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An Inset Groundwater-Flow Model to Evaluate the Effects of Layering Configuration on Model Calibration and Assess Managed Aquifer Recharge near Shellmound, Mississippi

Moussa Guira, Jonathan P. Traylor, Andrew T. Leaf, Alec R. Weisser, J.K. Arthur, P.M. Barlow · U.S. Geological Survey

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aquifer calibration configuration effects flow groundwater managed mississippi

usgs, geological survey, united states, science, government publication, usgs scientific investigations report, 2025, 5055, inset, groundwater, flow, model, evaluate, effects, layering, configuration, calibration, assess, managed, aquifer, recharge, near, shellmound, mississippi

Water Availability and Use Science Program Prepared in cooperation with U.S. Department of Agriculture Agricultural Research Service and the Mississippi Department of Environmental Quality

An Inset Groundwater-Flow Model to Evaluate the Effects of Layering Configuration on Model Calibration and Assess Managed Aquifer Recharge near Shellmound, Mississippi

Scientific Investigations Report 2025–5055

U.S. Department of the Interior U.S. Geological Survey

B C

Cover. A, Photograph showing Groundwater Transfer and Injection Pilot project injection well. Photograph by A.M. O’Reilly, U.S. Department of Agriculture, Agricultural Research. B, Photograph showing aerial view of the Delta region of Mississippi near Shellmound showing the Groundwater Transfer and Injection Pilot project injection site and surrounding soybean and corn fields. Drone photograph by U.S. Army Corps of Engineers, Vicksburg District. C, Photograph showing Groundwater Transfer and Injection Pilot project extraction well. Photograph by M. Van Hattem, Collier Consulting, Inc. D, Photograph showing aerial view of the Delta region of Mississippi near Shellmound showing the Groundwater Transfer and Injection Pilot project injection site and surrounding soybean and corn fields. Drone photograph by U.S. Army Corps of Engineers, Vicksburg District.

An Inset Groundwater-Flow Model to Evaluate the Effects of Layering Configuration on Model Calibration and Assess Managed Aquifer Recharge near Shellmound, Mississippi By Moussa Guira, Jonathan P. Traylor, Andrew T. Leaf, and Alec R. Weisser

Water Availability and Use Science Program Prepared in cooperation with U.S. Department of Agriculture Agricultural Research Service and the Mississippi Department of Environmental Quality

Scientific Investigations Report 2025–5055

U.S. Department of the Interior U.S. Geological Survey

U.S. Geological Survey, Reston, Virginia: 2025

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment—visit https://www.usgs.gov or call 1–888–392–8545. For an overview of USGS information products, including maps, imagery, and publications, visit https://store.usgs.gov/ or contact the store at 1–888–275–8747. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner. Suggested citation: Guira, M., Traylor, J.P., Leaf, A.T., and Weisser, A.R., 2025, An inset groundwater-flow model to evaluate the effects of layering configuration on model calibration and assess managed aquifer recharge near Shellmound, Mississippi: U.S. Geological Survey Scientific Investigations Report 2025–5055, 134 p., https://doi.org/10.3133/sir20255055. Associated data for this publication: Guira, M., and Weisser, A.R., 2025, Inset models used to evaluate the effects of layering configuration on model calibration from 1900 to 2018, and assess managed aquifer recharge near Shellmound, Mississippi, from 2019 to 2050: U.S. Geological Survey data release, https://doi.org/10.5066/P13DWA86. U.S. Geological Survey, 2020, USGS water data for the Nation: U.S. Geological Survey National Water Information System database, https://doi.org/10.5066/F7P55KJN. ISSN 2328-0328 (online)

iii

Acknowledgments The authors would like to acknowledge Connor Haugh, Leslie Duncan, J.R. Rigby, Wade Kress, Randy Hunt, and Mike Fienen for contributing to the discussions on conceptual modeling and the improvement of the modeling workflow from the onset of this project. The authors also thank Burke Minsley and Scott Ikard for iteratively providing airborne electromagnetic derived data for resistivity classes and hydraulic conductivity for testing the models as they evolved. Thank you to the U.S. Department of Agriculture Agricultural Research Service, Andy O’Reilly, and the Groundwater Transfer and Injection Pilot project management for providing soft knowledge about the modeled area; data related to extraction and injection wells and the observation wells; and operation data including pumping rates and observations data.

Contents Acknowledgments��iii Abstract��1 Introduction��1 Purpose and Scope��2 Study Area Description��2 Climate and Land Use��2 Surface-Water Features��2 Major Hydrogeologic Units��6 Groundwater and Water Use��7 Shellmound Groundwater-Flow Model��7 Parent Model��7 Conceptual Model��7 Inflows��11 Outflows��11 Model Construction��13 Spatial and Temporal Discretization��13 Hydrologic Boundaries��22 Areal Groundwater Recharge��22 Streams��22 Groundwater Pumping��22 Head Dependent Boundaries��22 MODFLOW 6 Solver Settings��22 Calibration��26 Observations��26 Observation Weighting��27 Parameterization��27 Aquifer Properties��27 Areal Recharge��39 Streamflow Routing��39 Water Use��39 Calibration Results and Best Model��39 Calibration Results for Model A��42 Calibrated Parameter Values��44 Aquifer Properties��44 Streambed Vertical Hydraulic Conductivity��83 Recharge��83 Water Use Parameters��83 Groundwater-Flow Model Budget Results��83 Managed Aquifer Recharge Scenario and Simulated Results��88 Groundwater Transfer and Injection Pilot (GTIP) Project��88 Forecast Model��89 Assumptions and Limitations��94 Summary��94 References Cited��96 Appendix 1. Additional Calibration Results from Model A��101 Appendix 2. Calibration and Modeling Results for Model B and Model C��108

Figures 1.

2. 3.

5. 6. 7.

8. 9.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Map showing the Shellmound model extent with streamlines and streamgage locations, the digital elevation model of the land surface, and boundaries of the Mississippi Embayment Regional Aquifer Study and the Mississippi Alluvial Plain��3 Graph showing groundwater-level elevation at U.S. Geological Survey site 334412090270301��4 Graph showing average monthly temperatures from 2010 to 2020 based on climate data from meteorological station USW00013978, near Greenwood, Mississippi��4 Graph showing average monthly precipitation from 2010 to 2020 based on climate data from meteorological station USW00013978, near Greenwood, Mississippi��5 Graph showing average daily mean streamflows for the Tallahatchie River at Money, Mississippi��5 Graphs showing plot of crop water use by crop type for the Shellmound model study area estimated from the Aquaculture and Irrigation Water-Use Model��8 Map showing the Shellmound model study area within the Mississippi Embayment Regional Aquifer System Mississippi Alluvial Plain, and Mississippi River Valley Alluvial aquifer extents��9 Map showing lateral inflow and outflow boundary segments (Guira and Weisser, 2025) as determined using 2016 potentiometric surface��10 Map showing surficial connectivity classifications based on the thickness of low electrical resistivity layers detected through airborne electromagnetic survey based on data from depths of 0 to 15 meters��12 Shellmound model grid showing model cells along with regularly spaced pilot points used as multipliers to aquifer properties during model calibration��14 Map showing electrical resistivity classes for the active area for layers 1–18 along with pilot points location in model A��15 Map showing electrical resistivity classes for the active area for layers 1–16 along with pilot points location in model B��16 Map showing electrical resistivity classes for the active area for layers 1–8 along with pilot points location in model C��17 Map showing yearly average net infiltration estimates from soil-water-balance model representing noncalibrated groundwater recharge��23 Map showing simulated stream reaches using the modular finite-difference flow model 6 Streamflow Routing package��24 Map showing average noncalibrated volumetric water use in cubic meters per year��25 Map showing field measurement and synthetic groundwater levels in the study area��28 Graphs showing north to south cross section of models A, B, and C showing noncalibrated hydraulic conductivity values��30 Graphs showing ensemble phi values from the calibration for model C��40 Graphs showing ensemble phi values for model B history matching��41 Graphs showing ensemble phi values for model C history matching��42 Graphs showing one-to-one plots comparing the Shellmound model outputs to field observations��43

vii

23. 24. 25.

26.

27. 28.

29. 30. 31. 32. 33. 34. 35. 36. 37.

Graphs showing time series of measured groundwater levels and simulated equivalents at selected wells��45 Graphs showing streamflow time series showing monthly averages of measured streamflows and simulated equivalents��46 Graphs showing horizontal hydraulic conductivity estimates for the Shellmound model, compared to electrical resistivity-based zones from the airborne electromagnetic survey��47 Graphs showing hydraulic conductivity vertical anisotropy estimates for the Shellmound model, compared to electrical resistivity-based zones from the airborne electromagnetic survey��56 Graphs showing specific yield estimates for the Shellmound model, compared to electrical resistivity-based zones from the airborne electromagnetic survey��65 Graphs showing specific storage estimates for the Shellmound model, compared to electrical resistivity-based zones from the airborne electromagnetic survey��74 Graphs showing simulated water table elevation along with estimates of streambed leakage in the Streamflow Routing package in two different conditions��84 Graphs showing comparative maps showing mean annual recharge��85 Graph showing total water use before and after calibration��86 Graph showing simulated annual net budget results for the Shellmound model��87 Schematic diagram of the Groundwater Transfer and Injection Project��88 Graph showing effective monthly average pumping rates at the extraction and injections sites used in the Groundwater Transfer and Injection Pilot project��91 Graphs showing time series plot of simulated water levels around the injection sites��91 Graphs showing simulated water table elevation of the study area at select stress periods��92 Graphs showing simulated water table elevation of the Groundwater Transfer and Injection Pilot project area at select stress periods��93

Tables 1. 2. 3. 4. 5. 6. 7. 8.

Hydrogeologic units represented in the Shellmound groundwater model framework��6 Temporal discretization in the Shellmound model��18 Parameter Estimation ++ Iterative Ensemble Smoother settings for calibration��26 Observations used in the model calibration as calibration targets��29 Calibration parameters used in model A��31 Calibration parameters used in model B��34 Calibration parameters used in model C��37 Ensemble phi values for models A–C following calibration run using Parameter Estimation++ Iterative Ensemble Smoother��40 9. Information for extraction and injection wells involved in the Groundwater Transfer and Injection Pilot project��90

viii

Conversion Factors International System of Units to U.S. customary units

Multiply

To obtain

Length centimeter (cm)

0.3937

inch (in.)

meter (m)

3.281

foot (ft)

kilometer (km)

0.6214

mile (mi)

kilometer (km)

0.5400

mile, nautical (nmi)

meter (m)

1.094

yard (yd)

square meter (m2)

0.0002471

Area acre

square kilometer (km2)

247.1

acre

square meter (m2)

10.76

square foot (ft2)

square kilometer (km2)

0.3861

square mile (mi2)

Volume cubic meter (m3) cubic meter (m3)

6.290 264.2

barrel (petroleum, 1 barrel = 42 gal) gallon (gal)

cubic meter (m3)

0.0002642

million gallons (Mgal)

cubic meter (m3)

35.31

cubic foot (ft3)

cubic meter (m3)

1.308

cubic yard (yd3)

cubic meter (m3)

0.0008107

acre-foot (acre-ft)

Flow rate centimeter per year (cm/yr) cubic meter per day (m3/d)

0.39370079 264.2

cubic meter per year (m3/yr)

0.000811

inches per year (in/yr) gallon per day (gal/d) acre-foot per year (acre-ft/yr)

Hydraulic conductivity meter per day (m/d)

3.281

foot per day (ft/d)

U.S. customary units to International System of Units

Multiply

To obtain

Length foot (ft)

0.3048

meter (m)

mile (mi)

1.609

kilometer (km)

square mile (mi2)

2.58998811

Area square mile (mi2)

640

square kilometer (km2) acre

Flow rate inch per year (in/yr)

2.54

centimeter per year (cm/yr)

cubic foot per second (ft3/s)

0.02831685

cubic meter per second (m3/s)

gallon per minute (gal/min)

0.06309

liter per second (L/s)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows: °F = (1.8 × °C) + 32.

Datum Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88). Horizontal coordinate information is referenced to North American Datum of 1983 (NAD 83). Altitude, as used in this report, refers to distance above the vertical datum.

Abbreviations Φ

phi, objective function

AEM

airborne electromagnetic

AIWUM

Aquaculture and Irrigation Water-Use Model

CHD

Constant Head

GTIP

Groundwater Transfer and Injection Pilot

IES

Iterative Ensemble Smoother

horizontal hydraulic conductivity

Kvani

hydraulic conductivity vertical anisotropy

MAP

Mississippi Alluvial Plain

MAR

managed aquifer recharge

MERAS

Mississippi Embayment River Aquifer Study

MODFLOW

modular finite-difference flow model

MRVA

Mississippi River Valley alluvial

NWIS

National Water Information System

PEST++

Parameter Estimation ++

PESTPP–IES

PEST++ Iterative Ensemble Smoother

SFR

Streamflow Routing

SWB soil-water-balance SWUDS

site-specific water-use data system

specific yield

USGS

U.S. Geological Survey

WEL Well

Abstract The U.S. Geological Survey has developed a high-resolution inset groundwater-flow model in the Mississippi Delta as part of an interdisciplinary collaboration coordinated by the Mississippi Alluvial Plain project to provide a tool that stakeholders can use to support water-resource management decisions. Groundwater withdrawals from the Mississippi River Valley alluvial (MRVA) aquifer have been vital to support agricultural production in the region, but substantial groundwater-level declines near Shellmound, Mississippi, have caused concerns for long-term sustainability of the aquifer. To better understand the subsurface and try to mitigate the long-term groundwater-level declines, stakeholders have undertaken actions including a Groundwater Transfer and Injection Pilot (GTIP) project using a riverbank filtration-based managed aquifer recharge approach. The pilot project consisted of extracting groundwater near the Tallahatchie River and reinjecting it into the aquifer 3 kilometers west where water levels have substantially declined. A high-resolution airborne electromagnetic (AEM) survey was also completed to collect electrical resistivity data to support the GTIP project and the development of the groundwater model. The inset groundwater-flow model was developed to (1) integrate the AEM data into the optimal layering configuration of the MRVA aquifer that the available observation data can support through calibration, and (2) assess the potential effect of the GTIP project on the groundwater levels. The AEM data were processed into three different layering configurations leading to the development of model A (18 layers), model B (16 layers), and model C (8 layers), all at a 100- x 100-meter cell spatial resolution using the U.S. Geological Survey modular finite-difference flow model 6 code with Newton-Raphson formulation. The model development process integrated recent advances in modeling, such as the incorporation of AEM data, the use of outputs from the soil-water-balance (SWB) model, and

the Aquaculture and Irrigation Water-Use Model, and was facilitated by robust automation using the open-source python packages Modflow-setup and SFRmaker. Using Parameter Estimation ++ Iterative Ensemble Smoother, the three numerical groundwater-flow models (models A, B, and C) were calibrated against a set of observations, which included aquifer groundwater levels, streamflows, stream stage, and aquifer transmissivity. Results indicate that the detailed representation of MRVA aquifer layers in model A produced the best calibrated model by history matching, and the integration of data representing surficial connectivity played a key role in improving groundwater recharge and enhancing the ability of the model to match groundwater levels in the cone of depression. A forecast model simulated the managed aquifer recharge approach, and the results indicated that, given average irrigation and recharge conditions (2010–15), the GTIP project has the potential to induce groundwater-level increases of as much as 3 meters around the injection site, but a sustained increase would require repetition in subsequent years of water transfer at 2022 rates or above.

Introduction Several numerical groundwater-flow models (hereafter referred to as “groundwater-flow models”) have been used for water management in the Mississippi Alluvial Plain (MAP) for decades (Sumner and Wasson, 1990; Arthur, 2001; Hart and others, 2008; Clark and Hart, 2009; Barlow and Clark, 2011; Haugh, 2012, 2016). The U.S. Geological Survey (USGS) Water Availability and Use Science Program, through the MAP project, has been updating these previously developed models by integrating new data and state-of-science software and methods to provide stakeholders with tools that can be used to support water-resource management decisions. Groundwater withdrawals from the Mississippi River Valley alluvial (MRVA) aquifer have been vital to support agricultural production, but groundwater-level declines have

2 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge heightened concerns about long-term sustainability. In a region near Shellmound, Mississippi (fig. 1), large groundwater-level declines (fig. 2) have prompted stakeholders to undertake several actions to better understand the subsurface and mitigate the declines. A Groundwater Transfer and Injection Pilot (GTIP) project was implemented by the U.S. Department of Agriculture, Agricultural Research Service whereby groundwater was extracted from the MRVA aquifer near the Tallahatchie River (fig. 1) and reinjected into the aquifer approximately 3 kilometers (km) west (O’Reilly and others, 2023). Additionally, a high-resolution airborne electromagnetic (AEM) survey was completed to collect geophysical data, help improve the current understanding of the subsurface, and support the GTIP project and groundwater modeling projects (Minsley and others, 2021). The MAP project supported the construction of a transient groundwater-flow model (the Shellmound model) using the modular finite-difference flow software (MODFLOW 6; Langevin and others, 2022). The model incorporates the hydrologic units inferred from the AEM data and serves as a tool to better understand processes associated with the groundwater system and the potential effects of GTIP project operations on groundwater levels.

Purpose and Scope The purpose of this report is to describe an inset groundwater-flow model, based on the regional model by Leaf and others (2023), of the MRVA aquifer including the model construction, calibration, simulation, and analysis of the simulated effects of groundwater extraction and injection by the GTIP project on groundwater levels near Shellmound, Miss. This report describes the approaches used to incorporate high-resolution AEM data in the model construction process through a detailed representation of the MRVA aquifer in the focused area (Minsley and others, 2021). The report describes how the same geophysical data were processed into three different vertical resolutions, each integrated into the construction of a groundwater-flow model with a different layering configuration of the MRVA aquifer. The report describes the construction and calibration of a historical model to simulate hydrologic conditions from 1900 to 2018 and a forecast model that simulates future conditions from 2019 to 2050, including water transfer using riverbank filtration and injection wells.

Study Area Description The Shellmound model study area covers the extent of the inset model domain, which lies entirely within the Mississippi River Delta and includes parts of Leflore, Sunflower, and Tallahatchie Counties (fig. 1). The area extends 35 km from the east to the west, 30 km from the north to the south, and covers a surface area of 1,050 square kilometers (km2; approximately 405 square miles [mi2]). The southeastern

corner of the model is 1 mile (mi) south of Greenwood, Miss. (fig. 1), and the western boundary goes through the town of Ruleville, Miss., which is 10 mi east of Cleveland, Miss. (fig. 1).

Climate and Land Use The climate in the Shellmound model study area is typical of the Mississippi River Delta (hereafter referred to as the “Delta”). Climate in the Delta is humid and subtropical (Arthur, 2001), and data from the meteorological station USW00013978 (National Centers for Environmental Information, 2022) near Greenwood, Miss. (fig. 1) indicate that the average minimum and maximum monthly temperatures were 11.6 degrees Celsius (°C) and 25 °C (53 °Fahrenheit [°F] to 77 °F), respectively. Long-term monthly averages indicate that the hottest months were July and August with temperatures around 32.2 °C (90 °F), whereas the coldest months were December and January with averages around 2 °C (35.6 °F; fig. 3; National Centers for Environmental Information, 2022). For the same period, 2010–20, the average annual precipitation was approximately 131 centimeters per year (cm/yr; 51.5 inches per year [in/yr]). April and December were the wettest months with an average precipitation of approximately 14 centimeters (5.5 inches) each (fig. 4). Land use in the Shellmound model study area is dominated by farmland with major agricultural crops including soybeans, corn, rice, and cotton. Farmlands in the area also include catfish ponds for aquaculture. Other land uses include wetlands, developed/urban, pasture, and forest (Wilson, 2021).

Surface-Water Features Surface-water features in the Shellmound model study area include streams, ponds, and oxbow lakes. Many of these surface-water features are not connected to the MRVA aquifer based on a spring 2016 potentiometric map by McGuire and others (2019). The major streams in the Shellmound model study area are the Tallahatchie, Quiver, and Big Sunflower Rivers (fig. 1). The Tallahatchie River flows north to south and meanders along the eastern portion of the study area until approximately 3 km north of the southern boundary where it merges with the Yalobusha River to become the Yazoo River (not shown). At the western boundary, the Big Sunflower River enters the study area approximately 10 km south of the northern boundary and runs south (fig. 1). Across the middle of the study area and flowing south is a network of small streams, most of which originate within the study area and are tributaries to the Quiver River (fig. 1). The average daily streamflow for the Tallahatchie River at Money, Miss. (USGS station 07281600; U.S. Geological Survey, 2020) from 1996 to 2018 was approximately 18.8 million cubic meters per day (m3/d; 7,700 cubic feet per second [ft3/s]; fig. 5). The average streamflow on the Quiver River near Sunflower, Miss.

33°48'

90°26'

90°24'

90°22'

90°20'

90°14'

90°12'

ug an

hi e

Ta llaha tc

Rattles n ake Bay

07288555

33°42'

334429090210101

Groundwater wells and identifier Groundwater Transfer and Injection Pilot groundwater wells

Qu ive rR iv

U.S. Geological Survey streamgage and identifier Teoc Little Cr Teoc eek CKENTUCKY MISSOURI

Shellmound

333603090164301 ou ay yB ke

Cleveland

Greenwood

33°30'

Base from U.S. Geological Survey and other Federal and State digital data, various scales; Albers Equal-Area Conic projection, standard parallels 29°30’ and 45°30’ N., central meridian 120° W.; North American Datum of 1983

430

er 0 0

CARROLL

Yazoo R

333136090244900

49W

TENNESSEE

Big S ARKANSAS and C reek

49E

07288580

k ree

333251090323801 07288500

RROLL

CA Mississippi embayment Potacoco wa regional aquifer systemCr e ek A' Cross-section for figure 18

07281600

33°34'

33°32'

High: 53.1 Yal oLow: a Riv e r bush28.5

07288555

LEFLORE SUNFLOWER

33°36'

89°58'

Land surface elevation, in meters above sea level

07288570

333742090303801

33°38'

90°

Shellmound model extent

er Riv er

90°02'

333950090230001 an

90°04'

Mississippi Alluvial Plain Bla c and Mississippi River Valleyk Creek alluvial aquifer ENADA

Pe c

442

lo w Big S u n f

33°40'

90°06'

TALLAHATCHIE LEFLORE

Ruleville 8

90°08'

334429090210101

334412090270301 33°44'

90°10'

EXPLANATION

Ba you

334538090303801

33°46'

90°16'

Bay

ell

90°18'

90°28'

ALABAMA

90°30'

90°32'

90°34'

Study area

LOUISIANA

MISSISSIPPI 6

12 KILOMETERS 6 MILES

Introduction 3

Figure 1. The Shellmound model extent with streamlines and streamgage locations, the digital elevation model of the land surface, and boundaries of the Mississippi Embayment Regional Aquifer Study and the Mississippi Alluvial Plain (Haugh and others, 2020a,b; Guira and Weisser, 2025).

4 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge 115 34

105 100

95 28 90 26

85 80

Groundwater-level elevation, in feet above North American Vertical Datum of 1988

Groundwater-level elevation, in meters above North American Vertical Datum of 1988

110

75 22 1975

1980

1985

1990

1995

2000

2005

2010

2015

2020

2025

Measurement date

Figure 2. Groundwater-level elevation at U.S. Geological Survey site 334412090270301 (133F0190 Sunflower; U.S. Geological Survey, 2020). 35

EXPLANATION Minimum temperature

80 25 70

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Monthly average temperature, in degrees Fahrenheit

Monthly average temperature, in degrees Celsius

Maximum temperature

Dec.

Month

Figure 3. Average monthly temperatures from 2010 to 2020 based on climate data from meteorological station USW00013978, near Greenwood, Mississippi (National Centers for Environmental Information, 2022).

Introduction 5

5 12 4

10 8

6 2 4 1

2 0

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Monthly average precipitation, in inches

Monthly average precipitation, in centimeters

Dec.

Month

Average discharge, in cubic meters per second

20,000 500

17,500 15,000

400

12,500 300

10,000 7,500

200

5,000 100 2,500 0

1996

2000

2004

2008

2012

2016

2020

2024

Date

Figure 5. Average daily mean streamflows for the Tallahatchie River at Money, Mississippi (U.S. Geological Survey station 07281600; U.S. Geological Survey, 2020).

Average discharge, in cubic feet per second

Figure 4. Average monthly precipitation from 2010 to 2020 based on climate data from meteorological station USW00013978, near Greenwood, Mississippi (National Centers for Environmental Information, 2022).

6 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge (USGS station 07288580) was 1.2 million cubic meters (m3) (500 ft3/s) based on 20 discrete streamflow measurements (from calendar year 1995 to 2014), and 2.7 million m3 (1,100 ft3/s) on the Big Sunflower River near Sunflower (USGS station 07288500) based on 257 discrete streamflow measurements (from calendar year 1940 to 2018).

Major Hydrogeologic Units The major hydrogeologic units in the Shellmound model study area are Quaternary and Tertiary units (table 1; Clark and Hart, 2009). The surficial MRVA aquifer is the uppermost unit and mainly consists of sand and gravel that were deposited during the Quaternary period. The uppermost layer of the MRVA aquifer generally is finer, with increased prevalence of silt and clay corresponding with lower vertical

hydraulic conductivity. The average thickness of the MRVA aquifer in the study area, as computed from land surface elevation to the interpreted base of the alluvial aquifer from recent AEM data (Minsley and others, 2021), is 38.3 meters (m; 126 feet [ft]) with a maximum of 49.2 m (161 ft) and a minimum of 23.5 m (77 ft). Underlying the MRVA aquifer are the older Tertiary hydrogeologic units, which mainly consist of undifferentiated sediments and include the upper and lower Claiborne aquifers, the middle Claiborne confining unit, and the middle and lower Wilcox aquifers (Hart and others, 2008; Clark and Hart, 2009; Leaf and others, 2023). The Tertiary deposits have a combined average thickness of 607 m (1,994 ft) with a maximum of 780.3 m (2,560 ft) and a minimum of 436 m (1,430 ft). Hydrogeologic units represented in the Shellmound groundwater model framework are shown in table 1.

Table 1. Hydrogeologic units represented in the Shellmound groundwater model framework. Modified from Hart and others (2008). [--, Group name does not exist]

Time-stratigraphic unit Era

System

Series

Pleistocene

Eocene

Tertiary

Cenozoic

Oligocene

Model C layers

Mississippi River 1 to 8 (within Valley, OuachitaMississippi Saline River, and Red Alluvial River alluvial aquifers Plain)

1 to 8

1 to 5

Vicksburg-Jackson confining unit

Missing in Shellmound

Cockfield Formation

Upper Claiborne aquifer

Missing in Shellmound

Cook Mountain Formation

Middle Claiborne confining unit

Sparta Sand

Middle Claiborne aquifer

Zilpha Clay Winona Sand Tallahata Formation

Lower Claiborne confining unit

Meridian Sand Member

Lower Claiborne aquifer

Undifferentiated

Upper, middle, and lower Wilcox aquifers

Alluvium, terrace, and loess deposits

Vicksburg

Vicksburg Formation

Jackson

Jackson Formation

Claiborne

Wilcox a

Model B layers

Formation

Holocene Quaternary

Model A layers

Group

Regional geohydrologic unit

Delta

1 to 21

9 to 18

6 to 16

2 to 8

Uniform and increasing thicknesses of layers to the depth of available airborne electromagnetic data prevent assignment of regional geohydrologic units to specific layers.

Shellmound Groundwater-Flow Model 7

Groundwater and Water Use The highly productive MRVA aquifer is the most important source of fresh water in the Mississippi embayment aquifer system (Clark and Hart, 2009), which fully encompasses the Shellmound model study area. Wells screened in the alluvial aquifer can pump between 1,635 and 16,350 m3/d (between 300 gallons per minute [gal/min] and 3,000 gal/min; Hewitt and others, 1949, Klein and others, 1950; Onellion, 1956; Bedinger and Reed, 1961). Outside of the Shellmound model study area, underlying Tertiary units were reported to have much lower well yield of 545 to 2,725 m3/day (100 to 500 gal/min) but can reach as much as 8,176 m3/day (1,500 gal/min; McKee and Hays, 2002; Clark and Hart, 2009). Killian and others (2019) reported that in 2000, groundwater withdrawal from the alluvial aquifer alone accounted for 10 percent of all groundwater use within the continental United States. Nearly all crop and catfish production is supported by groundwater pumping (Killian and others, 2019; Wilson, 2021; Bristow and Wilson, 2023; Leaf and others, 2023). Major crops in the Shellmound model study area and their estimated water use by the Aquaculture and Irrigation Water-Use Model (AIWUM) are shown in figure 6 (Bristow and Wilson, 2023). Other nonagricultural groundwater uses include municipal and industrial uses. Based on the geostatistical estimates for well screen elevation by Torak (2023), and the site-specific water-use data system (SWUDS) database (U.S. Geological Survey, 2020), it was determined that most groundwater use for crop and fish production within the limits of the Shellmound model study area is primarily supported by the MRVA aquifer, whereas the municipal and industrial groundwater use is supported by the underlying Tertiary units.

