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Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles From Estimated Groundwater Records in Massachusetts

Elizabeth A. Ahearn, Dee-Ann E. Crozier, D.E. Crozier, E.A. Ahearn, R.W. Dudley, G.A. Hodgkins · U.S. Geological Survey

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Prepared in cooperation with the Massachusetts Department of Environmental Protection

Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles From Estimated Groundwater Records in Massachusetts

Scientific Investigations Report 2024–5080

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

Cover. Photograph of U.S. Geological Survey groundwater monitoring well (415354069585201, MA–WNW 17R Wellfleet, MA) in Wellfleet, Massachusetts, on July 12, 2022. Photograph by Dale Tom, U.S. Geological Survey.

Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles From Estimated Groundwater Records in Massachusetts By Elizabeth A. Ahearn and Dee-Ann E. Crozier

Prepared in cooperation with the Massachusetts Department of Environmental Protection

Scientific Investigations Report 2024–5080

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

U.S. Geological Survey, Reston, Virginia: 2024

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: Ahearn, E.A., and Crozier, D.E., 2024, Estimating groundwater level records using MOVE.1 and computing monthly percentiles from estimated groundwater records in Massachusetts: U.S. Geological Survey Scientific Investigations Report 2024–5080, 39 p., https://doi.org/10.3133/sir20245080. Associated data for this publication: Crozier, D.E., and Ahearn, E.A., 2024, Data and R code to derive estimates of groundwater levels using MOVE.1 regression and compute monthly percentiles for select wells in Massachusetts: U.S. Geological Survey data release, https://doi.org/10.5066/P90PDI34. ISSN 2328-0328 (online)

iii

Contents Abstract��1 Introduction��1 Well Network��3 Development of MOVE.1 Models for the Extension of Groundwater Level Records��7 Selection of Well Pairs��7 Use of MOVE.1 for Record Extension��8 Evaluation of MOVE.1 Models��11 Accuracy and Limitations of Groundwater Level Records From MOVE.1��11 Comparison of Groundwater Level Records From MOVE.1 and Observed Records��14 Computation of Monthly Percentiles From Estimated Records��16 Future Studies for Estimating Monthly Percentiles��17 Summary��21 Acknowledgments��22 Selected References��22 Appendix 1. U.S. Geological Survey Climate Response Network of Groundwater Wells in Massachusetts, 2022��24 Appendix 2. Monthly Percentiles at Study Wells With Record Extensions��26

Figures 1.

Map showing the locations of U.S. Geological Survey Climate Response Network wells and drought regions for monitoring groundwater levels in Massachusetts��2 Map showing the locations of 29 U.S. Geological Survey groundwater wells selected for possible record extensions and 39 U.S. Geological Survey wells selected as index wells for monitoring groundwater levels in Massachusetts��7 Graphs showing A, correlation and B, model fit of the concurrent continuous data from the MOVE.1 method of the study well at site 414205070334701 and the index well at site 414219070313601, as part of a study for monitoring groundwater levels in Massachusetts��12 Graphs showing A, correlation and B, model fit of the concurrent continuous data from the MOVE.1 method of the study well at site 413930070190901 and the index well at site 414632070014901, as part of a study for monitoring groundwater levels in Massachusetts��13 Graphs showing A, correlation and B, model fit of the concurrent continuous data from the MOVE.1 method of the study well at site 423810072435401 and the index well at site 431540071452801, as part of a study for monitoring groundwater levels in Massachusetts��14 Graph of the magnitude of range of highest and lowest groundwater levels from the estimated MOVE.1 and observed records for 27 study wells for monitoring groundwater levels in Massachusetts��16 Graphs showing monthly depth changes for select wells for monitoring groundwater levels in Massachusetts at the 2d percentile attributed to the MOVE.1 record extensions��18 Boxplot graph showing monthly residuals for the MOVE.1 model of the study well at site 415453070434901 and the paired index well at site 415228070554601��21

Tables 1.

U.S. Geological Survey groundwater wells selected for record extensions for monitoring groundwater levels in Massachusetts��4 U.S. Geological Survey long-term groundwater wells in and near Massachusetts selected as index wells for extending groundwater level records at study wells for monitoring groundwater levels in Massachusetts��5 U.S. Geological Survey study wells with paired index wells and descriptive parameters of the Maintenance of Variance Extension type 1 (MOVE.1) models for monitoring groundwater levels in Massachusetts��9 U.S. Geological Survey study wells with paired index wells and performance metrics of the Maintenance of Variance Extension type 1 (MOVE.1) models for monitoring groundwater levels in Massachusetts��10 Range of highest and lowest groundwater levels from the estimated Maintenance of Variance Extension type 1 records and observed records for 27 study wells for monitoring groundwater levels in Massachusetts��15

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

Multiply

To obtain

foot (ft)

0.3048

meter (m)

mile (mi)

1.609

kilometer (km)

Datums Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88). Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Abbreviations CRN

Climate Response Network

MOVE.1

Maintenance of Variance Extension type 1

NSE

Nash-Sutcliffe efficiency coefficient

RMSE

root mean square error

USGS

U.S. Geological Survey

Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles From Estimated Groundwater Records in Massachusetts By Elizabeth A. Ahearn and Dee-Ann E. Crozier

Abstract

Introduction

The U.S. Geological Survey, in cooperation with the Massachusetts Department of Environmental Protection, performed record extensions on groundwater levels at select wells using the Maintenance of Variance Extension type 1 (MOVE.1) method. The groundwater levels estimated from these record extensions were used to compute monthly percentiles to improve future determinations of a groundwater index. In Massachusetts, 27 of 29 short-record study wells with continuous groundwater levels between 0.8 and 8.1 years were suitable for record extensions; 37 long-record index wells were used to extend the groundwater level records at the study wells. The index well selected to pair with a study well was chosen based on Pearson correlation coefficient values; cross-correlation between the two wells; geologic and topographic similarity; and smallest distance spanning the wells. Each study well and its corresponding index well have 1 or more years of concurrent, overlapping data; a Pearson correlation coefficient that exceeded a threshold value of 0.8; and a similar aquifer type and hydrologic characteristics. Of the 29 study wells, 2 showed poor correlations with all index wells and were not considered for record extensions. Performance metrics used to assess the accuracy of the MOVE.1 models indicated that most models provided reasonable estimates of groundwater levels. Root mean square error values ranged from 0.097 to 2.292 feet, with a median of 0.536 foot. Nash-Sutcliffe efficiency coefficient values ranged from 0.623 to 0.996, with a median value of 0.759. Generally, study wells in close geographical proximity to their index well resulted in stronger model performance. The average length of groundwater level records was extended by 14.1 years to a new average of 18.1 years. The estimated groundwater level records from the MOVE.1 models resulted in an increase in the range of highest and lowest groundwater levels at 23 of 27 wells. The increase in range of groundwater levels was between 0.08 to 7.95 feet. Monthly percentiles for State drought indices were computed from the estimated MOVE.1 records and observed records through December 31, 2021. Percentiles computed from estimated records show an average groundwater level about 1.0 foot lower than observed data at the 2d percentile and 0.1 foot lower at the 30th percentile.

The principal source of information for understanding groundwater conditions and characterizing the severity of a drought in Massachusetts comes from the records of groundwater levels from a statewide network of groundwater wells. Groundwater levels can vary greatly from season to season and from year to year in response to climatic and hydrologic conditions. Currently [2023], 72 wells in the U.S. Geological Survey (USGS) Climate Response Network (CRN) are used for monitoring groundwater levels in Massachusetts (fig. 1). CRN wells maximize the State’s ability to effectively prepare for and respond to drought conditions (Massachusetts Executive Office of Energy and Environmental Affairs and Massachusetts Emergency Management Agency, 2019). Groundwater levels are monitored using a combination of continuous monitoring wells and noncontinuous monitoring, discrete wells. Noncontinuous monitoring wells (with no automatic sensing or recording devices) require manual measurements. In Massachusetts, measurements are typically made at a scheduled monthly interval. With monthly monitoring, however, extreme water level fluctuations cannot be determined with certainty and hydraulic responses to groundwater stresses that happen between measurements may be missed. Continuous-monitoring wells provide the finest resolution, typically hourly or subhourly, of water level fluctuations and are the most helpful to use for monitoring fluctuations in groundwater levels during droughts. Since 2013, 29 wells have been equipped with 15-minute-interval recording devices and currently [2023] have between 0.8 and 8.1 years of continuous record. Many of the installations were prompted by the 2016–7 statewide drought and an increased awareness of the need for data for future drought analyses. Massachusetts has experienced widespread, severe drought many times. Single-season droughts in the State are becoming more common, with the majority of Massachusetts experiencing droughts in 2016, 2020, and 2022 (Lombard and others, 2020; McCarthy and others, 2023). In Massachusetts, groundwater levels are one of six indices (precipitation, streamflow, groundwater, lakes and impoundments, fire

2 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts 73°30'

73°00'

43°00'

72°30'

72°00'

71°30'

71°00'

70°30'

VERMONT

NEW HAMPSHIRE

NEW YORK

42°30'

29 68

65 61

EA OC

27 30

Map area

TIC AN

MASSACHUSETTS

23 58

L AT

IC ANT ATL EAN C O

70°00'

5 8 44

CONNECTICUT

42°00'

39 12

11 6

RHODE ISLAND

40 9

45 32

35 31 4 33 37 34 2

1 38

7 36

41°30' 46 3

0 0

50 KILOMETERS

EXPLANATION 3

Region Cape Cod Central Connecticut River Islands

50 MILES

Northeast Southeast Western

Groundwater well and identifier—Data from Crozier and Ahearn (2024)

Figure 1. Map showing the locations of U.S. Geological Survey Climate Response Network wells and drought regions for monitoring groundwater levels in Massachusetts. Wells are listed in appendix 1, table 1.1.

Well Network 3 danger, and evapotranspiration) used to assess the severity of a drought (Massachusetts Executive Office of Energy and Environmental Affairs and Emergency Management Agency, 2019). The methods for calculating the groundwater index are described in the Massachusetts drought management plan (Massachusetts Executive Office of Energy and Environmental Affairs and Emergency Management Agency, 2019). The 2019 plan aligns the drought categories and percentile ranges with the U.S. Drought Monitor, adopting a frequency of occurrence approach to determine drought severity as is used by the U.S. Drought Monitor and the USGS (National Drought Mitigation Center, 2023). The approach requires the computation of the monthly percentiles for individual CRN wells. Groundwater conditions are then characterized at a regional scale by the median of all the individual well percentiles within that region. Evaluating the potential effects of declining groundwater levels due to drought requires records beyond the observed groundwater levels available for many of the study CRN wells. Wells with shorter records generally do not capture the full range of long-term groundwater conditions. This lack of range renders drought determinations based on short-record wells less accurate than those based on long-record wells. Natural variations in groundwater levels at an annual scale, coupled with decadal variations, increase the need for the longest period of record possible. When monthly percentiles are computed from short records, particularly where the groundwater record excludes periods of droughts, the monthly percentiles for drought assessment can be unreliable. Robust estimation procedures such as record extensions use data from a well site with a long period of record to extend the data at a nearby well site with a shorter period of record when the sites are closely correlated. Historically, record extension methods have been widely used throughout the hydrologic community to extend streamflow records (Colarullo and others, 2018; Olson and Meyerhofer, 2019). Methods for extending groundwater levels have been developed to meet the needs for drought management and improvements in deriving the groundwater index (Dudley and others, 2018). The purpose of this study is to extend the groundwater level records at select study wells and compute monthly percentiles from the estimated historical groundwater level records to increase the State’s ability to characterize drought conditions in the seven drought regions in Massachusetts. This report presents the results of record extension efforts and includes (1) an overview of the selection of the study wells and long-term wells designated in this report as index wells; (2) discussion of the Maintenance of Variance Extension type 1 (MOVE.1) method to extend groundwater level records at wells on the basis of concurrent records at hydrologically similar index wells located in Massachusetts or surrounding States; and (3) evaluation of the MOVE.1 model accuracy. The report includes two appendices: appendix 1 contains a

list of groundwater wells in Massachusetts that are part of the USGS CRN and appendix 2 contains the monthly percentiles of groundwater levels for the study wells.

Well Network In 2023, the USGS operated a network of 79 wells in Massachusetts for monitoring groundwater levels. A subset of these wells (72 of 79) is part of the USGS CRN (U.S. Geological Survey, 2024). The CRN includes about 680 wells nationwide that report water level conditions that are minimally affected by human activities. The primary purpose of the USGS CRN is to monitor the effect of climate on groundwater levels. Because CRN wells are minimally affected by human activities, the groundwater level fluctuations reflect climatic variation rather than, for example, groundwater withdrawals or human-induced recharge. CRN wells provide critical information on groundwater levels for drought management. For this study, CRN wells in Massachusetts were reviewed and compiled as study wells or as index wells based on the individual lengths of continuous daily water level record. CRN wells in surrounding States with record lengths greater than 10 years and several undesignated CRN wells (sites 414831072173002 [CT–MS 80 Mansfield, Conn.], 414741072134501 [CT–MS 44 Mansfield, Conn.], 425024071413001 [NH–MOW 36, N.H.], 422622073410901 [Local number, Cb-1072, at Niverville, N.Y.], 414128073475201 [Local number, Du-1009, ST Park, Pleasant Valley, N.Y.], and 414737073563301 [Local number, Du-321, near Hyde Park, N.Y.]) with record lengths greater than 10 years were included as index wells to increase the spatial coverage and density of index wells in the study. Well data, including data from undesignated CRN wells, used in the study are considered to be predominantly natural, with no or little human-caused stresses. Most of the study wells include both continuous data and discrete data. Continuous data provide more accurate estimates of maximum and minimum water level fluctuations than discrete data. Discrete data include groundwater-level records based on measurements generally made at monthly intervals. For this study, study wells had continuous daily water-level data records 0.8 to 8.1 years long, as of December 31, 2021 (table 1). The average record length for the study wells is 4.0 years. An index well was required to have 9 or more years (consecutive or nonconsecutive) of daily water level records as of December 31, 2021 (table 2). The average record length for an index well was 20.8 years. On the basis of proximity of the paired wells and minimum data criteria, 29 study wells and 39 index wells were included in this study (fig. 2). The index wells include 26 wells in Massachusetts and 13 wells in nearby States: 4 in Connecticut, 3 in New Hampshire, 4 in New York, and 2 in Rhode Island (fig. 2).

Table 1. U.S. Geological Survey groundwater wells selected for record extensions for monitoring groundwater levels in Massachusetts.

Site ID

Site name

Decimal latitude

Decimal longitude

Period of record

Continuous (daily) record Start date

End date

No. of years

413930070190901

MA–A1W 306 Barnstable, MA

41.65844

−70.31863

1975–2021

11/5/2015

12/31/2021

6.2

422248071362401

MA–A9W 57, Berlin, MA

42.37989

−71.60678

2013–2021

7/21/2018

12/31/2021

3.4

414205070334701

MA–BHW 506–0206 (MW–21M3) Bourne, MA

41.70142

−70.56258

2019–2021

6/20/2019

12/31/2021

2.5

414455070325701

MA–BHW 507–0253 (MW–67M1) Bourne, MA

41.74874

−70.54872

2019–2021

3/2/2019

12/31/2021

2.8

421012072324301

MA–CMW 95R Chicopee, MA

42.17000

−72.54528

1983–2021

9/27/2017

12/31/2021

2.7

423810072435401

MA–CSW 8R Colrain, MA

42.63606

−72.73153

2016–2021

12/16/2017

12/31/2021

4.0

422733072532601

MA–CYW 13 Cummington, MA

42.45946

−72.89028

1986–2021

7/28/2017

12/31/2021

4.4

421438071165601

MA–DVW 10R Dover, MA

42.24389

−71.28222

1964–2021

2/25/2021

12/31/2021

0.8

412346070353403

MA–ENW 52 Edgartown, MA

41.39623

−70.59225

1976–2021

5/14/2019

12/31/2021

2.6

420305072581401

MA–GLW 6R Granville, MA

42.05140

−72.97068

1964–2021

2/28/2014

12/31/2021

7.8

422058072085101

MA–HHW 1R Hardwick, MA

42.34944

−72.14750

1964–2021

1/27/2018

12/31/2021

3.9

424249072493101

MA–HNW 19 Heath, MA

42.71378

−72.82528

2019–2021

5/3/2019

12/31/2021

2.7

415229070554301

MA–LKW 14R Lakeville, MA

41.87472

−70.92861

2018–2021

12/15/2018

12/31/2021

3.0

421240072490201

MA–M7W 19 Montgomery, MA

42.21127

−72.81700

1986–2021

9/23/2017

12/31/2021

4.3

420610071421402

MA–NXW 54 Northbridge, MA

42.10287

−71.70340

1984–2021

9/1/2017

12/31/2021

4.3

423441072170701

MA–ORW 63 Orange, MA

42.57814

−72.28481

1985–2021

2/5/2020

12/31/2021

1.9

415453070434901

MA–PWW 22 Plymouth, MA

41.91493

−70.72977

1956–2021

12/5/2014

12/31/2021

7.1

414405070312104

MA–SDW 483–0170 (MW–17M3) Sandwich, MA

41.73621

−70.52186

2019–2021

2/21/2019

12/31/2021

2.9

414712071175001

MA–SHW 275R Seekonk, MA

41.78667

−71.29722

2018–2021

9/14/2018

12/31/2021

3.3

420350073193601

MA–SJW 58R Sheffield, MA

42.06389

−73.32667

1987–2021

11/14/2013

12/31/2021

8.1

423715072042801

MA–TMW 3R Templeton, MA

42.62083

−72.07444

1957–2021

1/30/2020

12/31/2021

1.9

424055071435302

MA–TRW 13R Townsend, MA

42.68194

−71.73139

1964–2021

9/22/2017

12/31/2021

4.3

420206070045901

MA–TSW 89 Truro, MA

42.03523

−70.08257

1962–2021

11/3/2014

12/31/2021

7.2

415808070024301

MA–TSW 257–0034 Truro, MA

41.96899

−70.04475

1999–2021

6/14/2017

12/31/2021

4.6

421410072081101

MA–WUW 2R West Brookfield, MA

42.23611

−72.13639

1959–2021

9/27/2017

12/31/2021

4.3

423257071243702

MA–WWW 160 Westford, MA

42.54915

−71.41039

2001–2021

2/25/2021

12/31/2021

0.8

421923072451001

MA–WXW 20 Westhampton, MA

42.34120

−72.80621

1987–2021

9/22/2017

12/31/2021

4.3

424204072015201

MA–XNW 13 Winchendon, MA

42.70102

−72.03084

1939–2021

9/28/2017

12/31/2021

4.3

424057072010301

MA–XNW 48 Winchendon, MA

42.68265

−72.01765

2014–2021

9/26/2017

12/31/2021

4.3

Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

[Data are from Crozier and Ahearn (2024). ID, identifier; no., number; MA, Massachusetts]

