Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( Lock Locked padlock icon ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide PERMALINK Copy As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Mar 4;16:11952. doi: 10.1038/s41598-026-39531-2 Search in PMC Search in PubMed View in NLM Catalog Add to search Analysis of the performance of a virtual gauge-based method in hydrological modeling of basins with no precipitation stations Yanhong Dou Yanhong Dou 1 State Key Laboratory of Water Cycle and Water Security, Institute of Water Resources and Hydropower Research, Beijing, 100038 China 2 Research Center on Flood & Drought Disaster Prevention and Reduction of the Ministry of Water Resources, Beijing, 100038 China Find articles by Yanhong Dou 1, 2 , Xiangning Liu Xiangning Liu 1 State Key Laboratory of Water Cycle and Water Security, Institute of Water Resources and Hydropower Research, Beijing, 100038 China 2 Research Center on Flood & Drought Disaster Prevention and Reduction of the Ministry of Water Resources, Beijing, 100038 China Find articles by Xiangning Liu 1, 2 , Xiao Liu Xiao Liu 1 State Key Laboratory of Water Cycle and Water Security, Institute of Water Resources and Hydropower Research, Beijing, 100038 China 2 Research Center on Flood & Drought Disaster Prevention and Reduction of the Ministry of Water Resources, Beijing, 100038 China Find articles by Xiao Liu 1, 2 , Min Xie Min Xie 1 State Key Laboratory of Water Cycle and Water Security, Institute of Water Resources and Hydropower Research, Beijing, 100038 China 2 Research Center on Flood & Drought Disaster Prevention and Reduction of the Ministry of Water Resources, Beijing, 100038 China Find articles by Min Xie 1, 2 , Ronghua Liu Ronghua Liu 1 State Key Laboratory of Water Cycle and Water Security, Institute of Water Resources and Hydropower Research, Beijing, 100038 China 2 Research Center on Flood & Drought Disaster Prevention and Reduction of the Ministry of Water Resources, Beijing, 100038 China Find articles by Ronghua Liu 1, 2, ✉ Author information Article notes Copyright and License information 1 State Key Laboratory of Water Cycle and Water Security, Institute of Water Resources and Hydropower Research, Beijing, 100038 China 2 Research Center on Flood & Drought Disaster Prevention and Reduction of the Ministry of Water Resources, Beijing, 100038 China ✉ Corresponding author. Received 2025 Jul 17; Accepted 2026 Feb 5; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13069077 PMID: 41781515 Abstract This study evaluates the hydrological performance of the virtual gauge-based method (VG) for flood forecasting in basins devoid of precipitation stations. The Xiaoergou basin was selected as the study area, with flood-season data (2010–2019) including rainfall observations from adjacent basins, outlet streamflow records, and six precipitation products. The VG method divides the basin into multiple sub-regions based on the actual locations and density of the gauges, and then determines virtual gauge locations and precipitation using multi-source precipitation products, and integrates virtual with actual gauges to estimate rainfall fields and areal rainfall. As a control, the Thiessen polygon method was applied to estimate rainfall fields and areal rainfall from the observed rainfall. VG- and Thiessen-derived areal rainfall were used as inputs to hydrological model, with flood forecasting accuracy evaluated through multiple metrics. Results demonstrate that the VG method can adaptively adjust the number, location and rainfall of virtual gauges according to the spatial characteristic of rainfall fields, and dynamically optimizing the weighting of precipitation products. Compared with the Thiessen polygon method, VG-driven hydrological simulations achieved up to approximately 50% higher flood volume prediction accuracy and a notable increase in flood event pass rates. Consequently, the VG method demonstrates superior rainfall estimates and flood simulation capabilities in regions with no precipitation stations. Keywords: Virtual rainfall gauge, Multi-source precipitation products, Rainfall fields, Flood forecasting, Scarce gauge basins Subject terms: Climate sciences, Environmental sciences, Hydrology, Natural hazards Introduction Rainfall is a key driving factor in basin-scale hydrological modeling 1 and directly affects the accuracy of flood simulation 2 . Rainfall estimation methods can be generally categorized into two types: direct observations from ground-based rain gauges 3 , and indirect estimates based on ground-based radar 4 , satellite remote sensing 1 , 5 – 7 , and numerical models 8 . While gauge-based data has high accuracy near the gauge locations, the inadequate spatial coverage often results in missing rainfall center. In contrast, precipitation products can reflect the spatial heterogeneity of large-scale rainfall fields but have low accuracy. Therefore, merging multi-source rainfall data is an important method to improve the accuracy of rainfall estimation for regions with limited rainfall data 9 , 10 . Existing methods for merging multi-source rainfall data can be classified into the following categories: (1) bias correction-based methods 11 , 12 (using measured rainfall as the benchmark to correct rainfall products), such as quartile mapping 13 , geographical differential analysis 14 – 16 , and kriging method 17 ; (2) weighted averaging-based methods 18 , which mainly include optimal weighting 19 and Bayesian model averaging 20 , 21 ; and (3) machine learning-based methods 22 – 28 , including random forest 29 and artificial neural network 30 . These methods typically involve training the merging model in regions or grid cells with precipitation stations and then applying it on a grid-by-grid basis in regions or grid cells with no precipitation stations. However, these merging methods can only improve gauge-based rainfall estimates in regions where rain gauges are extremely sparsely