Shellmound Groundwater-Flow Model This section of the report describes the methodology used in the development of the Shellmound model. It includes a brief overview of the groundwater model used as the parent model. It also includes a description of the conceptual design, the three-dimensional groundwater-flow model, the model calibration approach, and the calibration results for the Shellmound model.

Parent Model An inset groundwater-flow model is one constructed from a previously developed and larger groundwater-flow model (Feinstein and others, 2010) that fully encompasses the inset model domain. The parent model used in the development of the Shellmound model is the three-dimensional groundwater-flow model described in Leaf and others (2023), which is an inset model. In this report, the parent model of the Shellmound model is hereafter referred to as the “Delta model.” The Delta model is a multilayer three-dimensional groundwater-flow model simulated by using the USGS

MODFLOW 6 code (Langevin and others, 2017) and focused on simulating hydrologic processes in the Mississippi Delta region (figs. 1 and 7). The purpose of the Delta model was to provide a tool for calibration in the Mississippi River Delta and for forecasting groundwater levels under specific climate and water use stresses (Leaf and others, 2023). The robust workflow was created to facilitate a somewhat fast development and parameterization of inset models and was subsequently modified for the purpose of developing the Shellmound model. More details on the Delta model development, calibration, and results are provided in Leaf and others (2023).

Conceptual Model Prior to the construction of the groundwater-flow model, the hydrologic system in the Shellmound model study area was conceptualized into a framework that accounts for the regional groundwater flow and its interactions with other components of the hydrologic system. The conceptualization led to a general understanding regarding the major budget components and physical processes that are within the study area. A conceptual model of groundwater flow is often presented as a narrative describing the occurrence and movement of groundwater along with physical characteristics such as aquifer properties and the largest inflows and outflows within the model domain (Peterson and others, 2016), and that approach has been taken in this report. The inset model domain was defined to cover the GTIP project area of operations and modified based on the coverage of the high-resolution AEM survey (Minsley and others, 2021). The modifications resulted in model boundary segments with fluctuating regimes of exchanges of groundwater between the model domain and the surrounding aquifer based on regional groundwater flow (fig. 8). At the onset of this study, a prototype version of the conceptual model was constructed for the MRVA aquifer using the newly interpreted base of the alluvial aquifer from the AEM survey (Minsley and others, 2021) as the base of the model. The constructed groundwater-flow model based on that conception was unstable and did not adequately account for the hydrologic contribution of the underlying Tertiary units; therefore, a more comprehensive approach was adopted to include the Tertiary units present in the study area. The conceptual model described in this report is not meant to accurately quantify each budget component of the Shellmound model. It is meant to provide a rough estimate of budget components to guide the calibration and help the reader understand the relative magnitude of each component. Thus, the 2016 conditions used to estimate most budget components indicate that approximately 52 percent of inflows were from stream leakage, 23 percent from storage, 15 percent from recharge, 5 percent from irrigation return flow, and 4 percent from cross boundary flow from surrounding aquifers. Approximately 88 percent of outflows were from groundwater irrigation, 11 percent from stream leakage, and 1 percent from groundwater evapotranspiration.

8 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge A. Catfish

B. Corn

C. Cotton

D. Rice

E. Soybeans

F. Other crops

10,000

Yearly water use, in million cubic meters

7,500 5,000 2,500 0

10,000 7,500 5,000 2,500 0 2000

2005

2010

2015

2020

2000

2005

2010

2015

2020

2000

2005

2010

2015

2020

Year

Figure 6. Plot of crop water use by crop type for the Shellmound model study area estimated from the Aquaculture and Irrigation Water-Use Model by Bristow and Wilson (2023). A, Catfish. B, Corn. C, Cotton. D, Rice. E, Soybeans. F, Other crops.

Shellmound Groundwater-Flow Model 9

36°

35°

OKLAHOMA

37°

94°

KANSAS

95°

93°

92°

91°

90°

89°

88°

87°

86°

NOIS

ILLI

KENTUCKY

MISSOURI

TENNESSEE

ARKANSAS

34°

ALABAMA 33°

32°

MISSISSIPPI TEXAS

LOUISIANA FLORIDA

31°

30°

GULF OF AMERICA 29° Base from U.S. Geological Survey and other Federal and State digital data, various scales; Albers Equal-Area Conic projection, standard parallels 29°30’ and 45°30’ N., central meridian 120° W.; North American Datum of 1983

0 0

60 30

120 60

180 90

120

240

300 KILOMETERS

150 MILES

EXPLANATION Mississippi Alluvial Plain and Mississippi River Valley alluvial aquifer

Grand Prairie model extent (Traylor and others, 2024)

Mississippi Embayment Regional Aquifer System

Shellmound model extent

Cache model extent (Traylor and others, 2024)

Delta model extent (Leaf and others, 2023)

Figure 7. The Shellmound model study area within the Mississippi Embayment Regional Aquifer System, Mississippi Alluvial Plain, and Mississippi River Valley Alluvial aquifer extents (Haugh and others, 2020a,b; Guira and Weisser, 2025).

ll B

90°20'

90°15'

90°10'

ayo

Ta lla hatchie R

90°05'

Nonirrigated

Shellmound model extent

Rattle s nake

Head boundary 38

Outflow

Streams

Qu ive rR iv

Su nflo wer R iv e r Big

Potentiometric contour lines, in meters (McGuire and 39 others, 2019)

c a n Ba y o

Teo c

C re

33°35'

cocowa Pota Creek

Inflow

Bayou

20 P

Yal obusha R e iv

Irrigated

Irrigated area

33°45'

33°40'

90°

EXPLANATION

ive

90°25'

Big S

and C

Tur

Bayo u

ive r

Yazoo R

w ay

33°30'

Roun d

reek

Pelu

cia B ayo u

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 8. Lateral inflow and outflow boundary segments (Guira and Weisser, 2025) as determined using 2016 potentiometric surface (McGuire and others, 2019). Background image shows irrigated and nonirrigated cells based on Aquaculture and Irrigation Water-Use Model data (Bristow and Wilson, 2023).

10 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

90°30'

Shellmound Groundwater-Flow Model 11

Inflows The two major inflows into the groundwater-flow system of the Shellmound model study area are (1) groundwater recharge, which consists of areal recharge and stream leakage; and (2) groundwater release from storage. Areal recharge represents the fraction of precipitation that infiltrates to the water table. The two minor inflows to the groundwater-flow system are from (1) lateral groundwater flow from areas surrounding the model domain and (2) irrigation return flow, which represents the portion of irrigation inefficiency that infiltrates back to the groundwater system. Below is a summary description of how each inflow component was calculated. Areal recharge estimates were taken from Clark and Hart (2009) where a calibrated recharge map provided average recharge rates by calibration zones. The map section that overlaps the Shellmound model study area contained zones 103 and 108 with respective average calibrated recharge rates of 2.85 and 0.19 in/yr (Clark and Hart; 2009). The average volumetric annual rate computed by using those rates for their respective areas was approximately 30.7 million cubic m per year (m3/yr). Irrigation return flow rates were computed using irrigation efficiencies based on the irrigation and crop type. A furrow irrigation efficiency of 65 percent and an irrigation return rate of 30 percent were used based on findings by Kandpal (2018) and Bryant and others (2021). Groundwater recharge is also affected by the thickness and permeability of the vadose zone. As a result, a spatially varying recharge rate was applied based on the surficial connectivity zones (fig. 9) generated by logarithmically binning “facies” classes of vertically averaged shallow electrical resistivity from AEM surveys (Minsley and others, 2021). The connectivity-based reduction resulted in an annual irrigation return rate estimated at 9.8 million m3/yr. The connection between streams and the groundwater system was examined using land surface elevations and the interpreted groundwater-level surface. A digital elevation model for land surface (U.S. Geological Survey, 2016) and a 2016 potentiometric surface by McGuire and others (2019) were used to compute the thickness of the unsaturated zone underlying all stream reaches. For this approximation, a stream segment was assumed to be in a losing condition if the unsaturated zone beneath was thicker than 1 ft; otherwise, the reach was assumed to be in a gaining condition. The assignments are based on the assumption that streambed elevation is likely lower compared to the digital elevation model altitude. Using stream length and width in each cell along with streambed vertical hydraulic conductivity and the distance between streambed elevation and the water table, an annual stream-leakage rate was computed for each stream reach (Barlow and others, 2000; McKay and others, 2012; Boyraz and Kazezyilmaz-Alhan, 2021). The estimation resulted in a net stream leakage to the groundwater-flow system of approximately 26.5 million m3/yr. It is important to note that the exchange between groundwater and surface

water could vary with time for each reach. The exchange also can vary in magnitude and direction seasonally depending on the hydraulic head gradient between the groundwater and surface water. Therefore, a gaining reach in February, prior to the start of agricultural irrigation pumping when groundwater levels are likely at their highest, can become a losing reach in October after the irrigation pumping throughout the growing season lowers groundwater levels. To account for change in groundwater storage, 17 wells across the Shellmound model study area were used to compute the average annual groundwater-level change from 1994 to 2016. The average groundwater-level change, along with the calibrated specific yield (Sy) of 0.3 (Clark and Hart, 2009), was used to approximate a rate of groundwater released from storage of 48 million m3/yr. Lateral groundwater movement across the model domain was estimated using 2016 equipotential lines from the potentiometric surface (McGuire and others, 2019). It was assumed that groundwater-flow direction is perpendicular to equipotential lines; therefore, drawing the flowlines in the vicinity of the boundary provided a snapshot of the groundwater-flow direction between the model domain and the surrounding aquifer. The head boundary segments where the study area is gaining from lateral groundwater flow are shown in figure 8. The 9.5 million m3/year net positive groundwater flow into the study area is consistent with the observation that a large portion of the area is irrigated, and groundwater pumping from the aquifer is decreasing groundwater levels, forming a regional cone of depression, and is responsible for the gradient that contributes to the influx. Influx along the eastern boundary is consistent with the overall regional groundwater flow as documented through previous studies and field water-level observation data (Arthur, 2001; McGuire and others, 2019, 2021; Leaf and others, 2023).

Outflows Hydrologic stresses that resulted in a net flow out of the Shellmound groundwater model study area consist of (1) irrigation pumping and (2) groundwater evapotranspiration. In this conceptual model, lateral groundwater flow out of the study area and groundwater discharge to streams as base flow were lower than their inflow counterparts. Below is a brief description of how flows out of the model were estimated. Irrigation water use for the conceptual model was estimated based on crop water demand by using the 2016 land use dataset (Meredith and Blais, 2019; USDA, 2020). Major crops in the Shellmound model study area include corn, cotton, rice, and soybeans. Crop water demand estimation also accounted for well-known and documented inefficiencies associated with irrigation practices in the region (Meredith and Blais, 2019). The estimation resulted in approximately 187 million m3 of extracted water for irrigation purposes per year. Nonagricultural water use was estimated at 67,875 m3/yr using USGS SWUDS data (Diehl and Harris, 2014; Harris and Diehl, 2019a, b).

90°15'

90°10'

Riv

Ta llah a

EXPLANATION

tc h

Surface connectivity

High

Yal obu s a Riv Low h er

a ck Shellmound model extent Cree

Bayou Rattl e snake

Potentiometric contour lines, in meters (McGuire and 42 others, 2019) acocowa Cree Pot k Streams

24lo w Big S u n f

35 34

B ay o u

er Riv er

28 27

33°40'

90°

90°05'

ayo

ll B

90°20'

B ill B

Burrell Bayou 33°45'

90°25'

Qu ive rR iv

Teoc

eek

18 33°35'

Big S

ay Bay

ive

Round a

Yazoo R

and C

reek

Pelu

ci a B a you

0 0

6 3

12 KILOMETERS 6 MILES

Figure 9. Surficial connectivity classifications based on the thickness of low electrical resistivity layers detected through airborne electromagnetic survey based on data from depths of 0 to 15 meters (Minsley and others, 2021).

12 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Wild

90°30'

Shellmound Groundwater-Flow Model 13 For this report, groundwater evapotranspiration is defined as the process by which plants uptake groundwater directly from the saturated zone through their roots and transpire that water to the atmosphere. Groundwater evapotranspiration is dependent on land cover and the thickness of the vadose zone, typically taking place in areas of shallow groundwater where plant roots reach the water table near gaining streams and in groundwater-fed swamps and marsh areas (Lubczynski, 2009). In most of the study area, the water table is deep enough that groundwater evapotranspiration is not expected, so plant water requirements are met predominantly by soil moisture in the vadose zone. Groundwater evapotranspiration is only expected in a small portion of the model domain along the gaining stream reaches. The estimates of groundwater evapotranspiration in the Shellmound model study area amounted to 2.5 million m3/yr.

Model Construction This section of the report describes the construction of the MODFLOW 6 Shellmound model by using the approach described in Leaf and others (2023). The process involved a robust automated workflow facilitated by the use of Python tools (Leaf and others, 2021; Leaf and Fienen, 2022) to expedite the construction. The workflow allowed for a stepwise approach in the model construction whereby complexity is added and tested one step at the time. The workflow also allows for quickly rebuilding the model at different spatial and temporal resolutions. The model was simulated using the USGS MODFLOW 6 code (Langevin and others, 2022).

Spatial and Temporal Discretization The plan view of the model domain footprint (the study area) is a rectangular shape that extends 30 km in the north to south direction and 35 km in the east to west direction (fig. 1). The model bounding box was chosen so that it aligns with the National Hydrologic Grid (Clark and others, 2018). The domain was spatially discretized into orthogonal blocks of 100 m by 100 m and organized in 300 rows and 350 columns (fig. 10). The Shellmound model development process included the exploration of the effect of increased complexity in layering configurations that resulted in three different vertical

discretizations corresponding to the three versions (models A, B, and C) of the Shellmound model. Model A retains the vertical discretization used in the Delta model and consists of uniform 5-meter-thick layers from land surface to the base of the MRVA aquifer as defined through the interpretation of the AEM data (Minsley and others, 2021). Below the base of the MRVA aquifer, the vertical discretization is represented by uniform and increasing thickness to the depth of the available AEM data, and then by nonuniform layer surfaces using the hydrostratigraphic surfaces described by Hart and others (2008). The Delta model layers 16–18 were inactive over the Shellmound model domain area and therefore were not represented in the inset model. Consequently, Shellmound model A layers 16, 17, and 18 correspond to the Delta model layers 19, 20, and 21, respectively. The discretization process resulted in 18 model layers for model A (fig. 11; table 1). More details on the Delta model layering and the extent of each layer are in Leaf and others (2023). Model B has a vertical discretization that defines 10-m constant thickness and horizontal layers from the highest elevation of the land surface to the base of the MRVA aquifer (Minsley and others, 2021). The vertical discretization of model B below the base of the MRVA aquifer is identical to that of model A, which resulted in 16 model layers for model B (fig. 12; table 1). The vertical discretization in model C is defined by a single layer that extends from land surface to the base of the MRVA aquifer as defined through the interpretation of AEM data (Minsely and others, 2021). The vertical discretization of model C below the base of the MRVA aquifer data is identical to those in models A and B, which resulted in eight model layers for model C (fig. 13; table 1). More information on the discretization for each model is provided in a USGS data release (Guira and Weisser, 2025). The temporal discretization of the Shellmound model is identical to that used in the Delta model (Leaf and others, 2023). A total of 148 stress periods of varying lengths were simulated from 1900 to 2018 (table 2). The period prior to April 2007 was subdivided into six stress periods of lengths of 1 year or more and represented varying stages of groundwater development within the MAP area as reported in previous studies (Clark and Hart, 2009; Leaf and others, 2023). The first stress period simulates a steady state condition, whereas stress periods 2 to 148 simulate transient conditions. The model simulates monthly stress periods from April 1, 2007, to January 1, 2019.

90°20'

90°15'

90°10'

90°05'

90°

ll B

ayo

Ta llah a tc h

B ill Bayou

90°25'

EXPLANATION Shellmound model extent

Wi l

Streams

YGroundwater Transfer alob u sInjection ha Riv e r Pilot and Bl groundwater wells a ck Cree k

33°45'

Rattl e snake

Pilot points for layers with multiple resistivity zones (layers 1–15) acocowa Cree Potlayers with k Pilot points for one resistivity zone (layers 16–17)

Bayou 26

24lo w Big S u n f

35 34

B ay o u

Shellmound grid

er Riv er

28 27

33°40'

49E

Qu ive rR iv

Teoc

eek

18 49W

Big S

33°35'

Round a

ay Bay

ive

Yazoo R

and C

reek

Pelu

ci a B a you

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 10. Shellmound model grid showing model cells along with regularly spaced pilot points used as multipliers to aquifer properties during model calibration (Guira and Weisser, 2025).

14 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

90°30'

90°25'

90°20'

90°15'

90°10'

90°05'

ll B

ayo

Ta llah a tc h

B ill Bayou

Burrell Bayou

Wi l

EXPLANATION Resistivity—Class

Yal 4ob

33°45'

u s ha Riv e r

Rattl e snake

a ck

Cree

Bayou

lo w Big S u n f

33°40'

90°

90°30'

acocowa Cree Pot k

16 17 18 19

er Riv er

B ay o u Qu ive rR iv

Shellmound model extent

Streams

Teoc Cr Groundwater Transfer eek and Injection Pilot groundwater wells

33°35'

Pilot points for layers 1–15 yo

Big S

ive Yazoo R

ay Bay

reek

Pelu

ci a B a you

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 11. Electrical resistivity classes (Minsley and others, 2021) for the active area for layers 1–18 along with pilot points location in model A (this is a layered .pdf; download at https://doi.org/10.3133/sir20255055).

Shellmound Groundwater-Flow Model 15

Round a

Ba ey rk

and C

90°20'

90°15'

90°10'

90°05'

ll B

ayo

Ta llah a tc h

B ill Bayou

Burrell Bayou

EXPLANATION 2

Wi l

Yal 4ob

33°45'

Resistivity—Class

u s ha Riv e r

35 34

28 27

acocowa Cree Pot k

Sunflower

Cree

B ay o u

er Riv er

a ck

Bayou

24lo w Big S u n f

Rattl e snake

33°40'

90°

90°25'

Qu ive rR iv

Shellmound model extent

Streams

Teoc Cr eek Groundwater Transfer and Injection Pilot groundwater wells

18 33°35'

Pilot points for layers 1–15 yo

Big S

ay Bay

ive Yazoo R

Round a

Ba ey rk

and C

reek

Pelu

ci a B a you

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 12. Electrical resistivity classes (Minsley and others, 2021) for the active area for layers 1–16 along with pilot points location in model B (this is a layered .pdf; download at https://doi.org/10.3133/sir20255055).

16 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

90°30'

90°25'

90°20'

90°15'

90°10'

90°05'

ll B

ayo

Ta llah a tc h

B ill Bayou

Burrell Bayou

Wi l

EXPLANATION Resistivity—Class

Yal o4b

33°45'

u s ha Riv e r

35 34

28 27

Cree

acocowa Cree Pot k

B ay o u

er Riv er

a ck

Bayou

24lo w Big S u n f

Rattl e snake

33°40'

90°

90°30'

Qu ive rR iv

Shellmound model extent

Streams

Teoc Cr Groundwater Transfer eek and Injection Pilot groundwater wells

18 33°35'

Pilot points for layers 1–7 yo

Big S

ive Yazoo R

ay Bay

reek

Pelu

ci a B a you

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 13. Electrical resistivity classes (Minsley and others, 2021) for the active area for layers 1–8 along with pilot points location in model C (this is a layered .pdf; download at https://doi.org/10.3133/sir20255055).

Shellmound Groundwater-Flow Model 17

Round a

Ba ey rk

and C

18 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Table 2. Temporal discretization in the Shellmound model (Guira and Weisser, 2025). [Dates shown as month/day/year]

Stress period number1

Start date

End date2

Length (days)

Number of timesteps

Timestep multiplier

Steady state

1/1/1900

12/31/1949

18,262

1.5

1/1/1950

12/31/1969

7,305

1.5

1/1/1970

3/31/1986

5,934

1.5

4/1/1986

9/30/1992

2,375

1.5

10/1/1992

3/31/1998

2,008

1.5

4/1/1998

3/31/2007

3,287

1.5

4/1/2007

4/30/2007

1.5

5/1/2007

5/31/2007

1.5

6/1/2007

6/30/2007

1.5

7/1/2007

7/31/2007

1.5

8/1/2007

8/31/2007

1.5

9/1/2007

9/30/2007

1.5

10/1/2007

10/31/2007

1.5

11/1/2007

11/30/2007

1.5

12/1/2007

12/31/2007

1.5

1/1/2008

1/31/2008

1.5

2/1/2008

2/29/2008

1.5

3/1/2008

3/31/2008

1.5

4/1/2008

4/30/2008

1.5

5/1/2008

5/31/2008

1.5

6/1/2008

6/30/2008

1.5

7/1/2008

7/31/2008

1.5

8/1/2008

8/31/2008

1.5

9/1/2008

9/30/2008

1.5

10/1/2008

10/31/2008

1.5

11/1/2008

11/30/2008

1.5

12/1/2008

12/31/2008

1.5

1/1/2009

1/31/2009

1.5

2/1/2009

2/28/2009

1.5

3/1/2009

3/31/2009

1.5

4/1/2009

4/30/2009

1.5

5/1/2009

5/31/2009

1.5

6/1/2009

6/30/2009

1.5

7/1/2009

7/31/2009

1.5

8/1/2009

8/31/2009

1.5

9/1/2009

9/30/2009

1.5

10/1/2009

10/31/2009

1.5

11/1/2009

11/30/2009

1.5

12/1/2009

12/31/2009

1.5

1/1/2010

1/31/2010

1.5

2/1/2010

2/28/2010

1.5

Shellmound Groundwater-Flow Model 19 Table 2. Temporal discretization in the Shellmound model (Guira and Weisser, 2025).—Continued [Dates shown as month/day/year]

Stress period number1

Start date

End date2

Length (days)

Number of timesteps

Timestep multiplier

3/1/2010

3/31/2010

1.5

4/1/2010

4/30/2010

1.5

5/1/2010

5/31/2010

1.5

6/1/2010

6/30/2010

1.5

7/1/2010

7/31/2010

1.5

8/1/2010

8/31/2010

1.5

9/1/2010

9/30/2010

1.5

10/1/2010

10/31/2010

1.5

11/1/2010

11/30/2010

1.5

12/1/2010

12/31/2010

1.5

1/1/2011

1/31/2011

1.5

2/1/2011

2/28/2011

1.5

3/1/2011

3/31/2011

1.5

4/1/2011

4/30/2011

1.5

5/1/2011

5/31/2011

1.5

6/1/2011

6/30/2011

1.5

7/1/2011

7/31/2011

1.5

8/1/2011

8/31/2011

1.5

9/1/2011

9/30/2011

1.5

10/1/2011

10/31/2011

1.5

11/1/2011

11/30/2011

1.5

12/1/2011

12/31/2011

1.5

1/1/2012

1/31/2012

1.5

2/1/2012

2/29/2012

1.5

3/1/2012

3/31/2012

1.5

4/1/2012

4/30/2012

1.5

5/1/2012

5/31/2012

1.5

6/1/2012

6/30/2012

1.5

7/1/2012

7/31/2012

1.5

8/1/2012

8/31/2012

1.5

9/1/2012

9/30/2012

1.5

10/1/2012

10/31/2012

1.5

11/1/2012

11/30/2012

1.5

12/1/2012

12/31/2012

1.5

1/1/2013

1/31/2013

1.5

2/1/2013

2/28/2013

1.5

3/1/2013

3/31/2013

1.5

4/1/2013

4/30/2013

1.5

5/1/2013

5/31/2013

1.5

6/1/2013

6/30/2013

1.5

7/1/2013

7/31/2013

1.5

8/1/2013

8/31/2013

1.5

20 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Table 2. Temporal discretization in the Shellmound model (Guira and Weisser, 2025).—Continued [Dates shown as month/day/year]

Stress period number1

Start date

End date2

Length (days)

Number of timesteps

Timestep multiplier

9/1/2013

9/30/2013

1.5

10/1/2013

10/31/2013

1.5

11/1/2013

11/30/2013

1.5

12/1/2013

12/31/2013

1.5

1/1/2014

1/31/2014

1.5

2/1/2014

2/28/2014

1.5

3/1/2014

3/31/2014

1.5

4/1/2014

4/30/2014

1.5

5/1/2014

5/31/2014

1.5

6/1/2014

6/30/2014

1.5

7/1/2014

7/31/2014

1.5

8/1/2014

8/31/2014

1.5

9/1/2014

9/30/2014

1.5

10/1/2014

10/31/2014

1.5

11/1/2014

11/30/2014

1.5

100

12/1/2014

12/31/2014

1.5

101

1/1/2015

1/31/2015

1.5

102

2/1/2015

2/28/2015

1.5

103

3/1/2015

3/31/2015

1.5

104

4/1/2015

4/30/2015

1.5

105

5/1/2015

5/31/2015

1.5

106

6/1/2015

6/30/2015

1.5

107

7/1/2015

7/31/2015

1.5

108

8/1/2015

8/31/2015

1.5

109

9/1/2015

9/30/2015

1.5

110

10/1/2015

10/31/2015

1.5

111

11/1/2015

11/30/2015

1.5

112

12/1/2015

12/31/2015

1.5

113

1/1/2016

1/31/2016

1.5

114

2/1/2016

2/29/2016

1.5

115

3/1/2016

3/31/2016

1.5

116

4/1/2016

4/30/2016

1.5

117

5/1/2016

5/31/2016

1.5

118

6/1/2016

6/30/2016

1.5

119

7/1/2016

7/31/2016

1.5

120

8/1/2016

8/31/2016

1.5

121

9/1/2016

9/30/2016

1.5

122

10/1/2016

10/31/2016

1.5

123

11/1/2016

11/30/2016

1.5

124

12/1/2016

12/31/2016

1.5

125

1/1/2017

1/31/2017

1.5

126

2/1/2017

2/28/2017

1.5

Shellmound Groundwater-Flow Model 21 Table 2. Temporal discretization in the Shellmound model (Guira and Weisser, 2025).—Continued [Dates shown as month/day/year]

Stress period number1

Start date

End date2

Length (days)

Number of timesteps

Timestep multiplier

127

3/1/2017

3/31/2017

1.5

128

4/1/2017

4/30/2017

1.5

129

5/1/2017

5/31/2017

1.5

130

6/1/2017

6/30/2017

1.5

131

7/1/2017

7/31/2017

1.5

132

8/1/2017

8/31/2017

1.5

133

9/1/2017

9/30/2017

1.5

134

10/1/2017

10/31/2017

1.5

135

11/1/2017

11/30/2017

1.5

136

12/1/2017

12/31/2017

1.5

137

1/1/2018

1/31/2018

1.5

138

2/1/2018

2/28/2018

1.5

139

3/1/2018

3/31/2018

1.5

140

4/1/2018

4/30/2018

1.5

141

5/1/2018

5/31/2018

1.5

142

6/1/2018

6/30/2018

1.5

143

7/1/2018

7/31/2018

1.5

144

8/1/2018

8/31/2018

1.5

145

9/1/2018

9/30/2018

1.5

146

10/1/2018

10/31/2018

1.5

147

11/1/2018

11/30/2018

1.5

148

12/1/2018

12/31/2018

1.5

1The first stress period designates a steady state; all other stress periods are transient. 2Stress periods end at midnight after the end date. For example, stress period 148 ends at midnight on 01/01/2019.

22 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Hydrologic Boundaries This section of the report describes the hydrologic boundary conditions, and the exchanges between the groundwater system in the study area and the surrounding environment. MODFLOW 6 uses boundary condition packages to model these exchanges and calculates the gains and losses for the groundwater system during each stress period.

Areal Groundwater Recharge Areal groundwater recharge was simulated in the Shellmound model using the MODFLOW 6 recharge package (Langevin and others, 2017). Input recharge grids for the Shellmound model were based on daily simulated net infiltration by the Shellmound soil-water-balance (SWB) model (Nielsen and Westenbroek, 2023). The Shellmound SWB model consists of 100×100-meter cells and computes a grid-based water budget of surface hydrology (from the vegetative canopy to the bottom of the root zone) that was constructed to provide inputs to the Shellmound model. Daily net infiltration rates were averaged to match the Shellmound model monthly temporal discretization from April 2007 to December 2018. The spatially distributed average daily net infiltration rates for 1999–2018 was used for the stress periods preceding 2007. The spatially distributed average net infiltration estimates from the SWB model are shown in figure 14 (Nielsen and Westenbroek, 2023).