Table 2. U.S. Geological Survey long-term groundwater wells in and near Massachusetts selected as index wells for extending groundwater level records at study wells for monitoring groundwater levels in Massachusetts. [Data are from Crozier and Ahearn (2024). ID, identifier; no., number; CT, Connecticut; MA, Massachusetts; NY, New York; RI, Rhode Island]

Site ID

Site name

Decimal latitude

Decimal longitude

Period of record

Continuous (daily) record Start date

End date

No. of years

CT–MB 32 Marlborough, CT

41.59313

−72.42642

1986–2021

9/30/2002

12/31/2021

19.3

414741072134501

CT–MS 44 Mansfield, CT

41.79502

−72.22864

1982–2021

10/1/2007

12/31/2021

14.3

414831072173002

CT–MS 80 Mansfield, CT

41.80853

−72.29211

2002–2021

3/1/2002

12/31/2021

19.8

414240072033201

CT–SC 22 Scotland, CT

41.71102

−72.05917

1984–2021

12/1/2007

12/31/2021

14.1

422241073274601

Local number, Cb-1071, Canaan, NY

42.37806

−73.46278

2004–2021

2/4/2004

12/31/2021

17.9

422622073410901

Local number, Cb-1072, at Niverville NY

42.43958

−73.68581

2005–2021

4/30/2006

12/31/2021

15.7

414128073475201

Local number, Du-1009, ST Park, Pleasant Valley, NY

41.69133

−73.79761

1965–2021

3/20/2002

12/31/2021

19.8

414737073563301

Local number, Du-321, near Hyde Park NY

41.79370

−73.94208

1948–2021

9/27/1978

12/31/2021

43.3

422812071244401

MA–ACW 158 Acton, MA

42.47011

−71.41188

1964–2021

10/23/2000

12/31/2021

21.2

414129070361401

MA–BHW 198 Bourne, MA

41.69150

−70.60336

1962–2021

5/19/2012

12/31/2021

9.6

414632070014901

MA–BMW 22R Brewster, MA

41.77556

−70.03028

1962–2021

12/5/2001

12/31/2021

20.1

414101070011001

MA–CGW 138R Chatham, MA

41.68361

−70.01944

1962–2021

5/24/2012

12/31/2021

9.6

420316070433501

MA–D4W 79R Duxbury, MA

42.05444

−70.72639

1964–2021

9/30/2007

12/31/2021

14.3

413801070322703

MA–FSW 239–0121, MA

41.63380

−70.54068

1993–2021

8/14/2008

12/31/2021

13.4

424841071004101

MA–HLW 23 Haverhill, MA

42.81161

−71.01162

1960–2021

10/17/1984

12/31/2021

37.2

415228070554601

MA–LKW 14 Lakeville, MA

41.87455

−70.92893

1964–2021

11/27/1984

12/10/2018

26.3

424520070562401

MA–NIW 27 Newbury, MA

42.75537

−70.93949

1959–2021

10/17/1984

12/31/2021

37.2

420544071173701

MA–NNW 27R Norfolk, MA

42.09556

−71.29361

1964–2021

8/10/2001

12/31/2021

20.4

422103072241102

MA–PDW 23 Pelham, MA

42.35092

−72.40258

1981–2021

10/1/1991

1/30/2017

25.4

422906072124301

MA–PHW 16 Petersham, MA

42.48508

−72.21144

1984–2021

5/17/2012

12/31/2021

9.6

422745073112001

MA–PTW 51 Pittsfield, MA

42.71378

−72.82528

1963–2021

10/19/1984

12/31/2021

37.2

414125070265901

MA–SDW 253R Sandwich, MA

41.69028

−70.44972

1962–2021

5/28/2012

12/31/2021

9.6

414219070313601

MA–SDW 525–0109 (MW–126S), MA

41.70542

−70.52600

2002–2021

1/10/2002

12/31/2021

20.0

414139070311501

MA–SDW 526–0040 (MW–145S), MA

41.69437

−70.52044

2002–2021

2/1/2002

12/31/2021

19.9

414124070311401

MA–SDW 527–0055 (90MW0063), MA

41.69013

−70.52013

2002–2021

1/10/2002

12/31/2021

20.0

414159070310501

MA–SDW 537–0107 Sandwich, MA

41.69998

−70.51775

2004–2021

1/21/2005

12/31/2021

17.0

423058071025401

MA–WAW 38R Wakefield, MA

42.51611

−71.04833

1964–2021

10/25/2000

12/31/2021

21.2

421853071220501

MA–WKW 2R Wayland, MA

42.31472

−71.36806

1965–2021

10/14/2010

12/31/2021

11.2

415354069585201

MA–WNW 17R Wellfleet, MA

41.89833

−69.98111

1962–2021

5/17/2012

12/31/2021

9.6

Well Network 5

413535072253701

[Data are from Crozier and Ahearn (2024). ID, identifier; no., number; CT, Connecticut; MA, Massachusetts; NY, New York; RI, Rhode Island]

Site ID

Site name

Decimal latitude

Decimal longitude

Period of record

Continuous (daily) record Start date

End date

No. of years

423506070491401

MA–WPW 76R Wenham, MA

42.58500

−70.82056

1964–2021

5/25/2012

12/31/2021

9.6

422341071464901

MA–WSW 26 West Boylston, MA

42.39478

−71.77985

1995–2021

5/14/2012

12/31/2021

9.6

423401071093801

MA–XMW 78 Wilmington, MA

42.56690

−71.15997

1951–2021

10/15/1984

12/31/2021

37.2

425024071413001

NH–MOW 36, NH

42.84009

−71.69118

1962–2021

10/1/1994

12/31/2021

27.3

431120071284201

NH–PBW 148 Pembroke, NH

43.18882

−71.47836

2000–2021

5/16/2000

12/31/2021

21.6

431540071452801

NH–WCW 1 Warner, NH

43.26119

−71.75730

1965–2021

3/12/1999

12/31/2021

22.8

413358071433801

RI–EXW 475 Exeter, RI

41.56621

−71.72673

1981–2021

10/5/1987

12/31/2021

34.3

412932071374302

RI–RIW 417 Richmond, RI

41.49232

−71.62812

1975–2021

10/5/1987

12/31/2021

34.3

6 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Development of MOVE.1 Models for the Extension of Groundwater Level Records 7 74°00'

73°30'

73°00'

72°30'

72°00'

71°30'

71°00'

70°30'

70°00'

69°30'

NH–WCW 1

ME VT

NH–PWB 148

NEW HAMPSHIRE

VERMONT

43°00'

IC ANT ATL EAN C O

NH–MOW 36

MA–CSW 8R

MA–SJW 58R

MA–GLW 6R

MA–WUW 2R MA–CMW 95R

MA–NXW 54

42°00'

MASSACHUSETTS Du-321 Du-1009

CT–MS 80

CONNECTICUT

MA–DVW 10R

CT–MS 44 CT–SC 22

CT–MB 32

MA–NNW 27R

RHODE ISLAND

MA–TSW 89

MA–D4W 79R

MA–TSW 257–0034

MA–PWW 22 MA–LKW 14R MA–SHW 275R MA–BHW 506–0206 MA–BHW 198

RI–EXW 475

MA–WNW 17R MA–BHW 507–0253 MA–SDW 483–0170 MA–SDW 525–0109 MA–BMW 22R MA–SDW 537–0107 MA–CGW 138R MA–A1W 306 MA–SDW 253R MA–FSW 239–0121

MA–SDW 526–0040 MA–SDW 527–0055

41°30'

MA–M7W 19

EA OC

MA–PDW 23 MA–WXW 20

Cb-1071

MA–NIW 27

MA–XMW MA–TMW 3R MA–WWW 160 78 MA–WPW 76R MA–PHW 16 MA–ACW 158 MA–WAW 38R MA–WSW 26 MA–A9W 57 MA–WKW 2R MA–HHW 1R

MA–ORW 63 MA–CYW 13

TIC AN

Cb-1072

MA–PTW 51

MA–TRW 13R

Map area

CT NJ

L AT

42°30'

MA–XNW MA–XNW 13 MA–XNW 48

MA–HNW 19

NEW YORK

MA–HLW 23

RI–RIW 417

MA–ENW 52

41°00' 25

50 MILES

50 KILOMETERS

EXPLANATION Groundwater well—Data from Crozier and Ahearn (2024)

Region Cape Cod Central Connecticut River Islands

Northeast Southeast Western

MA-CYW 13

Study well and name

Du-1009

Index well and name

Figure 2. Map showing the locations of 29 U.S. Geological Survey groundwater wells selected for possible record extensions and 39 U.S. Geological Survey wells selected as index wells in and near Massachusetts for monitoring groundwater levels in Massachusetts. Site names are in shortened forms; full study well site names are listed in table 1 and full index well site names are listed in table 2.

Development of MOVE.1 Models for the Extension of Groundwater Level Records Record extension uses information from a nearby longer-record index well site to extend the record (daily time-series data) at a short-record well site when the cross-correlation between the two sites is high. The index well characteristics of distribution shape, serial correlation, and seasonality are transferred to the short-record well site, with adjustments of location and scale appropriate to the

short-record well site. If the index well site and short-record well site have substantial differences in the characteristics, the record extension will perform poorly because these index well characteristics will be inaccurately attributed to the short-record well site.

Selection of Well Pairs It is important that the index well selected for extending groundwater-level records is hydrologically similar to the study well and characterized by similar types of groundwater level fluctuations. As an indicator of hydrologic similarity,

8 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts this study required that the index well and study well share the same physiographic province. The straight-line, Euclidean distance between individual study wells and index wells was calculated using geographic information system tools (tables 3 and 4). For this study, the maximum distance between paired wells for maintaining similar hydrologic characteristics was 30 miles (mi), which is about the average width of the drought regions in the Massachusetts drought management plan (Massachusetts Executive Office of Energy and Environmental Affairs and Emergency Management Agency, 2019). The paired wells more than 30 mi apart were flagged as suboptimal because the transfer of information from the index well to the study well may not be accurate over that distance (tables 3 and 4). In Massachusetts and its surrounding States, there are a very limited number of glacial till or bedrock wells. For this study, none of the well pairs in glacial till or bedrock aquifers were within a 30 mi span of one another and were therefore flagged as suboptimal. The criteria for selecting an index well to pair with a study well were (1) a Pearson correlation coefficient of 0.8 or greater; (2) similar geologic characteristics; (3) similar topographic characteristics, if applicable; and (4) a concurrent record of 1 or more years. A correlation coefficient exceeding a threshold value of 0.8 or greater is indicative of a strong linear relation between the index well and the study well; this provides reliable estimates of groundwater levels. Correlation testing was performed using all 37 index wells for each study well. Only well pairs with similar geologic characteristics and a correlation coefficient of 0.8 or greater were considered for further analysis. When multiple index wells show the same or similar correlation coefficient to a single study well, distance between the wells determined the most suitable index well. Well pairs with a shorter distance between the wells were given preference over well pairs that were further apart. In addition, well pairs with a longer concurrent record were preferred over well pairs with a shorter concurrent record. A longer concurrent record improves the MOVE.1 method to estimate groundwater levels because the model parameters can be estimated more precisely (Vogel and Kroll, 1991). Results from correlation testing on all possible pairs of wells indicated that 27 of 29 study wells have a Pearson correlation coefficient of 0.8 or greater to one or more index wells (table 4). The initial correlation testing resulted in a total of 75 possible pairs. Many of the possible pairs were dropped from further analysis because they did not meet the criterion for similarity in geologic and topographic characteristics. Two study wells—sites 420610071421402 (MA–NXW 54 Northbridge, Mass.) and 421410072081101 (MA–WUW 2R West Brookfield, Mass.)—had poor correlation coefficients (less than 0.8) and were dropped from further analysis. In several cases where the correlation coefficient is only slightly weaker at one or more index wells and the distance between the wells is similar, record extensions were performed on both wells and the performance metrics (described in the “Accuracy and Limitations of Groundwater Level Records From

MOVE.1” section of this report) from the MOVE.1 method were evaluated to determine the best index well to use for the final record extension.

Use of MOVE.1 for Record Extension The MOVE.1 method was used to estimate groundwater levels at 27 of 29 wells initially selected for extension. The MOVE.1 method is based on developing a linear relationship between the study well and the index well by assuming that the sample mean and sample variance of groundwater levels are maintained over time for the study well (Hirsch, 1982). Only the means and standard deviations for the concurrent record are used to define the MOVE.1 relation. The concurrent record is defined using continuous and discrete records. The MOVE.1 equation is then written as follows: Yi Y where

Sy Sx

X X ,(1) i

is the estimated groundwater level at the study well for day i,

Y̅

is the mean of the concurrent observed groundwater levels at the study well,

is the standard deviation of the concurrent observed groundwater levels at the study well,

is the standard deviation of the concurrent observed groundwater levels at the index well,

is the groundwater level at the index well for day i, and

X̅

is the mean of the concurrent observed groundwater levels at the index well.

The programming language R, along with the R package smwrStats, version 0.7.5 (Lorenz, 2017a, b, 2022), was used to perform the record extensions. R is an open-source programming language and software environment for statistical computing and graphics supported by the R Foundation for Statistical Computing. The R script reads the station identifiers; extracts groundwater level data from the National Water Information System database for both the index well and the study well; loops through each index well associated with the study wells, performing the MOVE.1 method using the index and study wells; outputs estimated groundwater levels for the study wells; computes residual statistics; and generates model residuals.

Table 3. U.S. Geological Survey study wells with paired index wells and descriptive parameters of the Maintenance of Variance Extension type 1 (MOVE.1) models for monitoring groundwater levels in Massachusetts. [Data are from Crozier and Ahearn (2024). Site names are in shortened forms; study well site names are listed in table 1 and index well site names are listed in table 2. ID, identifier; mi, mile; no., number; B, bedrock; Till, glacial till; SD, stratified drift]

Study well Site ID

Index well Site name

Site ID

Distance between wells (mi)

Site name

Aquifer type

No. of concurrent years

No. of extended years

MA–A1W 306

414632070014901

MA–BMW 22R

6.6

14.7

422248071362401

MA–A9W 57

414831072173002

CT–MS 80*

3.6

15.8

414205070334701

MA–BHW 506–0206

414219070313601

MA–SDW 525–0109

2.5

15.6

414455070325701

MA–BHW 507–0253

414219070313601

MA–SDW 525–0109

2.8

15.4

421012072324301

MA–CMW 95R

422622073410901

Cb-1072*

4.6

11.0

423810072435401

MA–CSW 8R

431540071452801

NH–WCW 1*

4.1

19.6

422733072532601

MA–CYW 13

422341071464901

MA–WSW 26*

4.7

5.4

421438071165601

MA–DVW 10R

422812071244401

MA–ACW 158

1.8

17.6

412346070353403

MA–ENW 52

414125070265901

MA–SDW 253R

3.0

7.2

420305072581401

MA–GLW 6R

422341071464901

MA–WSW 26*

7.9

2.2

422058072085101

MA–HHW 1R

422341071464901

MA–WSW 26

4.2

5.9

424249072493101

MA–HNW 19

413535072253701

CT–MB 32*

Till

2.7

16.7

415229070554301

MA–LKW 14R

421853071220501

MA–WKW 2R*

3.1

9.4

421240072490201

MA–M7W 19

422745073112001

MA–PTW 51

5.2

30.1

423441072170701

MA–ORW 63

422341071464901

MA–WSW 26

2.3

7.8

415453070434901

MA–PWW 22

415228070554601

MA–LKW 14

4.2

26.9

414405070312104

MA–SDW 483–0170

414159070310501

MA–SDW 537–0107

2.9

13.7

414712071175001

MA–SHW 275R

420544071173701

MA–NNW 27R

3.3

18.2

420350073193601

MA–SJW 58R

422622073410901

Cb-1072*

8.3

7.4

423715072042801

MA–TMW 3R

420544071173701

MA–NNW 27R*

2.7

18.8

424055071435302

MA–TRW 13R

422812071244401

MA–ACW 158

5.3

16.1

420206070045901

MA–TSW 89

414129070361401

MA–BHW 198*

7.7

3.5

415808070024301

MA–TSW 257–0034

415354069585201

MA–WNW 17R

4.6

6.7

423257071243702

MA–WWW 160

421853071220501

MA–WKW 2R

1.2

11.2

421923072451001

MA–WXW 20

422812071244401

MA–ACW 158*

4.8

16.6

424204072015201

MA–XNW 13

424520070562401

MA–NIW 27*

Till

5.3

32.9

424057072010301

MA–XNW 48

431120071284201

NH–PBW 148*

4.3

14.8

*The paired well is considered suboptimal for record extension (the distance between wells is greater than 30 miles).