distributed, such as regions with gauge densities of 8000 km²/gauge 31 or 13,000 km²/gauge 16 . In contrast, at higher gauge densities, such as 3,000–5,000 km²/gauge 32 , the accuracy of merged rainfall is inferior to that of spatial interpolation of purely measured rainfall, which nullifies the application value of existing merging methods. This performance bottleneck stems from indiscriminately merging rainfall products into each grid cell, which may interfere with the merging results. To address this, a strategy is needed that can dynamically select grid cells based on the spatial characteristics of different rainfall fields, and precipitation products are used only at these grid cells. Then combine these estimates with measured rainfall through spatial interpolation to dynamically supplement the key information on the spatial distribution of rainfall fields, while minimizing the interference caused by errors in precipitation products via dynamically adjusting the degree of utilization of precipitation products. In view of this, Dou et al. 32 proposed the virtual gauge-based method (VG), a multi-source rainfall data merging method capable of adaptively adjusting the degree of spatial utilization of precipitation products for different rainfall fields. The VG method dynamically identifies key locations (virtual gauges) where multi-source products suggest the presence of significant rainfall features missed by the physical gauge network, estimates rainfall at these points using a merging technique, and then integrates them with actual gauge observations via spatial interpolation. The VG method exhibited significant advantages in scenarios with different rainfall intensities, rainfall spatial distributions, and gauge densities. However, existing arithmetic examples of VG only analyzed the accuracy of the merged rainfall for regions with sparsely distributed gauges, while its performance in estimating areal rainfall in basins with no precipitation stations remains unexplored. Therefore, this study aims to fill this research gap by evaluating the performance of the virtual gauge method in a basin without any precipitation stations. The VG framework is applied to estimate areal rainfall, while the Thiessen polygon method serves as a control. Both rainfall datasets are used to drive the Xin’anjiang hydrological model, and the accuracy of model simulations is compared to indirectly assess the reliability of VG-based rainfall estimates in ungauged basins. The findings provide practical insights into the feasibility of applying the VG method for flood forecasting in data-scarce regions. Study area and data Study area Xiaoergou Basin is the control basin of Xiaoergou Hydrological Station in the middle reaches of the main stream of the Nuomin River, located between 121.73°E–123.88°E and 48.83°N–50.61°N in the upper reaches of the Nenjiang River, covering an area of 16,761 km². Nuomin River is an important western tributary of the Nenjiang River, originating in the Daxing’anling Prefecture, northern Inner Mongolia. Located in the temperate continental monsoon climate zone, the basin is cold and dry in winter and humid and rainy in summer, with short spring and fall seasons. The precipitation is unevenly distributed within the year, with approximately 80% of the annual precipitation concentrated in May to September. Gauge-based observation data No precipitation stations are deployed within the Xiaoergou Basin, while a small number of precipitation stations are located outside of the basin (within other basins in the immediate vicinity), making it a typical area with limited rainfall data availability, as shown in Fig. 1 . In this study, we collected the daily hydrological data for the flood season (May to September) from 2010 to 2019, including the observed flow at the Xiaoergou hydrological station at the outlet of the basin, the observed rainfall at 22 precipitation stations in the vicinity of the basin, and the observed evapotranspiration at three evapotranspiration stations in the vicinity of the basin. The location of the study area and the distribution of the hydrometeorological stations are shown in Fig. 1 . Fig. 1. Open in a new tab Location of the study area and distribution of hydrometeorological stations. The flow process was divided into 18 flood events, with the peak, volume, and type of each flood are shown in Fig. 2 . These events vary widely in terms of peak discharge, total flood volume, hydrograph shape, and temporal distribution. To be specific, the events cover a broad spectrum of flood peaks (from 247 m³/s to 1389 m³/s) and flood volume(from 3012.3 m³ to 18242.8 m³). Both single-peak and double-peak floods are included, reflecting different rainfall durations and basin response dynamics. Besides, the events are distributed throughout the 10-year study period (2010–2019), capturing the inter-annual variability of rainfall and runoff regimes. This diversity ensures that the hydrological model parameters calibrated on this dataset are robust and provides an objective basis for evaluating simulation accuracy during the validation period. Among the 18 floods, twelve were used for parameter calibration, and six were used to validate the flood simulation. The specific events assigned to each group are marked in Fig. 2 . Fig. 2. Open in a new tab Peaks, volumes, and peak patterns of flood events, the flood events within the box are used for validation, while the remaining flood events are used for calibration. Multi-source precipitation products We selected six daily real-time/short-latency precipitation products, namely, the satellite remote sensing products GSMaP-N and GSMaP-GN of the Japan Aerospace Exploration Agency 33 , 34 , the satellite remote sensing products IMERG-E and IMERG-L of the National Aeronautics and Space Administration 35 , 36 , the simulation and analysis product GRAPES of the China Meteorological Administration 37 , and the simulation and analysis products