Streams All streams in the Shellmound model were simulated using the MODFLOW 6 Streamflow Routing (SFR) package (Langevin and others, 2017). The SFR package simulated the stream water budget for each stream reach including gains and losses. In addition to the stream water budgets, the SFR package simulated surface runoff, stream stage, and routing between connected reaches. The runoff inputs to the SFR package were provided by the SWB model (Nielsen and Westenbroek, 2023). In addition to the budget components, the SFR package simulated the streambed conductance by using vertical hydraulic conductivity, streambed thickness, and channel geomorphology represented by Manning’s coefficient (Prudic and others, 2004; Langevin and others, 2017). The SFR package was built using NHDPlus version 2 data (McKay and others, 2012), the SFRmaker (Leaf and others, 2021), and MODFLOW 6 setup (Leaf and Fienen, 2022) following methodology described in Leaf and others (2023). Stream reaches and streamgages that were simulated in the Shellmound model are shown in figure 15.

Groundwater Pumping Groundwater pumping in the Shellmound model was simulated using the MODFLOW 6 Well (WEL) package (Langevin and others, 2017). A single WEL package was

used to simulate groundwater pumping for agricultural and nonagricultural use. Pumping locations and rates for stress periods prior to April 2007 were derived from the Mississippi Embayment River Aquifer Study (MERAS) 2.2 groundwater-flow model (Haugh and others, 2020a,b). There is no distinction between agricultural and nonagricultural water use in the Shellmound model prior to 2007. From April 2007 to December 2018, water-use data include pumping rates and locations for agricultural production and nonagricultural water use. Agricultural water use data were provided by the AIWUM version 1.1 (Wilson, 2021; Bristow and Wilson, 2023). The AIWUM estimates for annual average water use between 2000 and 2018 are shown in figure 16. Nonagricultural water-use data for the same period were provided by the USGS SWUDS and national estimates for water use associated with thermoelectric power generation (Diehl and Harris, 2014; Harris and Diehl, 2019a, b). Approximately 71.6 percent of all water from 1900 to 2018 were derived from the MERAS 2.2 model, whereas 28.3 and 0.09 percent were from AIWUM and SWUDS, respectively.

Head Dependent Boundaries Lateral groundwater flow into and out of the Shellmound model was simulated using the Constant Head (CHD) package (Leake and Prudic, 1991; Langevin and others 2017). The CHD package in MODFLOW 6, however, is classified as a hydrologic stress package where constant head values for specific cells were defined for every stress period (Langevin and others, 2017). Constant head boundary cells for the Shellmound model were specified at the perimeter boundary. Simulated groundwater levels from the parent model (Leaf and others, 2023) were used to specify hydraulic heads for every stress period in the CHD package. Lateral groundwater flow between the model and the surrounding aquifer for each stress period was computed based on the principle that groundwater flows downgradient, from higher groundwater levels to lower groundwater levels. The gradient between the CHD package cells and the neighboring cells determines the rates and direction of the exchange.

MODFLOW 6 Solver Settings The Shellmound model solved systems of equations to achieve mass balance of the stresses applied to the system during each of the 148 stress periods. The Integrated Model Solution package (Langevin and others, 2017) employed the Newton-Raphson formulation with the “complex” Integrated Model Solution package option to iteratively solve the water balance equation for each stress period. The “complex” option was selected to improve solution stability when simulating the nonlinearity associated with local unconfined layers. For convergence criteria, the maximum allowable absolute value in head change was set to 1.0 m for non-linear iterations, and 0.01 m for linear iterations. The maximum

90°25'

90°20'

90°15'

90°10'

90°05'

ll B

ayo

Ta llah a tc h

B ill Bayou

Burrell Bayou

Wi l

EXPLANATION Average yearly recharge, in meters

High: 0.67

Yal ob

33°45'

u s h0a Riv e r Low:

Bl a ck Shellmound model extent Cree

Rattl e snake

Streams Groundwater Transfer acocow and Injection PotPilot a Creek groundwater wells

Bayou 26

24lo w Big S u n f

35 34

Model archive and output files for net from Nielsen and Westenbroek, 2023

B ay o u

er Riv er

28 27

33°40'

90°

90°30'

Qu ive rR iv

Teoc

eek

18 33°35'

Big S

ive Yazoo R

ay Bay

reek

Pelu

ci a B a you

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 14. Yearly average (1999–2018) net infiltration estimates from soil-water-balance model representing noncalibrated groundwater recharge. Data from Nielsen and Westenbroek (2023).

Shellmound Groundwater-Flow Model 23

Round a

Ba ey rk

and C

90°20'

90°15'

90°10'

90°05'

ll B

ayo

Ta llah a tc h

B ill Bayou

Burrell Bayou

Wi l

EXPLANATION

Streams

Yal Streamflow obu s a Rivrouting network h er —U.S. Geological Survey, Bl a ck 2020 Cree k

33°45'

Shellmound model extent

Rattl e snake

07288555

07281600 442

er Riv er

B ay o u

49E

Qu ive rR iv

Teoc

eek

49W

518

33°35'

Groundwater Transfer and Injection Pilot groundwater wells acocowa Cree Pot k 07288555 Simulated streamgages and identifier— U.S. Geological Survey, 2020

Bayou

lo w Big S u n f

33°40'

90°

90°25'

Big S

and C

ay Bay

ive

Round a

Yazoo R

Ba ey

07288500

reek

Pelu

ci a B a you

430

0 0

Figure 15. Simulated stream reaches using the modular finite-difference flow model 6 Streamflow Routing package.

6 3

12 KILOMETERS 6 MILES

24 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

90°30'

90°25'

90°20'

90°15'

90°10'

90°05'

ll B

ayo

Ta llah a tc h

B ill Bayou

Burrell Bayou

Wi l

EXPLANATION Water use, in cubic meters per year (Bristow and Wilson, 2023)

TALLAHATCHIE

Yal obu s 3,500,000 High: ha Riv e r

33°45'

Rattl e snake

Groundwater Transfer and Injection Pilot groundwater wells

LEFLORE

B ay o u

SUNFLOWER

49E

Teoc

eek

CARROLL

49W

Big S

518

and C

ay Bay

reek

Pelu

ci a B a you

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 16. Average noncalibrated volumetric water use in cubic meters per year. Data processed from Aquaculture and Irrigation Water-Use Model estimates by Bristow and Wilson (2023).

Shellmound Groundwater-Flow Model 25

Round a

ive

Yazoo R

33°35'

Cree

acocowa Cree Pot k

Streams

Qu ive rR iv

er Riv er

a ck

Shellmound model extent GRENADA

442

Low: 0

Bayou

lo w Big S u n f

33°40'

90°

90°30'

26 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge number of iterations before convergence was set to 50 for non-linear iterations and 100 for linear iterations; the flow residual tolerance for linear iterations was set to 0.001. The same solver settings were used for all models and resulted in model run times of 58 minutes for model A, 28 minutes for model B, and 12 minutes for model C using MODFLOW 6 version 6.2.0.

Calibration After construction, the Shellmound model went through a process where selected model inputs were adjusted to improve the match between the model’s simulated outputs and historical observations or calibration targets. This process is called “model calibration” or “parameter estimation” (Fienen and others, 2022). The parameter estimation of the Shellmound model included the identification of the calibration targets based on available observation data, adjustment selection of model parameters, manual adjustments of some parameters, and automated calibration using Parameter Estimation ++ (PEST++; White and others 2020). Manual calibration consisted of a trial-and-error approach to minimize the sum of the squared weighted differences between model simulated values and the equivalent calibration targets, the sum of which is the objective function (Φ, phi). Phi is a measure of the degree of mismatch between observed and simulated conditions and is tracked though the entire calibration process as an indicator of how well the model is

capable of matching observations. The automated calibration of the groundwater model utilized PEST++ Iterative Ensemble Smoother (PESTPP–IES) software. The IES algorithm, along with select PEST++ and IES options (White, 2018; White and others, 2020), were activated to iteratively improve the model fit to the observations and reduce the uncertainty in parameter values during each iteration (table 3). The automated calibration process is based on Bayes’ Theorem (Tarantola, 2005; Fienen and others, 2022). It begins with a set of input parameter values known as the “prior,” which are then refined through a system conditioning step called the “update,” resulting in a new set of values referred to as the “posterior” (Fienen and others, 2022). The calibration process of the Shellmound model followed steps described in Leaf and others (2023) and Fienen and others (2022) using PEST++ (White and others, 2021), which was run on the USGS Denali supercomputer (Falgout and others, 2022).

Observations Calibration targets are observation values that the calibration process aims to reproduce by adjusting parameters and simulating the model. Calibration targets in the Shellmound model include field observations and derivatives computed as spatial and temporal differences generated using the Modflow-obs Python package (Leaf, 2024). Field measurements of groundwater levels and total streamflows were used to compute average values corresponding to stress

Table 3. Parameter Estimation ++ Iterative Ensemble Smoother (PESTPP–IES) settings for calibration. [PEST, Parameter Estimation; IES, Iterative Ensemble Smoother; --, option was not used]

PEST ++ and IES options

Model A

Model B

Model C

pestmode

Estimation

noptmax

svdmode

maxsing

250

eigthresh

0.000001

eigwrite

ies_num_reals

500

400

par_sigma_range

ies_bad_phi_sigma

2.5

overdue_giveup_fac

3.5

overdue_giveup_minutes

400

360

ies_save_rescov

False

ies_no_noise

False

True

ies_drop_conflicts

False

ies_pdc_sigma_distance

ies_autoadaloc

False

ies_lambda_mults

0.1, 1.0, 10.0, 100.0

lambda_scale_fac

0.75,0.9,1.0,1.1

ies_subset_size

Shellmound Groundwater-Flow Model 27 periods where there are available data. The USGS National Water Information System (NWIS) database (U.S. Geological Survey, 2020) was processed using methods described in two reports (Asquith and Seanor, 2019; Asquith and others, 2020) to produce synthetic groundwater-level observations, leading to 896 weighted and 375 non-weighted direct groundwater levels observations organized in six different observation groups (table 4). Only 30 of the groundwater-level observations were from the Tertiary deposits, 29 of which were weighted in the calibration, and represented 3 percent of weighted groundwater-level observations; the 97 percent remaining groundwater levels were measurements made in the MRVA aquifer. The number of field measurements and synthetic groundwater-level observations used for calibration in the Shellmound model are shown by the size of the circles on the map in figure 17. Streamflows and stage observations were processed from the NWIS database (U.S. Geological Survey, 2020) and from a random forest regression-based statistical model described in Dietsch and others (2022). Streamflow and stream stage observations were processed into monthly averages that resulted in 434 measured streamflow and 264 measured stage observations processed from the NWIS database and 142 estimated streamflow observations processed from the random forest model outputs (table 4). In addition to the measured and random forest output values, observations were also processed to produce secondary or derived observations based on long-term streamflow temporal differences. For details on how derived observations were produced, refer to Leaf and others (2023). Derived observations that were used in the calibration of the Shellmound model as calibration targets consisted of 1,937 groundwater-level temporal differences organized in four observation groups, 44 groundwater-level trends, 82 groundwater-level spatial differences, and 403 streamflow temporal differences organized in two observation groups (table 4).

is the residual associated with the ith observation and is calculated as observed minus simulated.

Initial observation weights were assigned based on uncertainty associated with the measurement and followed the approach used by Hunt and others (2013) and Leaf and others (2023). Weights were subsequently adjusted during manual calibration to approximately apportion the overall contribution of each observation group to the objective function (eq. 1) in accordance with the modeling objectives of simulating groundwater levels. This approach resulted in 2,462 weighted observations that included direct derivatives of groundwater-level measurements and 1,946 zero-weighted observations that included streamflows and some groundwater levels (table 4).

Parameterization Parameterization consisted of linking PESTPP–IES to specific model inputs. Parameterization of the Shellmound model extensively relied on the use of multipliers to adjust inputs imported from the parent model and other sources such as AIWUM (Bristow and Wilson, 2023) and the SWB model (Nielsen and Westenbroek, 2023). The overall approach is similar to the method used in Leaf and others (2023) and Fienen and others (2022) following the multiscale approach described in White and others (2021). Coarse- and fine-scale parameterization was facilitated by the PstFrom routine from the pyEMU python package by White and others (2016, 2021). Coarse-scale parameters were generally multipliers used to allow for input bias correction such as data source and processes used in data preparation. Fine-scale parameters were applied where needed to allow for changes owing to local heterogeneity.

Aquifer Properties

Observation Weighting The calibration process was primarily tracked by the objective function (eq. 1), which is a representation of the fit between the calibration targets and their equivalents from the model outputs. The difference between each observation and its equivalent in model outputs is referred to as a residual (Doherty, 2016; White and others, 2020) and was weighted using the equation of the objective function: Φ = ∑ ni=1 (wi ri) 2 where

is the objective function,

is the total number of observations,

is the assigned weight of the ith observation, and

(1)

Multiple levels of parameterization were applied to the aquifer properties, which comprise horizontal hydraulic conductivity (Kh), hydraulic conductivity vertical anisotropy (Kvani), Sy, and specific storage. Direct values were assigned to the two-dimensional grids based on zones defined by the resistivity classes (Minsley and others, 2021) for the MRVA aquifer section and hydrostratigraphic units defined in Hart and others (2008) for the underlying Tertiary layers. Cross sections of the Shellmound model with prior (noncalibrated) hydraulic conductivity values assigned based on resistivity classes are shown in figure 18. In addition to that initial coarse parameterization, multipliers for each zone and layer were added to allow for differences in zones based on layering. Finally, a dense network of regularly spaced pilot points (figs. 11–13) were added to Kh and Kvani layers. Pilot points for Sy were added to the first nine layers, which resulted in 40,150 aquifer-property parameters for model A; 39,202 for model B; and 23,780 for model C (tables 5–7).

90°25'

90°20'

90°15'

90°10'

90°05'

90°

EXPLANATION TALLAHATCHIE

33°45'

Elevation, in meters High: 53.1

Low: 28.5 Shellmound model extent Streams GRENADA Groundwater-level measurement count LEFLORE

1–14

33°40'

15–53 442

SUNFLOWER

54–121 Synthetic groundwater-level measurement count

49E

659–742 7

743–824 33°35'

825–852

49W

CARROLL

518

430

0 0

6 3

12 KILOMETERS 6 MILES

Figure 17. Field measurement and synthetic groundwater levels in the study area. The background image shows the digital elevation model of the land surface. Water-level measurements from U.S. Geological Survey (2020) and synthetic water-level measurements from Asquith and Seanor (2019) and Asquith and others (2020).

28 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

90°30'

Shellmound Groundwater-Flow Model 29 Table 4. Observations used in the model calibration as calibration targets. [--, not applicable]

Type

Derivation

Number of weighted observations

Number of zero-weighted observations

Total

heads_spinup

Direct heads

heads

Direct heads

270

364

heads_msemb

Direct heads

323

111

434

priority_wells_spinup

Direct heads

priority_wells

Direct heads

117

164

priority_wells_msemb

Direct heads

115

168

heads_tdiff

Derived heads

Temporal

625

198

823

priority_wells_tdiff

Derived heads

Temporal

188

169

357

heads_disp

Derived heads

Temporal

519

priority_wells_disp

Derived heads

Temporal

140

238

head_trend

Derived heads

Temporal

heads_sdiff

Derived heads

Spatial

flux_measured

Direct fluxes

264

flux_estimated

Direct fluxes

142

flux_measured_tdiff

Derived fluxes

Temporal

262

flux_estimated_tdiff

Derived fluxes

Temporal

141

stage_measured

Direct stage

264

transmissivity

Transmissivity

Observation group

30 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge A. Model a 60

–50 –100 –150

–200 –250

B. Model b

0 –50 –100

–150 –200 –250

C. Model c 0 –50

–100

Horizontal hydraulic conductivity, in meters per day

Elevation above North American Vertical Datum of 1988, in meters

–150 –200 –250

0 0

5,000

10,000

15,000

20,000

Distance from northern boundary, in meters

25,000

30,000

Figure 18. North to south cross section of models A, B, and C showing noncalibrated hydraulic conductivity values (Guira and Weisser, 2025).

Shellmound Groundwater-Flow Model 31 Table 5. Calibration parameters used in model A.

Parameter group

Description

Number of parameters

Mean starting value

Lower bound

Upper bound

Parameter type

Parameter style

k_zone_direct

Hydraulic conductivity by aquifer property zone

26.87

0.01

300

Zone

Direct

k_zone-lay_mult

Multiplier on hydraulic conductivity by aquifer property zone and layer

1.03

0.10

Zone

Multiplier

k_pp_layer0

Pilot point multiplier on horizontal hydraulic conductivity for layer 1

986

1.04

0.10

Pilot points

Multiplier

k_pp_layer1

Pilot point multiplier on horizontal hydraulic conductivity for layer 2

986

1.09

0.10

Pilot points

Multiplier

k_pp_layer2

Pilot point multiplier on horizontal hydraulic conductivity for layer 3

986

1.05

0.10

Pilot points

Multiplier

k_pp_layer3

Pilot point multiplier on horizontal hydraulic conductivity for layer 4

986

1.08

0.10

Pilot points

Multiplier

k_pp_layer4

Pilot point multiplier on horizontal hydraulic conductivity for layer 5

986

1.08

0.10

Pilot points

Multiplier

k_pp_layer5

Pilot point multiplier on horizontal hydraulic conductivity for layer 6

986

1.09

0.10

Pilot points

Multiplier

k_pp_layer6

Pilot point multiplier on horizontal hydraulic conductivity for layer 7

986

1.05

0.10

Pilot points

Multiplier

k_pp_layer7

Pilot point multiplier on horizontal hydraulic conductivity for layer 8

986

1.07

0.10

Pilot points

Multiplier

k_pp_layer8

Pilot point multiplier on horizontal hydraulic conductivity for layer 9

986

1.07

0.10

Pilot points

Multiplier

k_pp_layer9

Pilot point multiplier on horizontal hydraulic conductivity for layer 10

986

1.08

0.10

Pilot points

Multiplier

k_pp_layer10

Pilot point multiplier on horizontal hydraulic conductivity for layer 11

986

1.06

0.10

Pilot points

Multiplier

k_pp_layer11

Pilot point multiplier on horizontal hydraulic conductivity for layer 12

986

1.08

0.10

Pilot points

Multiplier

k_pp_layer12

Pilot point multiplier on horizontal hydraulic conductivity for layer 13

986

1.07

0.10

Pilot points

Multiplier

k_pp_layer13

Pilot point multiplier on horizontal hydraulic conductivity for layer 14

986

1.07

0.10

Pilot points

Multiplier

k_pp_layer14

Pilot point multiplier on horizontal hydraulic conductivity for layer 15

986

1.06

0.10

Pilot points

Multiplier

k_pp_layer15

Pilot point multiplier on horizontal hydraulic conductivity for layer 16

238

1.06

0.10

Pilot points

Multiplier

k_pp_layer16

Pilot point multiplier on horizontal hydraulic conductivity for layer 17

238

1.07

0.10

Pilot points

Multiplier

k_pp_layer17

Pilot point multiplier on horizontal hydraulic conductivity for layer 18

238

1.05

0.10

Pilot points

Multiplier

kvani_zone_direct

Hydraulic conductivity vertical anisotropy by aquifer property zone

155.97

1.00

10,000

Zone

Direct

kvani_zonelay_mult

Multiplier on hydraulic conductivity vertical anisotropy by aquifer property zone and layer

1.03

0.10

Zone

Multiplier

kvani_pp_layer0

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 1

986

1.08

0.10

Pilot points

Multiplier

32 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Table 5. Calibration parameters used in model A.—Continued

Number of parameters

Mean starting value

Lower bound

Upper bound

Parameter type

Parameter style

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 2

986

1.09

0.10

Pilot points

Multiplier

kvani_pp_layer2

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 3

986

1.06

0.10

Pilot points

Multiplier

kvani_pp_layer3

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 4

986

1.07

0.10

Pilot points

Multiplier

kvani_pp_layer4

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 5

986

1.08

0.10

Pilot points

Multiplier

kvani_pp_layer5

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 6

986

1.05

0.10

Pilot points

Multiplier

kvani_pp_layer6

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 7

986

1.07

0.10

Pilot points

Multiplier

kvani_pp_layer7

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 8

986

1.07

0.10

Pilot points

Multiplier

kvani_pp_layer8

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 9

986

1.07

0.10

Pilot points

Multiplier

kvani_pp_layer9

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 10

986

1.08

0.10

Pilot points

Multiplier

kvani_pp_layer10 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 11

986

1.09

0.10

Pilot points

Multiplier

kvani_pp_layer11 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 12

986

1.07

0.10

Pilot points

Multiplier

kvani_pp_layer12 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 13

986

1.08

0.10

Pilot points

Multiplier

kvani_pp_layer13 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 14

986

1.08

0.10

Pilot points

Multiplier

kvani_pp_layer14 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 15

986

1.08

0.10

Pilot points

Multiplier

kvani_pp_layer15 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 16

238

1.08

0.10

Pilot points

Multiplier

kvani_pp_layer16 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 17

238

1.09

0.10

Pilot points

Multiplier

kvani_pp_layer17 Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 18

238

1.10

0.10

Pilot points

Multiplier

ss_zone_direct

Specific storage by aquifer property zone

1.00E-05

Zone

Direct

ss_zone-lay_mult

Multiplier on specific storage by aquifer property zone and layer

1.03

0.10

Zone

Multiplier

sy_zone_direct

Specific yield by aquifer property zone

0.16

0.05

0.35

Zone

Direct

sy_zone-lay_mult Multiplier on specific yield by aquifer property zone and layer

1.15

0.10

Zone

Multiplier

sy_pp_layer0

Pilot point multiplier on specific yield layer 1

986

1.08

0.10

Pilot points

Multiplier

sy_pp_layer1

Pilot point multiplier on specific yield layer 2

986

1.05

0.10

Pilot points

Multiplier

sy_pp_layer2

Pilot point multiplier on specific yield layer 3

986

1.06

0.10

Pilot points

Multiplier

sy_pp_layer3

Pilot point multiplier on specific yield layer 4

986

1.08

0.10

Pilot points

Multiplier

Parameter group

Description

kvani_pp_layer1

9.85E-07 1.00E-07

Shellmound Groundwater-Flow Model 33 Table 5. Calibration parameters used in model A.—Continued

Parameter group

Description

Number of parameters

Mean starting value

Lower bound

Upper bound

Parameter type

Parameter style

sy_pp_layer4

Pilot point multiplier on specific yield layer 5

986

1.06

0.10

Pilot points

Multiplier

sy_pp_layer5

Pilot point multiplier on specific yield layer 6

986

1.06

0.10

Pilot points

Multiplier

sy_pp_layer6

Pilot point multiplier on specific yield layer 7

986

1.08

0.10

Pilot points

Multiplier

sy_pp_layer7

Pilot point multiplier on specific yield layer 8

986

1.08

0.10

Pilot points

Multiplier

sy_pp_layer8

Pilot point multiplier on specific yield layer 9

986

1.06

0.10

Pilot points

Multiplier

wel_datasource_ mult

Multiplier on pumping by data source

1.02

0.50

1.38333

Grid

Multiplier

rzonemult

Multiplier on recharge by surficial connectivity zone

0.18

0.01

1.5

Zone

Multiplier

rch_pp_mult

Pilot point multiplier on recharge

270

1.08

0.10

Pilot points

Multiplier

rchspmult

Recharge multiplier by stress period

148

0.54

0.01

1.5

Multiplier

wel_cn_mult

Multiplier on pumping by stress period

147

1.00

0.80

1.2

Multiplier

sfr_inflow_mult

SFR Package inflow multiplier by stream and stress period

429

1.00

0.80

1.2

Multiplier

sfr_runoff_mult

SFR Package runoff multiplier by surficial connectivity zone

715

1.03

0.20

Connectivity

Multiplier

sfr_kv_mult

SFR Package leakance multipliers, by surficial connectivity zone and by NHDPlus v2 COMID

145

0.17

0.00

Multiplier

42,012

Total

34 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Table 6. Calibration parameters used in model B.

Parameter group

Description

Number of parameters

Mean starting value

Lower bound

Upper bound

Parameter type

Parameter style

k_zone_direct

Hydraulic conductivity by aquifer property zone

25.16

0.01

300

Zone

Direct

k_zone-lay_mult

Multiplier on hydraulic conductivity by aquifer property zone and layer

1.00

0.1

Zone

Multiplier

k_pp_layer0

Pilot point multiplier on horizontal hydraulic conductivity for layer 1

986

1.08

0.1

Pilot points

Multiplier

k_pp_layer1

Pilot point multiplier on horizontal hydraulic conductivity for layer 2

986

1.07

0.1

Pilot points

Multiplier

k_pp_layer2

Pilot point multiplier on horizontal hydraulic conductivity for layer 3

986

1.07

0.1

Pilot points

Multiplier

k_pp_layer3

Pilot point multiplier on horizontal hydraulic conductivity for layer 4

986

1.06

0.1

Pilot points

Multiplier

k_pp_layer4

Pilot point multiplier on horizontal hydraulic conductivity for layer 5

986

1.12

0.1

Pilot points

Multiplier

k_pp_layer5

Pilot point multiplier on horizontal hydraulic conductivity for layer 6

986

1.09

0.1

Pilot points

Multiplier

k_pp_layer6

Pilot point multiplier on horizontal hydraulic conductivity for layer 7

986

1.06

0.1

Pilot points

Multiplier

k_pp_layer7

Pilot point multiplier on horizontal hydraulic conductivity for layer 8

986

1.09

0.1

Pilot points

Multiplier

k_pp_layer8

Pilot point multiplier on horizontal hydraulic conductivity for layer 9

986

1.07

0.1

Pilot points

Multiplier

k_pp_layer9

Pilot point multiplier on horizontal hydraulic conductivity for layer 10

986

1.07

0.1

Pilot points

Multiplier

k_pp_layer10

Pilot point multiplier on horizontal hydraulic conductivity for layer 11

986

1.09

0.1

Pilot points

Multiplier

k_pp_layer11

Pilot point multiplier on horizontal hydraulic conductivity for layer 12

986

1.08

0.1

Pilot points

Multiplier

k_pp_layer12

Pilot point multiplier on horizontal hydraulic conductivity for layer 13

986

1.07

0.1

Pilot points

Multiplier

k_pp_layer13

Pilot point multiplier on horizontal hydraulic conductivity for layer 14

986

1.08

0.1

Pilot points

Multiplier

k_pp_layer14

Pilot point multiplier on horizontal hydraulic conductivity for layer 15

986

1.09

0.1

Pilot points

Multiplier

k_pp_layer15

Pilot point multiplier on horizontal hydraulic conductivity for layer 16

238

1.07

0.1

Pilot points

Multiplier

kvani_zone_direct

Hydraulic conductivity vertical anisotropy by aquifer property zone

276.79

10,000

Zone

Direct

kvani_zonelay_mult

Multiplier on hydraulic conductivity vertical anisotropy by aquifer property zone and layer

1.06

0.1

Zone

Multiplier

kvani_pp_layer0

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 1

986

1.07

0.1

Pilot points

Multiplier

kvani_pp_layer1

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 2

986

1.08

0.1

Pilot points

Multiplier

Shellmound Groundwater-Flow Model 35 Table 6. Calibration parameters used in model B.—Continued

Parameter group

Description

Number of parameters

Mean starting value

Lower bound

Upper bound

Parameter type

Parameter style

kvani_pp_layer2

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 3

986

1.08

0.1

Pilot points

Multiplier

kvani_pp_layer3

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 4

986

1.08

0.1

Pilot points

Multiplier

kvani_pp_layer4

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 5

986

1.09

0.1

Pilot points

Multiplier

kvani_pp_layer5

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 6

986

1.07

0.1

Pilot points

Multiplier

kvani_pp_layer6

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 7

986

1.05

0.1

Pilot points

Multiplier

kvani_pp_layer7

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 8

986

1.10

0.1

Pilot points

Multiplier

kvani_pp_layer8

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 9

986

1.07

0.1

Pilot points

Multiplier

kvani_pp_layer9

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 10

986

1.07

0.1

Pilot points

Multiplier

kvani_pp_layer10

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 11

986

1.06

0.1

Pilot points

Multiplier

kvani_pp_layer11

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 12

986

1.08

0.1

Pilot points

Multiplier

kvani_pp_layer12

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 13

986

1.09

0.1

Pilot points

Multiplier

kvani_pp_layer13

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 14

986

1.05

0.1

Pilot points

Multiplier

kvani_pp_layer14

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 15

986

1.09

0.1

Pilot points

Multiplier

kvani_pp_layer15

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 16

238

1.10

0.1

Pilot points

Multiplier

ss_zone_direct

Specific storage by aquifer property zone

0.00

1E-07

ss_zonelay_mult

Multiplier on specific storage by aquifer property zone and layer

1.04

0.1

sy_zone_direct

Specific yield by aquifer property zone

0.17

sy_zonelay_mult

Multiplier on specific yield by aquifer property zone and layer

1.25

0.00001 Zone

Direct

Zone

Multiplier

0.05

0.35

Zone

Direct

0.1

Zone

Multiplier

36 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Table 6. Calibration parameters used in model B.—Continued

Parameter group

Description

Number of parameters

Mean starting value

Lower bound

Upper bound

Parameter type

Parameter style

sy_pp_layer0

Pilot point multiplier on specific yield layer 1

986

1.07

0.1

Pilot points

Multiplier

sy_pp_layer1

Pilot point multiplier on specific yield layer 2

986

1.08

0.1

Pilot points

Multiplier

sy_pp_layer2

Pilot point multiplier on specific yield layer 3

986

1.07

0.1

Pilot points

Multiplier

sy_pp_layer3

Pilot point multiplier on specific yield layer 4

986

1.09

0.1

Pilot points

Multiplier

sy_pp_layer4

Pilot point multiplier on specific yield layer 5

986

1.08

0.1

Pilot points

Multiplier

sy_pp_layer5

Pilot point multiplier on specific yield layer 6

986

1.08

0.1

Pilot points

Multiplier

sy_pp_layer6

Pilot point multiplier on specific yield layer 7

986

1.08

0.1

Pilot points

Multiplier

sy_pp_layer7

Pilot point multiplier on specific yield layer 8

986

1.09

0.1

Pilot points

Multiplier

sy_pp_layer8

Pilot point multiplier on specific yield layer 9

986

1.08

0.1

Pilot points

Multiplier

wel_datasource_ mult

Multiplier on pumping by data source

1.02

0.5

1.38333 Grid

Multiplier

rzonemult

Multiplier on recharge by surficial connectivity zone

0.19

0.01

1.5

Zone

Multiplier

rch_pp_mult

Pilot point multiplier on recharge

270

1.10

0.1

Pilot points

rchspmult

Recharge multiplier by stress period

148

0.54

0.01

1.5

Multiplier

wel_cn_mult

Multiplier on pumping by stress period

147

1.00

0.8

1.2

Multiplier

sfr_inflow_mult

SFR Package inflow multiplier by stream and stress period

429

1.00

0.8

1.2

Multiplier

sfr_runoff_mult

SFR Package runoff multiplier by surficial connectivity zone

715

1.01

0.2

Connectivity

Multiplier

sfr_kv_mult

SFR Package leakance multipliers, by surficial connectivity zone and by NHDPlus v2 COMID

145

0.14

0.0001

Multiplier

41,064

Total

Multiplier

Shellmound Groundwater-Flow Model 37 Table 7. Calibration parameters used in model C.