Development of MOVE.1 Models for the Extension of Groundwater Level Records 9

413930070190901

[Data are from Crozier and Ahearn (2024). Site names are in shortened forms; study well site names are listed in table 1 and index well site names are listed in table 2. ID, identifier; r, Pearson correlation coefficient; RMSE, root mean square error; NSE, Nash-Sutcliffe efficiency coefficient; Min, minimum; Q1, first quarter; Q3, third quarter; Max, maximum]

Study well Site ID

Index well Site name

Site ID

Site name

RMSE

NSE

Residuals Min

Max

413930070190901

MA–A1W 306

414632070014901

MA–BMW 22R

0.910

0.631

0.819

−2.95

−0.46

0.14

0.53

1.75

422248071362401

MA–A9W 57

414831072173002

CT–MS 80*

0.948

0.547

0.896

−2.65

−0.30

0.02

0.26

4.15

414205070334701

MA–BHW 506–0206

414219070313601

MA–SDW 525–0109

0.998

0.097

0.996

−0.37

−0.07

0.00

0.08

0.22

414455070325701

MA–BHW 507–0253

414219070313601

MA–SDW 525–0109

0.965

0.284

0.930

−0.61

−0.24

0.09

0.22

0.41

421012072324301

MA–CMW 95R

422622073410901

Cb-1072*

0.894

0.500

0.789

−1.36

−0.34

−0.03

0.34

2.18

423810072435401

MA–CSW 8R

431540071452801

NH–WCW 1*

0.866

1.150

0.732

−2.51

−0.84

0.15

0.80

2.24

422733072532601

MA–CYW 13

422341071464901

MA–WSW 26*

0.838

0.482

0.676

−2.93

−0.24

0.07

0.32

1.09

421438071165601

MA–DVW 10R

422812071244401

MA–ACW 158

0.880

0.532

0.759

−2.32

−0.31

0.08

0.40

2.25

412346070353403

MA–ENW 52

414125070265901

MA–SDW 253R

0.859

0.773

0.719

−3.19

−0.56

−0.06

0.67

1.94

420305072581401

MA–GLW 6R

422341071464901

MA–WSW 26*

0.842

0.943

0.684

−4.70

−0.47

0.14

0.62

2.27

422058072085101

MA–HHW 1R

422341071464901

MA–WSW 26

0.887

0.536

0.773

−2.50

−0.35

−0.02

0.36

2.90

424249072493101

MA–HNW 19

413535072253701

CT–MB 32*

0.886

2.292

0.772

−4.70

−1.50

0.13

1.77

5.61

415229070554301

MA–LKW 14R

421853071220501

MA–WKW 2R*

0.921

1.027

0.843

−2.75

−0.84

0.01

0.72

2.48

421240072490201

MA–M7W 19

422745073112001

MA–PTW 51

0.824

0.609

0.648

−3.05

−0.34

−0.01

0.38

1.39

423441072170701

MA–ORW 63

422341071464901

MA–WSW 26

0.825

0.495

0.650

−1.83

−0.23

0.10

0.32

1.52

415453070434901

MA–PWW 22

415228070554601

MA–LKW 14

0.906

0.643

0.812

−3.06

−0.46

−0.10

0.42

1.98

414405070312104

MA–SDW 483–0170

414159070310501

MA–SDW 537–0107

0.995

0.117

0.989

−0.24

−0.07

−0.01

0.05

1.13

414712071175001

MA–SHW 275R

420544071173701

MA–NNW 27R

0.916

0.370

0.833

−0.98

−0.27

−0.02

0.24

1.32

420350073193601

MA–SJW 58R

422622073410901

Cb-1072*

0.812

0.936

0.623

−2.21

−0.76

−0.03

0.72

2.06

423715072042801

MA–TMW 3R

420544071173701

MA–NNW 27R*

0.835

0.250

0.670

−0.94

−0.15

0.01

0.17

0.79

424055071435302

MA–TRW 13R

422812071244401

MA–ACW 158

0.861

0.679

0.723

−2.07

−0.42

0.00

0.48

2.08

420206070045901

MA–TSW 89

414129070361401

MA–BHW 198*

0.867

0.222

0.734

−0.69

−0.14

0.00

0.11

1.44

415808070024301

MA–TSW 257–0034

415354069585201

MA–WNW 17R

0.947

0.244

0.894

−0.61

−0.17

−0.02

0.12

0.88

423257071243702

MA–WWW 160

421853071220501

MA–WKW 2R

0.889

0.256

0.777

−1.33

−0.15

0.01

0.15

1.32

421923072451001

MA–WXW 20

422812071244401

MA–ACW 158*

0.842

1.803

0.684

−8.35

−0.80

0.16

1.11

4.47

424204072015201

MA–XNW 13

424520070562401

MA–NIW 27*

0.858

1.436

0.715

−5.55

−0.30

0.34

0.82

6.45

424057072010301

MA–XNW 48

431120071284201

NH–PBW 148*

0.855

0.501

0.711

−1.59

−0.33

−0.07

0.30

2.86

*The paired well is considered suboptimal for record extension (the distance between wells is greater than 30 miles).

Median

10 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Table 4. U.S. Geological Survey study wells with paired index wells and performance metrics of the Maintenance of Variance Extension type 1 (MOVE.1) models for monitoring groundwater levels in Massachusetts.

Development of MOVE.1 Models for the Extension of Groundwater Level Records 11

Evaluation of MOVE.1 Models Records were extended at 27 of the 29 wells initially selected for extensions. Plots of correlation, model fit, and statistical distribution of the residuals for the MOVE.1 models were evaluated for goodness of fit. The correlation plots of the concurrent records show the relation of index well to study well. The model-fit plots show the estimated groundwater levels and observed groundwater levels for the concurrent record. When extending records, the set of groundwater-level estimates and the statistical distribution of that set are important, rather than the individual estimates. Histogram plots were visually inspected and used to evaluate the data distribution. The distribution of residuals, representing the difference between the observed values and the estimated values, should be normally distributed with a mean of 0 for MOVE.1 modeling. Figures 3 through 5 not only show how accurately the models represent the groundwater-level range and data distribution at the study well but also provide insight into how well the models estimate groundwater levels and statistics for drought management. The three figures are examples of models ranging in quality from excellent (fig. 3) to fair (fig. 5), with the distance between the pared wells spanning 2, 17, and 66 mi. Visual inspection of the model fit and the interquartile range of the residuals were considered when evaluating the quality of the model. The aquifer systems of the three well pairs are stratified drift, which is the primary aquifer type of the study wells. The mean and distribution of the residuals for all the models indicated no clear bias in the estimated records. Figure 3 shows the correlation, model fit of the concurrent continuous data, and distribution of the residuals from the MOVE.1 method of the study well at site 414205070334701 (MA–BHW 506–0206 [MW–21M3] Bourne, Mass.) and the index well at site 414219070313601 (MA–SDW 525–0109 [MW–126S]). The paired wells are 2 mi apart with 2.5 years of concurrent data. The degree of correlation between study well and index well is considered very strong at 0.998 (fig. 3A). The model estimated daily groundwater levels from January 2002 to June 2018 (about 16 years of record). The model fit of the concurrent continuous data is considered excellent (fig. 3B). The residuals are very small, ranging from −0.37 to 0.22 foot (ft) with a mean of 0 ft and an interquartile range from −0.07 to 0.08 ft. The magnitude of the range of the groundwater data based on the record extension is 10.88 ft (a 6.08-ft change in range). Figure 4 shows the correlation, model fit of the concurrent continuous data, and distribution of the residuals from the MOVE.1 method of the study well at site 413930070190901 (MA–A1W 306 Barnstable, Mass.) and the index well at site 414632070014901 (MA–BMW 22R Brewster, Mass.). The paired wells are 17 mi apart with 6.6 years of concurrent data. The degree of correlation between study well and index well is considered strong at 0.910 (fig. 4A). The model estimated daily groundwater

levels from December 2001 to November 2015, along with several days in July 2016 and January 2019 (about 14 years of record). The estimated groundwater levels are considered a good model fit to the observed water levels (fig. 4B), with 50 percent of the estimated data within 0.5 ft of the observed data. The residuals range from −2.95 to 1.75 ft with an interquartile range of −0.46 to 0.53 ft. The magnitude of the range of the groundwater data based on the record extension is 8.35 ft (a 0.70-ft change in range). Figure 5 shows the correlation, model fit of the concurrent continuous data, and distribution of the residuals from the MOVE.1 method of the study well at site 423810072435401 (MA–CSW 8R Colrain, Mass.) and the index well at site 431540071452801 (NH–WCW 1 Warner, N.H.). The paired wells are 66 mi apart with 4.1 years of concurrent data. Because the wells span more than 30 mi, the paired wells are considered nonideal for record extension. The model estimated daily groundwater levels from March 1999 to December 2017 (about 18 years of record). The degree of correlation between the paired wells is considered good at 0.866 (fig. 5A). Figure 5B shows the estimated water levels appear as a fair model fit to the observed water levels with 50 percent of the estimated data within 0.8 ft of the observed. However, the plot does show the estimated water levels typically 1 to 1.5 ft deeper than the observed water levels during dry periods. The residuals range from −2.51 to 2.24 ft with an interquartile range from −0.84 to 0.80 ft. The magnitude of the range of the groundwater data based on the record extension is 16.41 ft (a 6.53-ft change in range).

Accuracy and Limitations of Groundwater Level Records From MOVE.1 The MOVE.1 models were developed from statistical variables (sample means and sample standard deviations of groundwater levels) that best explain the variability of groundwater levels and are subject to the limitations of the concurrent data used to develop the models. If the concurrent data used to calculate the sample mean and standard deviations are not representative of the population (true) mean and sample deviations of the two sites used in the record extension, the estimated values may not be very accurate. How well the estimated values represent the observed true values, or the accuracy of the MOVE.1 model, is an important consideration in the application of the model and the interpretation of the results. The accuracy of the estimates of groundwater level records from the MOVE.1 model is indicated by two statistics: the root mean square error (RMSE) and the Nash-Sutcliffe efficiency coefficient (NSE). The RMSE represents the mean of the absolute distance between the observed and estimated values. A lower RMSE indicates a better fit between the observed and estimated data. The units of RMSE are the same units as the groundwater levels. NSE is a normalized statistic that provides a measure of how well model output matches

Depth to water level in well MA–BHW 506–0206, in feet below land surface

12 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

A. Correlation plot

72 72 71 70 69

EXPLANATION MOVE.1 Regression

Water level, in feet

67 95.0

97.5

100.0

102.5

105.0

Depth to water level in well MA–SDW 525–0109, in feet below land surface

165

B. Model fit plot EXPLANATION

Groundwater level, in feet below land surface

MOVE.1 Observed daily data 168

171

174

2019

2020

2021

Year

Figure 3. Graphs showing A, correlation and B, model fit of the concurrent continuous data from the Maintenance of Variance Extension type 1 (MOVE.1) method of the study well at site 414205070334701 (MA–BHW 506-0206 [MW–21M3] Bourne, Mass.) and the index well at site 414219070313601 (MA–SDW 525–0109 [MW–126S]), as part of a study for monitoring groundwater levels in Massachusetts. The paired wells are 2 miles apart with 2.5 years of concurrent data.

measured data. NSE ranges from negative infinity to 1.0, with a value of 1.0 indicating a perfect match between model and observed data and a value of 0.0 or less indicating that the mean of the observed values is a better predictor than the model-estimated values. Both RMSE and NSE were reviewed collectively and used to determine whether the estimates of groundwater-level records are acceptable for the purpose of computing percentiles for drought determination. The Pearson correlation coefficient and the residual-regression statistics also provided a quantitative measure of the predictive value of data for each well. The Pearson correlation coefficient is a statistic that was used to determine how closely the concurrent data from index well and study well are related (table 4).

Overall, the performance metrics indicate the majority of MOVE.1 models estimated groundwater levels with reasonable accuracy (table 4). The interquartile range of the residuals shows that the groundwater level estimates are within 0.5 ft of the observed levels at about 20 wells. RMSE values ranged from 0.097 to 2.292 ft with a median of 0.536 ft. NSE values ranged from 0.623 to 0.996, with a median value of 0.759. In general, performance of the MOVE.1 model improves the closer the index well and study well are and the more geomorphological characteristics the wells share. RMSE values were generally smaller for study wells located closer to their index wells and larger for study wells located further from their index wells. For example, four wells—sites 414205070334701 (MA–BHW 506–0206

Development of MOVE.1 Models for the Extension of Groundwater Level Records 13

Depth to water level in well MA–A1W 306, in feet below land surface

A. Correlation plot

EXPLANATION

MOVE.1 Regression Water level, in feet

20 27

Depth to water level in well MA–BMW 22R, in feet below land surface

Groundwater level, in feet below land surface

20.0

B. Model fit plot

22.5

25.0

EXPLANATION

27.5

MOVE.1 Observed daily data 30.0

2015

2016

2017

2018

2019

2020

2021

Year

Figure 4. Graphs showing A, correlation and B, model fit of the concurrent continuous data from the Maintenance of Variance Extension type 1 (MOVE.1) method of the study well at site 413930070190901 (MA–A1W 306 Barnstable, Mass.) and the index well at site 414632070014901 (MA–BMW 22R Brewster, Mass.), as part of a study for monitoring groundwater levels in Massachusetts. The paired wells are 17 miles apart with 6.6 years of concurrent data.

[MW–21M3] Bourne, Mass.), 414455070325701 (MA–BHW 507–0253 [MW–67M1] Bourne, Mass.), 414405070312104 (MA–SDW 483–0170 [MW–17M3] Sandwich, Mass.), and 415808070024301 (MA–TSW 257–0034 Truro, Mass.)—have RMSE values less than 0.3 ft and are less than 6 mi from the index wells. Conversely, two wells—sites 423810072435401 (MA–CSW 8R Colrain, Mass.) and 415229070554301 (MA– LKW 14R Lakeville, Mass.)—have RMSE values greater than 1 ft and are 66 and 38 mi from the index wells, respectively. The RMSE and NSE values for site 421923072451001 (MA–WXW 20 Westhampton, Mass.) indicate low model accuracy. The poor performance of the model may be attributed to hydrologic differences and the distance from its index well (72 mi apart).

Because of the number of suitable index wells is limited, some index wells were used at more than one study well. Two index wells were used three or four times to extend the groundwater record at the study wells. One implication of using the same index well for multiple record extensions is the increase the intergroundwater level correlation in subsequent statistical analyses. When the estimates from the record extensions are compared to one another based on the same index well, the comparisons and inferences are unreliable. In any case, using the same index well for multiple record extensions will result in estimates that are all similar and introduce regional bias in the estimates.

Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Depth to water level in well MA–CSW 8R, in feet below land surface

A. Correlation plot

18 16 14 12

EXPLANATION MOVE.1 Regression

Water level, in feet 8

Groundwater level, in feet below land surface

Depth to water level in well NH–WCW 1, in feet below land surface

B. Model fit plot EXPLANATION MOVE.1 Observed daily data

2017

2018

2019

2020

2021

Year

Figure 5. Graphs showing A, correlation and B, model fit of the concurrent continuous data from the Maintenance of Variance Extension type 1 (MOVE.1) method of the study well at site 423810072435401 (MA–CSW 8R Colrain, Mass.) and the index well at site 431540071452801 (NH–WCW 1 Warner, N.H.), as part of a study for monitoring groundwater levels in Massachusetts. The paired wells are 66 miles apart with 4.1 years of concurrent data.

Comparison of Groundwater Level Records From MOVE.1 and Observed Records By using this method of record extension, the records for study wells—particularly those with very short records—were able to be substantially increased (table 3). Groundwater-level records averaged 4.0 years prior to the record extension and 18.1 years after the record extension. These longer records resulted in a wider range of groundwater levels for 23 of 27 wells (fig. 6; table 5). Higher (shallower) groundwater levels occurred at 18 wells and lower (deeper) groundwater levels occurred at 13 wells. Four wells— sites 421438071165601 (MA–DVW 10R Dover, Mass.), 422058072085101 (MA–HHW 1R Hardwick, Mass.), 415453070434901 (MA–PWW 22 Plymouth, Mass.), and

423715072042801 (MA–TMW 3R Templeton, Mass.)— showed no change in the range of groundwater levels after the record extensions. Although the records of these four wells are relatively short, the extreme highest and lowest groundwater levels were measured in the observed record. Even when the record extension results in no change in the range of groundwater levels, the extended records help minimize bias when certain data are overweighted, such as extremes in short-data records. With the additional data of an extended record, extremes are contextualized as outliers. The range of groundwater levels increased moderately in 16 wells, by between 0.1 and 3.0 ft, and increased substantially in 7 wells, by between 3.1 and 8.0 ft. Overall, the record extensions resulted in a much broader range of groundwater levels often associated with long-term conditions (fig. 6; table 5).