of the European Center for Medium-Range Weather Forecasts 38 , 39 . To match the flow data, we collected the daily rainfall data of the Xiaoergou Basin for the flood seasons (May to September) from 2010 to 2019 from the six precipitation products with a spatial resolution of 0.1°. Methods Multi-source rainfall data fusion method based on VG When actual gauges are sparsely distributed, the key information of the spatial distribution of the rainfall field is easily missing, and the direct spatial interpolation will homogenize the rainfall field. The rainfall estimation can be effectively improved if the spatial locations of the maximum and minimum rainfall and their corresponding rainfall in the real rainfall field are determined, supplementing these points as virtual gauges alongside the actual gauges, and then spatially interpolated, as shown in Fig. 3 , where and are the rainfall of actual gauges,, and is the rainfall of the grid cell to be estimated 32 . Fig. 3. Open in a new tab Schematic of the effect of virtual gauges, where and are the actual rainfall of gauge and , and are the estimated rainfall of virtual gauge and , denotes any grid cell in the rainfall field, indicates the estimated rainfall of the grid cell. Based on the above rationale, the main steps of VG method are as follows: (1) divide the area whose rainfall field is to be estimated into multiple sub-areas based on the locations and density of actual gauges; (2) determine the locations of virtual gauges in each sub-area in each period based on the spatial characteristics of the real-time updated multi-source precipitation products; (3) use existing grid-by-grid merging methods to estimate the rainfall in real-time at virtual gauges; and (4) utilize actual and virtual gauges for spatial interpolation, as shown in Fig. 4 . Fig. 4. Open in a new tab Flowchart of VG method. One of the key steps is the determination of the locations of virtual gauges, as shown in Fig. 5 . Since the spatial locations and the corresponding rainfall of the maximum and minimum rainfall in the real rainfall field are unknown, the locations of the virtual gauges need to be determined based on real-time updated multi-source precipitation products. It is assumed that if more than half of the precipitation products recommend a certain grid cell as a virtual gauge, the location does need to be supplemented with a virtual gauge. To highlight the spatial information of the precipitation products, the rainfall field estimated using each precipitation product at a single time step was normalized (0–1 scale) to obtain the normalized rainfall field for product i , . If a grid cell of is larger than and at the actual gauge, then the location of the grid cell occupied by product i is recommended as the location of the virtual gauge. Fig. 5. Open in a new tab Determination of the locations of virtual gauges, where denotes the normalized rainfall field of precipitation product , and indicate the normalized rainfall value at the location of actual gauge and , respectively. Control test setup for calculating areal rainfall in the basin To objectively evaluate the performance of the VG method in a basin without precipitation stations, a comparative experiment was established, comprising a test group and a control group. The test group employed the VG method, while the control group utilized the traditional Thiessen polygon method. The hydrological performance of the two rainfall inputs was then compared through flood simulations in the Xiaoergou Basin. The specific experimental setup is as follows. Test group: VG based rainfall estimation For the test group, the multi-source rainfall data were merged using VG to estimate the rainfall field in grid cells with a spatial resolution of 0.1° in the Xiaoergou Basin. This process includes two main steps: (1) determining the locations of virtual gauges and estimating their rainfall values using the random forest 40 algorithm, and (2) performing spatial interpolation with inverse distance weighting (IDW) by incorporating both actual and virtual gauges. The areal rainfall of the basin was then obtained by averaging the rainfall of all grid cells within the basin. The random forest merging process includes two main steps: Model training. A transfer model of dependent and independent variables was built based on random forest, with the rainfall measured at the actual gauges as the dependent variable and the rainfall estimates of the multi-source precipitation products at the actual gauge locations and other relevant covariates as the independent variables, as shown in Eq. ( 1 ). 1 where is the trained random forest transfer model; is the measured rainfall in period in the grid cell where the precipitation station is located; is the estimated rainfall of the product in period in the grid cell where the precipitation station is located; is the set of covariates associated with the precipitation station , including the measured rainfall at the two stations nearest to the precipitation station and the distances between the two stations nearest to the precipitation station and the precipitation station ; and is the model error. (b) Rainfall estimation. The rainfall at the virtual gauge, , is estimated using the trained random forest transfer model, as shown in Eq. ( 2 ). Only grid cells identified as virtual gauges were subjected to this merging process, ensuring that quantitative rainfall estimates from multi-source precipitation products were applied exclusively at these key locations. 