Parameter group

Description

Number of parameters

Mean starting value

Lower bound

Upper bound

Parameter type

Parameter style

k_zone_direct

Hydraulic conductivity by aquifer property zone

38.79

0.01

300

Zone

Direct

k_zone-lay_mult

Multiplier on hydraulic conductivity by aquifer property zone and layer

0.97

0.1

Zone

Multiplier

k_pp_layer0

Pilot point multiplier on horizontal hydraulic conductivity for layer 1

986

1.11

0.1

Pilot points

Multiplier

k_pp_layer1

Pilot point multiplier on horizontal hydraulic conductivity for layer 2

986

1.11

0.1

Pilot points

Multiplier

k_pp_layer2

Pilot point multiplier on horizontal hydraulic conductivity for layer 3

986

1.09

0.1

Pilot points

Multiplier

k_pp_layer3

Pilot point multiplier on horizontal hydraulic conductivity for layer 4

986

1.10

0.1

Pilot points

Multiplier

k_pp_layer4

Pilot point multiplier on horizontal hydraulic conductivity for layer 5

986

1.10

0.1

Pilot points

Multiplier

k_pp_layer5

Pilot point multiplier on horizontal hydraulic conductivity for layer 6

986

1.10

0.1

Pilot points

Multiplier

k_pp_layer6

Pilot point multiplier on horizontal hydraulic conductivity for layer 7

986

1.08

0.1

Pilot points

Multiplier

k_pp_layer7

Pilot point multiplier on horizontal hydraulic conductivity for layer 8

986

1.09

0.1

Pilot points

Multiplier

kvani_zone_direct

Hydraulic conductivity vertical anisotropy by aquifer property zone

126.00

10000

Zone

Direct

kvani_zonelay_mult

Multiplier on hydraulic conductivity vertical anisotropy by aquifer property zone and layer

1.18

0.1

Zone

Multiplier

kvani_pp_layer0

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 1

986

1.09

0.1

Pilot points

Multiplier

kvani_pp_layer1

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 2

986

1.09

0.1

Pilot points

Multiplier

kvani_pp_layer2

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 3

986

1.07

0.1

Pilot points

Multiplier

kvani_pp_layer3

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 4

986

1.08

0.1

Pilot points

Multiplier

kvani_pp_layer4

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 5

986

1.10

0.1

Pilot points

Multiplier

kvani_pp_layer5

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 6

986

1.07

0.1

Pilot points

Multiplier

kvani_pp_layer6

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 7

986

1.10

0.1

Pilot points

Multiplier

kvani_pp_layer7

Pilot point multiplier on hydraulic conductivity vertical anisotropy layer 8

986

1.09

0.1

Pilot points

Multiplier

38 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Table 7. Calibration parameters used in model C.—Continued

Parameter group

Description

Number of parameters

Mean starting value

Lower bound

Upper bound

1.00E-05 Zone

Direct

Parameter type

Parameter style

ss_zone_direct

Specific storage by aquifer property zone

0.00

1.00E-07

ss_zonelay_mult

Multiplier on specific storage by aquifer property zone and layer

0.95

0.1

Zone

Multiplier

sy_zone_direct

Specific yield by aquifer property zone

0.16

0.05

0.35

Zone

Direct

sy_zonelay_mult

Multiplier on specific yield by aquifer property zone and layer

1.14

0.1

Zone

Multiplier

sy_pp_layer0

Pilot point multiplier on specific yield layer 1

986

1.11

0.1

Pilot points

Multiplier

sy_pp_layer1

Pilot point multiplier on specific yield layer 2

986

1.08

0.1

Pilot points

Multiplier

sy_pp_layer2

Pilot point multiplier on specific yield layer 3

986

1.12

0.1

Pilot points

Multiplier

sy_pp_layer3

Pilot point multiplier on specific yield layer 4

986

1.08

0.1

Pilot points

Multiplier

sy_pp_layer4

Pilot point multiplier on specific yield layer 5

986

1.12

0.1

Pilot points

Multiplier

sy_pp_layer5

Pilot point multiplier on specific yield layer 6

986

1.10

0.1

Pilot points

Multiplier

sy_pp_layer6

Pilot point multiplier on specific yield layer 7

986

1.10

0.1

Pilot points

Multiplier

sy_pp_layer7

Pilot point multiplier on specific yield layer 8

986

1.10

0.1

Pilot points

Multiplier

wel_datasource_ mult

Multiplier on pumping by data source

0.94

0.5

1.38333

Grid

Multiplier

rzonemult

Multiplier on recharge by surficial connectivity zone

0.14

0.01

1.5

Zone

Multiplier

rch_pp_mult

Pilot point multiplier on recharge

270

1.14

0.1

Pilot points

Multiplier

rchspmult

Recharge multiplier by stress period

148

0.54

0.01

1.5

Multiplier

wel_cn_mult

Multiplier on pumping by stress period

147

1.00

0.8

1.2

Multiplier

sfr_inflow_mult

SFR Package inflow multiplier by stream and stress period

429

1.00

0.8

1.2

Multiplier

sfr_runoff_mult

SFR Package runoff multiplier by surficial connectivity zone

715

1.03

0.2

Connectivity

Multiplier

sfr_kv_mult

SFR Package leakance multipliers, by surficial connectivity zone and by NHDPlus v2 COMID

145

0.17

0.0001

Multiplier

25,642

Total

Shellmound Groundwater-Flow Model 39

Areal Recharge

Calibration Results and Best Model

Three levels of parameterization were applied to the areal groundwater recharge in the Shellmound model calibration. At the coarsest level, stress period multipliers were used to allow the calibration to correct for temporal bias in SWB model outputs. Additionally, recharge zone multipliers were added based on the surficial connectivity (fig. 9) and a spatial layer developed by Minsley and others (2021) based on electrical resistivity of the uppermost 15 m as interpreted by using the AEM survey data (Minsley and others, 2021). SWB model net infiltration does not simulate attenuation of recharge passing through the vadose zone that could affect recharge rates. Therefore, adding the surficial connectivity parameters improves the ability of the model to account for changes in recharge rates based on the degree of connection between the surface and the groundwater system. Finally, a network of pilot-point multipliers was added to account for local heterogeneity, which resulted in a total of 423 groundwater recharge parameters.

Following the construction and initial manual calibration, each model was transferred to the USGS Denali supercomputer (Falgout and others, 2022) for automated calibration. Calibration results were analyzed and evaluated for model fit and rationality of calibrated parameter values. One goal of this study was to explore the effects of integrating the AEM data (Minsley and others, 2021) and to evaluate which layering configuration (models A, B, or C) would yield the most useful model. The criteria used to decide on a good calibration included the value of Φ for the entire model, Φ for observations of particular interest, and calibrated parameters values. The IES method produces an ensemble of Φ values at the end of each iteration in the history matching process, corresponding to all realizations that successfully ran to completion, including the minimum error variance solution referred to as the “base realization.” Phi (Φ) values after four successive iterations for each model are shown in table 8. Mean Φ value for model A improved from 2,884.17 to 240.68 (table 8; fig. 19). Phi (Φ) values for models B and C changed from 2,473.32 to 231.03 and from 2,015.30 to 234.40, respectively (table 8; figs. 20 and 21). The “base” realization resulted in Φ values of 253.43, 258.72, and 265.25 for models A–C, respectively, after the second iteration. Calibration continued to improve throughout the process across all three models. However, to prevent potential overfitting of parameters, the analysis focused on results from the second iteration for the selection of one model configuration for the forecast. After the second iteration, model A outperformed models B and C. The global Φ value was not the sole indicator for optimal calibration but supported the observation that model A more accurately simulated water levels near the GTIP project operation sites. In addition to the acceptable calibration, the detailed representation of the MRVA aquifer in model A contributed to the decision to use model A for the forecast simulation. A good model calibration does not solely rely on achieving a satisfactory fit between simulated and observed values, leading to the smallest Φ; it is also crucial that the calibration yield a realistic set of parameters that are also in agreement with the general understanding of the conceptual model. A thorough review of the posterior “base” parameter set over the successive iterations, along with subsequent corresponding model inputs, led to the conclusion that the calibrated parameters values were acceptable. Within the “base” parameter realization after the second iteration, only 2 out of 42,012 parameters reached their maximum acceptable values (upper parameter bound) set through the calibration constraints, which further supports the conclusion that the parameters values were acceptable and not overfit to match observations. Parameters that reached the maximum acceptable values were those representing constant multipliers for AIWUM pumping rates and

Streamflow Routing Streams and their connection to the groundwater system were represented in the Shellmound model by the SFR package (Langevin and others, 2017). Parameterization of the SFR package inputs included surface-water inflows, surface runoff, and streambed vertical hydraulic conductivity. Multipliers to the inflows were added for stress periods 1 (steady-state), and 7–148 (monthly transient) and for the three inflow reaches. Surface runoff inputs were parameterized using multipliers by stress period but also by surficial connectivity (fig. 9) to account for the relation between infiltration capacity and runoff (Nielsen and Westenbroek, 2023). Unique multipliers were applied to streambed conductivity for each stream segment based on unique identifiers (COMID) associated with each stream segment in the NHDPlus version 2 (McKay and others, 2012). Additionally, coarse multiplier parameters were added based on the surficial connectivity. The parameterization of streamflow routing resulted in a total of 1,289 adjustable parameters (tables 5–7).

Water Use Water use estimates in the Shellmound model were parameterized by stress period and data source. One multiplier was assigned to each of the three data sources (AIWUM, SWUDS, and MERAS 2.2) that supplied pumping rates to the Shellmound model (Harris and Diehl, 2019a; Haugh and others, 2020b; Wilson, 2021). There was no pumping simulated during the first, steady-state stress period because it represented naturalized conditions prior to groundwater development; therefore, only 147 additional stress-period-based multipliers were applied throughout the simulation. The process resulted in a total of 150 adjustable parameters used to constrain pumping rates in the Shellmound model (tables 5–7).

40 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Table 8. Ensemble phi (Φ, objective function) values for models A–C following calibration run using Parameter Estimation++ Iterative Ensemble Smoother (PESTPP–IES) (White, 2018). Total runs Model A

Model B

Mean Phi value

Standard deviation

Model C

Model A

Model B

Model C

Model A

Model B

Model C

399

398

400

2,884.17

2,473.32

2,015.30

4,822.22

3,332.84

589.69

1,011

1,013

1,020

565.83

393.45

449.73

841.07

107.99

84.34

1,600

1,619

1,638

284.78

273.98

277.84

65.79

17.78

18.50

2,186

2,211

2,253

249.39

244.56

244.30

25.74

13.55

5.91

2,767

2,801

2,860

240.68

231.03

234.40

46.00

14.12

4.36

A. Ensemble phi by iteration

B. Iteration 2 phi distribution EXPLANATION

Iteration 2 base phi: 253 20

Ensemble member Base member

10,000

Phi

10 1,000 5

iES iteration

250

275

300

325

Phi

350

375

400

Figure 19. Ensemble phi (Φ, objective function) values from the calibration for model C. A, Reduction in the Φ value throughout iterations and B, histogram of ensemble members Φ values. In orange is Φ value for the base ensemble member.

Shellmound Groundwater-Flow Model 41 Table 8. Ensemble phi (Φ, objective function) values for models A–C following calibration run using Parameter Estimation++ Iterative Ensemble Smoother (PESTPP–IES) (White, 2018). —Continued Minimum Phi value

Maximum Phi value

Base realization Phi value

Model A

Model B

Model C

Model A

Model B

Model C

Model A

Model B

Model C

478.25

535.45

819.52

34,327.30

21,962.80

4,057.37

1,843.51

1,920.20

2,206.91

281.47

291.34

295.02

6,751.41

1,605.64

750.82

339.86

375.89

343.81

243.86

245.38

245.48

1,072.73

341.67

394.92

253.43

258.72

265.25

228.48

225.48

230.45

385.70

380.64

261.11

237.54

238.36

237.58

223.13

216.62

222.37

996.54

357.17

245.71

228.73

227.22

229.23

A. Ensemble phi by iteration

B. Iteration 2 phi distribution EXPLANATION Ensemble member Base member

10,000

Iteration 2 base phi: 259

16 14 12

Phi

10 8 1,000

6 4 2 0

iES iteration

260

280

300

320

Phi

Figure 20. Ensemble phi (Φ, objective function) values for model B history matching. A, Reduction in the Φ value throughout iterations and B, histogram of ensemble members Φ values. In orange is Φ value for the base ensemble member.

340

42 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge A. Ensemble phi by iteration

B. Iteration 2 phi distribution

4,000

EXPLANATION

3,000

Iteration 2 base phi: 265

Ensemble member Base member

2,000

Phi

15 1,000 10 600 400

300 200

iES iteration

240

260

280

300

320

340

360

380

400

Phi

Figure 21. Ensemble phi (Φ, objective function) values for model C history matching. A, Reduction in the Φ value throughout iterations and B, histogram of ensemble members Φ values. In orange is Φ value for the base ensemble member.

recharge in stress period 5 (“pname:wel_datasource_ mult_inst:0_ptype:gr_usecol:3_pstyle:m_idx0:iwum,” and “pname:rchspmult_inst:5_ptype:cn_pstyle:m”). All other posterior parameters in the “base” realization remained within bounds, further supporting that an acceptable calibration was achieved with model A. The “base” member parameter set for iteration 2 of model A most closely matched observations compared to those of models B and C. Therefore, model A was selected to use as the forecast model. Consequently, results from the calibration and water budget estimates presented in this section of the report will focus on the best calibration model—model A. More results from the calibration of model A are presented in appendix 1. Results from the calibration and water budget estimates for models B and C are presented in appendix 2. Model calibration input and output files are available for download from the associated USGS data release (Guira and Weisser, 2025). The best calibration of the Shellmound model was achieved with the improved representation of the interaction between surface water and groundwater. An earlier version of the model that used base flows as inflows to the SFR package and calibration targets did not yield realistic results and further exacerbated structural imperfections while accounting for the streambed leakance. The modeling approach was subsequently modified to employ streamflows as inputs and calibration targets at the streamgages. This approach was rendered possible thanks to the surface runoff inputs provided by the SWB model (Nielsen and Westenbroek, 2023). The use of the surficial connectivity layer (fig. 9; Minsley and others, 2021) to parameterize groundwater recharge substantially improved the calibration particularly

in the cone of depression. Because the SWB model does not account for potential barriers to vertical movement of water in the vadose zone, the net infiltration rates that the SWB model produces can be appreciably different from the actual net infiltration rates to the groundwater-flow system. The surficial connectivity zone multipliers adjusted during calibration showed a strong correlation between surficial connectivity and higher recharge. For example, the multiplier for zone 1 changed from 0.1 before automated calibration to approximately 0.07, thereby reducing SWB model recharge in that zone by approximately 25 percent. However, the multiplier for zone 5 during the same calibration changed from 0.4 to 0.53, resulting in a 20-percent increase of recharge in zone 5. Calibration of the Shellmound model employed pilot point (Doherty, 2003) multiplier parameters for aquifer properties (Kh, Kvani, and Sy) and groundwater recharge to account for possible local heterogeneity (figs. 11–13). Interpolation between pilot points was only allowed within zones (fig. 11; Minsley and others, 2021), and this contributed to maintaining the contrast of lithologic fabric between zones while allowing local heterogeneity.

Calibration Results for Model A Overall, the calibrated model achieved a good match for groundwater-level direct measurements and temporal trends such as seasonal fluctuations (fig. 22). Generally, groundwater-level measurements were collected biannually in April and October to capture seasonal high and low conditions at the end of the nongrowing (April) and growing seasons (October). A good fit between simulated and observed for

Shellmound Groundwater-Flow Model 43 B. Priority embayment heads

A. Shellmound heads

Simulated head, in meters

35.0

Mean error (ME): –0.45 meter Mean absolute error (MAE): 0.57 Root mean squared error (RMSE): 0.68 n: 47

32.5

ME: –0.36 meter MAE: 0.57 RMSE: 0.72 n: 115

30.0 27.5 25.0 22.5 20.0

Measured head, in meters

D. Heads

C. Embayment heads 40

Simulated head, in meters

ME: –0.21 meter MAE: 0.90 RMSE: 1.25 n: 323

Measured head, in meters

n: 406

n: 43

106 105 104 103 2

101 100 0 10

Measured head, in meters

F. Linear head trends

Simulated, in meters per day

Simulated, in cubic meters per day

E. Streamflow

107

108

ME: –0.42 meter MAE: 1.01 RMSE: 1.32 n: 270

102

104

106

Measured, in cubic meters per day

108

0.0002 0.0000 −0.0002 −0.0004 −0.0006

−0.0006 −0.0004 −0.0002 0.0000 0.0002

Measured, in meters per day

Figure 22. One-to-one plots comparing the Shellmound model outputs to field observations. A, Shellmound heads. B, Priority embayment heads. C, Embayment heads. D, Heads. E, Streamflow. F, Groundwater-level linear head trends.

44 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge observation groups “Shellmound heads,” “Priority embayment heads,” “Embayment heads,” and “Heads” with mean absolute errors of 0.57, 0.57, 0.90, and 1.01 m, respectively, are shown in figures 22A–D. Root-mean-squared error values for the same groups were 0.68, 0.72, 1.25, and 1.32 m, respectively. The mean absolute residual for weighted groundwater levels were 0.85 m and 4.40 m for the MRVA and Tertiary aquifers, respectively. The calibration did not yield a robust fit to the linear groundwater-level trends group (“head_trend”) even though only 7 out of 43 simulated trends were in the opposite direction compared to the observed trends, but the incorporation of that group appeared to help improve the fit in absolute groundwater level. Time series of groundwater levels for select observation sites purposefully chosen to cover the cone of depression and show the effect of the streams on groundwater levels from nearby wells are shown in figure 23. For USGS sites 334538090303801 (133F0600 Sunflower) and 334412090270301 (133F0190 Sunflower), located in the northwest corner of the Shellmound model domain (fig. 1), the model results show a good match between simulated and observed aquifer groundwater levels. The seasonal fluctuations between high water levels in April (the end of the nongrowing season) and low water levels in October (following the growing season) were well simulated (figs. 23A, B). Time series groundwater-level plots for USGS sites 334429090210101 (083A0602 Leflore), and 332733090252901 (083C0074 Leflore), located between the Tallahatchie and the Quiver Rivers, are shown in figures 23C–D. Both stations show a good match between simulated and observed groundwater levels although groundwater levels at station 083A0602 tend to be underestimated, whereas groundwater levels at station 083C0074 were overestimated. Similarly, figures 23E and F show time series groundwater levels plots for USGS stations 333742090303801 (L0027) and 333251090323801 (083F0534) with a good match between simulated and observed groundwater levels. Although use of the surficial connectivity layer (fig. 9; Minsley and others, 2021) during calibration improved the match between simulated and observed groundwater levels, most groundwater levels at stations in lower surficial connectivity zones were slightly overestimated. Simulated and observed time series for groundwater levels at USGS station 333603090164301 (083G0506 Sunflower) are shown in figure 23G. This station is 0.7 km from the Tallahatchie River and 0.8 km from the extraction site (fig. 1) used in the GTIP project. As a result, groundwater levels at this station are affected by stream seepage during seasonal high flows and long-term trends that remain relatively constant, thereby emphasizing interactions between surface water and groundwater. Time series of simulated and observed groundwater levels at USGS station 333251090323801 (02058 Sunflower) are shown in figure 23H. This plot shows a significant difference between simulated and observed groundwater

levels. Observed groundwater levels were approximately 5 m above the simulated groundwater levels and indicative of a perched system, which is consistent with findings from a previous study by O’Reilly and others (2020). Monthly average time series of observed and simulated streamflows at the Big Sunflower River at Sunflower, Miss. (USGS station 07288500), and Tallahatchie River at Money, Miss. (USGS station 07281600) are shown in figure 24. Simulated streamflows at the Big Sunflower River at Sunflower, Miss., generally follow the observed patterns (fig. 24A). However, simulated streamflows at the Tallahatchie River at Money, Miss., tend to overestimate high flows and underestimate low flows (fig. 24B). During calibration, there was a tradeoff between slight improvements in streamflows during low flows where residuals on groundwater levels remained significantly high and achieved a better match between observed groundwater levels and their simulated equivalents near the Tallahatchie River at the expense of obtaining high residuals on streamflows (fig. 24).

Calibrated Parameter Values This section of the report presents calibration results for model A. A combination of coarse-, medium-, and fine-scale parameters resulted in a satisfactory calibration using PESTPP–IES (White, 2018). The “base” ensemble member after iteration 2 was chosen as the best parameter set to represent a calibrated version of the model (fig. 19).

Aquifer Properties Calibrated aquifer properties by layer are shown in figures 25–28. Calibrated hydraulic conductivity for the entire model ranges from 0.02 meter per day (m/d) in the lower Claiborne confining unit to 300 m/d in the alluvial deposits, with an average value of 27 m/d. The MRVA aquifer portion of the model, as defined by aquifer material above the newly interpreted base using AEM data by Minsley and others (2021), calibrated to a slightly higher average Kh (27.6 m/d), whereas the Tertiary units calibrated to a lower average value (22.3 m/d). These hydraulic conductivity values were at the lower end of previously reported ranges of 1–500 m/d (Leaf and others, 2023). The calibrated hydraulic conductivity values in the MRVA aquifer were within the expected ranges and generally agree with the heterogeneity suggested by the interpretation of the AEM data. Anisotropy (ratio of Kh to the vertical hydraulic conductivity) was calibrated to an average value of 116.2 (dimensionless) and ranged from 1 (isotropic situation) to 3,400. Average anisotropy for MRVA aquifer was 103 and ranged from 1 to 758, whereas the Tertiary deposits calibrated to an average anisotropy of 126 and ranges from 1 to 3,400. Calibrated Sy and specific storage ranged from 0.05 to 0.35 and from 2.7x10−7 to 10−5, respectively, and were close to

Shellmound Groundwater-Flow Model 45

B. Head at USGS site 334412090270301 (133F0190 Sunflower) 32.5

32.5

Meters above sea level

35.0

A. Head at U.S. Geological Survey (USGS) site 334538090303801 (133F0600 Sunflower)

30.0 27.5 25.0 22.5 20.0 17.5

Zero-weighted spin-up period

30.0 27.5 25.0 22.5 20.0 17.5 15.0

Zero-weighted spin-up period

15.0

C. Head at USGS site 334429090210101 (083A0602 Leflore)

D. Head at USGS site 333950090230001 (083C0074 Leflore) 32.5

35.0

Meters above sea level

37.5

32.5 30.0 27.5 25.0 22.5 20.0

Zero-weighted spin-up period

30.0 27.5 25.0 22.5 20.0 17.5 15.0

F. Head at USGS site 333611090215901 (083F0534 Sunflower)

30.0

32.5

27.5

30.0

Meters above sea level

E. Head at USGS site 333742090303801 (L0027 Sunflower)

25.0 22.5 20.0 17.5 15.0 12.5

Zero-weighted spin-up period

27.5 25.0 22.5 20.0 17.5 15.0

Zero-weighted spin-up period

10.0

G. Head at USGS site 333603090164301 (083G0506 Sunflower)

H. Head at USGS site 333251090323801 (02058 Sunflower) 30.0

Meters above sea level

40.0 37.5 35.0 32.5 30.0 27.5 25.0 22.5

Zero-weighted spin-up period

2008

2010

27.5 25.0 22.5 20.0 17.5 15.0 12.5

2012

2014

Year

2016

2018

Zero-weighted spin-up period

2008

2010

2012

2014

Year

2016

2018

EXPLANATION Measured

Base member

Ensemble member

Figure 23. Time series of measured groundwater levels (U.S. Geological Survey, 2020) and simulated equivalents (Guira and Weisser, 2025) at selected wells. A, U.S. Geological Survey (USGS) site 334538090303801 (133F0600 Sunflower). B, USGS site 334412090270301 (133F0190 Sunflower). C, USGS site 334429090210101 (083A0602 Leflore). D, USGS site 332733090252901 (083C0074 Leflore). E, USGS site 333742090303801 (L0027). F, USGS site 333251090323801 (083F0534). G, USGS site 333603090164301 (083G0506 Sunflower). H, USGS site 333251090323801 (02058 Sunflower).

46 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Streamflow, in cubic meters per day

A. Streamflow at U.S. Geological Survey (USGS) site 07288500 (Big Sunflower River at Sunflower, Mississippi) 107

106

105

Zero-weighted spin-up period

2009

2011

2013

2015

2017

2019

2011

2013

2015

2017

2019

Streamflow, in cubic meters per day

Year B. Streamflow at USGS site 07281600 (Tallahatchie River at Money, Mississippi) 108

107

Zero-weighted spin-up period

2009

Year EXPLANATION Measured

Base member

Ensemble member

Figure 24. Streamflow time series showing monthly averages of measured streamflows (U.S. Geological Survey, 2020) and simulated equivalents (Guira and Weisser, 2025). A, Big Sunflower River at Sunflower, Mississippi (U.S. Geological Survey [USGS] station 07288500). B, Tallahatchie River at Money, Miss. (USGS station 07281600).

Shellmound Groundwater-Flow Model 47 B. Layer 1 'base' property zones

101

150 10

200 250

10−1

Model row

102

100

101

150 100

200 250

10−1 0

100

150

200

Model column

250

300

150 4 200 3

250

C. Layer 2 Kh minimum: 0.7351 maximum: 273.1 mean 29.08

100

D. Layer 2 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

Model row

Hydraulic conductivity, in meters per day

Model row

100

Electrical resistivity facies class

102

facies minimum: 3 facies maximum: 7 facies mode: 4

100

150 4 200 3

250

100

150

200

Model column

250

300

Electrical resistivity facies class

Model row

minimum: 0.6917 maximum: 300 mean 62.85

Hydraulic conductivity, in meters per day

A. Layer 1 hydraulic conductivity (Kh) 0

Figure 25. Horizontal hydraulic conductivity estimates for the Shellmound model (Guira and Weisser, 2025), compared to electrical resistivity-based zones from the airborne electromagnetic survey (James and Minsley, 2021; Minsley and others, 2021). A–JJ, Horizontal hydraulic conductivity and electrical resistivity zones for model layers 1–18.