Table 5. Range of highest and lowest groundwater levels from the estimated Maintenance of Variance Extension type 1 records and observed records for 27 study wells for monitoring groundwater levels in Massachusetts. [Data are from Crozier and Ahearn (2024). ID, identifier; ft, foot; MA, Massachusetts]

Site ID

Site name

Groundwater level extended record Groundwater level observed record (ft) (ft) Highest

Highest

MA–A1W 306 Barnstable, MA

20.83

29.18

8.35

20.83

28.48

Lowest

7.65

Range

0.70

422248071362401

MA–A9W 57, Berlin, MA

14.84

24.54

9.70

16.31

24.54

8.23

1.47

414205070334701

MA–BHW 506–0206 (MW–21M3) Bourne, MA

165.02

175.90

10.88

167.47

172.27

4.80

6.08

414455070325701

MA–BHW 507–0253 (MW–67M1) Bourne, MA

155.65

163.83

8.19

157.65

161.10

3.45

4.74

421012072324301

MA–CMW 95R Chicopee, MA

18.88

25.49

6.61

19.66

25.49

5.83

0.78

423810072435401

MA–CSW 8R Colrain, MA

4.68

21.08

16.41

9.52

19.40

9.88

6.53

422733072532601

MA–CYW 13 Cummington, MA

2.10

7.38

5.28

2.10

6.59

4.49

0.79

421438071165601

MA–DVW 10R Dover, MA

28.92

36.77

7.85

28.92

36.77

7.85

0.00

412346070353403

MA–ENW 52 Edgartown, MA

12.93

28.81

15.88

12.93

20.95

8.02

7.86

420305072581401

MA–GLW 6R Granville, MA

1.71

8.89

7.18

2.06

8.89

6.83

0.35

422058072085101

MA–HHW 1R Hardwick, MA

12.23

21.06

8.83

12.23

21.06

8.83

0.00

424249072493101

MA–HNW 19 Heath, MA

14.79

36.15

21.37

17.71

36.01

18.30

3.07

415229070554301

MA–LKW 14R Lakeville, MA

0.26

19.48

19.22

3.71

14.98

11.27

7.95

421240072490201

MA–M7W 19 Montgomery, MA

−0.68*

6.54

7.22

−0.68*

5.88

6.56

0.66

423441072170701

MA–ORW 63 Orange, MA

3.81

9.49

5.68

3.81

8.97

5.16

0.52

415453070434901

MA–PWW 22 Plymouth, MA

18.30

28.99

10.69

18.30

28.99

10.69

0.00

414405070312104

MA–SDW 483–0170 (MW–17M3) Sandwich, MA

118.68

125.41

6.73

120.23

124.05

3.82

2.91

414712071175001

MA–SHW 275R Seekonk, MA

0.59

6.99

6.40

2.67

6.34

3.67

2.73

420350073193601

MA–SJW 58R Sheffield, MA

7.95

16.09

8.14

8.27

16.09

7.82

0.32

423715072042801

MA–TMW 3R Templeton, MA

2.02

5.13

3.11

2.02

5.13

3.11

0.00

424055071435302

MA–TRW 13R Townsend, MA

8.25

17.45

9.20

9.25

17.45

8.20

1.00

420206070045901

MA–TSW 89 Truro, MA

10.12

12.96

2.84

10.20

12.96

2.76

0.08

415808070024301

MA–TSW 257–0034 Truro, MA

15.73

20.44

4.71

17.00

20.44

3.44

1.27

423257071243702

MA–WWW 160 Westford, MA

9.33

13.87

4.54

9.56

13.87

4.31

0.23

421923072451001

MA–WXW 20 Westhampton, MA

0.32

22.07

21.75

4.17

18.83

14.66

7.09

424204072015201

MA–XNW 13 Winchendon, MA

−0.57*

13.50

14.07

1.86

13.50

11.64

2.43

424057072010301

MA–XNW 48 Winchendon, MA

23.03

28.52

5.49

23.55

28.52

4.97

0.52

Development of MOVE.1 Models for the Extension of Groundwater Level Records 15

Range

413930070190901

*Negative values represent water levels above ground level, where the groundwater level is above the surface of the well.

Lowest

Change in range (ft)

16 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts 25

EXPLANATION Observed record

MA–XNW 48

MA–XNW 13

MA–WXW 20

MA–WWW 160

MA–TSW 89

MA–TSW 257–0034

MA–TRW 13R

MA–TMW 3R

MA–SJW 58R

MA–SHW 275R

MA–SDW 483–0170

MA–PWW 22

MA–ORW 63

MA–M7W 19

MA–HNW 19

MA–LKW 14R

MA–HHW 1R

MA–GLW 6R

MA–ENW 52

MA–CYW 13

MA–DVW 10R

MA–CSW 8R

MA–CMW 95R

MA–BHW 507–0253

MA–A9W 57

MA–BHW 506–0206

MA–A1W 306

Range between highest and lowest groundwater levels, in feet

Estimated MOVE.1 record

Study well

Figure 6. Graph of the magnitude of range of highest and lowest groundwater levels from the estimated Maintenance of Variance Extension type 1 (MOVE.1) and observed records for 27 study wells for monitoring groundwater levels in Massachusetts. Site names are in shortened forms; study well site names are listed in table 1.

Computation of Monthly Percentiles From Estimated Records The composite record of observed and estimated values from the record extension was used to compute monthly percentiles, which can be used for the Groundwater Index in the Massachusetts drought management plan (Massachusetts Executive Office of Energy and Environmental Affairs and Emergency Management Agency, 2019). Monthly percentiles were computed as a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it. For example, a monthly groundwater level at the 30th percentile is equal to or greater than 30 percent of the groundwater levels recorded in that month during all years with records. In addition, monthly percentiles were computed from available observed records for comparison purposes using records through December 31, 2021 (table 5). The R quantile function was used to compute the 2d, 10th, 20th, 30th, and 50th percentiles for each month of available data. This function allows the user to specify the type of interpolation (rounding) method to use to estimate percentiles. The type 6 interpolation method was used to perform the quantile function, and it is the commonly used interpolation method for hydrologic datasets (Helsel and others, 2020). The different interpolation methods to produce quantiles can be found in the R documentation on

sample quantiles (R Core Team, 2023). With large sample sizes of greater than about 100 observations, the type of interpolation has very little effect on the results. The 2d, 10th, 20th, and 30th monthly percentiles correspond with the index severity levels in the Massachusetts drought management plan (Massachusetts Executive Office of Energy and Environmental Affairs and Emergency Management Agency, 2019). Monthly percentiles were computed based on all continuous and discrete values parsed by month. Based on MOVE.1 record extensions, the average groundwater level is about 1.0 ft lower than the average groundwater level determined from observed data at index severity level 4, emergency drought, determined as the 2d percentile. Figure 7 shows the change in the groundwater level at 2d percentile for each well by month. For example, in January at the 2d percentile, study well 413930070190901 (MA–A1W 306 Barnstable, Mass.) has an estimated groundwater level of 28.7 ft and an observed groundwater level of 27.6 ft (a 1.1 ft decrease); study well 422248071362401 (MA–A9W 57, Berlin, Mass.) has an estimated level of 21.7 ft and an observed level of 19.4 ft (a 2.3 ft decrease); and study well 414205070334701 (MA–BHW 506–0206 [MW–21M3] Bourne, Mass.) has an estimated level of 175.8 ft and an observed level of 169.8 ft (a 6.0 ft decrease). The larger changes at 2d percentile tended to be in the winter months (January through March), as illustrated by the number

Computation of Monthly Percentiles From Estimated Records 17 of wells with points located outside the 1-ft change box (fig. 7). There is very little change at 30th percentile from the record extensions. The average extended-record groundwater level is about 0.1 ft lower than the average observed groundwater level at index severity level 0, mild drought, determined as the 30th percentile. Overall, the increase in the range of groundwater levels and the greater depths at many wells at the 2d percentile captures a broader range of groundwater conditions, typically observed with a longer climatic record.

Future Studies for Estimating Monthly Percentiles Estimated groundwater levels of several wells can be substantially overestimated or underestimated for some months, as shown by the monthly boxplots of MOVE.1

residuals (fig. 8). For example, monthly boxplots of the MOVE.1 residuals for study well at site 415453070434901 (MA–PWW 22 Plymouth, Mass.) and the paired index well at site 415228070554601 (MA–LKW 14 Lakeville, Mass.) show that 8 of 12 months contain a bias; months January to April and July to October show the interquartile range of the residuals had either overestimated or underestimated values (fig. 8). For this study, a single MOVE.1 model for each study well was developed to estimate the historical daily groundwater levels for the period of record. For future consideration, seasonal or month-specific MOVE.1 models could be developed to compute monthly percentiles more accurately. A recent study by Dudley and others (2018) estimating groundwater level records based on their relation to hydrologic and meteorological variables found including such variables in statistical models yielded successful models.

18 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

A. January

0 −2 −4 −6 −8 −10 2

B. February

Extended record minus observed record at 2d percentile, in feet

1 0 −1 −2 −3 −4 −5 −6 2

C. March

1 0 −1 −2 −3 −4 −5 −6 2

D. April

1 0 −1 −2 −3 −4

−6

MA–A1W 306 MA–A9W 57 MA–BHW 506–0206 MA–BHW 507–0253 MA–CMW 95R MA–CSW 8R MA–CYW 13 MA–DVW 10R MA–ENW 52 MA–GLW 6R MA–HHW 1R MA–HNW 19 MA–LKW 14R MA–M7W 19 MA–ORW 63 MA–PWW 22 MA–SDW 483–0170 MA–SHW 275R MA–SJW 58R MA–TMW 3R MA–TRW 13R MA–TSW 89 MA–TSW 257–0034 MA–WWW 160 MA–WXW 20 MA–XNW 13 MA–XNW 48

−5

Study well

Figure 7. Graphs showing monthly depth changes for select wells for monitoring groundwater levels in Massachusetts at the 2d percentile attributed to the Maintenance of Variance Extension type 1 (MOVE.1) record extensions (parts A through L represent depth changes for months January through December). Site names are in shortened forms; study well site names are listed in table 1. The box represents a 1-foot depth change.

Figure 7.—Continued −6

−5

Extended record minus observed record at 2d percentile, in feet

Computation of Monthly Percentiles From Estimated Records 19

E. May

−1

−2

−3

−4

−5

−6

F. June

−1

−2

−3

−4

−5

G. July

−1

−2

−3

−4

−5

H. August

−1

−2

−3

−4

Study well

Figure 7.—Continued −5

−8

Extended record minus observed record at 2d percentile, in feet

20 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts I. September

−1

−2

−3

−4

−5

J. October

−1

−2

−3

−4

K. November

−1

−2

−3

−4

−5

L. December

−1 0

−2

−3

−4

−5

−6

−7

Study well

Summary 21 5

122

129

161

164

162

156

133

111

EXPLANATION

MOVE.1 residual, in feet

3 94

Number of values Individual observation above 90th percentile

90th percentile 75th percentile

50th percentile (median)

−1

Interquartile range

25th percentile

−2

10th percentile

−3

Individual observation below 10th percentile

−4 −5

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Month

Figure 8. Boxplot graph showing monthly residuals for the Maintenance of Variance Extension type 1 (MOVE.1) model of the study well at site 415453070434901 (MA–PWW 22 Plymouth, Mass.) and the paired index well at site 415228070554601 (MA–LKW 14 Lakeville, Mass.).

Summary In Massachusetts, the severity of a drought is based on several indices described in the drought management plan. One of the indices is the groundwater index. The groundwater index provides a general overview of the status of the water level in aquifers relative to long-term groundwater conditions. Although groundwater level records from wells in the U.S. Geological Survey Climate Response Network are used for determining the groundwater index, not all Climate Response Network wells have the long-term, continuous data necessary for computing reliable groundwater statistics. Groundwater wells with shorter records generally do not capture the broader range of groundwater conditions. This lack of range in groundwater conditions renders drought determinations based on short-record wells less accurate than those based on long-record wells. The U.S. Geological Survey, in cooperation with the Massachusetts Department of Environmental Protection, conducted this study to extend groundwater level records at select wells in Massachusetts and compute monthly percentiles for the wells with record extensions. The record extensions increase the number of Climate Response Network wells that can be used for determining the groundwater index severity level. There are 29 study wells and 37 index wells included in this study. The criteria for record extension included that the study well and index well have one or more years of concurrent, overlapping data; a Pearson correlation coefficient that exceeded 0.8; and that they share similar aquifer type and

hydrologic attributes. Paired wells that were more than 30 miles (mi) apart were considered suboptimal for record extensions because of the differences in climatic characteristics over that distance. About half of the study wells are within a 30-mi span of the index well used for the record extension. The Pearson correlation coefficients for 27 wells ranged from 0.812 to 0.998. Two study wells, sites 420610071421402 (MA–NXW 54 Northbridge, Mass.) and 421410072081101 (MA–WUW 2R West Brookfield, Mass.), had a correlation coefficient less than 0.8 and were dropped from further analysis. The Maintenance of Variance Extension type 1 (MOVE.1) method was used to perform the record extensions on the remaining 27 of 29 study wells that met the criteria for record extension. Plots of correlation, model fit, and statistical distribution of the residuals for the MOVE.1 models indicated no clear bias in the estimated records. Performance metrics used to evaluate the MOVE.1 models include root mean square error (RMSE) and Nash-Sutcliffe efficiency coefficient (NSE). RMSE values ranged from 0.097 to 2.292 feet (ft), with a median of 0.536 ft. The median RMSE is about 50 percent smaller for paired wells less than 30 mi from one another than wells more than 30 mi apart. NSE values ranged from 0.623 to 0.996, with a median value of 0.759. Seven wells with NSE values less than 0.7 were considered to have moderate to poor predictor efficiency. Overall, smaller RMSE values and higher NSE values were found for study wells located nearer to their index well; model errors are less frequent when the paired wells are geographically close to one another, hydrologically similar, and share topographic characteristics.

22 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts Record extensions resulted in an increase in the groundwater level range at 23 of 27 wells. Higher (shallower) groundwater levels occurred at 18 wells and lower (deeper) groundwater levels occurred at 13 wells with records extensions. Four wells—sites 421438071165601 (MA– DVW 10R Dover, Mass.), 422058072085101 (MA–HHW 1R Hardwick, Mass.), 415453070434901 (MA–PWW 22 Plymouth, Mass.), and 423715072042801 (MA–TMW 3R Templeton, Mass.)—had no change in the range of highest and lowest groundwater levels. For the 27 study wells with record extensions, the average length of groundwater level records was extended by 14.1 years. Continuous-daily groundwater level records averaged 4.0 years prior to the record extension and 18.1 years after the record extension. The 2d, 10th, 20th, and 30th monthly percentiles correspond with the index severity levels in the Massachusetts drought management plan. These monthly percentiles were computed from the extended records and observed records using data through December 31, 2022. At the 2d percentile (index severity level 4, emergency drought), the average groundwater level from the record extensions is about 1.0 ft lower than the average groundwater level determined from observed data. At the 30th percentile (index severity level 0, mild drought), the average groundwater level from the record extensions is about 0.1 ft lower than the average groundwater level determined from observed data.

Acknowledgments The authors gratefully acknowledge Janet Barclay and John Mullaney of the U.S. Geological Survey for their assistance with the groundwater database and the R package smwrStats, which analyzes groundwater data. The authors deeply appreciate Janet Barclay and Robin Glas for their thorough peer reviews and thank U.S. Geological Survey personnel for their help collecting the groundwater data used in this report.

Selected References Barclay, J.R., and Mullaney, J.R., 2020, Updating data inputs, assessing trends, and evaluating a method to estimate probable high groundwater levels in selected areas of Massachusetts: U.S. Geological Survey Scientific Investigations Report 2020–5036, 45 p., accessed September 2022 at https://doi.org/10.3133/sir20205036. Colarullo, S.J., Sullivan, S.L., and McHugh, A.R., 2018, Implementation of MOVE.1, censored MOVE.1, and piecewise MOVE.1 low-flow regressions with applications at partial-record streamgaging stations in New Jersey: U.S. Geological Survey Open-File Report 2018–1089, 20 p., accessed June 5, 2022, at https://doi.org/10.3133/ ofr20181089.