2 where is the estimated rainfall of the product in period for the grid cell of the virtual gauge and is the set of covariates associated with the virtual gauge , including the measured rainfall of the two stations closest to the precipitation station and the distance from the two stations closest to the precipitation station to the precipitation station , which is set up according to the same idea of Eq. ( 1 ). It is worth noting that quantitative rainfall estimates from multi-source precipitation products have only been applied and merged at the virtual gauge. Control group: Thiessen polygon method For the control group, the Thiessen polygon method 41 , 42 was used to estimate the spatial distribution of rainfall and the areal rainfall in the Xiaoergou Basin based on measured rainfall at sparsely distributed gauges outside the basin. The rainfall intensity in the area within the Thiessen polygon is expressed in terms of the rainfall intensity at the only precipitation station contained within the polygon, so that the spatial distribution of rainfall within the basin can be estimated. The area of the portion of the polygon that intersects the basin is used as a weight to obtain the weighted average rainfall intensity within the corresponding area of the polygon to estimate the average areal rainfall in the basin. Figure 6 illustrates the Thiessen polygons for the sparse gauge divisions outside the Xiaoergou Basin, indicating that the Thiessen polygons for 9 of the 22 precipitation stations in the adjacent basins cover the Xiaoergou Basin. Fig. 6. Open in a new tab Division of precipitation station control regions using Thiessen polygons. Assessment of the hydrological performance of areal rainfall The areal rainfall estimates were used as input to the hydrological model for flow simulation. The performance of the hydrological model was evaluated using quantitative accuracy metrics to assess the impact of the different areal rainfall inputs on the simulation results, thereby reflecting its hydrological effectiveness. The Xin’anjiang model was employed to simulate floods in the Xiaoergou Basin. The hydrological model parameters were calibrated using the areal rainfall derived from both the VG method and the sparse external gauges. The technical roadmap of this paper is shown in Fig. 7 . Fig. 7. Open in a new tab Technical roadmap. The basic principles of the Xin’anjiang model are summarized below. The Xin’anjiang model comprises four components: evapotranspiration module, runoff production module, runoff separation module and runoff concentration module. First, the evapotranspiration module computes the actual evapotranspiration in the upper, lower, and deepest soil layers. Then, the total runoff generated from rainfall is calculated based on the saturation excess runoff concept, employing a basin storage capacity curve to account for the variability in runoff-contributing areas caused by the heterogeneity of underlying surfaces. Within the runoff separation module, the total runoff is partitioned into three components: surface runoff, interflow, and groundwater runoff. Last, the runoff concentration module uses the segmented continuous Muskingum method to calculate the runoff at the basin outlet. The detailed descriptions available in the literature 43 , 44 . In this paper, Particle Swarm Optimization (PSO) is chosen as the optimization algorithm for calibrating parameters. PSO is a population-based search algorithm developed by simulating the foraging behavior of bird flocks. It treats each potential solution as a particle within the search space. These particles update their velocity and position based on their own flight history and the collective experience of the entire swarm, specifically referring to the individual best solution and the global best solution. The specific procedure is as follows: First, a population of particles is randomly initialized. The fitness value of each particle is then evaluated, and based on this evaluation, the individual best and global best solutions are updated. Subsequently, the velocity and position of each particle are adjusted according to predefined update rules. This process is repeated iteratively until a predetermined termination criterion is met. A detailed description is provided in the cited reference 45 . The evaluation perspectives of flood simulation accuracy mainly include the degree of fit for flood processes and the accuracy of flood peak, flood volume, and time to peak flow. Therefore, in this study, we used the Nash–Sutcliffe efficiency ( ), the error of peak time ( ), the relative error of flood peak ( ), and the relative error of flood volume ( ) to evaluate the flood simulation accuracy. To comprehensively evaluate the flood simulation accuracy, the four metrics were integrated with equal weights into the relative membership degree ( ), which was used as the optimization objective of parameter calibration. The calculation methods for these metrics are described as follows: First, the simulation accuracy of flood events was calculated using Eq. ( 3 , 4 , 5 and 6 ). 3 4 5 6 where is the simulated flow for period , and are the simulated and observed time to peak flow for the flood event, and are the simulated and observed flood peak flows for the flood event, and and are the simulated and observed total flood volumes for the flood event, respectively. Then, the overall simulation accuracy evaluation metrics of multiple flood events were calculated: 1) Nash–Sutcliffe efficiency calculated for the flood flow of all flood events; 2) : mean absolute error in time to peak across all events; 3) : mean absolute value of the relative error of flood peak; and 4) mean absolute relative error in flood volume. Finally, , , , and were normalized and merged with equal weights into a comprehensive accuracy metric , with as the optimization objective of parameter calibration, , and larger represents higher accuracy of flood simulation. can be calculated by Eq. ( 7 ). 