48 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge F. Layer 3 'base' property zones

101

150 10

200 250

10−1

Model row

102

100

101

150 100

200 250

10−1 0

100

150

200

Model column

250

300

100

150 4 3

250

G. Layer 4 Kh minimum: 0.1446 maximum: 196.7 mean 17.2

200

H. Layer 4 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

Model row

Electrical resistivity facies class

100

facies minimum: 4 facies maximum: 6 facies mode: 5

100

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

102

Hydraulic conductivity, in meters per day

Model row

minimum: 1.34 maximum: 109.3 mean 18.41

Hydraulic conductivity, in meters per day

E. Layer 3 Kh 0

Model column

Shellmound Groundwater-Flow Model 49 I . Layer 5 Kh

150 10

200 250

10−1

Model row

102

100

101

150 10

200 250

10−1 0

100

150

200

Model column

250

300

100

150 4 3

250

K. Layer 6 Kh minimum: 0.1365 maximum: 237.3 mean 27.95

200

L. Layer 6 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

Model row

Electrical resistivity facies class

101

facies minimum: 5 facies maximum: 6 facies mode: 5

100

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

100

Model row

102

Hydraulic conductivity, in meters per day

minimum: 0.2025 maximum: 75.14 mean 25.62

Model row

J. Layer 5 'base' property zones

Hydraulic conductivity, in meters per day

Model column

50 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge N. Layer 7 'base' property zones

100

Model row

101

150 10

200 250

10−1

102

Model row

100

101

150 100

200 250

10−1 0

100

150

200

Model column

250

300

150 4

200 3

250

2 0

P. Layer 8 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 16

100

Model row

minimum: 0.09081 maximum: 219.6 mean 41.39

100

O. Layer 8 Kh

Hydraulic conductivity, in meters per day

Electrical resistivity facies class

102

facies minimum: 4 facies maximum: 6 facies mode: 5

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

Model row

minimum: 0.09433 maximum: 297.1 mean 30.4

Hydraulic conductivity, in meters per day

M . Layer 7 Kh 0

Model column

Shellmound Groundwater-Flow Model 51

101

150 10

200 250

10−1

minimum: 0.4002 maximum: 300 mean 101.8

102

100

101

150 100

200 250

10−1 0

100

150

200

Model column

250

300

100

150 4 200 3

250

S. Layer 10 Kh

Model row

facies minimum: 3 facies maximum: 6 facies mode: 5

Electrical resistivity facies class

100

R. Layer 9 'base' property zones

T. Layer 10 'base' property zones

facies minimum: 3 facies maximum: 5 facies mode: 4

100

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

102

Model row

minimum: 0.5972 maximum: 184.7 mean 41.18

Hydraulic conductivity, in meters per day

Q. Layer 9 Kh

Hydraulic conductivity, in meters per day

Model column

52 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

101

150 100

200 250

10−1

minimum: 0.4529 maximum: 300 mean 44.91

102

100

101

150 100

200 250

10−1 0

100

150

200

Model column

250

300

100

150 4 200 3

250

W. Layer 12 Kh

Model row

X. Layer 12 'base' property zones

facies minimum: 2 facies maximum: 5 facies mode: 3

100

Model row

100

facies minimum: 3 facies maximum: 5 facies mode: 4

Electrical resistivity facies class

102

V. Layer 11 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

Model row

minimum: 0.4407 maximum: 274.3 mean 56.38

Hydraulic conductivity, in meters per day

U. Layer 11 Kh

Hydraulic conductivity, in meters per day

Model column

Shellmound Groundwater-Flow Model 53

101

150 100

200 250

10−1

minimum: 0.4708 maximum: 174.6 mean 6.412

102

100

101

150 100

200 250

10−1 0

100

150

200

Model column

250

300

100

150 4 200 3

250

AA. Layer 14 Kh

Model row

BB. Layer 14 'base' property zones

facies minimum: 2 facies maximum: 4 facies mode: 3

100

Model row

100

facies minimum: 2 facies maximum: 4 facies mode: 3

Electrical resistivity facies class

102

Z. Layer 13 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

Model row

minimum: 0.3555 maximum: 300 mean 10.84

Hydraulic conductivity, in meters per day

Y. Layer 13 Kh

Hydraulic conductivity, in meters per day

Model column

54 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

101

150 100

200 250

10−1

Model row

102

100

101

150 100

200 250

10−1 100

200

Model column

150 4

200

250

FF. Layer 16 'base' property zones

minimum: 0.02496 maximum: 0.1386 mean 0.07186

100

EE. Layer 16 Kh (single zone representing the Lower Claiborne confining unit)

facies minimum: 2 facies maximum: 3 facies mode: 3

300

Electrical resistivity facies class

100

DD. Layer 15 'base' property zones

20.0

facies minimum: -facies maximum: -facies mode: 18

19.5 19.0

100

18.5

150

18.0

200

17.5 17.0

250

16.5 0

100

200

300

Electrical resistivity facies class

102

Model row

minimum: 0.279 maximum: 3.706 mean 0.9486

Hydraulic conductivity, in meters per day

CC. Layer 15 Kh

Hydraulic conductivity, in meters per day

16.0

Model column

150 100

200 250

10−1

II. Layer 18 Kh (single zone representing the Wilcox aquifer [undifferentiated]) minimum: 0.8406 maximum: 8.173 mean 2.595

Model row

102

100

101

150 100

200 250

10−1 0

100

200

Model column

300

facies minimum: -facies maximum: -facies mode: 19

100

150 200

17 250 16

JJ. Layer 18 'base' property zones

facies minimum: -facies maximum: -facies mode: 20

50 100

150 200

17 250 0

100

200

300

Electrical resistivity facies class

101

Electrical resistivity facies class

100

HH. Layer 17 'base' property zones

Model row

102

Model row

minimum: 0.3252 maximum: 2.123 mean 1.109

Hydraulic conductivity, in meters per day

GG. Layer 17 Kh (single zone representing the Lower Claiborne aquifer)

Hydraulic conductivity, in meters per day

Shellmound Groundwater-Flow Model 55

Model column

56 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

103

Model row

100 102

150 200

101

250

B. Layer 1 'base' property zones

facies minimum: 3 facies maximum: 7 facies mode: 4

100

Model row

minimum: 2.417 maximum: 642.5 mean 145.4

150 4 200 3

250

Electrical resistivity facies class

A. Layer 1 hydraulic conductivity vertical anisotropy (Kh/Kv)

Hydraulic conductivity vertical anisotropy, dimensionless

2 0

103

Model row

100 102

150 200

101

250

100

150

200

Model column

250

300

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 19.63 maximum: 758.3 mean 133

D. Layer 2 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

C. Layer 2 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

Model column

Figure 26. Hydraulic conductivity vertical anisotropy estimates for the Shellmound model (Guira and Weisser, 2025), compared to electrical resistivity-based zones from the airborne electromagnetic survey (James and Minsley, 2021; Minsley and others, 2021). A– JJ, Hydraulic conductivity vertical anisotropy and resistivity zones for model layers 1–18.

Shellmound Groundwater-Flow Model 57

103

Model row

100 102

150 200

101

250

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 33.2 maximum: 353.9 mean 109.8

F. Layer 3 'base' property zones

150 4 200 3

250

Electrical resistivity facies class

E. Layer 3 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

2 0

103

Model row

100 102

150 200

101

250

100

150

200

Model column

250

300

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 21.86 maximum: 304.8 mean 92.13

H. Layer 4 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

G. Layer 4 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

Model column

58 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

103

Model row

100 102

150 200

101

250

facies minimum: 5 facies maximum: 6 facies mode: 5

100

Model row

minimum: 23.03 maximum: 463.7 mean 102.2

J. Layer 5 'base' property zones

150 4

200 3

250

Electrical resistivity facies class

I. Layer 5 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

2 0

103

Model row

100 102

150 200

101

250

100

150

200

Model column

250

300

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 8.703 maximum: 484.1 mean 77.54

L. Layer 6 'base' property zones

150 4

200 3

250

100

150

200

250

300

Electrical resistivity facies class

K. Layer 6 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

Model column

Shellmound Groundwater-Flow Model 59

103

Model row

100 102

150 200

101

250

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 11.88 maximum: 434.6 mean 119.7

N. Layer 7 'base' property zones

150 4 200 3

250

Electrical resistivity facies class

M. Layer 7 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

2 0

103

Model row

100 102

150 200

101

250

100

150

200

Model column

250

300

facies minimum: 4 facies maximum: 6 facies mode: 16

100

Model row

minimum: 10.48 maximum: 514.4 mean 178.7

P. Layer 8 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

O. Layer 8 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

Model column

60 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

103

Model row

100 102

150 200

101

250

facies minimum: 3 facies maximum: 6 facies mode: 5

100

Model row

minimum: 5.957 maximum: 306 mean 79.8

R. Layer 9 'base' property zones

150 4 200 3

250

Electrical resistivity facies class

Q. Layer 9 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

2 0

103

Model row

100 102

150 200

101

250

100

150

200

Model column

250

300

facies minimum: 3 facies maximum: 5 facies mode: 4

100

Model row

minimum: 4.482 maximum: 356 mean 89.56

T. Layer 10 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

S. Layer 10 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

Model column

Shellmound Groundwater-Flow Model 61

103

Model row

100 102

150 200

101

250

facies minimum: 3 facies maximum: 5 facies mode: 4

100

Model row

minimum: 4.366 maximum: 593.1 mean 99.52

V. Layer 11 'base' property zones

150 4 200 3

250

Electrical resistivity facies class

U.. Layer 11 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

2 0

103

Model row

100 102

150 200

101

250

100

150

200

Model column

250

300

facies minimum: 2 facies maximum: 5 facies mode: 3

100

Model row

minimum: 7.043 maximum: 359.1 mean 52.46

X. Layer 12 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

W. Layer 12 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

Model column

62 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

103

Model row

100 102

150 200

101

250

facies minimum: 2 facies maximum: 4 facies mode: 3

100

Model row

minimum: 8.608 maximum: 377.4 mean 36.8

Z. Layer 13 'base' property zones

150 4 200 3

250

Electrical resistivity facies class

Y. Layer 13 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

2 0

103

Model row

100 102

150 200

101

250

100

150

200

Model column

250

300

facies minimum: 2 facies maximum: 4 facies mode: 3

100

Model row

minimum: 4.97 maximum: 365.7 mean 25.88

BB. Layer 14 'base' property zones

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

AA. Layer 14 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

Model column

Shellmound Groundwater-Flow Model 63

103

100 102

150 200

101

250

DD. Layer 15 'base' property zones

facies minimum: 2 facies maximum: 3 facies mode: 3

Model row

minimum: 2.58 maximum: 34.11 mean 9.232

Model row

100

150 4

200

250

Electrical resistivity facies class

CC. Layer 15 Kh/Kv

Hydraulic conductivity vertical anisotropy, dimensionless

100 102

150 200

101

250 0

100

200

Model column

300

FF. Layer 16 'base' property zones

20.0

facies minimum: -facies maximum: -facies mode: 18

19.5 19.0

100

18.5

150

18.0

200

17.5 17.0

250

16.5 0

100

200

300

Electrical resistivity facies class

103

Model row

minimum: 343.3 maximum: 3,400 mean 1,261

Model row

Hydraulic conductivity vertical anisotropy, dimensionless

EE. Layer 16 Kh/Kv (single zone representing the Lower Claiborne confining unit)

16.0

Model column

64 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

102

150 200

101

250

facies minimum: -facies maximum: -facies mode: 19

100 18

150 200

17 250 16

II. Layer 18 Kh/Kv (single zone representing the Wilcox aquifer [undifferentiated]) 0

Model row

103

100 102

150 200

101

250 0

100

200

Model column

300

JJ. Layer 18 'base' property zones

facies minimum: -facies maximum: -facies mode: 20

Model row

minimum: 12.03 maximum: 100.4 mean 28.58

Hydraulic conductivity vertical anisotropy, dimensionless

100 18

150 200

17 250 0

100

200

Electrical resistivity facies class

100

HH. Layer 17 'base' property zones

300

Electrical resistivity facies class

103

Model row

minimum: 15.78 maximum: 132.6 mean 44.05

Model row

Hydraulic conductivity vertical anisotropy, dimensionless

GG. Layer 17 Kh/Kv (single zone representing the Lower Claiborne aquifer)

Model column

Shellmound Groundwater-Flow Model 65

100

0.25

150

0.20

200

0.15

250

0.10

B. Layer 1 'base' property zones

facies minimum: 3 facies maximum: 7 facies mode: 4

100

150 4 200 3

250

0.05

C. Layer 2 Sy

0.30

100

0.25

150

0.20

200

0.15

250

0.10

100

150

200

Model column

250

300

0.05

D. Layer 2 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

0.35

minimum: 0.073 maximum: 0.35 mean 0.30

Specific yield, dimensionless

Electrical resistivity facies class

0.30

Model row

minimum: 0.050 maximum: 0.35 mean 0.17

Model row

0.35

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

A. Layer 1 Sy

Specific yield, dimensionless

Model column

Figure 27. Specific yield estimates for the Shellmound model (Guira and Weisser, 2025), compared to electrical resistivity-based zones from the airborne electromagnetic survey (James and Minsley, 2021; Minsley and others, 2021). A–JJ, Specific yield and resistivity zones for model layers 1–18.

66 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

100

0.25

150

0.20

200

0.15

250

0.10

F. Layer 3 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

150 4 200 3

250

0.05

G. Layer 4 Sy

0.30

100

0.25

150

0.20

200

0.15

250

0.10

100

150

200

Model column

250

300

0.05

H. Layer 4 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

0.35

minimum: 0.052 maximum: 0.35 mean 0.17

Specific yield, dimensionless

Electrical resistivity facies class

0.30

Model row

minimum: 0.083 maximum: 0.35 mean 0.29

Model row

0.35

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

E. Layer 3 Sy

Specific yield, dimensionless

Model column

Shellmound Groundwater-Flow Model 67

100

0.25

150

0.20

200

0.15

250

0.10

J.. Layer 5 'base' property zones

facies minimum: 5 facies maximum: 6 facies mode: 5

100

150 4 200 3

250

0.05

K. Layer 6 Sy

0.30

100

0.25

150

0.20

200

0.15

250

0.10

100

150

200

Model column

250

300

0.05

L. Layer 6 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 0.050 maximum: 0.35 mean 0.11

Model row

0.35

Specific yield, dimensionless

Electrical resistivity facies class

0.30

Model row

minimum: 0.050 maximum: 0.35 mean 0.17

Model row

0.35

150 4 200 3

250

100

150

200

250

300

Model column

Electrical resistivity facies class

I. Layer 5 Sy

Specific yield, dimensionless

68 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

100

0.25

150

0.20

200

0.15

250

0.10

N. Layer 7 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

150 4 200 3

250

0.05

O. Layer 8 Sy

0.30

100

0.25

150

0.20

200

0.15

250

0.10

100

150

200

Model column

250

300

0.05

P. Layer 8 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 16

100

Model row

0.35

minimum: 0.080 maximum: 0.35 mean 0.28

Specific yield, dimensionless

Electrical resistivity facies class

0.30

Model row

minimum: 0.056 maximum: 0.35 mean 0.18

Model row

0.35

150 4 200 3

250

100

150

200

250

300

Model column

Electrical resistivity facies class

M. Layer 7 Sy

Specific yield, dimensionless

Shellmound Groundwater-Flow Model 69

100

0.25

150

0.20

200

0.15

250

0.10

R. Layer 9 'base' property zones

facies minimum: 3 facies maximum: 6 facies mode: 5

100

150 4 200 3

250

0.05

S. Layer 10 Sy

0.30

100

0.25

150

0.20

200

0.15

250

0.10

100

150

200

Model column

250

300

0.05

T. Layer 10 'base' property zones

facies minimum: 3 facies maximum: 5 facies mode: 4

100

Model row

0.35

minimum: 0.084 maximum: 0.21 mean 0.15

Specific yield, dimensionless

Electrical resistivity facies class

0.30

Model row

minimum: 0.051 maximum: 0.35 mean 0.15

Model row

0.35

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

Q. Layer 9 Sy

Specific yield, dimensionless

Model column

70 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

100

0.25

150

0.20

200

0.15

250

0.10

V. Layer 11 'base' property zones

facies minimum: 3 facies maximum: 5 facies mode: 4

100

150 4 200 3

250

0.05

0.30

100

0.25

150

0.20

200

0.15

250

0.10

100

150

200

Model column

250

300

0.05

X. Layer 12 'base' property zones

facies minimum: 2 facies maximum: 5 facies mode: 3

100

Model row

0.35

minimum: 0.13 maximum: 0.24 mean 0.16

Specific yield, dimensionless

W. Layer 12 Sy

Electrical resistivity facies class

0.30

Model row

minimum: 0.087 maximum: 0.16 mean 0.10

Model row

0.35

150 4 200 3

250

100

150

200

250

300

Electrical resistivity facies class

U. Layer 11 Sy

Specific yield, dimensionless

Model column

Shellmound Groundwater-Flow Model 71

100

0.25

150

0.20

200

0.15

250

0.10

Z. Layer 13 'base' property zones

facies minimum: 2 facies maximum: 4 facies mode: 3

100

150 4 200 3

250

0.05

AA. Layer 14 Sy

0.30

100

0.25

150

0.20

200

0.15

250

0.10

100

150

200

Model column

250

300

0.05

BB. Layer 14 'base' property zones

facies minimum: 2 facies maximum: 4 facies mode: 3

100

Model row

0.35

minimum: 0.079 maximum: 0.22 mean 0.095

Specific yield, dimensionless

Electrical resistivity facies class

0.30

Model row

minimum: 0.093 maximum: 0.35 mean 0.12

Model row

0.35

150 4 200 3

250

100

150

200

250

300

Model column

Electrical resistivity facies class

Y. Layer 13 Sy

Specific yield, dimensionless)

72 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

100

0.25

150

0.20

200

0.15

250

0.10

DD. Layer 15 'base' property zones

facies minimum: 2 facies maximum: 3 facies mode: 3

100

150 4

200

250

0.05

0.30

100

0.25

150

0.20

200

0.15

250

0.10 0

100

200

Model column

300

0.05

FF. Layer 16 'base' property zones

20.0

facies minimum: -facies maximum: -facies mode: 18

Model row

0.35

minimum: 0.12 maximum: 0.12 mean 0.12

Specific yield, dimensionless

EE. Layer 16 Sy (single zone representing the Lower Claiborne confining unit)

Electrical resistivity facies class

0.30

Model row

minimum: 0.17 maximum: 0.25 mean 0.19

Model row

0.35

19.5 19.0

100

18.5

150

18.0

200

17.5 17.0

250

16.5 0

100

200

300

Electrical resistivity facies class

CC. Layer 15 Sy

Specific yield, dimensionless

16.0

Model column

100

0.25

150

0.20

200

0.15

250

0.10

HH. Layer 17 'base' property zones

facies minimum: -facies maximum: -facies mode: 19

100 18

150 200

17 250

0.05

0.30

100

0.25

150

0.20

200

0.15

250

0.10 0

100

200

Model column

300

0.05

JJ. Layer 18 'base' property zones

facies minimum: -facies maximum: -facies mode: 20

Model row

minimum: 0.18 maximum: 0.18 mean 0.18

Model row

0.35

Specific yield, dimensionless

II. Layer 18 Sy (single zone representing the Wilcox aquifer [undifferentiated])

100 18

150 200

17 250 0

100

200

300

Electrical resistivity facies class

0.30

Model row

minimum: 0.098 maximum: 0.098 mean 0.098

Model row

0.35

Specific yield, dimensionless

GG. Layer 17 Sy (single zone representing the Lower Claiborne aquifer)

Electrical resistivity facies class

Shellmound Groundwater-Flow Model 73

Model column

74 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

4.0 3.5

Model row

100

3.0 2.5

150

2.0 200

1.5 1.0

250

B.. Layer 1 'base' property zones

facies minimum: 3 facies maximum: 7 facies mode: 4

100

Model row

minimum: 7.5e-07 maximum: 1.5e-06 mean 1.4e-06

150 4 200 3

250

0.5

C. Layer 2 Ss

1e−6 4.0 3.5

100

Model row

3.0 2.5

150

2.0 200

1.5 1.0

250

D.. Layer 2 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 8.8e-07 maximum: 1.1e-06 mean 1.0e-06

Specific storage, dimensionless

150 4 200 3

250

0.5 0

100

150

200

Model column

250

300

Electrical resistivity facies class

1e−6

100

150

200

250

300

Electrical resistivity facies class

A. Layer 1 specific storage (Ss)

Specific storage, dimensionless

Model column

Figure 28. Specific storage estimates for the Shellmound model (Guira and Weisser, 2025), compared to electrical resistivity-based zones from the airborne electromagnetic survey (James and Minsley, 2021; Minsley and others, 2021). A–JJ, Specific storage and resistivity zones for model layers 1–18.

Shellmound Groundwater-Flow Model 75

4.0 3.5

Model row

100

3.0 2.5

150

2.0 200

1.5 1.0

250

F. Layer 3 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 9.5e–07 maximum: 1.7e–06 mean 1.5e–06

150 4 200 3

250

0.5

G. Layer 4 Ss

1e−6 4.0 3.5

100

Model row

3.0 2.5

150

2.0 200

1.5 1.0

250

H.. Layer 4 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 3.4e–07 maximum: 2.3e–06 mean 1.1e–06

Specific storage, dimensionless

150 4 200 3

250

0.5 0

100

150

200

Model column

250

300

Electrical resistivity facies class

1e−6

100

150

200

250

300

Electrical resistivity facies class

E. Layer 3 Ss

Specific storage, dimensionless

Model column

76 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

4.0 3.5

Model row

100

3.0 2.5

150

2.0 200

1.5 1.0

250

J. Layer 5 'base' property zones

facies minimum: 5 facies maximum: 6 facies mode: 5

100

Model row

minimum: 6.8e–07 maximum: 1.2e–06 mean 8.0e–07

150 4 200 3

250

0.5

K. Layer 6 Ss

1e−6 4.0 3.5

100

Model row

3.0 2.5

150

2.0 200

1.5 1.0

250

L. Layer 6 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 7.3e–07 maximum:: 1.7 1.7ee–06 mean 1.7e–06

Specific storage, dimensionless

150 4 200 3

250

0.5 0

100

150

200

Model column

250

300

Electrical resistivity facies class

1e−6

100

150

200

250

300

Electrical resistivity facies class

I. Layer 5 Ss

Specific storage, dimensionless

Model column

Shellmound Groundwater-Flow Model 77

4.0 3.5

Model row

100

3.0 2.5

150

2.0 200

1.5 1.0

250

N. Layer 7 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 5

100

Model row

minimum: 4.0e–07 maximum: 2.7e–06 mean 1.5e–06

150 4 200 3

250

0.5

O. Layer 8 Ss

1e−6 4.0 3.5

100

Model row

3.0 2.5

150

2.0 200

1.5 1.0

250

P. Layer 8 'base' property zones

facies minimum: 4 facies maximum: 6 facies mode: 16

100

Model row

minimum: 4.1e–07 maximum: 1.8e–06 mean 6.8e–07

Specific Storage, dimensionless

150 4 200 3

250

0.5 0

100

150

200

Model column

250

300

Electrical resistivity facies class

1e−6

100

150

200

250

300

Electrical resistivity facies class

M. Layer 7 Ss

Specific Storage, dimensionless

Model column

minimum: 3.8e–07 maximum: 4.5e–06 mean 2.1e–06

4.0 3.5

Model row

100

3.0 2.5

150

2.0 200

1.5

facies minimum: 3 facies maximum: 6 facies mode: 5

100

150 4 200

1.0

250

R. Layer 9 'base' property zones

250

0.5

S. Layer 10 Ss

1e−6 4.0 3.5

100

Model row

3.0 2.5

150

2.0 200

1.5 1.0

250

T. Layer 10 'base' property zones

facies minimum: 3 facies maximum: 5 facies mode: 4

100

Model row

minimum: 6.8e–07 maximum: 1.6e–06 mean 1.2e–06

Specific storage, dimensionless

150 4 200 3

250

0.5 0

100

150

200

Model column

250

300

Electrical resistivity facies class

1e−6

100

150

200

250

300

Electrical resistivity facies class

Q. Layer 9 Ss

Model row

Specific storage, dimensionless

78 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Model column

Shellmound Groundwater-Flow Model 79

4.0 3.5

Model row

100

3.0 2.5

150

2.0 200

1.5 1.0

250

V. Layer 11 'base' property zones

facies minimum: 3 facies maximum: 5 facies mode: 4

100

Model row

minimum: 5.4e–07 maximum: 1.3e–06 mean 1.0e–06

150 4 200 3

250

0.5

W. Layer 12 Ss

1e−6 4.0 3.5

100

Model row

3.0 2.5

150

2.0 200

1.5 1.0

250

X. Layer 12 'base' property zones

facies minimum: 2 facies maximum: 5 facies mode: 3

100

Model row

minimum: 2.8e–07 maximum: 1.9e–06 mean 1.1e–06

Specific storage, dimensionless

150 4 200 3

250

0.5 0

100

150

200

Model column

250

300

Electrical resistivity facies class

1e−6

100

150

200

250

300

Electrical resistivity facies class

U. Layer 11 Ss

Specific storage, dimensionless

Model column

80 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

4.0 3.5

Model row

100

3.0 2.5

150

2.0 200

1.5 1.0

250

Z. Layer 13 'base' property zones

facies minimum: 2 facies maximum: 4 facies mode: 3

100

Model row

minimum: 7.4e–07 maximum: 1.1e–06 mean 8.5e–07

150 4 200 3

250

0.5

AA. Layer 14 Ss

1e−6 4.0 3.5

100

Model row

3.0 2.5

150

2.0 200

1.5 1.0

250

BB. Layer 14 'base' property zones

facies minimum: 2 facies maximum: 4 facies mode: 3

100

Model row

minimum: 2.7e–07 maximum: 1.6e–06 mean 7.7e–07

Specific storage, dimensionless

150 4 200 3

250

0.5 0

100

150

200

Model column

250

300

Electrical resistivity facies class

1e−6

100

150

200

250

300

Electrical resistivity facies class

Y. Layer 13 Ss

Specific storage, dimensionless

Model column

Shellmound Groundwater-Flow Model 81

0 4

100

150 2 200 1

250

DD. Layer 15 'base' property zones

facies minimum: 2 facies maximum: 3 facies mode: 3

Model row

minimum: 4.7e-07 maximum: 4.9e-07 mean 4.9e-07

Model row

1e−6

100

150 4

200

250

Electrical resistivity facies class

CC. Layer 15 Ss

Specific storage, dimensionless

100

150 2 200 1

250 0

100

200

Model column

300

FF. Layer 16 'base' property zones

20.0

facies minimum: -facies maximum: -facies mode: 18

19.5 19.0

100

18.5

150

18.0

200

17.5 17.0

250

16.5 0

100

200

300

Electrical resistivity facies class

Model row

minimum: 5.2e-07 maximum: 5.2e-07 mean 5.2e-07

Model row

1e−6

Specific storage, dimensionless

EE. Layer 16 Ss (single zone representing the Lower Claiborne confining unit)

16.0

Model column

82 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

150 2

200

250

Model row

100

150 2

200

250 0

100

200

Model column

300

150 200

0 4

100

250

1e−6

minimum: 1.5e–06 maximum: 1.5e–06 mean 1.5e–06

JJ. Layer 18 'base' property zones

facies minimum: -facies maximum: -facies mode: 20

Model row

II. Layer 18 Ss (single zone representing the Wilcox aquifer [undifferentiated])

facies minimum: -facies maximum: -facies mode: 19

100 18

150 200

17 250 0

100

200

Electrical resistivity facies class

HH. Layer 17 'base' property zones

300

Electrical resistivity facies class

100

Model row

Specific storage, dimensionless

minimum: 1.4e–06 maximum: 1.4e-06 mean 1.4e–06

Model row

1e−6

Specific storage, dimensionless

GG. Layer 17 Ss (single zone representing the Lower Claiborne aquifer)

Model column

Shellmound Groundwater-Flow Model 83 values (0.19 to 0.32, and 2.4x10−6 to 3.8x10−5, respectively) reported by Arthur (2001), Clark and Hart (2009), and Leaf and others (2023).

figure 30C shows mean value −9.74 in/yr. The mean calibrated recharge value (1.09 in/yr) is less than one-half of the 2.84-in/ yr value reported by Clark and Hart (2009).

Streambed Vertical Hydraulic Conductivity

Water Use Parameters

Calibrated streambed vertical hydraulic conductivity ranged from 10−5 to 1.37 m/d with an average value of 6.67x10−2 m/d. Streambed vertical hydraulic conductivity plays an important role in the magnitude of the interactions between groundwater and surface water through base flows or stream leakage. Stream leakage immediately following dry (September 2016) and wet (February 2018) conditions, respectively, is shown in figures 29B and 29D. During dry conditions (fig. 29B), the simulation shows that segments of the Tallahatchie River gained base flows, whereas most reaches from the Quiver River and the Big Sunflower River lost water to the aquifer, and some reaches dried out. During wet conditions (fig. 29D), the simulation shows that most stream reaches including the Tallahatchie River lost water to the aquifer. During dry and wet conditions, reaches of the Yazoo River, as it meanders back to the model domain and around the City of Greenwood (fig. 1), remained dry in the simulation. This is mostly due to a structural error that resulted in no SFR inflows at that location. The model boundary truncated the Tallahatchie River (fig. 29B, D), which would otherwise route water to that dry stream reach.