Crozier, D.E., and Ahearn, E.A., 2024, Data and R code to derive estimates of groundwater levels using MOVE.1 regression and compute monthly percentiles for select wells in Massachusetts: U.S. Geological Survey data release, https://doi.org/10.5066/P90PDI34. Dudley, R.W., Hodgkins, G.A., Nielsen, M.G., and Qi, S.L., 2018, Estimating historical groundwater levels based on relations with hydrologic and meteorological variables in the U.S. glacial aquifer system: Journal of Hydrology, v. 562, p. 530–543, accessed November 2023 at https://doi.org/10.1016/j.jhydrol.2018.05.019. Helsel, D.R., Hirsch, R.M., Ryberg, K.R., Archfield, S.A., and Gilroy, E.J., 2020, Statistical methods in water resources: U.S. Geological Survey Techniques and Methods, book 4, chap. A3, 458 p., accessed September 2022 at https://doi.org/10.3133/tm4A3. [Supersedes USGS Techniques of Water-Resources Investigations, book 4, chap. A3, version 1.1.] Helsel, D.R., and Hirsch, R.M., 2000, Statistical methods in water-resources (4th impression): Amsterdam, Netherlands, Elsevier Science B.V. Studies in Environmental Science, v. 49, 529 p. Hirsch, R.M., 1979, An evaluation of some record reconstruction techniques: Water Resources Research, v. 15, no. 6, p. 1781–1790. [Also available at https://doi.org/10.1029/ WR015i006p01781.] Hirsch, R.M., 1982, A comparison of four streamflow record extension techniques: Water Resources Research, v. 18, no. 4, p. 1081–1088. [Also available at https://doi.org/ 10.1029/WR018i004p01081.] Lombard, P.J., Barclay, J.R., and McCarthy, D.E., 2020, 2020 drought in New England (ver. 1.1, February 2021): U.S. Geological Survey Open-File Report 2020–1148, 12 p., accessed December 20, 2022, at https://doi.org/ 10.3133/ofr20201148. Lorenz, D.L., 2015, smwrBase—An R package for managing hydrologic data, version 1.1.1: U.S. Geological Survey Open-File Report 2015–1202, 7 p., accessed September 13, 2022, at https://doi.org/10.3133/ ofr20151202. Lorenz, D.L., 2017a, Streamflow record extension example: U.S. Geological Survey software repository, 8 p., accessed September 13, 2022, at https://rdrr.io/github/USGS-R/ smwrStats/f/inst/doc/RecordExtension.pdf. Lorenz, D.L., 2017b, USGS-R/smwrStats—R functions to support statistical methods in water resources, version 0.7.6: U.S. Geological Survey software repository webpage, accessed September 13, 2022, at https://rdrr.io/github/ USGS-R/smwrStats/.

Selected References 23 Lorenz, D.L., 2022, R/smwrStats-package.R: U.S. Geological Survey software repository webpage, accessed May 23, 2024, at https://rdrr.io/github/USGS-R/smwrStats/src/R/ smwrStats-package.R.

R Core Team, 2023, Sample quantiles: R Foundation for Statistical Computing web page, accessed May 23, 2024, at https://search.r-project.org/R/refmans/stats/html/ quantile.html.

Matalas, N.C., and Jacobs, B., 1964, A correlation procedure for augmenting hydrologic data: U.S. Geological Survey Professional Paper 434–E, 7 p., accessed May 9, 2019, at https://doi.org/10.3133/pp434E.

U.S. Geological Survey, 2018, USGS water data for the nation: U.S. Geological Survey National Water Information System database, accessed July 20, 2022, at https://doi.org/ 10.5066/F7P55KJN.

McCarthy, D.E., LeNoir, J.M., and Lombard, P.J., 2023, 2022 drought in New England: U.S. Geological Survey Scientific Investigations Report 2023–5016, 34 p., accessed January 30, 2023, at https://doi.org/10.3133/sir20235016.

U.S. Geological Survey, 2023, Groundwater climate response network: U.S. Geological Survey website, accessed March 25, 2024, at https://rconnect.usgs.gov/crn-map/ CRNmap.html.

Massachusetts Executive Office of Energy and Environmental Affairs and Massachusetts Emergency Management Agency, 2019, Massachusetts drought management plan: Executive Office of Energy and Environmental Affairs, 115 p., accessed September 2022, at https://www.mass.gov/ doc/massachusetts-drought-management-plan.

U.S. Geological Survey, 2024, Groundwater climate response network: U.S. Geological Survey database map interface, accessed August 2, 2024, at https://rconnect.usgs.gov/crn- map/CRNmap.html.

National Drought Mitigation Center, 2023, Drought classification: National Drought Mitigation Center U.S. Drought Monitor web page, accessed March 25, 2024, at https://droughtmonito r.unl.edu/About/AbouttheData/DroughtClassification.aspx. Olson, S.A., and Meyerhofer, A.J., 2019, Development and evaluation of a record extension technique for estimating discharge at selected stream sites in New Hampshire: U.S. Geological Survey Scientific Investigations Report 2019–5066, 23 p., accessed September 12, 2022, at https://doi.org/10.3133/sir20195066. R Core Team, 2020, R—A language and environment for statistical computing—Version 4.0.2.: R Foundation for Statistical Computing web page, accessed September 15, 2022, at http://www.r-project.org/index.html.

U.S. Geological Survey, [undated], smwrStats: U.S. Geological Survey data repository, accessed July 15, 2022, at https://github.com/USGS-R/smwrStats. Vogel, R.M., and Kroll, C.N., 1991, The value of streamflow record augmentation procedures in low-flow and flood-flow frequency analysis: Journal of Hydrology, v. 125, nos. 3–4, p. 259–276, accessed June 4, 2023, at https://doi.org/ 10.1016/0022-1694(91)90032-D. Vogel, R.M., and Stedinger, J.R., 1985, Minimum variance streamflow record augmentation procedures: Water Resources Research, v. 21, no. 5, p. 715–723, accessed March 25, 2024, at https://doi.org/10.1029/ WR021i005p00715.

24 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Appendix 1. U.S. Geological Survey Climate Response Network of Groundwater Wells in Massachusetts, 2022 Table 1.1. Groundwater wells of the U.S. Geological Survey Climate Response Network in Massachusetts in 2022. [Data are from Crozier and Ahearn (2024). Map label refers to the numbers of station labels on the map of figure 1. ID, identifier; MA, Massachusetts]

Map label (fig. 1)

Site ID

Site name

Decimal latitude

Decimal longitude

County

414154070165002

MA–A1W 247R Barnstable, MA

41.69833

−70.28056

Barnstable

413525070291904

MA–MIW 29 Mashpee, MA

41.59039

−70.48808

Barnstable

411555070021901

MA–NBW 228 Nantucket, MA

41.26540

−70.03807

Nantucket

414400070242901

MA–SDW 252R Sandwich, MA

41.73333

−70.40806

Barnstable

420056070575701

MA–EBW 30 East Bridgewater, MA

42.01566

−70.96532

Plymouth

414518070435701

MA–WFW 51 Wareham, MA

41.75516

−70.73202

Plymouth

414518070015801

MA–BMW 21R Brewster, MA

41.75500

−70.03278

Barnstable

415449071155201

MA–ATW 83R Attleboro, MA

41.91361

−71.26444

Bristol

415217070393102

MA–PWW 494 Plymouth, MA

41.87149

−70.65809

Plymouth

420317070432901

MA–D4W 80 Duxbury, MA

42.05482

−70.72421

Plymouth

415228070554601

MA–LKW 14 Lakeville, MA

41.87455

−70.92893

Plymouth

414706071045001

MA–F3W 23R Freetown, MA

41.78500

−71.08056

Bristol

420924072422602

MA–WVW 152 Westfield, MA

42.15676

−72.70676

Hampden

422103072241102

MA–PDW 23 Pelham, MA

42.35092

−72.40258

Hampshire

423845070542501

MA–TQW 1 Topsfield, MA

42.64629

−70.90674

Essex

422650071213801

MA–CTW 167R Concord, MA

42.44722

−71.36056

Middlesex

423503073075401

MA–CJW 2 Cheshire, MA

42.58438

−73.13133

Berkshire

422559072332402

MA–S6W 68 Sunderland, MA

42.43314

−72.55620

Franklin

420355070520201

MA–HGW 76R Hanson, MA

42.06528

−70.86722

Plymouth

422819071065701

MA–XOW 14 Winchester, MA

42.47204

−71.11533

Middlesex

422627071154002

MA–LTW 104 Lexington, MA

42.44093

−71.26061

Middlesex

422520071483001

MA–SYW 177 Sterling, MA

42.42231

−71.80785

Worcester

423641071102501

MA–AJW 462 Andover, MA

42.61148

−71.17311

Essex

423311072355801

MA–DFW 44R Deerfield, MA

42.55314

−72.59898

Franklin

421851071312601

MA–SSW 12 Southborough, MA

42.31426

−71.52340

Worcester

424322070592201

MA–GCW 168R Georgetown, MA

42.72278

−70.98944

Essex

421550073025101

MA–A3W 12 Becket, MA

42.26411

−73.04685

Berkshire

421228072585301

MA–BEW 9 Blandford, MA

42.20787

−72.98094

Hampden

423339072524101

MA–HMW 8 Hawley, MA

42.56092

−72.87760

Franklin

420912072042801

MA–OTW 7R Otis, MA

42.15333

−73.07444

Berkshire

414139070311501

MA–SDW 526–0040 (MW–145S)

41.69437

−70.52044

Barnstable

414159070310501

MA–SDW 537–0107 Sandwich, MA

41.69998

−70.51775

Barnstable

414129070361401

MA–BHW 198 Bourne, MA

41.69150

−70.60336

Barnstable

414125070265901

MA–SDW 253R Sandwich, MA

41.69028

−70.44972

Barnstable

414219070313601

MA–SDW 525–0109 (MW–126S)

41.70542

−70.52600

Barnstable

Appendix 1. U.S. Geological Survey Climate Response Network of Groundwater Wells in Massachusetts, 2022 25 Table 1.1. Groundwater wells of the U.S. Geological Survey Climate Response Network in Massachusetts in 2022.—Continued [Data are from Crozier and Ahearn (2024). Map label refers to the numbers of station labels on the map of figure 1. ID, identifier; MA, Massachusetts]

Map label (fig. 1)

Site ID

Site name

Decimal latitude

Decimal longitude

County

414101070011001

MA–CGW 138R Chatham, MA

41.68361

−70.01944

Barnstable

414124070311401

MA–SDW 527–0055 (90MW0063)

41.69013

−70.52013

Barnstable

413930070190901

MA–A1W 306 Barnstable, MA

41.65844

−70.31863

Barnstable

415453070434901

MA–PWW 22 Plymouth, MA

41.91493

−70.72977

Plymouth

415354069585201

MA–WNW 17R Wellfleet, MA

41.89833

−69.98111

Barnstable

420305072581401

MA–GLW 6R Granville, MA

42.05140

−72.97068

Hampden

420316070433501

MA–D4W 79R Duxbury, MA

42.05444

−70.72639

Plymouth

420206070045901

MA–TSW 89 Truro, MA

42.03523

−70.08257

Barnstable

414714071175901

MA–SHW 275 Seekonk, MA

41.78732

−71.29922

Bristol

414632070014901

MA–BMW 22R Brewster, MA

41.77556

−70.03028

Barnstable

412346070353403

MA–ENW 52 Edgartown, MA

41.39623

−70.59225

Dukes

423506070491401

MA–WPW 76R Wenham, MA

42.58500

−70.82056

Essex

423257071243702

MA–WWW 160 Westford, MA

42.54915

−71.41039

Middlesex

423058071025401

MA–WAW 38R Wakefield, MA

42.51611

−71.04833

Middlesex

423715072042801

MA–TMW 3R Templeton, MA

42.62083

−72.07444

Worcester

424055071435302

MA–TRW 13R Townsend, MA

42.68194

−71.73139

Middlesex

422103072241103

MA–PDW 24 Pelham, MA

42.35092

−72.40258

Hampshire

420544071173701

MA–NNW 27R Norfolk, MA

42.09556

−71.29361

Norfolk

424204072015201

MA–XNW 13 Winchendon, MA

42.70102

−72.03084

Worcester

421923072451001

MA–WXW 20 Westhampton, MA

42.34120

−72.80621

Hampshire

421012072324301

MA–CMW 95R Chicopee, MA

42.17000

−72.54528

Hampden

421240072490201

MA–M7W 19 Montgomery, MA

42.21127

−72.81700

Hampden

423401071093801

MA–XMW 78 Wilmington, MA

42.56690

−71.15997

Middlesex

422341071464901

MA–WSW 26 West Boylston, MA

42.39478

−71.77985

Worcester

420610071421402

MA–NXW 54 Northbridge, MA

42.10287

−71.70340

Worcester

421438071165601

MA–DVW 10R Dover, MA

42.24389

−71.28222

Norfolk

422906072124301

MA–PHW 16 Petersham, MA

42.48508

−72.21144

Worcester

424520070562401

MA–NIW 27 Newbury, MA

42.75537

−70.93949

Essex

422058072085101

MA–HHW 1R Hardwick, MA

42.34944

−72.14750

Worcester

421853071220501

MA–WKW 2R Wayland, MA

42.31472

−71.36806

Middlesex

423441072170701

MA–ORW 63 Orange, MA

42.57814

−72.28481

Franklin

421410072081101

MA–WUW 2R West Brookfield, MA

42.23611

−72.13639

Worcester

422733072532601

MA–CYW 13 Cummington, MA

42.45946

−72.89028

Hampshire

424841071004101

MA–HLW 23 Haverhill, MA

42.81161

−71.01162

Essex

420350073193601

MA–SJW 58R Sheffield, MA

42.06389

−73.32667

Berkshire

422745073112001

MA–PTW 51 Pittsfield, MA

42.46258

−73.18844

Berkshire

422812071244401

MA–ACW 158 Acton, MA

42.47011

−71.41188

Middlesex

26 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Appendix 2. Monthly Percentiles at Study Wells With Record Extensions

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts. [Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record

P10

P20

P30

P50

P10

January

28.69

27.37

26.79

26.05

25.51

27.56

27.36

February

28.79

26.96

26.60

25.75

24.99

26.89

March

28.84

26.39

25.89

25.45

24.27

26.62

April

28.20

25.58

25.29

24.84

23.86

May

27.81

25.26

24.92

24.48

23.71

June

27.46

25.25

24.69

24.44

July

27.79

25.70

25.20

August

28.40

26.14

25.76

September

28.77

26.47

October

29.00

26.71

November

29.12

December

28.65

P20

Extended record minus observed record P30

P50

P10

P20

P30

P50

26.29

26.18

25.70

−1.13

−0.01

−0.50

0.13

0.18

26.67

26.04

25.82

24.43

−1.90

−0.29

−0.56

0.07

−0.56

26.39

25.71

25.53

23.96

−2.21

0.00

−0.18

0.09

−0.31

25.98

25.55

25.40

25.25

23.43

−2.22

−0.03

0.11

0.41

−0.43

26.25

25.26

25.14

24.87

23.35

−1.57

0.00

0.22

0.38

−0.36

23.88

25.77

25.24

25.02

24.64

23.79

−1.69

−0.01

0.33

0.20

−0.09

24.77

24.18

26.11

25.64

25.35

24.73

24.12

−1.68

−0.06

0.15

−0.04

−0.06

25.26

24.77

26.29

26.05

25.80

25.22

24.71

−2.11

−0.09

0.04

−0.04

−0.07

26.13

25.74

25.33

26.86

26.31

25.97

25.72

25.18

−1.91

−0.16

−0.02

−0.15

26.47

26.20

25.66

27.14

26.61

26.37

26.11

25.23

−1.86

−0.10

−0.09

−0.43

27.05

26.76

26.42

25.76

27.31

27.02

26.72

26.51

25.29

−1.81

−0.03

−0.04

0.09

−0.47

27.46

26.67

26.36

25.84

27.49

27.31

26.55

26.31

25.56

−1.16

−0.15

−0.12

−0.05

−0.28

MA–A1W 306 Barnstable, Mass.

January

21.69

19.95

19.25

18.56

18.02

19.42

18.05

17.98

17.87

17.75

−2.27

−1.90

−1.27

−0.69

−0.27

February

19.86

19.11

18.81

18.65

18.39

20.06

18.33

18.23

18.08

17.79

0.19

−0.78

−0.58

−0.57

−0.60

March

19.95

18.76

18.45

18.18

17.84

18.47

18.18

18.09

17.99

17.86

−1.48

−0.58

−0.36

−0.19

0.02

April

19.32

18.54

18.04

17.79

17.37

18.40

18.13

17.96

17.82

17.44

−0.92

−0.41

−0.09

0.03

0.07

May

18.99

18.64

18.46

18.28

17.98

19.25

18.51

18.29

18.13

17.81

0.26

−0.13

−0.18

−0.15

−0.17

June

20.01

19.67

19.44

19.23

18.93

20.71

19.98

19.55

19.39

19.15

0.70

0.32

0.11

0.16

0.22

July

21.16

20.82

20.53

20.35

19.94

21.36

21.10

20.64

20.39

20.10

0.20

0.28

0.11

0.04

0.15

August

22.34

21.96

21.56

21.35

20.50

22.58

22.04

21.61

21.43

20.73

0.24

0.08

0.05

0.08

0.23

September

23.31

22.92

22.54

22.12

21.31

23.03

22.55

22.30

22.02

21.49

−0.28

−0.36

−0.23

−0.10

0.18

October

23.85

23.36

22.76

22.44

21.65

22.81

22.69

22.42

22.23

21.83

−1.04

−0.67

−0.34

−0.21

0.18

November

23.84

22.95

22.38

21.83

20.55

22.33

21.82

21.74

21.65

20.56

−1.52

−1.13

−0.64

−0.18

0.01

December

23.65

22.66

21.19

20.24

18.55

21.22

19.74

18.72

18.59

18.27

−2.43

−2.92

−2.47

−1.65

−0.28

MA–BHW 506-0206 (MW-21M3) Bourne, Mass. January

175.87

173.67

173.20

171.79

170.52

169.83

169.74

169.64

169.56

169.47

−6.04

−3.92

−3.55

−2.23

−1.06

February

175.69

173.78

173.48

172.04

170.65

170.24

170.16

170.05

170.01

169.11

−5.46

−3.61

−3.43

−2.03

−1.54

March

174.13

173.84

172.53

171.83

170.54

170.66

170.53

170.48

170.40

170.20

−3.47

−3.32

−2.05

−1.44

−0.34

April

175.13

174.20

172.71

172.21

170.70

170.91

170.86

170.81

170.73

170.03

−4.22

−3.34

−1.90

−1.47

−0.67

Appendix 2. Monthly Percentiles at Study Wells With Record Extensions 27

MA–A9W 57, Berlin, Mass.

[Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record P2

P10

P20

Extended record minus observed record

P10

P20

P30

P50

P30

May

174.64

174.07

172.74

171.72

170.58

171.17

171.14

171.07

171.04

June

174.79

173.08

172.27

171.29

170.38

171.37

171.33

171.27

July

175.02

172.84

171.80

170.45

169.94

171.57

171.52

171.46

August

175.21

172.86

171.79

170.88

169.99

171.79

171.72

September

175.37

172.93

171.85

170.71

169.96

172.03

171.97

October

175.52

173.05

171.71

170.70

169.97

172.23

November

175.70

173.24

171.87

171.01

170.00

December

175.87

173.44

172.05

171.38

170.14

January

163.81

162.16

161.80

160.74

159.79

159.46

159.38

159.28

February

163.68

162.24

162.02

160.93

159.88

159.82

159.75

March

162.50

162.29

161.30

160.77

159.88

160.13

160.03

April

163.26

162.56

161.43

161.06

159.94

160.29

May

162.89

162.46

161.46

160.69

159.83

160.48

June

163.00

161.71

161.09

160.58

159.68

July

163.17

161.53

160.75

159.73

August

163.32

161.55

160.80

160.06

September

163.44

161.60

160.86

October

163.55

161.69

160.69

November

163.69

161.83

December

163.81

161.98

P50

P10

P20

P30

P50

169.52

−3.47

−2.93

−1.67

−0.68

−1.07

171.22

169.22

−3.42

−1.75

−1.00

−0.07

−1.16

171.39

169.07

−3.45

−1.32

−0.34

0.94

−0.87

171.67

171.61

169.01

−3.42

−1.14

−0.12

0.73

−0.98

171.91

171.83

169.14

−3.34

−0.96

0.06

1.12

−0.82

172.17

172.11

172.06

169.32

−3.29

−0.88

0.40

1.36

−0.65

172.27

172.25

172.21

172.16

169.52

−3.43

−0.99

0.34

1.15

−0.48

172.20

172.10

172.04

171.98

169.65

−3.67

−1.34

−0.01

0.60

−0.49

159.19

159.09

−4.35

−2.78

−2.52

−1.55

−0.70

159.65

159.61

159.12

−3.86

−2.49

−2.36

−1.32

−0.76

159.94

159.86

159.44

−2.37

−2.26

−1.36

−0.91

−0.44

160.25

160.17

160.12

159.07

−2.97

−2.31

−1.26

−0.94

−0.87

160.43

160.38

160.34

158.75

−2.41

−2.03

−1.08

−0.36

−1.08

160.64

160.60

160.55

160.52

158.50

−2.36

−1.11

−0.54

−0.06

−1.19

159.35

160.76

160.73

160.70

160.68

158.24

−2.41

−0.80

−0.05

0.94

−1.11

159.39

160.87

160.84

160.80

160.77

158.23

−2.45

−0.71

0.01

0.71

−1.16

159.93

159.36

161.02

160.98

160.94

160.89

158.37

−2.42

−0.62

0.08

0.96

−1.00

159.92

159.37

161.08

161.05

161.03

161.01

158.56

−2.47

−0.64

0.35

1.09

−0.81

160.81

160.16

159.39

161.07

161.01

160.95

160.89

158.79

−2.62

−0.82

0.14

0.73

−0.61

160.88

160.43

159.50

160.90

160.80

160.74

160.67

159.06

−2.91

−1.18

−0.14

0.23

−0.44

MA–BHW 506-0206 (MW-21M3) Bourne, Mass.—Continued

MA–BHW 507–0253 (MW–67M1) Bourne, Mass.

MA–CMW 95R Chicopee, Mass. January

25.27

24.41

23.39

22.96

22.19

24.67

24.53

24.12

23.03

22.28

−0.60

0.12

0.72

0.07

0.09

February

25.26

24.07

23.40

22.89

22.40

24.09

23.89

23.61

22.79

22.06

−1.17

−0.18

0.21

−0.09

−0.34

March

24.64

23.58

23.15

22.88

21.97

23.85

23.33

23.04

22.92

22.00

−0.79

−0.25

−0.11

0.04

0.03

April

23.99

23.62

22.96

22.89

21.68

23.48

22.96

22.94

22.93

21.90

−0.50

−0.66

−0.02

0.04

0.22

May

23.83

23.31

22.86

22.67

21.21

23.38

22.77

22.69

22.62

21.53

−0.45

−0.54

−0.17

−0.05

0.32

June

23.98

23.35

22.86

22.33

21.45

23.21

22.84

22.68

22.34

21.72

−0.77

−0.51

−0.18

0.01

0.26

July

24.24

23.42

23.01

22.27

21.88

23.36

23.15

22.98

22.39

22.01

−0.88

−0.27

−0.03

0.12

0.13

August

24.45

23.70

23.23

22.55

22.09

23.76

23.23

23.21

22.64

22.10

−0.68

−0.47

−0.02

0.09

0.01

28 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts.—Continued

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts.—Continued [Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record

P10

P20

P30

P50

P10

P20

September

24.67

23.94

23.29

22.88

22.29

24.26

23.32

23.25

October

24.92

24.34

23.34

23.10

22.28

24.47

24.35

November

25.07

24.25

23.54

23.35

22.37

24.33

24.26

December

25.19

24.46

23.59

23.27

22.41

24.59

24.49

Extended record minus observed record P30

P50

P10

P20

P30

P50

23.03

22.47

−0.42

−0.62

−0.04

0.14

0.18

23.38

23.24

22.37

−0.44

0.01

0.04

0.14

0.09

23.54

23.45

22.47

−0.73

0.00

0.10

23.55

23.33

22.55

−0.60

0.03

−0.04

0.06

0.14

MA–CMW 95R Chicopee, Mass.—Continued

MA–CSW 8R Colrain, Mass. 18.29

16.93

15.88

15.20

14.74

16.63

16.12

16.06

15.90

14.74

−1.66

−0.81

0.18

0.70

0.00

February

18.16

16.78

15.53

15.07

14.00

15.53

15.15

14.43

13.54

13.01

−2.63

−1.64

−1.10

−1.53

−1.00

March

17.40

15.96

15.45

14.49

13.55

13.93

13.66

13.37

12.48

12.20

−3.47

−2.30

−2.08

−2.01

−1.35

April

15.14

13.66

13.04

12.53

11.61

13.00

12.87

12.43

12.01

11.60

−2.14

−0.79

−0.61

−0.52

−0.01

May

13.43

12.62

12.05

11.66

10.93

12.20

12.05

11.93

11.79

11.56

−1.23

−0.56

−0.12

0.13

0.63

June

14.04

13.47

13.04

12.81

11.87

13.77

13.63

13.45

13.26

12.93

−0.26

0.16

0.41

0.46

1.06

July

15.53

14.83

14.31

13.85

12.82

15.29

15.04

14.87

14.72

14.37

−0.23

0.21

0.56

0.87

1.55

August

16.81

16.10

15.50

14.87

13.74

16.50

16.30

16.09

15.85

15.32

−0.31

0.20

0.58

0.98

1.58

September

17.85

16.98

16.57

16.05

14.95

17.40

17.17

16.99

16.80

16.41

−0.45

0.19

0.42

0.76

1.46

October

18.58

17.59

17.03

16.28

15.36

18.01

17.75

17.61

17.54

17.22

−0.57

0.16

0.57

1.26

1.86

November

18.44

18.10

16.96

16.14

15.43

18.49

18.40

18.16

18.01

17.54

0.05

0.30

1.20

1.87

2.11

December

18.35

18.05

16.31

15.96

15.20

18.23

18.13

18.06

17.60

16.17

−0.12

0.08

1.74

1.64

0.97

January

6.10

5.21

4.98

4.80

4.51

5.31

5.18

4.88

4.65

4.43

−0.79

−0.03

−0.09

−0.15

−0.08

February

5.25

5.08

4.96

4.85

4.66

5.40

5.18

5.07

4.96

4.70

0.15

0.10

0.11

0.04

March

5.16

5.00

4.71

4.50

4.17

5.17

5.07

4.92

4.56

4.30

0.01

0.07

0.21

0.06

0.13

April

4.71

4.32

4.10

3.97

3.80

4.73

4.43

4.19

4.03

3.81

0.02

0.11

0.09

0.06

0.01

May

5.12

4.94

4.80

4.69

4.46

5.30

4.89

4.69

4.58

4.29

0.18

−0.06

−0.11

−0.18

June

5.75

5.61

5.39

5.23

5.07

5.79

5.68

5.63

5.54

5.28

0.04

0.07

0.24

0.31

0.21

July

6.09

5.81

5.70

5.59

5.39

6.14

5.87

5.77

5.71

5.54

0.05

0.06

0.07

0.12

0.15

August

6.52

6.22

6.06

5.96

5.81

6.31

6.13

5.99

5.94

5.74

−0.21

−0.09

−0.07

−0.02

−0.07

September

7.07

6.66

6.42

6.27

6.08

6.31

6.24

6.16

6.09

5.84

−0.75

−0.42

−0.27

−0.18

−0.24

October

7.03

6.79

6.72

6.50

6.10

6.20

6.14

6.06

5.90

5.49

−0.83

−0.65

−0.66

−0.60

−0.61

November

6.86

6.74

6.45

5.95

5.37

5.85

5.44

5.33

5.21

4.91

−1.01

−1.30

−1.12

−0.74

−0.46

December

6.86

6.38

5.57

5.33

4.92

5.51

5.37

5.12

4.86

4.52

−1.36

−1.01

−0.45

−0.48

−0.41

MA–CYW 13 Cummington, Mass.

Appendix 2. Monthly Percentiles at Study Wells With Record Extensions 29

January

[Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record

P10

P20

P30

P50

P10

January

35.17

34.78

34.41

34.06

32.87

36.71

35.35

February

35.08

34.30

34.11

33.72

33.01

36.51

March

34.93

33.95

33.50

33.28

32.39

35.25

April

34.56

33.25

32.76

32.41

31.97

May

34.38

33.14

32.83

32.42

31.82

June

34.17

33.42

33.07

32.74

July

34.43

33.85

33.35

August

34.84

34.34

33.82

September

35.21

34.73

October

35.42

35.05

November

35.45

December

35.12

January

P20

Extended record minus observed record P30

P50

P10

P20

P30

P50

34.65

34.15

33.47

1.54

0.56

0.24

0.09

0.60

35.00

33.87

33.58

32.54

1.43

0.70

−0.24

−0.14

−0.47

33.64

32.67

32.37

32.15

0.31

−0.31

−0.83

−0.91

−0.25

34.24

32.78

32.17

32.15

32.12

−0.32

−0.47

−0.59

−0.26

0.15

34.03

33.00

32.40

32.28

32.17

−0.36

−0.14

−0.43

−0.14

0.35

32.31

33.92

33.24

32.65

32.55

32.37

−0.25

−0.17

−0.42

−0.19

0.06

33.16

32.78

34.34

33.80

33.26

33.09

32.65

−0.09

−0.05

−0.09

−0.07

−0.13

33.66

33.27

34.79

34.36

33.94

33.64

33.01

−0.06

0.02

0.12

−0.02

−0.26

34.27

34.10

33.77

35.31

34.79

34.45

34.21

33.58

0.10

0.06

0.18

0.12

−0.19

34.55

34.43

34.04

35.59

35.17

34.71

34.46

33.87

0.18

0.13

0.16

0.02

−0.17

35.08

34.68

34.61

33.87

35.92

35.29

34.75

34.60

33.83

0.47

0.21

0.07

−0.01

−0.04

34.95

34.79

34.52

33.75

35.94

35.11

34.50

34.10

32.86

0.82

0.17

−0.29

−0.42

−0.89

21.45

20.49

19.37

19.16

18.60

20.41

19.86

19.00

18.54

18.41

−1.04

−0.62

−0.38

−0.61

−0.19

February

20.91

20.10

19.24

18.73

18.51

20.52

19.71

18.58

18.52

18.46

−0.39

−0.66

−0.21

−0.05

March

20.66

20.09

18.80

18.38

17.75

20.37

19.07

18.43

18.31

18.01

−0.28

−1.02

−0.37

−0.07

0.25

April

20.11

18.90

17.99

17.85

17.25

19.79

18.55

17.91

17.83

17.43

−0.32

−0.36

−0.09

−0.02

0.18

May

20.00

18.19

17.81

17.57

17.11

19.66

17.86

17.54

17.42

15.72

−0.35

−0.34

−0.27

−0.15

−1.40

June

19.79

18.31

18.00

17.53

17.18

19.32

17.54

17.31

17.24

14.93

−0.47

−0.77

−0.69

−0.28

−2.25

July

20.04

18.71

18.24

17.89

17.30

18.73

17.70

17.37

17.24

15.12

−1.32

−1.01

−0.87

−0.65

−2.19

August

20.40

19.24

18.73

18.24

17.68

19.09

18.06

17.78

17.63

15.64

−1.32

−1.18

−0.94

−0.61

−2.04

September

20.74

19.77

19.15

18.74

18.03

19.54

18.52

18.26

18.11

16.41

−1.19

−1.25

−0.90

−0.62

−1.62

October

21.17

20.02

19.32

19.09

18.34

20.05

18.92

18.66

18.50

17.13

−1.11

−1.10

−0.66

−0.59

−1.21

November

21.52

20.24

19.48

19.16

18.51

20.47

19.23

18.98

18.88

17.79

−1.05

−1.01

−0.50

−0.28

−0.73

December

20.62

20.40

19.55

19.08

18.66

20.39

19.78

19.08

19.04

18.25

−0.23

−0.61

−0.47

−0.04

−0.42

MA–DVW 10R Dover, Mass.

MA–ENW 52 Edgartown, Mass.

MA–GLW 6R Granville, Mass. January

7.24

6.05

5.38

5.12

4.54

6.52

5.77

5.31

4.81

4.21

−0.72

−0.28

−0.07

−0.31

−0.33

February

6.13

5.57

5.29

5.13

4.67

6.14

5.81

5.34

5.11

4.43

0.01

0.24

0.06

−0.02

−0.24

March

5.58

5.03

4.53

4.18

3.48

5.60

5.08

4.64

4.24

3.52

0.02

0.05

0.11

0.06

0.04

April

4.77

4.02

3.69

3.43

3.13

4.78

3.98

3.61

3.40

3.08

0.01

−0.04

−0.08

−0.03

−0.05

30 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts.—Continued

Month

Extended record P2

P10

P20

Observed record P30

P50

P10

P20

Extended record minus observed record P30

P50

P10

P20

P30

P50

MA–GLW 6R Granville, Mass.—Continued 6.20

5.42

5.12

4.85

4.17

6.24

5.52

5.09

4.67

3.98

0.04

0.10

−0.03

−0.18

−0.19

June

7.26

6.66

6.38

5.96

5.38

7.26

6.83

6.46

6.23

5.62

0.01

0.17

0.08

0.27

0.24

July

8.10

7.54

7.18

6.74

6.19

8.16

7.59

7.31

7.04

6.42

0.06

0.05

0.13

0.30

0.23

August

8.27

8.03

7.70

7.36

6.85

8.27

8.08

7.86

7.59

6.93

0.00

0.04

0.16

0.23

0.08

September

8.46

8.23

7.94

7.76

7.41

8.46

8.30

7.96

7.78

7.45

0.00

0.07

0.02

0.03

0.04

October

8.45

8.22

7.97

7.77

7.06

8.23

8.02

7.82

7.57

6.82

−0.22

−0.20

−0.15

−0.20

−0.24

November

8.63

7.77

6.59

6.34

5.69

7.81

7.18

6.22

5.93

5.49

−0.81

−0.60

−0.36

−0.41

−0.20

December

8.63

6.58

6.21

5.95

4.88

6.55

6.21

5.95

5.69

4.26

−2.08

−0.37

−0.26

−0.62

January

19.62

18.04

17.42

17.13

16.60

20.15

18.48

17.68

16.73

16.44

0.53

0.44

0.26

−0.40

−0.16

February

19.34

17.63

17.33

17.13

16.81

19.80

18.32

17.51

17.34

16.60

0.46

0.69

0.18

0.22

−0.21

March

18.12

17.32

17.16

16.68

16.27

18.80

17.30

17.20

16.71

16.38

0.68

−0.03

0.04

0.02

0.11

April

17.64

16.98

16.39

16.12

15.88

18.19

17.18

16.97

16.56

15.98

0.55

0.20

0.58

0.44

0.10

May

17.97

17.29

17.09

16.88

16.49

18.40

17.15

16.79

16.60

16.18

0.42

−0.14

−0.30

−0.28

−0.31

June

18.47

17.90

17.67

17.58

17.30

18.89

18.15

17.82

17.67

17.30

0.42

0.25

0.16

0.09

0.00

July

19.12

18.49

18.23

18.05

17.78

19.40

18.80

18.35

18.16

17.75

0.28

0.30

0.12

0.10

−0.03

August

19.54

19.11

18.81

18.63

18.26

19.65

19.09

18.78

18.61

17.94

0.11

−0.02

−0.03

−0.02

−0.33

September

20.13

19.67

19.35

19.15

18.78

20.06

19.36

19.11

18.92

18.48

−0.07

−0.30

−0.25

−0.22

−0.30

October

20.27

19.77

19.65

19.43

19.02

20.03

19.40

19.19

19.07

18.48

−0.25

−0.37

−0.46

−0.36

−0.54

November

19.87

19.68

19.47

18.91

18.34

20.17

19.34

18.88

18.80

18.17

0.30

−0.34

−0.59

−0.11

−0.17

December

19.85

19.54

18.52

18.00

17.32

19.82

18.74

18.00

17.44

16.89

−0.02

−0.80

−0.52

−0.56

−0.43

MA–HHW 1R Hardwick, Mass.