7 where , , , and are normalized to , , , and , respectively. Results and discuss Comparison of rainfall field estimates Figure 8 shows the rainfall field and areal rainfall in the Xiaoergou Basin estimated by VG and the sparse gauge-based Thiessen polygon method, using three representative days as example. The figure also displays the locations and rainfall values of the virtual gauges to analyze their contribution to estimating the rainfall field and areal rainfall. Fig. 8. Open in a new tab Rainfall fields estimated using the two methods (3 arbitrary days as an example), where the numbers in the lower-right corner indicate the areal rainfall of the basin. For 2011-06-03, shown in Fig. 8 a, five virtual gauges were constructed based on VG in the center of the basin. The rainfall at the virtual gauges was higher than the observed rainfall at the actual gauges, effectively supplementing the rainfall center. As a result, the areal rainfall estimated by VG was 20.29 mm, significantly higher than the 8.99 mm estimated using the sparse gauge method. For 2012-07-02, shown in Figure 8 b, the rainfall at the virtual gauges estimated by VG was close to that observed at the control stations of the Thiessen polygon at the corresponding locations. Here, the VG method served to shorten the distance between gauges to facilitate interpolation. Hence, the areal rainfall of 15.25 mm estimated using VG was close to the areal rainfall of 15.98 mm estimated by the sparse gauge method. For 2015-07-22, shown in Figure 8 c, VG set up several virtual gauges in the basin. The rainfall at the virtual gauges was lower than the observed rainfall at the actual gauges; therefore, the areal rainfall estimated using VG (11.45 mm) was significantly lower than the areal rainfall estimated using the sparse gauge method (24.23 mm). Therefore, VG can adaptively adjust the number, location, and rainfall of virtual gauges in response to the spatial characteristics of different rainfall fields and dynamically adjust the degree of utilization of precipitation products. It is impossible to judge the accuracy of the rainfall field and areal rainfall directly based on observed rainfall because no actual precipitation stations are deployed in the basin. Therefore, in the next section, areal rainfall estimates obtained from VG and the sparse gauge-based Thiessen polygon method are used respectively to drive the hydrological model for simulating the basin outlet flow, which is then evaluated against observed data from hydrological station. Comparison of the hydrological performance of areal rainfall The two areal rainfall estimates were separately used to drive the Xin’anjiang model, with parameter calibration and validation performed respectively. The accuracy of the two rainfall estimates was evaluated from the perspective of hydrological performance, thereby further illustrating the improvement provided by the multi-source precipitation products on the rainfall observations at sparse gauges in the Xiaoergou Basin. For the convenience of presentation, driving the Xin’anjiang model with the VG-estimated areal rainfall is referred to as Approach I, and driving the Xin’anjiang model with the sparse gauge-estimated areal rainfall is referred to as Approach II. Table 1 shows the hydrological performance of the two areal rainfall estimates through the flood simulation accuracies of Approaches I and II for the calibration period and the validation period, with metrics, including the , , , , and , for the calibration and validation periods. In the calibration period, the of Approach I was 0.88, significantly exceeding that of Approach II (0.61). Specifically, Approach I outperformed Approach II in terms of the four evaluation metrics that make up RMS, with the most noticeable difference observed for , at 12.99% for Approach I and 27.64% for Approach II. The accuracy of Approach I was 53% higher than that of Approach II. In the validation period, Approach I outperformed Approach II, with of 0.85 and 0.72, respectively. Among the four evaluation metrics, the greatest difference was observed for , at 1.5 days for Approach I and 3.3 days for Approach II. The two approaches performed similarly for the other metrics. Therefore, VG-estimated areal rainfall exhibited better hydrological performance than sparse gauge-estimated areal rainfall. Table 1. Accuracy of flood simulation driven by different rainfall estimates in the Xiaoergou Basin 46 . Period Evaluation metrics Approach I (VG-estimated rainfall) Approach II (sparse gauge-estimated rainfall) Calibration Nash–Sutcliffe efficiency 0.84 0.73 Error of peak time (days) 1.2 2.2 Relative error of flood peak (%) 18.03 24.66 Relative error of flood volume (%) 12.99 27.64 Comprehensive accuracy metric 0.88 0.61 Validation Nash–Sutcliffe efficiency 0.85 0.87 Error of peak time (days) 1.5 3.3 Relative error of flood peak (%) 19.70 15.72 Relative error of flood volume (%) 15.42 18.18 Comprehensive accuracy metric 0.85 0.72 Open in a new tab Figure 9 presents the flood event simulation accuracies of Approaches I and II for analyzing the reliability of the hydrologic performance of the two areal rainfall estimates. As can be seen from Fig. 9 a, using Approach I, three flood events (events 2, 4, and 13) had below 0.8, compared to seven using Approach II (events 2, 4, 7, 9, 11, 12, and 13). Figure 9 b shows the for each approach. While did not exceed 2 days for either approach, the for events 2 and 13 under Approach II was significantly higher than that for Approach I. Figure 9 c shows flood events with exceeding plus or minus 20%, with four flood events for Approach I (2, 12, 16, and 17) and eight for Approach II (1, 2, 9, 10, 11, 12, 13, and 16). Figure 9 d shows flood events with exceeding plus or minus 20%, showing three for Approach I (2, 13, and 16) and seven for Approach II (1, 2, 6, 11, 12, 13, and 16). Therefore, compared with Approach II, Approach I had a higher pass rate for flood event simulation, indicating higher reliability of the hydrological performance of areal rainfall estimated by VG. Fig. 9. Open in a new tab Accuracy of flood event simulations driven by different rainfall estimates in the Xiaoergou Basin. Analysis of the role of virtual gauges in flood simulation Taking flood events 11 and 12 as examples, we analyze the specific role of the VG in improving the accuracy of flood simulation