The calibration led to a 20-percent reduction of pumping rate multipliers for data imported from the MERAS 2.2 model, which covers simulation periods prior to April 2007, and a reduction of 1 percent for SWUDS. However, multipliers for pumping rates processed from AIWUM, which covers the simulation period starting from April 2007, increased by 25 percent. The average stress-period-based multipliers for the water use was 1.00 and ranged from 0.88 to 1.09. The minimum reduction happened in stress period 143 (July 2018), whereas the maximum increase was noted in stress period 1 (April 2014). Overall, the calibration resulted in a slight increase of water use. Yearly total water use from 2007 to 2018 before and after calibration is shown in figure 31.

Recharge Average SWB model and calibrated groundwater recharge maps from 2007 to 2018 are shown in figure 30. The surficial connectivity zone multipliers, along with pilot points and stress-period-based multipliers used in the calibration, contributed to a successful calibration of the model that required reduction in recharge particularly in areas with low surficial connectivity (Minsley and others, 2021). The lowest values for recharge multipliers corresponded to the zone with the lowest surficial connectivity (0.04) and pilot points (0.48). This spatial distribution and magnitude of the multipliers are consistent with the interpretation of the AEM data by Minsley and others (2021) that showed the existence of a low conductivity layer, potentially acting as a barrier, could significantly reduce effective groundwater recharge. The spatial mean annual recharge from the base member of the ensemble in for model A calibration was 1.09 in/yr (fig. 30A), whereas mean SWB model net infiltration (passed the root zone) was 10.82 in/yr (fig. 30B). The difference between SWB model net infiltration and calibrated recharge presented on

Groundwater-Flow Model Budget Results This section of the report presents water budget results for the calibrated groundwater-flow model. Budgets for the groundwater-flow system were computed for the entire model domain to produce yearly net terms for each budget component. Simulated net budget components for the Shellmound model are shown in figure 32. Budget terms were summarized into averaged daily rates for the spin-up multiyear stress periods from 1900 to 2007 and averaged daily rates for each year from 2007 to 2018. The budget shows that groundwater pumping has been the largest outflow from the system since 1970, often approaching 100 percent of all outflows (for example, 2008, 2015–17). The second largest net outflow was the change in storage for some years (for example, 2009 and 2018). A negative change in storage represents water replenishing aquifer storage during years with high recharge and less pumping. The net storage change results in an inflow (release from storage) for most years, which represents an inflow of water to the groundwater-flow system as water leaving aquifer storage to help meet pumping demand. Prior to 1950, net outflows were dominated by groundwater discharge to the streams as base flows and lateral groundwater flows out of the model domain. Simulated net inflows include areal recharge, lateral groundwater flows, change in storage, and stream leakage.

84 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge A. Simulated water table elevations (dry conditions) 1,205,000

B. Simulated stream leakage (dry conditions)

38.00

1,200,000

.00

26.00

1,195,000 32.00

.00

24.00

34.

1,190,000

36.00

22.00

1,180,000

34.00

1,185,000 28.00

Northing, EPSG: 5070 meters

2016-10-01 (model stress period 121)

38.00

0 30.0

2016-10-01 (model stress period 121)

22.

Dry Stream flow routing (SFR) reaches are indicated in black

20.00

505,000 510,000 515,000 520,000 525,000 530,000 535,000

Easting, EPSG: 5070 meters 15

Easting, EPSG: 5070 meters

Water table elevation, in meters

–105

10 1

10 3

10 5

2018-03-01 (model stress period 138)

38.00

28.00 30

.00

20.00

1,190,000

36.

22.00

1,195,000

24.0

32.00

.00

36.00

Dry SFR reaches are indicated in black

22.0

1,180,000

.00

1,185,000

34.00

30.00

Northing, EPSG: 5070 meters

1,200,000

D. Simulated stream leakage (wet conditions)

26.

2018-03-01 (model stress period 138)

–101

Average leakage at each stream reach, in cubic meters per day

C. Simulated water table elevations (wet conditions) 1,205,000

–103

505,000 510,000 515,000 520,000 525,000 530,000 535,000

Easting, EPSG: 5070 meters 20

Water table elevation, in meters

Easting, EPSG: 5070 meters 55

–105

−103

−101

10 1

10 3

10 5

Average leakage at each stream reach, in cubic meters per day

Figure 29. Simulated water table elevation along with estimates of streambed leakage in the Streamflow Routing package in two different conditions. A, Water table elevation with equipotential contour lines in a dry condition (September 2016). B, Streamflow segments in dry conditions with average leakage at each stream reach. C, Water table elevation with equipotential contour lines in a wet condition (February 2018). D, Streamflow segments in wet conditions with average leakage at each stream reach.

Shellmound Groundwater-Flow Model 85

1,200,000

1,195,000

10 8

1,190,000

6 1,185,000

4 2

1,180,000 505,000 510,000 515,000 520,000 525,000 530,000 535,000

1,195,000

10 8

1,190,000

6 1,185,000

4 2

1,180,000

Easting, NAD 83 Albers (EPSG: 5070)

10.0 7.5

1,200,000

5.0

1,195,000

2.5 0.0

1,190,000

−2.5 1,185,000

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

1,205,000

14 1,200,000

505,000 510,000 515,000 520,000 525,000 530,000 535,000

Easting, NAD 83 Albers (EPSG: 5070) C. Recharge difference Spatial mean: –9.74 inches per year

1,205,000

−5.0

1,180,000

−7.5 505,000 510,000 515,000 520,000 525,000 530,000 535,000

−10.0

Easting, NAD 83 Albers (EPSG: 5070)

Figure 30. Comparative maps showing mean annual recharge. A, Shellmound calibrated recharge. B, soil-water-balance model (Nielsen and Westenbroek, 2023). C, Recharge difference between the soil-water-balance estimated and the calibrated.

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

1,205,000

B. Net infiltration estimated by SWB (2007–18) Spatial mean: 10.82 inches per year

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

A. Calibrated recharge (2007–18) Spatial mean: 1.09 inches per year

86 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge 80,000

300

70,000 60,000 200

50,000 40,000

150

30,000

100

20,000 50

10,000

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2018

Year EXPLANATION Noncalibrated

Calibrated

Figure 31. Total water use before and after calibration. Water-use data prior to calibration includes estimated rates from Aquaculture and Irrigation Water-Use Model (Bristow and Wilson, 2023) and nonagricultural rates from the U.S. Geological Survey site-specific water-use data system and national estimates for water use associated with thermoelectric power generation in 2010 and 2015 (Diehl and Harris, 2014; Harris and Diehl, 2019a,b).

Total water use, in gallons

Total water use, in cubic meters

250

Shellmound Groundwater-Flow Model 87 0.8

200

150

0.4

100

0.2

0.0

–0.2

–50

–100

–0.4

–150

–0.6

–200

–0.8 1900 1950 1970 1986 1992 1998 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Year EXPLANATION [SFR, Streamflow Routing; CHD, Constant Head; RCH, Recharge; WEL, Well]

net-storage net-SFR

net-CHD net-RCH

Figure 32. Simulated annual net budget results for the Shellmound model.

net-WEL

Rates, in million gallons per day

Rates, in million cubic meters per day

0.6

88 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Managed Aquifer Recharge Scenario and Simulated Results Groundwater Transfer and Injection Pilot (GTIP) Project Following the construction and calibration of the historical version of the Shellmound model, a forecast scenario model was developed to simulate the extraction and reinjection of groundwater to and from the aquifer in accordance with the objectives of the GTIP project. The GTIP project is an interagency collaborative effort focused on finding sustainable solutions to long-term groundwater-level decline in the Delta. Partners in this collaboration include the U.S. Department of Agriculture Agricultural Research Service (in charge of leading the research and funding) and the U.S. Army Corps of Engineers Vicksburg District (in charge of operations design and construction), with support from stakeholders in the Delta including the Delta Council, Delta Farmers Advocating Resource Management, Mississippi Department of Environmental Quality, Mississippi Farm Bureau Federation, the Mississippi Soil and Water Conservation Commission, U.S. Department of Agriculture Natural Resources Conservation Service, USGS, and Yazoo Mississippi Delta Joint Water Management District. With increases in agricultural development in the region during the past century, groundwater withdrawals by high-capacity wells to support agricultural production have increased concerns about long-term sustainability of the MRVA aquifer. The GTIP project, along with other studies such as the high-resolution AEM data collection were initiated to improve understanding of the subsurface and explore potential solutions to groundwater-level declines. The GTIP project uses

a managed aquifer recharge (MAR) approach to artificially replenish the groundwater. MAR is the purposeful recharge of water to aquifers to support subsequent aquifer recovery for agricultural and (or) environmental benefits (Dillon and others, 2009). There is a history of successful MAR implementation worldwide (Pyne, 2005; Dillon and others, 2019; Zheng and others, 2021) to mitigate flood, meet legal obligations, protect and (or) restore ecosystems, enhance water quality, manage water supply, and restore or protect aquifers, among others. Many methods can be used in the implementation of MAR. The ideal method used for a specific site incorporates factors such as hydrogeology, topography, hydrology, and land use around the site (Dillon and others, 2022). The MAR technique employed in this project is the bank filtration, which consists of pumping groundwater near a surface-water body to drive seepage caused by the cone of depression, combined with direct injection of the extracted groundwater, into the depleted aquifer at another location. For the GTIP project, bank filtration is induced by extracting groundwater near the Tallahatchie River, and the extracted groundwater is transferred 3 km west before it is reinjected into the aquifer (fig. 33). Because of the high transmissivity of the MRVA aquifer at the injection site, water is injected into the aquifer by gravity flow, and the injection wells are not pressurized. The extraction well was constructed 35 m from the river, has a screen that extends from approximately 19 to 34 m below land surface, and is equipped with a high-capacity pump with variable frequency drive (500–1,500 gal/min). The injection site is organized into two injection wells approximately 150 m apart with screens extending from approximately 24 to 37 m below land surface and is equipped with submersible pumps for periodic backflushing to mitigate clogging. Each injection well can receive as much as 750 gal/min as allowed by the underground injection control permitted issued by the Mississippi Department of Environmental Quality.

East

Injection wells A and B

Extraction well Tallahatchie River

3 Km Figure 33. Schematic diagram of the Groundwater Transfer and Injection Project.

Managed Aquifer Recharge Scenario and Simulated Results 89

Forecast Model The Shellmound forecast groundwater-flow model was constructed using the calibrated model inputs from the “base” realization of iteration 2. To ensure a smooth transition into “future” stress periods, the forecast model includes all stress periods in the historical model and 384 additional monthly stress periods from January 1, 2019, to January 1, 2051. Historical input data from 2010 to 2015 for recharge, water use, and lateral groundwater movement were processed into monthly averages for the forecast period. In addition to stresses simulated in the historical model, the forecast model construction included a new WEL package (Langevin and others, 2017) to simulate the GTIP project. The new WEL package only includes wells at the extraction and injection locations. Relevant information used for setting up the extraction and injection wells in the new WEL package is shown in table 9. Well screen information was used to apply pumping to the appropriate model layers and rates to be applied based on the proportion of the screen that intersects each layer. As a result, one-third of the pumping rate is applied to layers 5 and 6 individually, whereas one-sixth of the pumping rate was applied to layers 4 and 7 individually. Following the same process at the injection sites, one-half of the injection rate at injection well A was applied to layer 6, whereas one-quarter of the rate was applied to layers 5 and 7 individually. The same ratios of injection were applied at injection well B using the injection rates provided for well B. Effective extraction and injection rates accounted for times when pumping rate was reduced or stopped for maintenance purposes such as backflushing. During test periods 1 and 2 of the pilot project completed in 2021 and 2022, respectively, field operation data on extraction and injection rates and water levels at select observation wells were collected (O’Reilly and others, 2023). Effective monthly extraction and injection rates (fig. 34) were computed from the hourly data collection and applied to the Shellmound forecast model. Time series of simulated water levels at select observation sites around the injection wells, along with the available equivalent field observations collected during the two test periods of the GTIP project operations, are shown in figure 35. Water levels from a test simulation that did not account for the GTIP operations are also included. Declining groundwater levels prior to the end of the calibration period and the start of the GTIP project operations are consistent with general observations in wells around the area. The forecast results indicate a rise in simulated water levels at all

observation sites starting in April 2021 when the water transfer operations began. Observed water levels also indicate rising water levels although the forecast shows an underestimation bias. Input data for the forecast (from January 2019) were average values computed from historical (2010–15) data and do not represent field conditions from a specific time. Simulated water table elevation maps for selected stress periods are shown in figures 36 and 37. The full extent of the inset model domain is shown in figure 36, whereas figure 37 shows areas zoomed in around the GTIP project operation sites. Simulated water table elevation on January 1, 1900, prior to extensive groundwater development and water-level declines, is shown in figures 36A and 37A. Simulated water table elevation on December 31, 2018 (end of the calibration model), indicates significant declines in water levels, particularly on the western half of the model domain, leading to a cone of depression (figs. 36B and 37B). Simulated water table elevations on June 30, 2021, and February 28, 2022, when the GTIP project was in full operation and applying the maximum pumping rates during test periods 1 and 2, respectively, are shown in figures 36C–D and 37C–D. The rise in water table elevation around the injection sites resulted in groundwater mounding west of the contour line, delineating 30 m of altitude. Simulated water table elevation on August 31, 2022, when GTIP project operations for test period 2 ended, is shown in figures 36E and 37E. Simulated water table elevation shows that the groundwater mound had gently spread, indicating that the rise in water levels resulting from water transfer and injection in the area cannot be sustained for extended periods of time if operation is not continuous. Finally, simulated water table elevation on May 31, 2050, indicating an increase in water table elevation of as much as 3m around the injection site, is shown in figures 36F and 37F. Contour lines indicate that water levels at the injection sites are still below water levels near the extraction site. Long-term injection of groundwater by the wells of the GTIP project could result in the reversal of the hydraulic head gradient between the extraction and injection sites, effectively leading to a “recirculation” situation whereby water pumped from the extraction site and injected into the aquifer at the injection sites would eventually flow back to the extraction well. Results of the forecast simulation indicate that for the 2022 GTIP project operation rates and average (2010–15) pumping and recharging conditions, yearly repetition until 2051 would not result in substantial water re-circulation and has the potential to increase groundwater levels around the injection site.

[ft, feet; NAVD 88, North American Vertical Datum 88; BLS, below land surface; MRVAA, Mississippi River Valley Alluvial Aquifer ; INJ, injection site; EXT, extraction site; OW, observation well; --, not applicable]

Site name

Site number

Latitude

Longitude

Purpose

Measuring point elevation, in ft NAVD 88

Extraction well (G-0190)

33.603637

−90.270658

Extract source groundwater

136.36

63–113

71–21

4–7

Injection well A (G-0191)

33.596349

−90.301489

Inject source water

137.04

80–120

55–15

5–7

Injection well B (G-0192)

Screen interval, in ft BLS

Screen interval, in ft NAVD 88

Layers of screen intersection

33.596516

−90.30057

Inject source water

136.9

80–120

55–15

5–7

OW-1 (G-0182)

333535090180301

33.593108

−90.300935

MRVAA OW at INJ

127.62

65.1–75.1

60–50

OW-2 (G-0178)

333550090174201

33.597175

−90.295013

MRVAA OW at INJ

133.82

63.7–73.7

68–58

4–5

OW-3 (G-0175)

333547090180301

33.596458

−90.300921

MRVAA OW at INJ

135.25

65.1–75.1

68–58

4–5

OW-4 (G-0179)

333452090181301

33.581052

−90.303559

MRVAA OW at INJ

124.52

63.7–73.7

59–49

OW-5

333613090162801

33.603493

−90.274374

MRVAA OW at EXT

131.86

65.3–75.3

67–57

4–5

OW-6 (G-0177)

333611090161501

33.602947

−90.270733

MRVAA OW at EXT

135.56

65.1–75.1

68–58

4–5

OW-8

333611090155401

33.602983

−90.265069

MRVAA OW at EXT

130.62

65.3–75.3

63–53

OW-9 (G-0176)

333621090161401

33.605903

−90.270626

MRVAA OW at EXT

137.87

65.1–75.1

70–60

4–5

OW-10

333600090161701

33.600109

−90.271448

MRVAA OW at EXT

136.87

63.7–73.7

71–61

4–5

OW-12

333602090140501

33.600515

−90.234608

MRVAA OW at EXT

137.79

65.3–75.3

70–60

4–5

OW-13 (G-0181)

333545090184601

33.595871

−90.312677

MRVAA OW at INJ

127.11

65.1–75.1

60–50

4–5

OW-14

333631090182501

33.608669

−90.306819

MRVAA OW at INJ

131.08

66.8–76.8

62–52

4–5

MDEQ-EXT-MRVAA (G-0162)

333613090161402

33.603688

−90.270617

MRVAA OW at EXT (4-in diameter)

136.24

130–140

4 to −6

MDEQ-EXT-US (G-0166)

333614090161401

33.603733

−90.270658

Upper Sparta OW at EXT (4-in diameter)

136.88

180–190

−45 to −55

10–11

MDEQ-EXT-LS (G-0183)

333612090161401

33.6034

−90.270615

Lower Sparta OW at EXT

137.08

270–280

−135 to −145

MDEQ-INJ-MRVAA

333548090180601

33.596587

−90.301457

MRVAA OW at INJ

135.55

90–100

43–33

MDEQ-INJ-US (G-0165)

333547090180501

33.596444

−90.3015

Upper Sparta OW at INJ (4-in diameter)

134.79

190–200

−58 to −68

10–11

90 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Table 9. Information for extraction and injection wells involved in the Groundwater Transfer and Injection Pilot project (U.S. Geological Survey, 2020).

Managed Aquifer Recharge Scenario and Simulated Results 91

Pumping rates, in cubic meters per day

8,000

EXPLANATION

7,000

Extraction rate 6,000

Injection rate, well A

5,000

Injection rate, well B

4,000 3,000 2,000 1,000 0 4/1/2021

9/1/2021

2/1/2022

7/1/2022

12/1/2022

Date (Month/day/year)

Figure 34. Effective monthly average pumping rates at the extraction and injections sites used in the Groundwater Transfer and Injection Pilot project.

A. Observation well 1 (G–0182)

32.0

Meters above sea level

30.5

B. Observation well 3 (G–0175)

31.5 30.0

31.0 30.5

29.5

30.0 29.0

29.5 29.0

28.5 2010

2015

2020

2025

2030

2035

2040

2045

2050

28.5

2010

2015

2020

2025

Date

Meters above sea level

30.5

2030

2035

2040

2045

2050

2035

2040

2045

2050

Date

C. Observation well 14

D. MDEQ–INJ–MRVAA 32.0 31.5

30.0

31.0 29.5

30.5 30.0

29.0

29.5 29.0

28.5

28.5 2010

2015

2020

2025

2030

2035

2040

2045

2050

2010

2015

Date

2020

2025

2030

Date EXPLANATION

Measured

Simulated with Groundwater Transfer and Injection Pilot (GTIP)

Simulated without GTIP

Figure 35. Time series plot of simulated water levels around the injection sites (U.S. Geological Survey, 2020; Guira and Weisser, 2025).

92 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge A. Water table on January 1, 1900

150

35 23

200

100

200

45 31

100 150

B. Water table on December 31, 2018 27

Model row

250

C. Water table on June 30, 2021

D. Water table on February 28, 2022 27

50 40

250

26 4 2 22

150 200 250

15 0

100

150

200

Model column

250

300

100

150

200

Model column

30 37

40 100

F. Water table on May 31, 2050

200

25 31

100 4 150 2

E. Water table on August 31, 2022

250

200 19

250

200

Model row

35 150

150

35 38

Model row

100

25 20

250

Figure 36. Simulated water table elevation of the study area at select stress periods (Guira and Weisser, 2025).

25 20

300

Managed Aquifer Recharge Scenario and Simulated Results 93 A. Water table around the Groundwater Transfer and Injection Pilot (GTIP) site on January 1, 1900 180

180

B. Water table around the GTIP site on December 31, 2018 29

43.5 190

43.0

190

42.5

200

210

42.0

210 26 220 30

C. Water table around the GTIP site on June 30, 2021

41.0

180

24 180

D. Water table around the GTIP site on February 28, 2022 29

32 31

Model row

200

210

220 30

220

210

190

30 29

200

190

41.5

220

200

Model row

24 180

E. Water table around the GTIP site on August 31, 2022

180

F. Water table around the GTIP site on May 31, 2050 33

32 31

190 29

200

30 28

Model row

200

190

210

220

230

Model column

240

250

27 26

24 200

220 31

28 30

220

210 26

210

200

210

220

230

240

250

Model column

Figure 37. Simulated water table elevation of the Groundwater Transfer and Injection Pilot project area at select stress periods (Guira and Weisser, 2025).

94 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Assumptions and Limitations As in any modeling effort, the Shellmound model construction is an attempt to represent complex natural processes of the real world to address specific hydrologic questions, which requires some approximations and simplifications. This section of the report discusses some of the assumptions made in the model development and calibration and the limitations of the model capabilities. The 100×100-meter cell resolution used in spatial discretization is considered a high resolution but still required summarizing input data that were spatially distributed within a 10,000-square-meter model cell into a single value. The use of the CHD package to simulate lateral groundwater flow could be an unrealistic infinite source (or sink) of water, but in this simulation, the flow was constrained by realistic estimates of lateral groundwater flow from the conceptual model. To explore a more constrained representation of lateral groundwater flow, a prototype version of the Shellmound model used a specified flux boundary condition simulated using a MODFLOW 6 WEL package (Langevin and others, 2017) in lieu of the CHD package. Lateral groundwater-flow rates were extracted from the parent model using the USGS ZoneBudget software (Harbaugh, 1990) for boundary cells and converted into well pumping rates. The same approach was successfully used in Traylor and others (2024), but that did not yield a more stable Shellmound model; therefore, this approach was not used. Input data such as hydraulic heads used as boundary conditions derived from the parent model come with the uncertainty associated with the parent model. Hydraulic head values used in the CHD package were constant during calibration, which most likely resulted in some changes in other parameters in places where calibration would potentially perform better if hydraulic heads were allowed to slightly fluctuate. The model did not accurately simulate streamflow routing in the Yazoo River as it re-enters the model domain near Greenwood, Miss. This inaccuracy only affected a small section of the study area but resulted in a dried-out stream reach for a substantial portion of the entire simulation time where it normally remains wet. The inaccuracy also led to lower simulated groundwater levels in the area immediately surrounding that stream reach. The model did not account for the perched aquifer in the southwest corner of the model domain, which was documented in previous studies (O’Reilly and others, 2020; Leaf and others, 2023). Simulation of perched aquifers requires a specific package in MODFLOW 6 that was not used in this study because the perched system was not an important component to the aquifers of interest such as the MRVA and Claiborne aquifers. Because of the thickness of the unsaturated zone in the area, the model could potentially be improved with the use of the Unsaturated Zone Flow package (Langevin and others, 2017) that could better simulate the lag between net infiltration as simulated by the SWB model and groundwater recharge.

Limitations of the forecast model include the limited capability to accurately predict water levels because of the lack of accurate input data. Most stresses in the forecast section were simulated by using averaged historical inputs from 2010 to 2015; therefore, the forecast model can be useful for making approximations based on how future conditions compare to the average conditions during this period. It is also useful for approximating how long the groundwater mound around the injection sites can be sustained based on average conditions, but results were not a definitive indication of future conditions.

Summary The U.S. Geological Survey (USGS) Water Availability and Use Science Program, through the Mississippi Alluvial Plain (MAP) project, has been updating groundwater-flow models of the Mississippi Embayment and Mississippi River Valley alluvial (MRVA) aquifers to provide stakeholders with tools that can be used to support water-resource management decisions. Groundwater withdrawals from the MRVA aquifer have been vital to support a multibillion-dollar agricultural industry, but groundwater-level declines have heightened concerns about long-term sustainability. In a region near Shellmound, Mississippi, large groundwater-level declines have prompted stakeholders to undertake several actions to better understand the subsurface hydrogeology and mitigate water-level declines. The Groundwater Transfer and Injection Pilot project (GTIP) was implemented whereby groundwater was extracted from the MRVA aquifer near the Tallahatchie River and reinjected into the aquifer approximately 3 kilometers (km) (1.8 miles) west of the extraction point. Additionally, a high-resolution airborne electromagnetic (AEM) survey was completed to collect geophysical data, help improve current understanding of the subsurface, and support the GTIP project and groundwater modeling projects. The MAP project supported the construction of the Shellmound model, a transient groundwater-flow model using the modular finite-difference flow model (MODFLOW 6), which integrates the AEM data to serve as a tool to better understand processes associated with the groundwater system and the potential effects of GTIP project operations on groundwater levels. The Shellmound model domain is within the Mississippi Delta (hereafter referred to as the “Delta”), including parts of Leflore, Sunflower, and Tallahatchie Counties, and extends 35 km east to west and 30 km north to south. The climate in the area is typical of the Delta, which is humid and subtropical; the average annual precipitation from 2010 to 2020 was approximately 131 centimeters per year. The average annual temperature ranged from 11.6 to 25 degrees Celsius. Land use in the area is dominated by farmland with major agricultural crops being soybeans, corn, rice, and cotton, but also includes catfish ponds, wetlands, developed/urban, pasture, and forest.

Summary 95 Surface-water features in the Shellmound model study area include streams, ponds, and oxbow lakes, many of which are not connected to the groundwater system. Streams in the area include the Tallahatchie, Quiver, and Big Sunflower Rivers. The average daily mean streamflow for the Tallahatchie River at the Money, Miss., streamgage (USGS station 07281600), from 1996 to 2018 was approximately 18.8 million cubic meters per day (m3/d). The major hydrogeologic units in the Shellmound model study area are Quaternary and Tertiary units. The MRVA aquifer, which is present at land surface throughout the study area, mainly consists of sand and gravel with an average thickness of 38.3 meters (m), ranging from 23.5 to 49.2 m. The uppermost layer of the MRVA aquifer generally is finer grained, with increased prevalence of silt and clay that limits areal recharge. Underlying the MRVA aquifer are the older Tertiary hydrogeologic units, which mainly consist of undifferentiated sediments, and include the upper and lower Claiborne aquifers, the middle Claiborne confining unit, and the middle and lower Wilcox aquifers. The Tertiary deposits have a combined average thickness of 607 m, ranging from 436 to 780.3 m. The highly productive alluvial aquifer is the most important source of fresh water supply in the study area. Wells screened in the alluvial aquifer can pump between 1,635 and 16,350 m3/d. The underlying Tertiary units were reported to have a much lower well yield of 545 to 2,725 m3/d. In 2000, groundwater withdrawal from the alluvial aquifer alone accounted for 10 percent of all groundwater use within the continental United States. Other nonagricultural groundwater uses include municipal and industrial purposes. Most crop and fish production within the limits of the Shellmound model study area is primarily supported by the MRVA aquifer, whereas the municipal and industrial groundwater use is supported by the underlying Tertiary units. The Shellmound model is a high-resolution (100-m cell size) inset model that uses the regional-scale Delta model (500-m cell size) as its parent model. The development process included the exploration of the effect of layering configurations of varying complexity that resulted in three different vertical discretizations corresponding to the three versions (models A, B, and C). Model A retains the vertical discretization used in the Delta model and consists of uniform 5-m-thick layers from land surface to the base of the MRVA aquifer as defined through the interpretation of the AEM data. Below the base of the MRVA aquifer, the vertical discretization is represented by uniform and increasing thickness to the depth of the available AEM data, and then by nonuniform layer surfaces following hydrostratigraphic surfaces. Because the Delta model layers 16, 17, and 18 were inactive over the Shellmound model domain, they were not represented in the inset models which resulted in 18 model layers for model A. Model B has a vertical discretization that defines 10-m constant thickness and horizontal layers from the highest elevation of the land surface to the deepest extent of the AEM data, but its vertical discretization is identical to

model A below the depth of the AEM data and resulted in 16 model layers for model B. The vertical discretization in model C is defined by a single layer that extends from land surface to the deepest extent of the AEM data. The vertical discretization of model C below the deepest extent of the AEM data is identical to those in models A and B, which resulted in eight model layers for model C. The temporal discretization of the Shellmound model defines 148 stress periods simulated from 1900 to 2018 with varying stress period lengths. The period prior to April 2007 was subdivided into six stress periods with lengths of 1 year or more and represented varying stages of groundwater development within the MAP area as reported in previous studies. The first stress period simulates a steady state condition, whereas stress periods 2 to 148 simulate transient conditions. The model simulates monthly stress periods from April 1, 2007, to January 1, 2019. Areal groundwater recharge was simulated in the Shellmound model using the MODFLOW 6 recharge package. Input recharge grids for the Shellmound model were based on simulated net infiltration by the Shellmound soil-water-balance (SWB) model, which runs on a daily time step. The Shellmound SWB model computes grid-based water budget of surface hydrology (from the vegetative canopy to the bottom of the root zone) with 100×100-m cells that was specifically constructed to provide inputs to the Shellmound model. Daily net infiltration rates were averaged to match the Shellmound model monthly temporal discretization from April 2007 through December 2018. An average rate between 1999 and 2018 was used for the stress periods preceding 2007. All streams in the Shellmound model were simulated using the MODFLOW 6 Streamflow Routing (SFR) package. The SFR package simulated the stream water budget for each stream reach including gains and losses. Other budget components simulated by the SFR package include surface runoff, stream stage, and routing between connected reaches. The runoff inputs to the SFR package were provided by the SWB model. The SFR package was built using NHDPlus version 2 data, and the open-source python packages SFRmaker, and Modflow-setup. Groundwater use in the Shellmound model was simulated using the MODFLOW 6 well (WEL) package. Pumping well locations and rates for stress periods prior to April 2007 were derived from the Mississippi Embayment Regional Aquifer Study 2.2 groundwater-flow model. There is no distinction between agricultural and nonagricultural water use in the Shellmound model prior to 2007. From April 2007 to December 2018, water-use data included pumping rates and locations for agricultural production and nonagricultural water use. Agricultural water use data were provided by the AIWUM version 1.1. Nonagricultural water-use data for the same period were provided by the USGS site-specific water-use data system and national estimates for water use associated with thermoelectric power generation.

