Bias Correction of Satellite-Derived Climatic Datasets for Water Balance Estimation

Abstract

The satellite-derived climatic variables offer extensive spatial and temporal coverage for research; however, their inherent biases can subsequently reduce their accuracy for water balance estimate. This study evaluates the effectiveness of bias correction in improving the Tropical Rainfall Measuring Mission (TRMM) rainfall and the Global Land Data Assimilation System (GLDAS) land surface temperature (LST) data and illustrates their long-term (2000–2019) hydrological assessment. The novelty lies in coupling the bias-corrected climate variables with the Thornthwaite–Mather water balance model as well as land use land cover (LULC) for improved predictive hydrological modeling. Bias correction significantly improved the agreement with ground observations, enhancing the R² value from 0.89 to 0.96 for temperature and from 0.73 to 0.80 for rainfall, making targeted inputs ready to predict hydrological dynamics. LULC mapping showed a predominance of agricultural land (64.5%) in the area followed by settlements (20.0%), forest (7.3%), barren land (6.5%), and water bodies (1.7%), with soils being silt loam, clay loam, and clay. With these improved datasets, the model found seasonal rise in potential evapotranspiration (PET), peaking at 120.7 mm in June, with actual evapotranspiration (AET) following a similar trend. The annual water balance showed a surplus of 523.8 mm and deficit of 121.2 mm, which proves that bias correction not only enhances the reliability of satellite data but also reinforces the credibility of hydrological indicators, with a direct, positive impact on evidence-based irrigation planning and flood mitigation and drought management, especially in data-scarce regions.

1. Introduction

Accurate assessment of hydrological components remains one of the most persistent challenges in water resources research, particularly in regions with sparse ground-based meteorological observations. In recent decades, climate change has intensified variability in precipitation and temperature, increasing uncertainty in water availability and placing greater demands on precise and reliable hydrological assessments [1,2,3]. Traditional hydrological models rely heavily on dense weather station networks, which are often inadequate in remote or developing regions [4,5]. This limitation necessitates the integration of remote sensing products into hydrological modeling, enabling improved spatial and temporal coverage where observational gaps persist.

Satellite-based climatic datasets are reliable alternatives to conventional station records [6,7,8,9]. The Tropical Rainfall Measuring Mission (TRMM) provides high-resolution precipitation data with near-global coverage [10,11]. It has been validated in many tropical and subtropical regions. However, regional biases still occur, particularly in areas with high rainfall intensity or complex terrain [12,13,14,15,16]. The Global Land Data Assimilation System (GLDAS) combines satellite observations with land surface models. It produces climate variables that better capture spatial variability than interpolated station data, especially in poorly monitored basins. Many studies in diverse climatic and physiographic settings have confirmed the accuracy of these datasets when compared with ground observations [17,18,19,20,21,22]. This evidence supports their suitability for hydrological modeling and water resource studies.

Despite their advantages, satellite datasets are not entirely free from error. Systematic biases can arise from sensor calibration limitations, retrieval algorithm uncertainties, and region-specific atmospheric conditions [23,24]. If uncorrected, these biases propagate through hydrological simulations, leading to over- or underestimation of key water balance components. Bias correction is therefore an essential step in ensuring the accuracy of satellite-derived climatic inputs, especially for long-term basin-scale assessments [25,26,27,28].

In this context, the Thornthwaite–Mather water balance framework offers a practical approach for data-scarce regions due to its minimal input requirements and ability to integrate bias-corrected satellite datasets [29,30,31]. However, its performance depends heavily on the quality of input variables. While satellite datasets have been applied in water balance studies globally, few investigations have integrated bias-corrected TRMM and GLDAS products within this framework for multi-decadal hydrological analysis in eastern India [32,33,34,35]. The existing studies often rely on uncorrected satellite records or short-term datasets, limiting their ability to capture decadal-scale hydrological variability essential for informed water management [36,37].

To address research gaps in long-term hydrological assessment in data-scarce regions, this study advances the state of knowledge by explicitly integrating bias-corrected TRMM precipitation and GLDAS land surface temperature into the Thornthwaite–Mather water balance framework, thereby improving the reliability of long-term hydrological assessments in such regions. The specific objectives are (i) to evaluate the effectiveness of bias correction in improving the accuracy of satellite-derived climatic variables, (ii) to quantify seasonal and annual water balance components over a multi-decadal period, and (iii) to assess the implications of improved climatic datasets for basin-scale hydrological assessments. By combining satellite-based climatic datasets with bias correction and GIS-supported spatial analysis, this research advances hydrological modeling capabilities in data-scarce regions. The outcomes provide a stronger scientific basis for climate-resilient water resource management and can inform strategies to mitigate water scarcity risks, particularly in regions vulnerable to climatic variability.