in regions with no precipitation stations in terms of supplementing virtual gauges for large rainfall and the virtual gauge for small rainfall, respectively. Approach I slightly underestimated the flood volume and second flood peak of flood event 11, while Approach II significantly underestimated the flood peak and flood volume (Fig. 10 a). During this flood event, the areal rainfall estimated using sparse gauges was slightly lower than areal rainfall estimated using VG almost every day, so the cumulative total rainfalls of the events estimated using the sparse gauges were significantly lower than those estimated using VG. Figure 10 b presents the rainfall field and areal rainfall estimated using VG and the sparse gauge-based Thiessen polygon method, using the rainfall in the 13th period of the flood as an example. For the rainfall field on that day, four virtual gauges were set up based on VG in the central part of the basin. The rainfall at the virtual gauges was higher than that observed by the control gauges of the Thiessen polygon at those locations, which enlarged the range of the rainfall center. Therefore, the areal rainfall of 24.27 mm estimated using VG was higher than the areal rainfall of 18.84 mm estimated using the sparse gauges. Fig. 10. Open in a new tab Rainfall inputs and flood simulation results of Flood 11 for the two approaches. As shown in Fig. 11 a, the peak and volume of flood event 12 have been overestimated by both Approaches I and II, with a more pronounced effect in Approach II. In contrast to flood 11, the areal rainfall estimated using sparse gauges was slightly higher than that estimated using VG almost every day during flood 12. Figure 11 b illustrates the rainfall field and areal rainfall estimated by VG and the sparse gauge-based Thiessen polygon method in period 7 of this flood event; VG deployed several virtual gauges within the basin and the rainfall at the virtual gauges was lower than that observed at the control gauges used in the Thiessen polygon, leading to the areal rainfall estimated using VG (24.49 mm) being significantly lower than the areal rainfall estimated using the sparse gauge method (35.37 mm). Figures 10 and 11 indicate that VG can enhance flood simulation accuracy by improving the spatial distribution of rainfall estimated from sparse gauges. Fig. 11. Open in a new tab Simulation results for flood event 12 in different rainfall input scenarios. Uncertainty and variability While the VG method demonstrated a clear overall superiority, an analysis of individual flood events reveals inherent uncertainties and variability in simulation performance, as visualized in Fig. 9 . For instance, both Approaches I and II struggled to accurately simulate the peak of Flood Event 12, leading to notable overestimation. Conversely, events like Flood 11 were simulated with significantly higher accuracy using the VG method. This event-dependent variability is a common challenge in hydrological modeling and can be attributed to several factors. Floods generated by highly localized, convective storm cells or those occurring under exceptional antecedent soil moisture conditions may not be fully captured by the available precipitation inputs or may push the hydrological model structure to its limits. In terms of overall performance variability, the comprehensive accuracy metric (RMD) for Approach I ranged from 0.85 to 0.88 across calibration and validation periods, indicating relatively stable performance. In contrast, Approach II exhibited greater variability, with RMD ranging from 0.61 to 0.72. This suggests that the VG method not only improves average performance but also provides more consistent simulation accuracy across different periods and events. Conclusions We applied VG to a basin with no precipitation stations and evaluated its hydrological performance via a hydrologic model. Three key conclusions are as follows: Daily rainfall data during the flood seasons from 2010 to 2019 in the Xiaoergou Basin were employed to compare and analyze the rainfall field and areal rainfall estimated by VG and the sparse gauge-based Thiessen polygon method. Results show that VG can adaptively adjust the number, locations, and rainfall of virtual gauges in response to the spatial characteristics of different rainfall fields and dynamically adjust the degree of utilization of precipitation products. Two types of areal rainfall were used to calibrate and validate the hydrological model parameters. During both the calibration and validation periods, the hydrological model driven by areal rainfall of VG had higher flood simulation accuracy, with the greatest improvement in total flood volume accuracy (up to approximately 50%) compared to the sparse gauge method. The results indicate that VG demonstrates strong hydrological performance in the area with no precipitation stations. The specific role of VG in enhancing flood simulation accuracy in regions with no precipitation stations was analyzed by taking two flood events as examples. VG improves the rainfall field estimated using the sparse gauge method by dynamically constructing virtual gauges, thereby improving the accuracy of flood simulation. Although the VG method shows promising performance in ungauged basins, several limitations should be acknowledged. First, the accuracy of VG-based rainfall estimation remains dependent on the quality and resolution of the input precipitation products, which may vary under different satellite sensors or numerical models. Second, the representativeness of the results is constrained by the specific climatic and topographic conditions of the Xiaoergou Basin; therefore, further validation across basins with diverse rainfall regimes is needed. Future research will focus on improving the robustness of VG through adaptive parameterization and uncertainty analysis to enhance its transferability to broader hydrological applications. Author contributions Y.H.D. conceived and