96 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge Lateral groundwater flow into and out of the Shellmound model was simulated using the Constant Head (CHD) package. Constant head boundary cells for the Shellmound model were specified at the perimeter boundary. Simulated groundwater-level values from the parent model were used to specify hydraulic heads for every stress period in the CHD package. Lateral groundwater flow between the model and the surrounding aquifer for each stress period was computed based on the gradient between the CHD package cells and the neighboring cells. The parameter estimation of the Shellmound model consisted of the identification of the calibration targets, the selection of model parameters to adjust, some manual adjustments of parameters, and automated calibration. The calibration process of the Shellmound model employed the high-performance computing software Parameter Estimation ++ (PEST++) using the USGS Denali supercomputing resources. Calibration results show that mean phi (Φ, objective function) value, which is a measure of the degree of mismatch between observed and simulated conditions, for model A improved from 2,884.17 to 240.68, whereas Φ values for models B and C changed from 2,473.32 to 231.03 and from 2,015.30 to 234.40, respectively. The minimum error variance set of “base” realization resulted in Φ values of 253.43, 258.72, and 265.25 for models A, B, and C, respectively, after the second iteration. Simulated budgets for model A indicate that groundwater pumping is the largest outflow from the system since 1970 often approaching 100 percent of all outflows. The second largest net outflow is change in storage representing water replenishing aquifer storage during years with high recharge and less pumping, although the net storage change results in an inflow for most years. Prior to 1950, net outflows were dominated by groundwater discharge to the streams as base flows and lateral groundwater flows out of the model domain. Calibration results also show a good fit between simulated and calibration targets. For observation groups “Shellmound heads,” “Priority embayment heads,” “Embayment heads,” and “Heads” with mean absolute errors of 0.57, 0.57, 0.90, and 1.01 m, respectively, whereas root-mean-squared error for the same groups were 0.68, 0.72, 1.25, and 1.32 m. Many assumptions were made in the development of the forecast model. Stresses such as groundwater pumping and recharge rates applied to the future stress period were obtained by computing monthly averages from the calibration period. Although this allows to see the potential effects of the GTIP operations, the forecast simulation outputs do not represent predictions under any climate forecasting scenario. The Shellmound forecast groundwater-flow model was constructed using model A calibrated parameters and, in addition to the historical period, covers another 384 additional monthly stress periods from January 1, 2019, to January 1, 2051. A new WEL package was used to simulate the groundwater transfer and only included wells at the extraction

and injection locations. Extraction rates were distributed so that one-third of the pumping rate was applied to layers 5 and 6 individually, whereas one-sixth of the pumping rate was applied to layers 4 and 7 individually. Following the same process at the injection sites, one-half of the injection rate at injection well A was applied to layer 6, whereas one-quarter was applied to layers 5 and 7 individually. The same ratios of injection were applied at injection well B using the injection rates provided for well B. Results indicate a notable groundwater-level rise of as much as 3 m around the injection sites and indicate that under average (2010–15) irrigation and recharge conditions, the GTIP project has the potential to increase groundwater levels around the injection site, but sustained mounding requires yearly repetition of GTIP project operations.

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Torak, L.J., 2023, Digital surfaces and site data of well-screen top and bottom altitudes defining the irrigation production zone of the Mississippi River Valley alluvial aquifer within the Mississippi Alluvial Plain project region: U.S. Geological Survey data release, accessed December 30, 2024, at https://doi.org/10.5066/P9TSDEAC. Traylor, J.P., Duncan, L.L., Leaf, A.T., Weisser, A.R., Dietsch, B.J., and Guira, M., 2024, Inset groundwater-flow models for the Cache and Grand Prairie Critical Groundwater Areas, northeastern Arkansas: U.S. Geological Survey Scientific Investigations Report 2024–5088, 152 p., accessed on December 30, 2024, at https://doi.org/10.3133/ sir20245088. U.S. Department of Agriculture, 2020, Census of agriculture for 2012: National Agricultural Statistics Service digital data, accessed November 1, 2020, at http://www.agcensus. usda.gov/. U.S. Geological Survey, 2016, USGS National Elevation Dataset (NED) 1 arc-second downloadable data collection from The National Map 3D Elevation Program (3DEP)— National Geospatial Data Asset (NGDA) National Elevation Data Set (NED): U.S. Geological Survey digital data, accessed September 2021 at https://data.globalchange.gov/ dataset/usgs-national-elevation-dataset-ned-1-arc-second. U.S. Geological Survey, 2020, USGS water data for the Nation: U.S. Geological Survey National Water Information System database, accessed December 2020 at https://doi.org/10.5066/F7P55KJN.

White, J.T., Hunt, R.J., and Fienen, M.N., and Doherty, J.E., 2020, Approaches to highly parameterized inversion— PEST++ Version 5, a software suite for parameter estimation, uncertainty analysis, management optimization and sensitivity analysis: U.S. Geological Survey Techniques and Methods, book 7, chap. C26. 52 p., accessed October 2, 2023, at https://doi.org/10.3133/tm7C26. White, J.T., Hemmings, B., Fienen, M.N., and Knowling, M.J., 2021, Towards improved environmental modeling outcomes—Enabling low-cost access to high-dimensional, geostatistical-based decision-support analyses: Environmental Modelling & Software, v. 139, art. 105022, 9 p. [Also available at https://doi.org/10.1016/j.envsoft. 2021.105022.] Wilson, J.L., 2021, Aquaculture and Irrigation Water-Use Model (AIWUM) version 1.0—An agricultural water-use model developed for the Mississippi Alluvial Plain, 1999–2017: U.S. Geological Survey Scientific Investigations Report 2021–5011, 36 p., accessed October 2, 2023, at https://doi.org/10.3133/sir20215011. Zheng, Y., Ross, A., Villholth, K.G., and Dillon, P., eds., 2021, Managing aquifer recharge—A showcase for resilience and sustainability: Paris, United Nations Educational, Scientific and Cultural Organization, 379 p., accessed October 2, 2023, at https://unesdoc.unesco.org/ark:/48223/ pf0000379962.

Appendix 1. Additional Calibration Results from Model A 101

Appendix 1. Additional Calibration Results from Model A Below are additional figures from the results of the model A calibration using the “base” realization after the second iteration of the Parameter Estimation ++ Iterative Ensemble Smoother run (Guira and Weisser, 2025). For figures 1.1–1.5, a histogram shows the distribution of ensemble values distribution organized in bins by count. Also emphasized on

these plots are prior and posterior parameter values of the base member within the ensemble. Direct parameter values for hydraulic conductivity, hydraulic conductivity, vertical anisotropy, specific yield, and specific storage for model A are shown in figures 1.1–1.4. Pumping data source multipliers for model A are shown in figure 1.5.

parval1: 1.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.24e+00 ens. geomean: 1.44e+00

Frequency

B. Zone 3

12 10 8

C. Zone 4 parval1: 1.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.46e+00 ens. geomean: 7.28e–01

20 15 10

6 4

2 0

E. Zone 6

Frequency

30 25

5 0

Frequency

0 H. Zone 17 parval1: 0.18 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.92e–01 ens. geomean: 2.24e–01

10.0

20.0

parval1: 65.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 6.46e+01 ens. geomean: 5.29e+01

17.5 15.0 12.5 10.0

7.5

5.0

2.5

0.0

0.0 10−2

J. Zone 19 parval1: 0.6 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.01e–01 ens. geomean: 1.19e–01

5.0

I. Zone 18 16

12.5

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 2.68e+01 ens. geomean: 2.54e+01

15.0

17.5

G. Zone 16

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 9.15e+01 ens. geomean: 5.93e+01

D. Zone 5

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 9.77e+01 ens. geomean: 7.95e+01

F. Zone 7

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 4.87e+00 ens. geomean: 4.62e+00

K. Zone 20 35

parval1: 7.4 parlbnd: 0.01 parubnd: 300.0 ens. base: 2.21e+00 ens. geomean: 1.28e+00

14 12 10

parval1: 7.4 parlbnd: 0.01 parubnd: 300.0 ens. base: 4.90e+00 ens. geomean: 3.31e+00

30 25

10−1

10 0

10 1

102

Horizontal hydraulic conductivity, in meters per day EXPLANATION

Posterior distribution

Base member in prior distribution

Base member in posterior distribution

0 10−2

10–1

10 0

10 1

10 2

Horizontal hydraulic conductivity, in meters per day

0 10−2

10−1

10 0

10 1

10 2

Horizontal hydraulic conductivity, in meters per day

0 10−2

10−1

10 0

10 1

10 2

Horizontal hydraulic conductivity, in meters per day

Figure 1.1. Model A histogram of hydraulic conductivity direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 16. H, Zone 17. I, Zone 18. J, Zone 19. K, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values].

102 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

A. Zone 2

A. Zone 2 17.5

parval1: 20.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 3.97e+01 ens. geomean: 3.06e+01

15.0

Frequency

12.5

C. Zone 4 parval1: 20.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.30e+01 ens. geomean: 4.40e+00

30 25

12.5

7.5

5.0

2.5

0.0

parval1: 45.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.57e+02 ens. geomean: 1.28e+02

14 12 10 8

F. Zone 7

Frequency

2.5 0.0 100

12 10

7.5

5.0

2.5

0 100

0.0 100

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

104

0 100

102

103

104

EXPLANATION Posterior distribution

101

Hydraulic conductivity vertical anisotropy, dimensionless

parval1: 105.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 4.76e+01 ens. geomean: 4.08e+01

Hydraulic conductivity vertical anisotropy, dimensionless

5.0

parval1: 89.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 3.71e+01 ens. geomean: 4.05e+01

12.5

104

7.5

K. Zone 20

15.0

103

10.0

0.0

10.0

102

12.5

2.5

101

15.0

5.0

17.5

7.5

20.0

parval1: 74.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 5.20e+01 ens. geomean: 6.83e+01

Base member in prior distribution Base member in posterior distribution

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

104

Figure 1.2. Model A histogram of hydraulic conductivity vertical anisotropy direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 16. H, Zone 17. I, Zone 18. J, Zone 19. K, Zone 20.[parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

Appendix 1. Additional Calibration Results from Model A 103

20.0

10.0

J. Zone 19

parval1: 500.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.10e+03 ens. geomean: 8.60e+02

H. Zone 17 parval1: 43.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 3.25e+01 ens. geomean: 4.82e+01

12.5

15.0

17.5

parval1: 5.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 4.47e+00 ens. geomean: 5.23e+00

I. Zone 18

G. Zone 16

7.5

parval1: 51.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.02e+02 ens. geomean: 3.18e+01

10.0

parval1: 58.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.33e+02 ens. geomean: 6.64e+01

15.0

D. Zone 5

17.5

10.0

E. Zone 6

Frequency

B. Zone 3

B. Zone 3 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.43e–01 ens. mean: 1.54e–01

17.5

Frequency

15.0 12.5

C. Zone 4 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.34e–01 ens. mean: 1.40e–01

20 15

10.0 5.0

12 10

2.5 0.0

E. Zone 6 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.88e–01 ens. mean: 1.81e–01

Frequency

12 10

10 8

2 0

7.5

5.0

2.5

0.0

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.96e–01 ens. mean: 2.05e–01

10 8

12 10

12 10 8 6

K. Zone 20 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.26e–01 ens. mean: 1.34e–01

15.0 12.5

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.38e–01 ens. mean: 1.48e–01

17.5

H. Zone 17 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.88e–01 ens. mean: 1.88e–01

J. Zone 19

Frequency

10.0

I. Zone 18 14

12.5

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.81e–01 ens. mean: 1.91e–01

15.0

G. Zone 16

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.64e–01 ens. mean: 1.79e–01

17.5

F. Zone 7

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.68e–01 ens. mean: 1.86e–01

7.5

D. Zone 5

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.35e–01 ens. mean: 1.55e–01

14 12 10

0.10

0.15

0.20

0.25

0.30

0.35

Specific yield, dimensionless

EXPLANATION

10.0

Posterior distribution

7.5

Base member in prior distribution

5.0

Base member in posterior distribution

2.5

0.10

0.15

0.20

0.25

0.30

Specific yield, dimensionless

0.35

0.0

0.10

0.15

0.20

0.25

0.30

Specific yield, dimensionless

0.35

0.10

0.15

0.20

0.25

0.30

0.35

Specific yield, dimensionless

Figure 1.3. Model A histogram of specific yield direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 16. H, Zone 17. I, Zone 18. J, Zone 19. K, Zone 20.[parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

104 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

A. Zone 2 20.0

A. Zone 2 16 14 12

Frequency

B. Zone 3

10 8

D. Zone 5 16

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.66e–06 ens. geomean: 1.73e–06

14 12 10

12 10

F. Zone 7 17.5

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 8.15e–07 ens. geomean: 9.90e–07

14 12 10

G. Zone 16

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.16e–06 ens. geomean: 1.31e–06

15.0 12.5

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.17e–06 ens. geomean: 1.07e–06

E. Zone 6

Frequency

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 6.47e–07 ens. geomean: 5.99e–07

H. Zone 17 parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 7.44e–07 ens. geomean: 7.14e–07

14 12 10

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 5.55e–07 ens. geomean: 5.89e–07

12 10 8

10.0

7.5

5.0

2.5

0.0

0 −7 10

8 6

J. Zone 19 16

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 7.45e–07 ens. geomean: 7.86e–07

16 14 12 10

12 10

14 12 10

0 10−7

10−5

Specific storage, dimensionless

10−5

Specific storage, dimensionless

10−5

EXPLANATION Posterior distribution

10−6

Specific storage, dimensionless

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.29e–06 ens. geomean: 1.16e–06

10−6

K. Zone 20

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.54e–06 ens. geomean: 1.25e–06

Base member in prior distribution Base member in posterior distribution

0 10−7

10−6

10−5

Specific storage, dimensionless

Figure 1.4. Model A histogram of specific storage direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 16. H, Zone 17. I, Zone 18. J, Zone 19. K, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

Appendix 1. Additional Calibration Results from Model A 105

I. Zone 18

Frequency

C. Zone 4

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 5.03e–07 ens. geomean: 6.09e–07

106 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge A. Data source: AIWUM

Frequency

200 150

parval1: 1.0 parlbnd: 0.5 parubnd: 1.25 ens. base: 1.25e+00 ens. mean: 1.23e+00

B. Data source: MERAS 2 20 15 10

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

WEL (well) data source multiplier, dimensionless

12 10 8

100

parval1: 1.0 parlbnd: 0.5 parubnd: 1.4 ens. base: 8.03e–01 ens. mean: 8.22e–01

C. Data source: SWUDS 14

parval1: 1.0 parlbnd: 0.5 parubnd: 1.5 ens. base: 9.98e–01 ens. mean: 9.85e–01

6 4 2 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

WEL data source multiplier, dimensionless

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

WEL data source multiplier, dimensionless

EXPLANATION Posterior distribution

Figure 1.5. Histogram of well data source multiplier parameter ensemble following second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). Well data sources comprise the Aquaculture and Irrigation Water-Use Model (Bristow and Wilson, 2023), Mississippi Embayment Regional Aquifer Study 2 (Hunt and others, 2021) and site-specific water-use data system (U.S. Geological Survey, 2020). A, Data source: Aquaculture and Irrigation Water-Use Model (AIWUM, Bristow and Wilson, 2023). B, Data source: Mississippi Embayment River Aquifer Study (MERAS, Hart and others, 2008) 2. C, Data source: site-specific water-use data system (SWUDS, U.S. Geological Survey, 2020). [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

Appendix 1. Additional Calibration Results from Model A 107

References Cited Bristow, E.L., and Wilson, J.L., 2023, Aquaculture and irrigation water-use model (AIWUM) version 1.1 estimates and related datasets for the Mississippi Alluvial Plain: U.S. Geological Survey data release, accessed October 2, 2024, at https://doi.org/10.5066/P9RGZOBZ. Guira, M., and Weisser, A.R., 2025, Inset models used to evaluate the effects of layering configuration on model calibration from 1900 to 2018, and assess managed aquifer recharge near Shellmound, Mississippi, from 2019 to 2050: U.S. Geological Survey data release, https://doi.org/ 10.5066/P13DWA86.

Hart, R.M., Clark, B.R., and Bolyard, S.E., 2008, Digital surfaces and thicknesses of selected hydrogeologic units within the Mississippi Embayment Regional Aquifer Study (MERAS): U.S. Geological Survey Scientific Investigations Report 2008–5098, 33 p., accessed October 2, 2023, at https://doi.org/10.3133/sir20085098. Hunt, R.J., White, J.T., Duncan, L.L., Haugh, C.J., and Doherty, J., 2021, Evaluating lower computational burden approaches for calibration of large environmental models: Groundwater, v. 59, no. 6, p. 788–798 [Also available at https://doi.org/10.1111/gwat.13106.] U.S. Geological Survey, 2020, USGS water data for the Nation: U.S. Geological Survey National Water Information System database, accessed December 2020 at https://doi.org/10.5066/F7P55KJN.

108 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Appendix 2. Calibration and Modeling Results for Model B and Model C This section of the report presents results from the calibration and the historical modeling for models B and C (Guira and Weisser, 2025). Calibration performance for models B and C allows for comparison with model A.

Calibration and Groundwater Budget Results for Models B Below are figures from the Parameter Estimation++ Iterative Ensemble Smoother (PESTPP–IES) calibration results of model B. Direct parameter values for hydraulic conductivity, hydraulic conductivity vertical anisotropy, specific yield, and specific storage for model B are shown in figures 2.1–2.4. Pumping data source multipliers for model B are shown in figure 2.5. In each instance, the posterior ensemble values distribution histogram shows parameters

organized in bins based on resistivity classes developed by Minsley and others (2021), and hydrostratigraphic layers defined in by Hart and others (2008). Also emphasized on these plots are prior and poster parameter values of the base member within the distribution. One-to-one plots for aquifer direct heads, streamflows, and linear head derivatives are shown in figure 2.6. Measured and simulated aquifer heads and streamflows are shown in figures 2.7 and 2.8. Net infiltration estimates were determined from the SWB model (fig. 2.9A; Nielsen and Westenbroek, 2023), model B calibrated recharge (fig. 2.9B), and the spatial difference between SWB model estimates and model B calibrated recharge (fig. 2.9C). Noncalibrated and calibrated water use for model B is shown in figure 2.10. Noncalibrated water use data, which were processed from the Aquaculture and Irrigation Water-Use Model estimates, are lower than the calibrated water use across the simulation period. Net annual budgets simulated by model B are shown in figure 2.11.

A. Zone 1

B. Zone 2

parval1: 0.42 parlbnd: 0.01 parubnd: 300.0 ens. base: 6.95e–01 ens. geomean: 8.86e–01

Frequency

12 10

8 6

D. Zone 4

parval1: 5.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 6.55e+00 ens. geomean: 4.20e+00

30 25 20

E. Zone 5

F. Zone 6

G. Zone 7 25

parval1: 55.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 4.68e+00 ens. geomean: 7.11e+00

I. Zone 18

J. Zone 19 parval1: 0.6 parlbnd: 0.01 parubnd: 300.0 ens. base: 8.02e–02 ens. geomean: 1.43e–01

20 15

17.5 15.0 12.5

15.0 12.5 10.0 7.5 5.0 2.5 0.0 10 −2

K. Zone 20

parval1: 7.4 parlbnd: 0.01 parubnd: 300.0 ens. base: 2.52e+00 ens. geomean: 1.64e+00

20 15

10.0

parval1: 7.4 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.81e+00 ens. geomean: 1.44e+00

10 0

10 1

10 2

EXPLANATION Posterior distribution

5.0

10 −1

Horizontal hydraulic conductivity, in meters per day

Base member in prior distribution

7.5

5 0 10 −2

20.0

parval1: 80.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 2.53e+01 ens. geomean: 2.38e+01

17.5

H. Zone 8

parval1: 60.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 6.59e+01 ens. geomean: 5.60e+01

10 5

Base member in posterior distribution

2.5 10 −1

10 0

10 1

10 2

Horizontal hydraulic conductivity, in meters per day

0.0 10 −2

10 −1

10 0

10 1

10 2

Horizontal hydraulic conductivity, in meters per day

0 10 −2

10 −1

10 0

10 1

10 2

Horizontal hydraulic conductivity, in meters per day

Figure 2.1. Model B histogram of hydraulic conductivity direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 1. B, Zone 2. C, Zone 3. D, Zone 4. E, Zone 5. F, Zone 6. G, Zone 7. H, Zone 8. I, Zone 18. J, Zone 19. K, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

Appendix 2. Calibration and Modeling Results for Model B and Model C 109

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 3.66e+01 ens. geomean: 2.73e+01

parval1: 40.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.30e+02 ens. geomean: 9.33e+01

Frequency

parval1: 1.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 2.64e+00 ens. geomean: 1.99e+00

12 8

Frequency

C. Zone 3

parval1: 20.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 2.85e+00 ens. geomean: 3.56e+00

70 60

Frequency

B. Zone 2

50 40

C. Zone 3 parval1: 20.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.00e+01 ens. geomean: 7.26e+00

20 15

20.0

Frequency

15.0 12.5

15.0 12.5 10.0 7.5

7.5 5.0

5.0

2.5

0.0

I. Zone 18 17.5 15.0

Frequency

parval1: 45.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.17e+02 ens. geomean: 6.63e+01

12.5

10.0 7.5

2.5

0.0

H. Zone 8 parval1: 5.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 5.29e+00 ens. geomean: 5.43e+00

12.5

6 4 2 0 0 10

K. Zone 20

15.0

parval1: 50.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 2.69e+01 ens. geomean: 2.63e+01

parval1: 89.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.11e+02 ens. geomean: 8.69e+01

17.5

parval1: 500.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.80e+03 ens. geomean: 1.64e+03

12.5

5.0

J. Zone 19

parval1: 58.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 7.44e+02 ens. geomean: 3.40e+02

15.0

G. Zone 7

17.5

10.0

17.5

F. Zone 6

parval1: 51.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.95e+02 ens. geomean: 5.68e+01

17.5

E. Zone 5

parval1: 20.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 9.65e+00 ens. geomean: 4.50e+00

D. Zone 4

parval1: 105.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 2.68e+01 ens. geomean: 2.44e+01

14 12 10

10 1

10 2

10 3

Hydraulic conductivity vertical anisotropy, dimensionless

EXPLANATION

10.0

Posterior distribution

7.5

Base member in prior distribution

5.0

Base member in posterior distribution

2.5

0.0 100

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

0.0 100

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

0 100

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

Figure 2.2. Model B histogram of hydraulic conductivity anisotropy direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 1. B, Zone 2. C, Zone 3. D, Zone 4. E, Zone 5. F, Zone 6. G, Zone 7. H, Zone 8. I, Zone 18. J, Zone 19. K, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

110 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

A. Zone 1 80

A. Zone 1 12

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.76e–01 ens. mean: 1.75e–01

Frequency

B. Zone 2 14

D. Zone 4 17.5

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.33e–01 ens. mean: 1.56e–01

15.0 12.5

12.5

10.0

7.5

5.0

2.5

0.0

G. Zone 7

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 2.64e–01 ens. mean: 2.48e–01

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 2.20e–01 ens. mean: 2.20e–01

12 10 8

H. Zone 8 16

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.33e–01 ens. mean: 1.55e–01

12 10

15 10

I. Zone 18 17.5

J. Zone 19 16

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.55e–01 ens. mean: 1.58e–01

15.0 12.5

12 10

10.0 7.5

K. Zone 20 14

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.74e–01 ens. mean: 1.86e–01

2.5

0.0

0.35

Specific yield, dimensionless

0.35

EXPLANATION

Base member in posterior distribution

0.30

Base member in prior distribution

0.25

Posterior distribution

0.20

5.0

0.15

0.10

Specific yield, dimensionless parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.46e–01 ens. mean: 1.51e–01

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.58e–01 ens. mean: 1.69e–01

0.10

0.15

0.20

0.25

0.30

0.35

Specific yield, dimensionless

0.10

0.15

0.20

0.25

0.30

0.35

Specific yield, dimensionless

Figure 2.3. Model B histogram of specific yield direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 1. B, Zone 2. C, Zone 3. D, Zone 4. E, Zone 5. F, Zone 6. G, Zone 7. H, Zone 8. I, Zone 18. J, Zone 19. K, Zone 20.[parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

Appendix 2. Calibration and Modeling Results for Model B and Model C 111

F. Zone 6 14

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.21e–01 ens. mean: 1.31e–01

15.0

Frequency

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.74e–01 ens. mean: 1.78e–01

E. Zone 5

Frequency

C. Zone 3 17.5

12 10

Frequency

B. Zone 2

12 10 8

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 6.36e–07 ens. geomean: 8.25e–07

14 12 10 8

12 10 8

E. Zone 5 12 10 8

F. Zone 6

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.32e–06 ens. geomean: 1.48e–06

17.5 15.0 12.5 10.0

G. Zone 7

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 8.42e–07 ens. geomean: 9.05e–07

12 10 8

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 4.86e–07 ens. geomean: 4.61e–07

Frequency

D. Zone 4

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 8.73e–07 ens. geomean: 8.00e–07

H. Zone 8 16

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 2.12e–06 ens. geomean: 1.85e–06

14 12 10

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.27e–06 ens. geomean: 1.35e–06

7.5

5.0

2.5

0.0

0 10 −7

I. Zone 18 parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 6.50e–07 ens. geomean: 7.05e–07

14 12 10

16 14 12 10

J. Zone 19

Frequency

C. Zone 3

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 3.89e–07 ens. geomean: 3.76e–07

K. Zone 20 16

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.43e–06 ens. geomean: 1.30e–06

10−6

10−5

Specific storage, dimensionless parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 7.52e–07 ens. geomean: 8.05e–07

14 12 10

EXPLANATION Posterior distribution

Base member in prior distribution

Base member in posterior distribution

0 10−7

10−6

10−5

Specific storage, dimensionless

0 10−7

10−6

10−5

Specific storage, dimensionless

0 10−7

10−6

10−5

Specific storage, dimensionless

Figure 2.4. Model B histogram of specific storage direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 1. B, Zone 2. C, Zone 3. D, Zone 4. E, Zone 5. F, Zone 6. G, Zone 7. H, Zone 8. I, Zone 18. J, Zone 19. K, Zone 20.[parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

112 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

A. Zone 1 14

Appendix 2. Calibration and Modeling Results for Model B and Model C 113 A. Data source: AIWUM 300

Frequency

250 200 150

B. Data source: MERAS 2 20.0

parval1: 1.0 parlbnd: 0.5 parubnd: 1.25 ens. base: 1.25e+00 ens. mean: 1.24e+00

17.5 15.0

C. Data source: SWUDS 14

parval1: 1.0 parlbnd: 0.5 parubnd: 1.4 ens. base: 8.32e–01 ens. mean: 8.49e–01

12 10

12.5

10.0

7.5

100

5.0

2.5

0 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

WEL (well) data source multiplier, dimensionless

parval1: 1.0 parlbnd: 0.5 parubnd: 1.5 ens. base: 9.88e–01 ens. mean: 1.02e+00

0 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

WEL data source multiplier, dimensionless

EXPLANATION Posterior distribution

Base member in prior distribution

Base member in posterior distribution

Figure 2.5. Model B histogram of well (WEL) package (Langevin and others, 2017) data source multiplier parameter ensemble following second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Data source: Aquaculture and Irrigation Water-Use Model (AIWUM). B, Data source: Mississippi Embayment River Aquifer Study (MERAS) 2. C, Data source: site-specific water-use data system (SWUDS). [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

114 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge B. Priority embayment heads

Mean error (ME): –0.58 meter Mean absolute error (MAE): 0.59 Root mean squared error (RMSE): 0.72 n: 47

35.0

Simulated head, in meters

A. Shellmound heads

32.5

ME: –0.36 meter MAE: 0.60 RMSE: 0.77 n: 115

30.0 27.5 25.0 22.5 20.0

Measured head, in meters

ME: –0.52 meter MAE: 1.14 RMSE: 1.54 n: 323

Simulated head, in meters

Measured head, in meters

n: 43

Simulated, in meters per day

106 105 104 103 2

101 100 0 10

Measured head, in meters

F. Linear head trends

E. Streamflow n: 406

Simulated, in cubic meters per day

ME: –0.59 meter MAE: 1.13 RMSE: 1.46 n: 270

107

108

D. Heads

C. Embayment heads 40

Measured head, in meters

102

104

106

Measured, in cubic meters per day

108

0.0002 0.0000 –0.0002 –0.0004 –0.0006

–0.0006 –0.0004 –0.0002 0.0000 0.0002

Measured, in meters per day

Figure 2.6. Model B one-to-one plots comparing the Shellmound model outputs (Guira and Weisser, 2025) to field observations. A, Shellmound heads. B, Priority embayment heads. C, Embayment heads. D, Heads. E, Streamflow (U.S. Geological Survey, 2020). F, Linear head trends.