MA–HNW 19 Heath, Mass. January

31.82

27.71

24.44

22.78

21.27

23.04

22.66

22.38

22.27

22.02

−8.79

−5.06

−2.06

−0.51

0.75

February

26.95

23.85

23.06

22.56

21.79

23.93

23.77

23.64

23.54

22.84

−3.02

−0.08

0.58

0.98

1.05

March

23.48

22.61

21.55

21.00

20.19

23.19

23.05

22.05

21.12

20.75

−0.29

0.44

0.49

0.12

0.56

April

24.43

21.38

20.46

19.89

19.06

21.40

21.05

20.94

20.80

20.49

−3.04

−0.33

0.48

0.91

1.43

May

23.73

22.87

22.18

21.63

20.64

23.23

22.76

21.79

21.57

20.43

−0.49

−0.11

−0.39

−0.06

−0.21

June

26.46

25.56

25.02

24.33

23.20

27.19

26.35

25.77

25.21

23.96

0.73

0.79

0.75

0.88

0.75

July

29.35

28.22

27.64

27.26

25.93

27.93

27.72

27.55

27.28

25.00

−1.41

−0.50

−0.09

0.01

−0.93

August

32.21

30.47

29.80

29.15

27.58

29.82

29.19

28.54

28.11

27.24

−2.39

−1.28

−1.26

−1.04

−0.34

Appendix 2. Monthly Percentiles at Study Wells With Record Extensions 31

May

[Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record

P10

P20

P30

P50

P10

P20

September

34.14

32.93

32.24

31.50

29.33

33.00

32.60

32.11

October

35.82

34.46

33.74

32.96

28.61

36.04

35.66

November

36.10

34.27

32.38

31.13

26.12

35.33

33.40

December

34.92

33.32

28.12

25.31

22.25

28.13

27.39

Extended record minus observed record P30

P50

P10

P20

P30

P50

31.56

30.69

−1.14

−0.33

−0.13

0.06

1.36

34.84

34.51

33.81

0.21

1.20

1.10

1.54

5.20

32.39

31.52

30.35

−0.77

−0.87

0.01

0.39

4.23

25.47

24.34

22.85

−6.79

−5.94

−2.65

−0.96

0.60

MA–HNW 19 Heath, Mass.—Continued

MA–LKW 14R Lakeville, Mass. January

14.22

11.98

11.28

10.83

10.22

10.54

10.40

10.26

10.21

8.05

−3.68

−1.58

−1.02

−0.62

−2.17

February

14.68

11.08

10.75

10.43

10.06

10.44

10.02

9.98

9.70

8.30

−4.24

−1.05

−0.77

−0.72

−1.76

March

11.77

10.38

9.94

9.69

9.24

9.96

9.85

9.63

9.42

8.65

−1.81

−0.53

−0.31

−0.27

−0.59

April

11.30

9.94

9.16

8.80

7.08

9.53

9.25

9.02

8.82

5.86

−1.77

−0.69

−0.14

0.03

−1.22

May

11.35

10.55

9.98

9.69

8.24

9.99

9.56

9.10

8.92

6.80

−1.35

−0.98

−0.88

−0.77

−1.44

June

13.31

11.68

11.18

10.75

9.81

11.03

10.64

10.03

9.75

8.96

−2.28

−1.04

−1.15

−1.00

−0.85

July

15.21

13.68

12.57

12.14

11.36

11.37

10.93

10.42

10.24

9.62

−3.85

−2.75

−2.15

−1.90

−1.74

August

17.05

15.32

13.67

13.28

12.67

13.24

12.92

12.42

11.73

10.58

−3.81

−2.40

−1.24

−1.56

−2.09

September

18.43

16.13

15.03

14.30

13.69

14.50

14.18

13.76

13.40

11.80

−3.93

−1.96

−1.27

−0.90

−1.90

October

18.47

16.35

14.94

14.67

13.57

14.96

14.85

14.75

14.63

12.54

−3.51

−1.50

−0.19

−0.04

−1.03

November

15.85

14.55

13.94

13.77

12.71

14.36

13.84

13.79

13.65

11.86

−1.49

−0.71

−0.15

−0.12

−0.85

December

14.65

13.28

12.87

12.32

11.28

13.16

11.54

11.23

10.62

9.33

−1.49

−1.74

−1.64

−1.71

−1.95

January

4.04

2.40

1.83

1.75

1.46

3.21

2.47

2.14

1.43

1.17

−0.83

0.06

0.31

−0.33

−0.29

February

2.45

1.97

1.80

1.66

1.52

2.32

1.89

1.58

1.47

1.37

−0.13

−0.08

−0.22

−0.20

−0.15

March

2.64

1.82

1.71

1.60

1.40

1.85

1.67

1.53

1.43

1.19

−0.79

−0.15

−0.17

−0.21

April

2.04

1.60

1.40

1.17

1.05

1.93

1.72

1.35

1.04

0.86

−0.11

0.12

−0.05

−0.13

−0.19

May

1.72

1.53

1.43

1.26

1.13

2.13

1.70

1.46

1.19

0.95

0.40

0.17

0.03

−0.07

−0.18

June

2.37

2.07

1.80

1.65

1.37

2.49

2.31

2.19

2.06

1.78

0.12

0.24

0.39

0.41

July

3.48

2.95

2.69

2.40

2.05

3.16

2.94

2.80

2.68

2.36

−0.32

−0.01

0.11

0.28

0.31

August

4.22

3.90

3.59

3.21

2.55

4.24

3.86

3.42

3.19

2.44

0.02

−0.04

−0.17

−0.02

−0.12

September

5.03

4.64

4.37

4.11

3.15

4.60

4.32

3.89

3.63

2.78

−0.43

−0.32

−0.48

−0.37

October

5.33

4.99

4.61

4.13

2.98

4.76

4.50

3.95

3.65

2.59

−0.57

−0.49

−0.66

−0.48

−0.39

November

5.48

4.81

3.59

2.72

2.04

2.92

2.67

2.53

2.45

2.12

−2.56

−2.14

−1.06

−0.27

0.08

December

4.90

3.06

2.28

1.85

1.61

3.00

2.91

2.30

1.58

1.22

−1.89

−0.14

0.02

−0.27

−0.39

MA–M7W 19 Montgomery, Mass.

32 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts.—Continued

Month

Extended record P2

P10

P20

Observed record P30

P50

P10

P20

Extended record minus observed record P30

P50

P10

P20

P30

P50

MA–ORW 63 Orange, Mass. 8.36

7.54

7.30

7.15

6.72

8.40

7.94

7.56

7.27

6.64

0.04

0.40

0.26

0.12

−0.08

February

8.07

7.34

7.25

7.09

6.95

8.26

7.92

7.70

7.30

7.07

0.19

0.58

0.45

0.21

0.12

March

7.57

7.29

7.21

6.95

6.70

8.10

7.38

7.27

7.24

7.05

0.54

0.09

0.06

0.29

0.35

April

7.37

7.16

6.71

6.52

6.35

7.63

7.34

7.23

7.17

6.55

0.26

0.18

0.51

0.65

0.20

May

7.47

7.27

7.14

7.00

6.75

7.83

7.25

6.88

6.75

6.52

0.36

−0.02

−0.26

−0.25

−0.23

June

7.84

7.55

7.49

7.43

7.30

8.15

7.60

7.49

7.37

7.15

0.32

0.05

0.00

−0.06

−0.15

July

8.30

8.06

7.86

7.73

7.61

8.36

8.13

8.06

7.89

7.55

0.06

0.07

0.20

0.15

−0.07

August

8.74

8.51

8.31

8.17

7.91

8.61

8.54

8.43

8.29

7.71

−0.12

0.03

0.12

−0.20

September

9.21

8.85

8.71

8.60

8.27

8.82

8.75

8.68

8.62

7.90

−0.39

−0.10

−0.03

0.02

−0.37

October

9.17

8.95

8.88

8.78

8.43

8.83

8.80

8.56

8.30

7.71

−0.34

−0.15

−0.33

−0.48

−0.72

November

9.02

8.91

8.69

8.25

7.96

8.74

8.11

8.08

8.01

7.50

−0.28

−0.80

−0.61

−0.23

−0.46

December

9.02

8.60

7.90

7.50

7.20

8.32

7.72

7.35

7.22

7.17

−0.70

−0.88

−0.55

−0.28

−0.03

January

26.94

25.86

25.01

24.75

24.33

27.14

26.93

26.31

25.55

24.81

0.20

1.08

1.30

0.80

0.48

February

26.21

25.60

24.73

24.37

23.80

26.74

26.05

25.42

24.93

23.96

0.52

0.45

0.69

0.56

0.16

March

25.92

24.72

24.06

23.74

23.16

26.09

25.56

24.50

24.01

23.62

0.17

0.84

0.44

0.27

0.46

April

25.30

24.41

23.64

23.08

22.55

25.96

24.33

23.93

23.85

22.59

0.66

−0.08

0.30

0.77

0.04

May

24.82

23.95

23.56

23.17

22.62

25.31

23.91

23.82

23.69

22.40

0.49

−0.04

0.25

0.52

−0.22

June

24.72

24.09

23.73

23.51

23.00

25.33

24.03

23.72

23.60

22.87

0.61

−0.06

−0.01

0.09

−0.13

July

25.36

24.83

24.44

24.11

23.74

25.59

24.66

24.08

23.94

23.58

0.23

−0.17

−0.36

−0.17

−0.16

August

26.26

25.43

25.07

24.76

24.33

26.24

25.26

24.81

24.36

24.04

−0.02

−0.17

−0.26

−0.40

−0.29

September

26.89

25.93

25.62

25.31

24.85

26.52

25.87

25.25

25.03

24.64

−0.37

−0.06

−0.38

−0.28

−0.21

October

27.07

26.37

25.83

25.57

25.20

26.80

26.27

25.77

25.46

25.10

−0.27

−0.10

−0.06

−0.11

−0.10

November

27.02

26.52

25.96

25.66

25.30

26.83

26.60

26.06

25.86

25.28

−0.19

0.08

0.10

0.20

−0.02

December

26.91

26.12

25.68

25.36

24.87

27.08

26.87

26.21

25.80

24.81

0.17

0.75

0.53

0.44

−0.06

MA–PWW 22 Plymouth, Mass.

MA–SDW 483–0170 (MW–17M3) Sandwich, Mass. January

125.35

125.09

124.01

123.29

122.76

122.13

122.06

121.98

121.87

121.77

−3.22

−3.03

−2.03

−1.42

−1.00

February

125.35

125.20

124.12

123.68

122.69

123.34

122.54

122.41

122.34

122.18

−2.01

−2.66

−1.70

−1.34

−0.51

March

125.33

125.23

124.01

123.78

122.65

122.73

122.65

122.56

122.49

122.40

−2.60

−2.59

−1.45

−1.29

−0.25

April

125.38

124.82

123.90

123.21

122.70

122.99

122.95

122.86

122.76

122.13

−2.39

−1.87

−1.04

−0.45

−0.57

Appendix 2. Monthly Percentiles at Study Wells With Record Extensions 33

January

[Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record P50

P10

P20

Extended record minus observed record

P10

P20

P30

May

125.22

124.16

123.28

123.05

122.54

123.26

123.20

123.13

123.05

June

125.08

123.72

123.40

122.77

122.38

123.45

123.42

123.37

July

124.87

123.71

123.26

122.67

122.04

123.62

123.57

123.51

August

124.73

123.81

122.92

122.72

122.05

123.76

123.72

September

124.70

124.00

123.02

122.85

122.20

123.90

123.86

October

124.80

124.22

123.29

122.97

122.42

124.01

November

124.91

124.44

123.58

123.19

122.44

December

125.02

124.71

123.87

123.34

122.69

January

5.02

4.32

4.05

3.88

3.63

3.38

3.33

3.30

February

4.78

4.43

4.23

4.05

3.74

3.33

3.28

March

4.58

4.24

4.00

3.77

3.51

3.34

3.29

April

4.50

4.25

3.76

3.53

3.27

3.29

May

4.43

4.19

4.05

3.90

3.68

3.62

June

5.21

4.85

4.63

4.48

4.16

July

5.97

5.64

5.43

5.27

August

6.47

6.07

5.87

5.71

September

6.84

6.33

6.03

October

6.26

5.92

5.72

November

5.78

5.40

December

5.57

5.03

P50

P10

P20

P30

P50

121.88

−1.96

−0.96

−0.15

0.00

−0.66

123.30

121.66

−1.63

−0.30

−0.03

0.53

−0.72

123.47

121.52

−1.25

−0.14

0.25

0.80

−0.52

123.69

123.65

121.53

−0.97

−0.09

0.78

0.93

−0.52

123.83

123.79

121.64

−0.80

−0.14

0.81

0.94

−0.56

123.98

123.95

123.93

121.75

−0.79

−0.24

0.66

0.95

−0.67

124.04

124.03

124.01

124.00

121.84

−0.87

−0.41

0.43

0.81

−0.60

124.02

123.99

123.94

123.90

121.90

−1.00

−0.72

0.07

0.56

−0.79

3.27

3.21

−1.64

−0.99

−0.75

−0.61

−0.42

3.24

3.22

3.18

−1.45

−1.15

−0.99

−0.83

−0.56

3.26

3.23

3.16

−1.24

−0.95

−0.74

−0.54

−0.35

3.22

3.20

3.14

3.10

−1.21

−1.03

−0.56

−0.38

−0.17

3.43

3.36

3.31

3.22

−0.81

−0.76

−0.69

−0.60

−0.46

4.52

4.23

3.80

3.71

3.51

−0.69

−0.62

−0.84

−0.77

−0.65

4.94

5.48

5.33

5.04

4.64

4.08

−0.49

−0.32

−0.39

−0.62

−0.86

5.24

5.98

5.88

5.75

5.57

5.07

−0.49

−0.19

−0.12

−0.14

−0.17

5.76

5.44

6.31

6.23

6.08

5.66

5.38

−0.53

−0.10

0.05

−0.10

−0.06

5.48

4.93

6.33

6.19

5.62

5.28

4.05

0.07

0.27

−0.10

−0.20

−0.88

5.09

4.73

4.16

4.39

4.33

4.16

4.03

3.42

−1.39

−1.08

−0.93

−0.69

−0.75

4.62

4.27

3.59

3.55

3.48

3.41

3.32

3.23

−2.03

−1.55

−1.21

−0.95

−0.36

MA–SDW 483–0170 (MW–17M3) Sandwich, Mass.—Continued

MA–SHW 275R Seekonk, Mass.