designed the study. X.N.L. performed data processing, hydrological modeling, and drafted the manuscript. X.L. contributed to software development and visualization. M.X. assisted in data analysis and result interpretation. R.H.L. supervised the project, provided critical revisions, and approved the final manuscript. All authors read and approved the submitted version. Funding This research was funded by “Gansu Provincial Water Resources Science and Technology Program, grant number 26GSLK135”, “The National Key Research and Development Program of China, grant number 2023YFC3006700” and “Ningbo Municipal Water Resources Science and Technology Program Project, grant number NSKA202507”. Data availability The datasets used and analyzed during the current study are available from the corresponding author on reasonable request. Declarations Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References 1. Dou, Y., Ye, L., Zhang, J., Zhang, C. & Zhou, H. Evaluation of seven Near-Real-Time Satellite-Based precipitation products for wet seasons in the Nierji Basin, China. Remote Sens. 13 , 4552. 10.3390/rs13224552 (2021). [ Google Scholar ] 2. Miao, C., Gou, J., Hu, J. & Duan, Q. Impacts of Different Satellite-Based Precipitation Signature Errors on Hydrological Modeling Performance Across China. Earth’s Future 12 , e2024EF004954. 10.1029/2024EF004954 (2024). [ Google Scholar ] 3. Chacon-Hurtado, J. C., Alfonso, L. & Solomatine, D. P. Rainfall and streamflow sensor network design: a review of applications, classification, and a proposed framework. Hydrol. Earth Syst. Sci. 21 , 3071–3091. 10.5194/hess-21-3071-2017 (2017). [ Google Scholar ] 4. Hou, T., Kong, F., Chen, X., Lei, H. & Hu, Z. Evaluation of radar and automatic weather station data assimilation for a heavy rainfall event in Southern China. Adv. Atmos. Sci. 32 , 967–978. 10.1007/s00376-014-4155-7 (2015). [ Google Scholar ] 5. Luo, Z. et al. A new method to improve precipitation estimates by blending multiple satellite/reanalysis-based precipitation products and considering observations and terrestrial water budget balance. J. Hydrol. 635 , 131188. 10.1016/j.jhydrol.2024.131188 (2024). [ Google Scholar ] 6. Gavahi, K., Foroumandi, E. & Moradkhani, H. A deep learning-based framework for multi-source precipitation fusion. Remote Sens. Environ. 295 , 113723. 10.1016/j.rse.2023.113723 (2023). [ Google Scholar ] 7. Tang, M. et al. Coupling distributed hydrological model with spatially discrete altimetry data for distributed prediction in ungauged basins. J. Hydrol. 662 , 134103. 10.1016/j.jhydrol.2025.134103 (2025). [ Google Scholar ] 8. Cai, C., Wang, J. & Li, Z. Assessment and modelling of uncertainty in precipitation forecasts from TIGGE using fuzzy probability and bayesian theory. J. Hydrol. 577 , 123995. 10.1016/j.jhydrol.2019.123995 (2019). [ Google Scholar ] 9. Boluwade, A. Spatial-Temporal Evaluation of Satellite-Derived Rainfall Estimations for Water Resource Applications in the Upper Congo River Basin. Remote Sensing 16 , 3868 (2024). [ Google Scholar ] 10. Gao, Z. et al. Evaluation of Multiple Satellite, Reanalysis, and Merged Precipitation Products for Hydrological Modeling in the Data-Scarce Tributaries of the Pearl River Basin, China. Remote Sensing 15 , 5349 (2023). [ Google Scholar ] 11. Chen, H. et al. A novel Real-Time error adjustment method with considering four factors for correcting hourly Multi-Satellite precipitation estimates. IEEE Trans. Geosci. Remote Sens. 60 , 1–11. 10.1109/TGRS.2021.3131238 (2022). [ Google Scholar ] 12. Martel, J. L. et al. Improved historical reconstruction of daily flows and annual maxima in gauged and ungauged basins. J. Hydrol. 623 , 129777. 10.1016/j.jhydrol.2023.129777 (2023). [ Google Scholar ] 13. Vernimmen, R. R. E., Hooijer, A., Mamenun, Aldrian, E., van Dijk, A. & I. J. M. Evaluation and bias correction of satellite rainfall data for drought monitoring in Indonesia. Hydrol. Earth Syst. Sci. 16 , 133–146. 10.5194/hess-16-133-2012 (2012). [ Google Scholar ] 14. Chao, L. et al. Geographically weighted regression based methods for merging satellite and gauge precipitation. J. Hydrol. 558 , 275–289. 10.1016/j.jhydrol.2018.01.042 (2018). [ Google Scholar ] 15. Chen, Y. et al. A new downscaling-integration framework for high-resolution monthly precipitation estimates: combining rain gauge observations, satellite-derived precipitation data and geographical ancillary data. Remote Sens. Environ. 214 , 154–172. 10.1016/j.rse.2018.05.021 (2018). [ Google Scholar ] 16. Bai, X., Wu, X. & Wang, P. Blending long-term satellite-based precipitation data with gauge observations for drought monitoring: considering effects of different gauge densities. J. Hydrol. 577 , 124007. 10.1016/j.jhydrol.2019.124007 (2019). [ Google Scholar ] 17. Yan, X. et al. A Downscaling–Merging scheme for improving daily Spatial precipitation estimates based on random forest and Cokriging. Remote Sens. 13 , 2040. 10.3390/rs13112040 (2021). [ Google Scholar ] 18. Cheng, S., Wang, W. & Chen, Z. Blending gauge, multi-satellite and atmospheric reanalysis precipitation products to facilitate drought monitoring. J. Hydrol. 647 , 132254. 10.1016/j.jhydrol.2024.132254 (2025). [ Google Scholar ] 19. Beck, H. E. et al. MSWEP V2 global 3-Hourly 0.1° precipitation: methodology and quantitative assessment. Bull. Am. Meteorol. Soc. 100 , 473–500. 10.1175/BAMS-D-17-0138.1 (2019). [ Google Scholar ] 20. Yumnam, K., Kumar Guntu, R., Rathinasamy, M. & Agarwal, A. Quantile-based bayesian model averaging approach towards merging of precipitation products. J. Hydrol. 604 , 127206. 10.1016/j.jhydrol.2021.127206 (2022). [ Google Scholar ] 21. Rahman, K., Shang, S., Shahid, M., Wen, Y. & Khan, Z. Application of a dynamic clustered bayesian model averaging (DCBA) algorithm for merging multisatellite precipitation products over Pakistan. J. Hydrometeorol. 21 , 17–37. 