Appendix 2. Calibration and Modeling Results for Model B and Model C 115

B. Head at USGS site 334412090270301 (133F0190 Leflore) 32.5

32.5

Meters above sea level

35.0

A. Head at U.S. Geological Survey (USGS) site 334538090303801 (133F0600 Sunflower)

30.0 27.5 25.0 22.5 20.0 17.5

Zero-weighted spin-up period

30.0 27.5 25.0 22.5 20.0 17.5 15.0

Zero-weighted spin-up period

15.0

C. Head at USGS site 334429090210101 (083A0602 Leflore)

35.0 32.5 30.0 27.5 25.0 22.5 20.0

D. Head at USGS site 333950090230001 (083C0074 Leflore) 32.5

Meters above sea level

37.5

Zero-weighted spin-up period

E. Head at USGS site 333742090303801 (L0027 Sunflower) 27.5

Meters above sea level

25.0 22.5 20.0 17.5

32.5

30.0

25.0 22.5 20.0 17.5

12.5

27.5

15.0

17.5

15.0

30.0

Zero-weighted spin-up period

27.5 25.0 22.5 20.0 17.5 15.0

H. Head at USGS site 333251090323801 (02058 Sunflower) 30.0

Meters above sea level

Zero-weighted spin-up period

12.5

40.0 37.5 35.0 32.5 30.0 27.5

22.5

F. Head at USGS site 333611090215901 (083F0534 Sunflower)

30.0

G. Head at USGS site 333603090164301 (083G0506 Sunflower)

25.0

Zero-weighted spin-up period

2008

2010

27.5 25.0 22.5 20.0 17.5 15.0 12.5

2012

2014

2016

2018

Zero-weighted spin-up period

2008

2010

2012

2014

2016

2018

EXPLANATION Measured

Base member

Ensemble member

Figure 2.7. Model B time series of measured heads and simulated equivalents at selected wells (U.S. Geological Survey, 2020; Guira and Weisser, 2025). A, U.S. Geological Survey (USGS) site 334538090303801 (133F0600 Sunflower). B, USGS site 334412090270301 (133F0190 Leflore). C, USGS site 334429090210101 (083A0602 Leflore). D, USGS site 333950090230001 (083C0074 Leflore). E, USGS site 333742090303801 (L0027 Sunflower). F, USGS site 333611090215901 (083F0534 Sunflower). G, USGS site 333603090164301 (083G0506 Sunflower). H, USGS site 333251090323801 (02058 Sunflower).

116 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Streamflow, in cubic meters per day

A. Streamflow at U.S. Geological Survey (USGS) site 07288500 (Big Sunflower River at Sunflower, Mississippi) 107

106

zero-weighted spin-up period

105 2007

2009

2011

2013

2015

2017

2019

2017

2019

Streamflow, in cubic meters per day

B. Streamflow at USGS site 07281600 (Tallahatchie River at Money, Mississippi) 108

107

2007

2009

2011

2013

2015

EXPLANATION Measured

Base member

Ensemble member

Figure 2.8. Model B streamflows time series showing monthly averages of measured streamflows (U.S. Geological Survey, 2020) and simulated equivalents (Guira and Weisser, 2025). A, U.S. Geological Survey station 07288500 (Big Sunflower River at Sunflower, Mississippi). B, U.S. Geological Survey station 07281600 (Tallahatchie River at Money, Mississippi). Simulated streamflows include base flows and surface runoff estimates from the soil-water-balance model by Nielsen and Westenbroek (2023).

Appendix 2. Calibration and Modeling Results for Model B and Model C 117

1,200,000

1,195,000

10 8

1,190,000

6 1,185,000

4 2

1,180,000 505,000 510,000 515,000 520,000 525,000 530,000 535,000

1,195,000

10 8

1,190,000

6 1,185,000

4 2

1,180,000

Easting, NAD 83 Albers (EPSG: 5070)

10.0 7.5

1,200,000

5.0

1,195,000

2.5 0.0

1,190,000

−2.5 1,185,000

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

1,205,000

14 1,200,000

505,000 510,000 515,000 520,000 525,000 530,000 535,000

Easting, NAD 83 Albers (EPSG: 5070) C. Recharge difference Spatial mean: –9.62 inches per year

1,205,000

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

1,205,000

B. Net infiltration estimated by SWB (2007–18) Spatial mean: 10.82 inches per year

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

A. Simulated recharge (2007–18) Spatial mean: 1.21 inches per year

−5.0

1,180,000

−7.5 505,000 510,000 515,000 520,000 525,000 530,000 535,000

−10.0

Easting, NAD 83 Albers (EPSG: 5070)

Figure 2.9. Comparative maps showing mean annual recharge for model B. A, Simulated recharge (Guira and Weisser, 2025). B, Net infiltration simulated by soil-water-balance (Nielsen and Westenbroek, 2023). C, Recharge difference between soil-water-balance estimate and calibrated.

118 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge 300 70,000 60,000 200

50,000 40,000

150

30,000

100

20,000 50

10,000

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2018

Year EXPLANATION Noncalibrated

Calibrated

Figure 2.10. Model B total water use before and after calibration. Water-use data prior to calibration includes estimated rates from Aquaculture and Irrigation Water-Use Model (Bristow and Wilson, 2023) and nonagricultural rates from the U.S. Geological Survey site-specific water-use data system (U.S. Geological Survey, 2020) and national estimates for water use associated with thermoelectric power generation in 2010 and 2015 (Diehl and Harris, 2014; Harris and Diehl, 2019a,b).

Total water use, in gallons

Total water use, in cubic meters

250

Appendix 2. Calibration and Modeling Results for Model B and Model C 119 0.8

200

0.6

150

100

Rates, in million gallons per day

Rates, in million cubic meters per day

0.4

0.2

0.0

–0.2

–50

–0.4

–100

–150

–0.6

–200

–0.8 1900 1950 1970 1986 1992 1998 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Year EXPLANATION [SFR, Streamflow Routing; CHD, Constant Head; RCH, Recharge; WEL, Well]

net-storage net-SFR

net-CHD net-RCH

net-WEL

Figure 2.11. Model B simulated annual net budget results for the Shellmound model (Guira and Weisser, 2025).

120 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Calibration and Groundwater Budget Results for Model C Below are figures from the PESTPP–IES calibration results of model C. In each instance, a histogram shows the ensemble values distribution organized in bins. Also emphasized on these plots are prior and poster parameter values of the base member within the ensemble. Direct parameter values for hydraulic conductivity, hydraulic conductivity vertical anisotropy, specific yield, and specific storage for model C are shown in figures 2.12–2.15. Pumping data source multipliers for model C are shown in figure 2.16.

One-to-one plots for aquifer direct heads, streamflows, and linear head derivatives are shown in figure 2.17. Time series plots showing measured and simulated heads and streamflows for model C are shown in figures 2.18 and 2.19. Net infiltration estimates were determined from SWB model (fig. 2.20A), model C calibrated recharge (fig. 2.20B) and the spatial difference between SWB model recharge estimates and calibrated recharge (fig. 2.20C). Noncalibrated and calibrated water use for model C are shown in figure 2.21. Net annual budgets simulated by model C are shown in figure 2.22.

A. Zone 2 parval1: 1.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 7.73e+00 ens. geomean: 5.50e+00

Frequency

B. Zone 3

30 25

E. Zone 6

20 15 10

F. Zone 7

G. Zone 18 25

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.67e+02 ens. geomean: 1.09e+02

80 60

parval1: 0.6 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.74e–01 ens. geomean: 1.78e–01

0 10−2

101

102

Horizontal hydraulic conductivity, in meters per day

parval1: 7.4 parlbnd: 0.01 parubnd: 300.0 ens. base: 2.79e+00 ens. geomean: 2.13e+00

100

parval1: 7.4 parlbnd: 0.01 parubnd: 300.0 ens. base: 3.22e+00 ens. geomean: 2.28e+00

14 12 8

10−1

I. Zone 20

H. Zone 19

6 4 2 10−1

100

101

102

Horizontal hydraulic conductivity, in meters per day

0 10−2

10−1

100

101

102

Horizontal hydraulic conductivity, in meters per day

EXPLANATION Posterior distribution

Base member in prior distribution

Base member in posterior distribution

5 0 10−2

10−1

100

101

102

Horizontal hydraulic conductivity, in meters per day

Figure 2.12. Model C histogram of hydraulic conductivity direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 18. H, Zone 19. I, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

Appendix 2. Calibration and Modeling Results for Model B and Model C 121

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.98e+00 ens. geomean: 2.06e+00

100

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 3.15e+01 ens. geomean: 2.80e+01

Frequency

D. Zone 5 35

parval1: 50.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 1.25e+02 ens. geomean: 6.41e+01

Frequency

parval1: 1.0 parlbnd: 0.01 parubnd: 300.0 ens. base: 9.94e+00 ens. geomean: 6.99e+00

C. Zone 4

parval1: 20.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.20e+01 ens. geomean: 1.09e+01

Frequency

B. Zone 3

12 10

15.0 12.5

D. Zone 5 16

parval1: 58.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.92e+02 ens. geomean: 9.41e+01

17.5 15.0 12.5

12 10

7.5

5.0

2.5

0.0

F. Zone 7 parval1: 45.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 2.10e+01 ens. geomean: 1.98e+01

14 12 10 8

G. Zone 18 parval1: 5.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 6.21e+00 ens. geomean: 5.27e+00

30 25 20

14 12 10

H. Zone 19 14

parval1: 500.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 6.28e+02 ens. geomean: 6.22e+02

0 10 0

0 100

I. Zone 20 16

parval1: 105.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 7.75e+01 ens. geomean: 4.43e+01

14 12 10 8

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

parval1: 89.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 2.04e+01 ens. geomean: 1.37e+01

parval1: 51.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.28e+01 ens. geomean: 1.23e+01

10.0

E. Zone 6

Frequency

parval1: 20.0 parlbnd: 1.0 parubnd: 10,000.0 ens. base: 1.63e+02 ens. geomean: 7.23e+01

17.5

20.0

10.0

Frequency

C. Zone 4

20.0

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

0 100

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

EXPLANATION Posterior distribution

Base member in prior distribution

Base member in posterior distribution

2 0 100

101

102

103

Hydraulic conductivity vertical anisotropy, dimensionless

Figure 2.13. Model C histogram of hydraulic conductivity anisotropy direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 18. H, Zone 19. I, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

122 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

A. Zone 2

A. Zone 2 14

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.43e–01 ens. mean: 1.54e–01

Frequency

B. Zone 3

10 8

C. Zone 4 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.48e–01 ens. mean: 1.52e–01

20 15 10

6 4

2 0

E. Zone 6 16

Frequency

12 10

15.0 12.5

10.0

7.5

5.0

2.5

0.0

G. Zone 18 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.35e–01 ens. mean: 1.45e–01

16 14 12 10

H. Zone 19 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.75e–01 ens. mean: 1.83e–01

20.0 17.5 15.0 12.5

10.0

7.5

5.0

2.5

8 6

12 10 8

0.10 0.15 0.20 0.25 0.30 0.35

Specific yield, dimensionless parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.83e–01 ens. mean: 2.04e–01

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.46e–01 ens. mean: 1.52e–01

17.5

I. Zone 20

Frequency

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.80e–01 ens. mean: 1.87e–01

0.10 0.15 0.20 0.25 0.30 0.35

Specific yield, dimensionless

0.0

parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.43e–01 ens. mean: 1.49e–01

0.10 0.15 0.20 0.25 0.30 0.35

Specific yield, dimensionless

EXPLANATION Posterior distribution

Base member in prior distribution

Base member in posterior distribution

2 0

0.10 0.15 0.20 0.25 0.30 0.35

Specific yield, dimensionless

Figure 2.14. Model C histogram of specific yield direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 18. H, Zone 19. I, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

Appendix 2. Calibration and Modeling Results for Model B and Model C 123

F. Zone 7 parval1: 0.15 parlbnd: 0.05 parubnd: 0.35 ens. base: 1.67e–01 ens. mean: 1.72e–01

D. Zone 5

B. Zone 3 parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 7.63e–07 ens. geomean: 7.73e–07

Frequency

15.0 12.5 10.0

14 12 10 8

D. Zone 5

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.32e–06 ens. geomean: 1.22e–06

14 12 10

12 10

5.0

2.5

0.0

F. Zone 7

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 6.66e–07 ens. geomean: 8.82e–07

12 10 8

G. Zone 18

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 1.69e–06 ens. geomean: 1.79e–06

16 14 12 10

H. Zone 19

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 9.33e–07 ens. geomean: 1.04e–06

16 14 12 10

12 10 8

0 10−7

I. Zone 20 17.5

Specific storage, dimensionless

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 9.08e–07 ens. geomean: 1.09e–06

15.0 12.5

10−6

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 6.48e–07 ens. geomean: 7.14e–07

parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 9.29e–07 ens. geomean: 9.86e–07

7.5

Frequency

E. Zone 6

Frequency

C. Zone 4 parval1: 1e–06 parlbnd: 1e–07 parubnd: 1e–05 ens. base: 8.21e–07 ens. geomean: 7.17e–07

10−6

Specific storage, dimensionless

0 10−7

10−6

Specific storage, dimensionless

EXPLANATION

10.0

Posterior distribution

7.5

Base member in prior distribution

5.0

Base member in posterior distribution

2.5 0.0 10−7

10−6

Specific storage, dimensionless

Figure 2.15. Model C histogram of specific storage direct value parameters ensemble by zone after second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Zone 2. B, Zone 3. C, Zone 4. D, Zone 5. E, Zone 6. F, Zone 7. G, Zone 18. H, Zone 19. I, Zone 20. [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

124 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

A. Zone 2 17.5

Appendix 2. Calibration and Modeling Results for Model B and Model C 125 A. Data source: AIWUM 50

Frequency

B. Data source: MERAS 2

parval1: 1.0 parlbnd: 0.5 parubnd: 1.25 ens. base: 1.15e+00 ens. mean: 1.15e+00

25 20

parval1: 1.0 parlbnd: 0.5 parubnd: 1.4 ens. base: 8.32e–01 ens. mean: 8.47e–01

C. Data source: SWUDS 12 10 8

parval1: 1.0 parlbnd: 0.5 parubnd: 1.5 ens. base: 8.38e–01 ens. mean: 8.93e–01

0 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

WEL data source multiplier, dimensionless

WEL (well) data source multiplier, dimensionless

EXPLANATION Posterior distribution

Base member in prior distribution

Base member in posterior distribution

Figure 2.16. Model C histogram of well (WEL) package (Langevin and others, 2017) data source multiplier parameter ensemble following second iteration of Iterative Ensemble Smoother calibration run (Guira and Weisser, 2025). A, Data source: Aquaculture and Irrigation Water-Use Model (AIWUM). B, Data source: Mississippi Embayment River Aquifer Study (MERAS) 2. C, Data source: site-specific water-use data system (SWUDS). [parval1, parameter starting value; parlbnd, lower bound of parameter range; parubnd, upper bound of parameter range; ens. base, parameter value for the base member of the ensemble; ens. geomean, geometric mean of the ensemble parameter values]

126 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge B. Priority embayment heads

A. Shellmound heads 35.0

Mean error (ME): –0.47 meter Mean absolute error (MAE): 0.52 Root mean squared error (RMSE): 0.73 n: 47

Simulated head, in meters

32.5

ME: –0.25 meter MAE: 0.63 RMSE: 0.78 n: 115

30.0 27.5 25.0 22.5 20.0

20 20

Measured head, in meters

ME: –0.16 meter MAE: 1.07 RMSE: 1.46 n: 323

Simulated head, in meters

ME: –0.78 meter MAE: 1.31 RMSE: 1.61 n: 270

Measured head, in meters 108

n: 406

n: 43

Simulated, in meters per day

Simulated, in cubic meters per day

F. Linear head trends

E. Streamflow

106 105 104 103 2

101 100 0 10

Measured head, in meters

107

D. Heads

C. Embayment heads 40

Measured head, in meters

102

104

106

Measured, in cubic meters per day

108

0.0002 0.0000 −0.0002 −0.0004 −0.0006

−0.0006 −0.0004 −0.0002 0.0000 0.0002

Measured, in meters per day

Figure 2.17. Model C one-to-one plots comparing the Shellmound model outputs (Guira and Weisser, 2025) to field observations (U.S. Geological Survey, 2020). A, Shellmound heads. B, Priority embayment heads. C, Embayment heads. D, Heads. E, Streamflow. F, Linear head trends.

Appendix 2. Calibration and Modeling Results for Model B and Model C 127 A. Head at U.S. Geological Survey (USGS) site 334538090303801 (133F0600 Sunflower)

B. Head at USGS site 334412090270301 (133F0190 Leflore) Meters above sea level

Meters above sea level

35.0 32.5 30.0 27.5 25.0 22.5 20.0 17.5

Zero-weighted spin-up period

32.5 30.0 27.5 25.0 22.5 20.0 17.5 15.0

Zero-weighted spin-up period

15.0

C. Head at USGS site 334429090210101 (083A0602 Leflore)

D. Head at USGS site 333950090230001 (083C0074 Leflore) 32.5

Meters above sea level

37.5 35.0 32.5 30.0 27.5 25.0 22.5 20.0

Zero-weighted spin-up period

30.0 27.5 25.0 22.5 20.0 17.5 15.0

30.0 27.5 25.0 22.5 20.0 17.5 15.0 12.5

F. Head at USGS site 333611090215901 (083F0534 Sunflower) Meters above sea level

Meters above sea level

E. Head at USGS site 333742090303801 (L0027 Sunflower)

Zero-weighted spin-up period

30.0 27.5 25.0 22.5 20.0 17.5 15.0

Meters above sea level

40.0 37.5 35.0 32.5 30.0 27.5 22.5

Zero-weighted spin-up period

12.5

G. Head at USGS site 333603090164301 (083G0506 Sunflower)

25.0

Zero-weighted spin-up period

2010

30.0 27.5 25.0 22.5 20.0 17.5 15.0

Zero-weighted spin-up period

2008

H. Head at USGS site 333251090323801 (02058 Sunflower)

12.5

2012

2014

2016

2018

Zero-weighted spin-up period

2008

2010

2012

2014

2016

2018

EXPLANATION Measured

Base member

Ensemble member

Figure 2.18. Model C time series of measured heads and simulated equivalents (Guira and Weisser, 2025) at selected wells (U.S. Geological Survey, 2020). A, U.S. Geological Survey (USGS) site 334538090303801 (133F0600 Sunflower). B, USGS site 334412090270301 (133F0190 Leflore). C, USGS site 334429090210101 (083A0602 Leflore). D, USGS site 333950090230001 (083C0074 Leflore). E, USGS site 333742090303801 (L0027 Sunflower). F, USGS site 333611090215901 (083F0534 Sunflower). G, USGS site 333603090164301 (083G0506 Sunflower). H, USGS site 333251090323801 (02058 Sunflower).

128 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Streamflow, in cubic meters per day

A. Streamflow at U.S. Geological Survey (USGS) site 07288500 (Big Sunflower River at Sunflower, Mississippi) 107

106

Zero-weighted spin-up period

105 2007

2009

2011

2013

2015

2017

2019

2017

2019

Streamflow, in cubic meters per day

B. Streamflow at USGS site 07281600 (Tallahatchie River at Money, Mississippi) 108

107

Zero-weighted spin-up period

2007

2009

2011

2013

2015

EXPLANATION Measured

Base member

Ensemble member

Figure 2.19. Model C streamflows time series showing monthly averages of measured streamflows (U.S. Geological Survey, 2020) and simulated equivalents (Guira and Weisser, 2025). A, U.S. Geological Survey station 07288500 (Big Sunflower River at Sunflower, Mississippi). B, U.S. Geological Survey station 07281600 (Tallahatchie River at Money, Mississippi). Simulated streamflows include base flows and surface runoff estimates from the soil-water-balance model by Nielsen and Westenbroek (2023).

Appendix 2. Calibration and Modeling Results for Model B and Model C 129

1,200,000

1,195,000

10 8

1,190,000

6 1,185,000

4 2

1,180,000 505,000 510,000 515,000 520,000 525,000 530,000 535,000

1,195,000

10 8

1,190,000

6 1,185,000

4 2

1,180,000

Easting, NAD 83 Albers (EPSG: 5070)

10.0 7.5

1,200,000

5.0

1,195,000

2.5 0.0

1,190,000

−2.5 1,185,000

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

1,205,000

14 1,200,000

505,000 510,000 515,000 520,000 525,000 530,000 535,000

Easting, NAD 83 Albers (EPSG: 5070) C. Recharge difference Spatial mean: –9.94 inches per year

1,205,000

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

1,205,000

B. Net infiltration estimated by SWB (2007–18) Spatial mean: 10.82 inches per year

Annual inches

Northing, NAD 83 Albers (EPSG: 5070)

A. Simulated recharge (2007–18) Spatial mean: 0.89 inch per year

−5.0

1,180,000

−7.5 505,000 510,000 515,000 520,000 525,000 530,000 535,000

−10.0

Easting, NAD 83 Albers (EPSG: 5070)

Figure 2.20. Comparative maps showing mean annual recharge for model C. A, Simulated recharge (Guira and Weisser, 2025). B, Net infiltration estimated by soil-water-balance (Nielsen and Westenbroek, 2023). C, Recharge difference between soil-water-balance estimate and calibrated.

130 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge 80,000

300

70,000 60,000 200

50,000 40,000

150

30,000

100

Total water use, in gallons

Total water use, in cubic meters

250

20,000 50

10,000

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

2018

Year EXPLANATION Noncalibrated

Calibrated

Figure 2.21. Model C total water use before and after calibration. Water-use data prior to calibration includes estimated rates from Aquaculture and Irrigation Water-Use Model (Bristow and Wilson, 2023) and nonagricultural rates from the U.S. Geological Survey site-specific water-use data system (U.S. Geological Survey, 2020) and national estimates for water use associated with thermoelectric power generation in 2010 and 2015 (Diehl and Harris, 2014; Harris and Diehl, 2019a,b).

Appendix 2. Calibration and Modeling Results for Model B and Model C 131 0.8

200

150

0.4

100

0.2

0.0

–0.2

–50

–0.4

–100

–150

–0.6

–0.8

Rates, in million gallons per day

Rates, in million cubic meters per day

0.6

–200 1900 1950 1970 1986 1992 1998 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Year EXPLANATION [SFR, Streamflow Routing; CHD, Constant Head; RCH, Recharge; WEL, Well]

net-storage net-SFR

net-CHD net-RCH

net-WEL

Figure 2.22. Model C simulated annual net budget results for the Shellmound model (Guira and Weisser, 2025).

132 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

Comparison of Recharge and Water Use A comparative plot for annual average calibrated groundwater recharge simulated by models A, B, and C is shown in figure 2.23. Calibrated recharge rates have similar patterns for the entire simulation period for all three models.

Minor differences can be perceived primarily for the steady state and during the multiyear spin-up period. However, after 2007, calibrated recharge rates for all three models were similar except for 2013 and 2018, when rates in model C were notably higher. Comparative plots of calibrated average annual water use simulated by models A, B, and C are shown in figure 2.24.

0.25

EXPLANATION

Model B

0.2

Model C

0.15

30 0.1 20

Recharge, in million gallons per day

Recharge, in million cubic meters per day

Model A

0.05 10

1900 1950 1970 1986 1992 1998 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Year

Figure 2.23. Comparative plot of calibrated annual groundwater recharge by models A, B, and C (Guira and Weisser, 2025).

0.7

0.6

200

EXPLANATION Model A

175

Model B Model C

150

0.5 125 0.4

100

0.3

0.2

0.1

0.0

1900 1950 1970 1986 1992 1998 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

Year

Figure 2.24. Comparative plot of calibrated annual water use by models A, B, and C (Guira and Weisser, 2025).

Groundwater withdrawals, in million gallons per day

Groundwater withdrawals, in million cubic meters per day

Appendix 2. Calibration and Modeling Results for Model B and Model C 133

134 Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge

References Cited Guira, M., and Weisser, A.R., 2025, Inset models used to evaluate the effects of layering configuration on model calibration from 1900 to 2018, and assess managed aquifer recharge near Shellmound, Mississippi, from 2019 to 2050: U.S. Geological Survey data release, https://doi.org/ 10.5066/P13DWA86. Bristow, E.L., and Wilson, J.L., 2023, Aquaculture and irrigation water-use model (AIWUM) version 1.1 estimates and related datasets for the Mississippi Alluvial Plain: U.S. Geological Survey data release, accessed October 2, 2024, at https://doi.org/10.5066/P9RGZOBZ.

Hart, R.M., Clark, B.R., and Bolyard, S.E., 2008, Digital surfaces and thicknesses of selected hydrogeologic units within the Mississippi Embayment Regional Aquifer Study (MERAS): U.S. Geological Survey Scientific Investigations Report 2008–5098, 33 p., accessed October 2, 2023, at https://doi.org/10.3133/sir20085098. Langevin, C.D., Hughes, J.D., Banta, E.R., and Niswonger, R.G., Panday, S., and Provost, A.M., 2017, Documentation for the MODFLOW 6 Groundwater Flow Model: U.S. Geological Survey Techniques and Methods, book 6, chap. A55, 197 p., accessed October 2, 2023, at https://doi.org/10.3133/tm6A55.

Diehl, T.H., and Harris, M.A., 2014, Withdrawal and consumption of water by thermoelectric power plants in the United States, 2010: U.S. Geological Survey Scientific Investigations Report 2014–5184, 28 p. [Also available at https://doi.org/10.3133/sir20145184.]

Harris, M.A., and Diehl, T.H., 2019a, Withdrawal and consumption of water by thermoelectric power plants in the United States, 2015: U.S. Geological Survey Scientific Investigations Report 2019–5103, 15 p. [Also available at https://doi.org/10.3133/sir20195103.]

Nielsen, M.G. and Westenbroek, S.M, 2023, Updated estimates of water budget components for the Mississippi Embayment Region, 2000–2020: U.S. Geological Survey Scientific Investigations Report 2023–5080, 58 p., accessed October 2, 2024, at https://doi.org/10.3133/sir20235080.

Harris, M.A., and Diehl, T.H., 2019b, Water withdrawal and consumption estimates for thermoelectric power plants in the United States, 2015: U.S. Geological Survey data release, accessed October 2, 2023, at https://doi.org/ 10.5066/P9V0T04B.

U.S. Geological Survey, 2020, USGS water data for the Nation: U.S. Geological Survey National Water Information System database, accessed December 2020 at https://doi.org/10.5066/F7P55KJN.

For more information about this publication, contact: Director, USGS Nebraska Water Science Center 5231 South 19th Street Lincoln, NE 68512 402–328–4100 For additional information, visit: https://www.usgs.gov/ centers/ne-water Publishing support provided by the Rolla and Sacramento Publishing Service Centers

Guira and others—Inset Groundwater-Flow Model to Evaluate Effects of Layering Configuration and Assess Managed Aquifer Recharge—SIR 2025–5055

ISSN 2328-0328 (online) https://doi.org/10.3133/sir20255055

An Inset Groundwater-Flow Model to Evaluate the Effects of Layering Configuration on Model Calibration and Assess Managed Aquifer Recharge near Shellmound, Mississippi

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