MA–SJW 58R Sheffield, Mass. January

15.82

15.13

14.01

13.29

12.27

15.85

15.57

15.07

14.70

13.23

0.03

0.44

1.05

1.41

0.96

February

15.32

14.87

14.00

13.29

12.52

15.37

15.16

14.84

14.22

13.32

0.05

0.30

0.84

0.93

0.79

March

15.05

14.93

13.58

13.12

12.57

15.07

14.98

14.88

13.82

13.12

0.02

0.05

1.30

0.70

0.55

April

14.94

14.30

13.23

12.92

12.05

14.97

14.83

14.15

13.53

12.60

0.02

0.53

0.92

0.61

0.55

May

14.63

13.98

13.42

12.94

11.46

14.73

14.35

13.97

13.46

12.36

0.10

0.37

0.55

0.52

0.90

June

14.29

13.88

13.62

12.60

11.58

14.34

14.25

13.85

13.73

12.64

0.05

0.37

0.23

1.13

1.06

July

14.43

14.00

13.70

12.74

11.79

14.53

14.27

13.97

13.84

13.12

0.11

0.27

1.10

1.33

August

14.91

14.24

13.87

12.60

12.17

14.98

14.62

14.23

13.99

12.66

0.07

0.38

0.36

1.39

0.49

34 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts.—Continued

Month

Extended record

Observed record

P10

P20

P30

P50

P10

P20

September

15.38

14.76

13.69

12.95

12.38

15.42

15.11

14.71

October

15.76

15.22

13.63

13.19

12.34

15.77

15.55

November

16.02

15.48

13.88

13.43

12.55

16.06

15.84

December

15.99

15.47

14.15

13.48

12.15

15.99

15.86

Extended record minus observed record P30

P50

P10

P20

P30

P50

14.45

13.14

0.05

0.35

1.02

1.50

0.76

15.19

15.01

13.32

0.01

0.33

1.56

1.82

0.98

15.39

15.18

13.44

0.04

0.36

1.51

1.75

0.89

15.41

14.86

13.48

0.00

0.39

1.27

1.38

1.33

MA–SJW 58R Sheffield, Mass.—Continued

MA–TMW 3R Templeton, Mass. 4.11

3.81

3.67

3.60

3.49

4.00

3.80

3.70

3.62

3.45

−0.11

−0.01

0.03

0.02

−0.04

February

4.00

3.84

3.75

3.67

3.56

3.90

3.81

3.70

3.66

3.55

−0.10

−0.03

−0.05

−0.02

−0.01

March

3.90

3.75

3.64

3.54

3.43

3.72

3.58

3.49

3.40

3.32

−0.18

−0.17

−0.15

−0.14

−0.12

April

3.87

3.75

3.56

3.44

3.33

3.78

3.66

3.56

3.42

3.31

−0.09

−0.08

0.00

−0.02

May

3.88

3.76

3.69

3.63

3.51

4.01

3.82

3.77

3.69

3.54

0.13

0.06

0.08

0.06

0.03

June

4.29

4.09

3.99

3.92

3.78

4.50

4.25

4.14

4.06

3.95

0.22

0.15

0.14

0.17

July

4.58

4.40

4.30

4.22

4.07

4.61

4.35

4.22

4.16

4.04

0.03

−0.05

−0.07

−0.06

−0.03

August

4.79

4.58

4.49

4.41

4.19

4.77

4.53

4.44

4.33

4.14

−0.02

−0.05

−0.08

−0.06

September

4.95

4.69

4.53

4.42

4.25

4.71

4.55

4.46

4.40

4.04

−0.23

−0.14

−0.07

−0.02

−0.21

October

4.63

4.50

4.41

4.29

4.01

4.49

4.46

4.06

3.84

3.71

−0.14

−0.04

−0.35

−0.44

−0.30

November

4.45

4.28

4.09

3.95

3.71

4.01

3.79

3.71

3.65

3.47

−0.44

−0.49

−0.39

−0.30

−0.24

December

4.35

4.10

3.91

3.74

3.48

3.85

3.71

3.58

3.54

3.38

−0.51

−0.40

−0.33

−0.20

−0.10

January

15.47

15.04

14.59

14.18

13.61

15.91

14.28

13.91

13.82

13.56

0.44

−0.76

−0.68

−0.36

−0.04

February

15.37

14.44

14.24

13.81

13.17

15.83

14.13

13.57

13.51

13.14

0.46

−0.31

−0.67

−0.30

−0.03

March

15.21

14.05

13.54

13.38

12.60

15.33

13.53

13.37

13.16

12.52

0.12

−0.52

−0.17

−0.23

−0.08

April

14.81

13.24

12.94

12.58

11.92

14.43

13.20

13.11

12.30

11.85

−0.37

−0.04

0.18

−0.27

−0.07

May

14.57

13.09

12.77

12.43

11.60

14.10

12.80

12.56

12.03

11.50

−0.46

−0.28

−0.21

−0.40

−0.10

June

14.32

13.43

13.03

12.72

12.17

14.29

12.82

12.58

12.50

12.02

−0.03

−0.61

−0.45

−0.22

−0.15

July

14.64

13.90

13.33

13.05

12.70

14.53

13.30

12.96

12.85

12.55

−0.11

−0.61

−0.37

−0.20

−0.15

August

15.09

14.26

13.82

13.61

13.19

14.91

13.70

13.44

13.18

12.76

−0.18

−0.56

−0.38

−0.43

September

15.49

14.72

14.32

14.10

13.75

15.34

14.22

14.02

13.73

13.32

−0.15

−0.50

−0.31

−0.37

−0.43

October

15.74

15.07

14.67

14.55

14.01

15.13

14.57

14.38

14.00

13.81

−0.61

−0.49

−0.29

−0.55

−0.20

November

15.78

15.35

14.90

14.77

14.10

15.68

14.95

14.76

14.22

13.55

−0.11

−0.40

−0.14

−0.56

−0.55

December

15.40

15.19

15.01

14.62

13.70

15.55

14.66

14.40

14.19

13.63

0.16

−0.53

−0.61

−0.43

−0.07

MA–TRW 13R Townsend, Mass.

Appendix 2. Monthly Percentiles at Study Wells With Record Extensions 35

January

[Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record

P10

P20

P30

P50

P10

January

12.33

12.04

11.89

11.80

11.64

12.39

12.05

February

12.35

11.85

11.63

11.57

11.48

12.41

March

12.27

11.73

11.65

11.48

11.25

12.31

April

12.08

11.65

11.53

11.25

11.09

May

12.10

11.75

11.50

11.26

11.11

June

12.26

11.83

11.61

11.47

July

12.48

11.99

11.81

August

12.62

12.19

11.97

September

12.67

12.29

October

12.60

12.30

November

12.51

December

12.45

January

P20

Extended record minus observed record P30

P50

P10

P20

P30

P50

11.93

11.84

11.63

0.06

0.01

0.04

−0.01

11.94

11.67

11.58

11.44

0.06

0.09

0.04

0.01

−0.04

11.74

11.67

11.61

11.28

0.05

0.01

0.02

0.13

0.03

12.28

11.66

11.56

11.30

11.09

0.20

0.01

0.03

0.05

0.00

12.22

11.81

11.53

11.30

11.14

0.12

0.06

0.03

0.04

0.03

11.32

12.30

11.89

11.80

11.51

11.34

0.04

0.06

0.19

0.04

0.02

11.65

11.53

12.50

12.13

11.83

11.79

11.59

0.02

0.15

0.02

0.14

0.06

11.90

11.70

12.66

12.35

12.07

11.95

11.85

0.04

0.16

0.10

0.05

0.15

12.16

12.02

11.78

12.70

12.46

12.22

12.13

11.96

0.03

0.17

0.06

0.11

0.18

12.07

12.01

11.84

12.65

12.38

12.14

12.06

11.95

0.04

0.08

0.07

0.04

0.11

12.17

12.04

11.99

11.77

12.53

12.23

12.05

12.00

11.76

0.02

0.06

0.01

−0.01

12.12

12.00

11.92

11.71

12.46

12.14

12.04

11.95

11.65

0.01

0.02

0.04

0.03

−0.06

19.94

19.84

19.72

19.54

19.10

19.73

19.72

19.69

18.81

18.65

−0.21

−0.12

−0.03

−0.73

−0.45

February

19.80

19.75

19.65

19.35

18.68

19.73

19.69

19.61

18.63

18.33

−0.07

−0.04

−0.72

−0.35

March

19.57

19.50

19.24

18.64

18.26

19.58

19.55

19.52

18.28

18.22

0.01

0.05

0.28

−0.36

−0.04

April

19.50

19.41

18.57

18.34

18.05

19.53

19.46

19.44

18.13

17.99

0.03

0.05

0.87

−0.21

−0.06

May

19.44

19.13

18.48

18.38

17.88

19.46

19.43

17.88

17.81

0.02

0.30

0.95

−0.50

−0.07

June

19.47

19.13

18.69

18.48

17.97

19.51

19.44

19.39

18.39

17.83

0.04

0.31

0.70

−0.09

−0.14

July

19.59

19.44

18.92

18.58

18.21

19.61

19.56

19.38

18.27

18.14

0.02

0.12

0.45

−0.31

−0.07

August

19.75

19.64

19.21

18.94

18.52

19.77

19.70

19.50

18.49

18.29

0.02

0.06

0.28

−0.45

−0.23

September

19.80

19.71

19.50

19.23

18.88

19.77

19.69

19.65

18.88

18.47

−0.04

−0.02

0.15

−0.35

−0.41

October

19.93

19.69

19.58

19.41

19.15

19.69

19.66

19.60

19.21

18.74

−0.24

−0.03

0.02

−0.20

−0.42

November

20.04

19.75

19.58

19.51

19.38

19.62

19.53

19.46

19.41

18.87

−0.42

−0.22

−0.12

−0.10

−0.51

December

20.11

19.82

19.64

19.59

19.23

19.66

19.62

19.54

19.33

18.79

−0.45

−0.19

−0.10

−0.26

−0.44

MA–TSW 89 Truro, Mass.

MA–TSW 257–0034 Truro, Mass.

MA–WWW 160 Westford, Mass. January

12.25

11.70

11.52

11.40

11.16

11.91

11.31

11.07

11.00

10.94

−0.34

−0.39

−0.45

−0.41

−0.22

February

12.37

11.47

11.39

11.31

11.19

11.53

11.25

11.12

11.05

10.96

−0.84

−0.22

−0.27

−0.26

−0.23

March

11.64

11.29

11.17

11.09

10.88

10.99

10.90

10.88

10.86

10.83

−0.65

−0.39

−0.30

−0.23

−0.05

April

11.52

11.17

10.94

10.82

10.47

11.02

11.00

10.95

10.91

10.84

−0.50

−0.17

0.01

0.09

0.36

36 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts.—Continued

Month

Extended record

Observed record

P10

P20

P30

P50

P10

P20

May

11.54

11.33

11.18

11.04

10.71

11.25

10.96

10.91

June

12.03

11.63

11.49

11.38

11.15

12.11

11.47

July

12.51

12.14

11.87

11.77

11.58

13.09

11.97

August

12.99

12.64

12.18

12.09

11.89

13.24

September

13.32

12.92

12.55

12.41

12.15

13.86

October

13.33

12.81

12.69

12.40

12.09

November

12.67

12.34

12.21

12.12

December

12.40

12.03

11.90

11.76

January

19.28

18.09

16.96

February

19.00

16.28

March

18.54

15.56

April

17.44

May

16.89

June

Extended record minus observed record P30

P50

P10

P20

P30

P50

10.86

10.73

−0.29

−0.37

−0.27

−0.18

0.01

11.30

11.22

11.06

0.08

−0.16

−0.19

−0.16

−0.09

11.71

11.35

10.84

0.58

−0.17

−0.16

−0.42

−0.74

12.74

11.90

11.35

11.05

0.25

0.10

−0.28

−0.74

−0.84

12.90

12.05

11.42

10.92

0.54

−0.02

−0.50

−0.99

−1.23

13.28

12.56

11.89

11.19

10.97

−0.05

−0.25

−0.80

−1.21

−1.12

11.84

12.40

11.73

11.37

10.93

10.70

−0.27

−0.61

−0.84

−1.19

−1.14

11.46

12.54

11.48

10.93

10.86

10.81

0.14

−0.54

−0.97

−0.90

−0.65

15.89

12.74

17.22

14.79

14.60

14.16

12.27

−2.07

−3.30

−2.37

−1.73

−0.47

16.05

14.82

12.52

15.36

13.69

12.83

11.84

11.39

−3.64

−2.58

−3.21

−2.98

−1.13

14.21

13.54

11.56

14.84

12.22

12.11

11.48

10.86

−3.70

−3.34

−2.10

−2.06

−0.70

13.40

11.99

11.15

9.94

11.86

11.14

10.54

10.37

9.68

−5.58

−2.26

−1.45

−0.78

−0.26

13.03

12.16

10.84

8.91

12.12

9.49

8.44

8.09

7.79

−4.77

−3.55

−3.72

−2.75

−1.12

16.22

13.93

12.86

11.81

10.27

12.21

10.89

10.37

10.06

9.42

−4.02

−3.05

−2.49

−1.75

−0.86

July

17.04

15.21

13.64

12.96

12.05

14.07

12.82

12.45

12.31

11.69

−2.98

−2.39

−1.19

−0.65

−0.36

August

18.29

16.61

15.02

14.57

13.57

15.62

14.69

14.40

13.99

12.90

−2.67

−1.92

−0.62

−0.57

−0.67

September

19.33

17.63

16.35

15.88

15.13

16.86

16.12

15.80

15.48

14.81

−2.47

−1.51

−0.55

−0.39

−0.32

October

19.98

18.34

17.25

16.94

16.08

17.36

17.09

16.85

16.55

15.66

−2.61

−1.25

−0.40

−0.39

−0.42

November

20.11

18.77

17.70

17.44

15.98

17.60

17.55

17.40

17.25

15.16

−2.51

−1.22

−0.30

−0.19

−0.82

December

19.06

18.55

18.06

17.36

14.60

17.53

17.33

16.79

16.01

14.51

−1.53

−1.22

−1.27

−1.35

−0.09

MA–WWW 160 Westford, Mass.—Continued

MA–XNW 13 Winchendon, Mass. January

11.15

7.57

6.59

5.95

4.63

9.47

6.26

5.45

4.70

4.01

−1.68

−1.31

−1.14

−1.25

−0.62

February

9.43

6.95

6.12

5.57

4.70

7.85

5.99

5.17

4.92

4.46

−1.58

−0.96

−0.95

−0.65

−0.24

March

8.10

6.19

4.93

4.33

3.71

5.93

5.26

4.41

4.14

3.82

−2.16

−0.93

−0.52

−0.19

0.11

April

5.96

5.07

4.47

3.97

3.18

4.83

4.58

4.27

3.93

3.40

−1.13

−0.49

−0.21

−0.04

0.22

May

7.05

5.85

5.08

4.65

3.88

6.18

5.09

4.67

4.41

4.04

−0.88

−0.75

−0.41

−0.24

0.16

June

8.67

7.63

6.94

6.38

5.47

8.62

7.63

7.05

6.51

5.83

−0.05

0.00

0.11

0.13

0.36

July

10.23

9.62

9.09

8.48

7.52

10.45

9.64

9.25

8.63

7.42

0.21

0.01

0.16

−0.10

August

11.57

10.94

10.56

10.21

9.21

11.78

11.04

10.72

10.18

8.76

0.21

0.10

0.16

−0.03

−0.45

Appendix 2. Monthly Percentiles at Study Wells With Record Extensions 37

MA–WXW 20 Westhampton, Mass.

[Data are from Crozier and Ahearn (2024). P2, 2d percentile; P10, 10th percentile; P20, 20th percentile; P30, 30th percentile; P50, 50th percentile]

Month

Extended record

Observed record

P10

P20

P30

P50

P10

P20

September

12.35

11.86

11.39

10.82

9.85

12.28

11.86

11.61

October

12.54

12.13

11.46

11.05

9.89

12.63

12.26

November

12.63

11.02

10.15

9.58

7.74

12.82

11.77

December

12.26

9.79

8.34

7.01

5.60

12.26

6.81

Extended record minus observed record P30

P50

P10

P20

P30

P50

11.08

10.14

−0.06

0.00

0.22

0.26

0.28

11.69

11.46

10.86

0.09

0.13

0.22

0.41

0.97

10.87

8.70

6.16

0.19

0.75

0.72

−0.88

−1.58

5.96

5.78

4.75

0.00

−2.98

−2.38

−1.23

−0.85

MA–XNW 13 Winchendon, Mass.—Continued

MA–XNW 48 Winchendon, Mass. January

27.20

26.04

25.75

25.61

25.39

25.67

25.39

25.24

25.12

24.96

−1.53

−0.65

−0.51

−0.50

−0.43

February

26.73

26.02

25.86

25.75

25.53

25.92

25.74

25.47

25.24

25.05

−0.81

−0.27

−0.39

−0.51

−0.48

March

25.99

25.69

25.53

25.31

25.06

25.93

25.72

25.53

25.43

25.20

−0.06

0.03

0.00

0.12

0.14

April

26.02

25.28

25.02

24.87

24.43

26.55

25.50

25.29

25.16

24.79

0.53

0.22

0.27

0.29

0.36

May

26.16

25.56

25.30

25.10

24.77

27.21

26.00

25.58

25.26

24.82

1.05

0.44

0.28

0.15

0.05

June

27.21

26.05

25.81

25.58

25.27

28.12

27.16

26.28

26.12

25.96

0.90

1.11

0.47

0.54

0.69

July

27.13

26.51

26.16

26.00

25.74

27.74

27.05

26.78

26.43

26.16

0.61

0.54

0.62

0.43

0.42

August

27.62

27.13

26.75

26.50

26.15

27.74

27.44

27.19

26.70

25.98

0.12

0.31

0.44

0.20

−0.17

September

28.04

27.52

27.13

26.88

26.64

28.02

27.69

27.56

26.71

26.35

−0.02

0.17

0.43

−0.17

−0.29

October

28.11

27.61

27.09

26.87

26.62

27.92

27.60

27.03

26.74

26.54

−0.19

−0.01

−0.06

−0.13

−0.09

November

27.82

26.92

26.65

26.40

26.02

27.03

26.90

26.37

26.18

25.24

−0.79

−0.02

−0.28

−0.22

−0.78

December

27.75

26.32

26.03

25.86

25.46

26.31

25.96

25.61

25.48

25.34

−1.44

−0.36

−0.42

−0.38

−0.12

38 Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts

Table 2.1. Monthly percentiles for 27 groundwater wells with record extensions used in a study monitoring groundwater levels in Massachusetts.—Continued

For more information, contact Director, New England Water Science Center U.S. Geological Survey 10 Bearfoot Road Northborough, MA 01532 dc_[email protected] or visit our website at https://www.usgs.gov/centers/new-england-water-science-center Publishing support provided by the Pembroke Publishing Service Center

Ahearn and Crozier—Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles in Massachusetts—SIR 2024–5080

ISSN 2328-0328 (online) https://doi.org/10.3133/sir20245080

Estimating Groundwater Level Records Using MOVE.1 and Computing Monthly Percentiles From Estimated Groundwater Records in Massachusetts

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