10.1175/JHM-D-19-0087.1 (2020). [ Google Scholar ] 22. Zhang, Y. et al. QRF4P-NRT: Probabilistic Post-Processing of Near-Real-Time Satellite Precipitation Estimates Using Quantile Regression Forests. Water Resour. Res. 58 , e2022WR032117. 10.1029/2022WR032117 (2022). [ Google Scholar ] 23. Xu, Y., Tang, G., Li, L. & Wan, W. Multi-source precipitation Estimation using machine learning: clarification and benchmarking. J. Hydrol. 635 , 131195. 10.1016/j.jhydrol.2024.131195 (2024). [ Google Scholar ] 24. Wang, C., Tang, G. & Gentine, P. PrecipGAN: merging microwave and infrared data for satellite precipitation Estimation using generative adversarial network. Geophys. Res. Lett. 48 , e2020GL092032. 10.1029/2020GL092032 (2021). [ Google Scholar ] 25. Kossieris, P. et al. Precipitation data merging via machine learning: revisiting conceptual and technical aspects. J. Hydrol. 637 , 131424. 10.1016/j.jhydrol.2024.131424 (2024). [ Google Scholar ] 26. Fan, Z. et al. A comparative study of four merging approaches for regional precipitation Estimation. IEEE Access. 9 , 33625–33637. 10.1109/ACCESS.2021.3057057 (2021). [ Google Scholar ] 27. Zhang, L. et al. Merging multiple satellite-based precipitation products and gauge observations using a novel double machine learning approach. J. Hydrol. 594 , 125969. 10.1016/j.jhydrol.2021.125969 (2021). [ Google Scholar ] 28. Papacharalampous, G. Comparison of Tree-Based Ensemble Algorithms for Merging Satellite and Earth-Observed Precipitation Data at the Daily Time Scale. Hydrology 10 , 50. 10.3390/hydrology10020050 (2023). [ Google Scholar ] 29. Nguyen, G. V. et al. Application of random forest algorithm for merging multiple satellite precipitation products across South Korea. Remote Sens. 13 , 4033. 10.3390/rs13204033 (2021). [ Google Scholar ] 30. Yang, X. et al. Correcting the bias of daily satellite precipitation estimates in tropical regions using deep neural network. J. Hydrol. 608 , 127656. 10.1016/j.jhydrol.2022.127656 (2022). [ Google Scholar ] 31. Chen, S. et al. Improving daily Spatial precipitation estimates by merging gauge observation with multiple satellite-based precipitation products based on the geographically weighted ridge regression method. J. Hydrol. 589 , 125156. 10.1016/j.jhydrol.2020.125156 (2020). [ Google Scholar ] 32. Dou, Y., Ye, L., Ai, J., Zhang, C. & Zhou, H. A framework for merging precipitation retrievals and gauge-based observations based on a novel concept namely virtual gauges. J. Hydrol. 620 , 129506. 10.1016/j.jhydrol.2023.129506 (2023). [ Google Scholar ] 33. Kubota, T. et al. Satellite Precipitation Measurement: Volume 1 355–373 (Springer International Publishing, 2020). [ Google Scholar ] 34. Kubota, T. et al. Global precipitation map using Satellite-Borne microwave radiometers by the GSMaP project: production and validation. IEEE Trans. Geosci. Remote Sens. 45 , 2259–2275. 10.1109/TGRS.2007.895337 (2007). [ Google Scholar ] 35. Huffman, G. J. et al. Integrated Multi-satellitE Retrievals for GPM (IMERG) Technical Documentation (NASA Goddard Space Flight Center, 2019). [ Google Scholar ] 36. Huffman, G. J. et al. NASA Global Precipitation Measurement (GPM) Integrated Multi-Satellite Retrievals for GPM (IMERG). Algorithm Theoretical Basis Doc . Version 06. (2019). https://docserver.gesdisc.eosdis.nasa.gov/public/project/GPM/IMERG_ATBD_V06.pdf 37. Li, Z. & Han, W. Impact of HY-2B SMR radiance assimilation on CMA global medium-range weather forecasts. Q. J. R. Meteorol. Soc. 150 , 937–957. 10.1002/qj.4630 (2024). [ Google Scholar ] 38. Berner, J., Shutts, G., Leutbecher, M., Palmer, T. A. & Spectral Stochastic,. Kinetic Energy Backscatter Scheme and Its Impact on Flow-Dependent Predictability in the ECMWF Ensemble Prediction System. J. Atmospheric Sci. - J. ATMOS. SCI. 10.1175/2008JAS2677.1 (2009). [ Google Scholar ] 39. Buizza, R., Leutbecher, M. & Isaksen, L. Potential use of an ensemble of analyses in the ECMWF ensemble prediction system. Q. J. R. Meteorol. Soc. 134 , 2051–2066. 10.1002/qj.346 (2008). [ Google Scholar ] 40. Liu, M., Zuo, J., Tan, J. & Liu, D. Comparing and optimizing four machine learning approaches to Radar-Based quantitative precipitation Estimation. Remote Sens. 16 , 4713. 10.3390/rs16244713 (2024). [ Google Scholar ] 41. Zhang, Y. et al. Impacts of reference precipitation on the assessment of global precipitation measurement precipitation products. Remote Sens. 17 , 624. 10.3390/rs17040624 (2025). [ Google Scholar ] 42. Croley, T. E. & Hartmann, H. C. Resolving Thiessen polygons. J. Hydrol. 76 , 363–379. 10.1016/0022-1694(85)90143-X (1985). [ Google Scholar ] 43. Ren-Jun, Z. The Xinanjiang model applied in China. J. Hydrol. 135 , 371–381. 10.1016/0022-1694(92)90096-E (1992). [ Google Scholar ] 44. Zhao, J., Duan, Y., Hu, Y., Li, B. & Liang, Z. The numerical error of the Xinanjiang model. J. Hydrol. 619 , 129324. 10.1016/j.jhydrol.2023.129324 (2023). [ Google Scholar ] 45. Kennedy, J. & Eberhart, R. in Proceedings of ICNN’95 - International Conference on Neural Networks. 1942–1948 vol.1944. 46. Liu, H. et al. Performance of datasets in hydrological simulation in various basin scales: an investigation on hydrological lumped effect in the Lancang-Mekong region. J. Hydrology: Reg. Stud. 62 , 102769. 10.1016/j.ejrh.2025.102769 (2025). [ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Data Availability Statement The datasets used and analyzed during the current study are available from the corresponding author on reasonable request. Articles from Scientific Reports are provided here courtesy of Nature Publishing Group ACTIONS View on publisher site PDF (3.5 MB) Cite Collections Permalink PERMALINK Copy RESOURCES Similar articles Cited by other articles Links to NCBI Databases Cite Copy Download .nbib .nbib Format: AMA APA MLA NLM Add to Collections Create a new collection Add to an existing collection Name your collection * Choose a collection Unable to load your collection due to an error Please try again Add Cancel Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top