2. Materials and Methods

2.1. Study Area Description

Samastipur District (Figure 1), located in North Bihar, extends between 25°30′ to 26°05′ N latitude and 85°37′50″ to 86°23′30″ E longitude, encompassing an area of approximately 2904 km² at an average elevation of ~52 m above mean sea level (MSL). The district is geographically bounded by the Bagmati River in the north, Vaishali and Muzaffarpur Districts in the west, the Ganges River in the south, and Begusarai and Khagaria Districts in the east [38]. The salient geographical, hydro-climatological, and agricultural attributes of the study area are presented in

Table 1. Summary of Key Characteristics of Samastipur District, Bihar.

Category	Attribute	Details
Geographical	Location Coordinates	25°30′–26°05′ N; 85°37′50″–86°23′30″ E
	Area	2904 km2
	Elevation	~52 m above mean sea level (MSL)
	Boundaries	North: Bagmati River South: Ganges River East: Begusarai and Khagaria Districts West: Vaishali and Muzaffarpur Districts
Hydro-climatological	Major Rivers	Burhi Gandak (tributary of Ganges River)
	Groundwater Depth (Pre-monsoon)	7.2–11.1 m below ground level (m bgl)
	Groundwater Depth (Post-monsoon)	3.2–6.4 m bgl
	Rainfall	1100–1250 mm/year
	Climate Type	Semi-arid to subtropical monsoon
	Temperature Range	6 °C (winter min)–45 °C (summer max)
Agricultural	Agro-Ecological Zone	Zone I (North-West Alluvial Plains)
	Soil Type	Fertile alluvial soil; clay loam texture
	Soil pH	5.8–8.0
	Soil Calcium Carbonate (CaCO3) Content	3–10%
	Major Crops	Rice (30%), Wheat (31%), Maize (32%), Sugarcane, Potatoes, Pulses, Vegetables

.

2.2. Data Collection and Processing

The analysis utilizes multiple datasets covering a 20-year period from 2000 to 2019 to estimate water balance components, incorporating satellite-derived precipitation, LST, and multispectral imagery. The TRMM 3B43 dataset provides monthly rainfall estimates, while GLDAS Noah LST (GLDAS-2.1) supplies LST data for PET estimation [39,40].

Additionally, high-resolution LANDSAT-8 imagery for land cover classification and soil data from National Bureau of Soil Survey and Land Use Planning (NBSS and LUP), Nagpur, India, is used for soil texture characterization. A summary of the datasets used in this study is presented in

Table 2. Data used in the study.

Dataset	Temporal Coverage	Spatial Resolution	Key Parameters	Source
TRMM 3B43 Precipitation	1998–2020	0.25° × 0.25°	Monthly Rainfall Estimates	https://disc.gsfc.nasa.gov/datasets/TRMM_3B43_7/summary?keywords=trmm (accessed on 12 March 2021)
GLDAS Noah LST (GLDAS-2.1)	2000–Present	0.25° × 0.25°	Land Surface Temperature	https://disc.gsfc.nasa.gov/datasets?keywords=GLDAS (accessed on 25 March 2021)
LANDSAT-8	(Acquisition Year: 2019)	30 m (OLI), 15 m (PAN), and 100 m (TIRS)	Multispectral and Thermal Bands	https://earthexplorer.usgs.gov/ (accessed on 5 June 2021)
Soil Data	-	Varies	Soil Texture; Classification	https://bhoomigeoportal-nbsslup.in/ (accessed on 19 May 2021)

.

2.3. Rainfall and Temperature

Monthly TRMM rainfall data and LST from GLDAS were extracted for all grid points within the study area using Esri’s ArcMap Model Builder tool. Daily climatic variables, including maximum and minimum temperatures, pan evaporation, and sunshine hours, were obtained from the meteorological station of Dr. Rajendra Prasad Central Agricultural University (RPCAU), Pusa, covering a 20-year period from 2000 to 2019. The daily data were processed and aggregated to a monthly scale for validating satellite-based climatic variables.

Due to the limited network of meteorological stations within the district, the station located at Pusa was selected for comparison and validation. Following Subramanya [41], the observed and satellite-derived temperature and rainfall data for selected grid points (GP-44 to GP-47, GP-53 to GP-56, GP-60 to GP-63, GP-65, and GP-66) within a circumferential area of 3000 km² around the station at Pusa (Figure 1) were considered for analysis and validation. This approach ensured that the comparison accounted for spatial variability in a predominantly flat terrain. Statistical methods such as Pearson correlation coefficient (PCC), root mean square error (RMSE), mean error (ME), and bias (B), as presented in

Table 3. Statistical parameters used for validation.

Metric	Formula	Description
PCC	$PCC = {\displaystyle \frac{{\sum }_{j=1}^N\left\{\left(O_{ij}-{\overline{O}}_i\right)\left(S_{ij}-\overline{S_i}\right)\right\}}{\sqrt{{\sum }_{j=1}^N{\left(O_{ij}-{\overline{O}}_i\right)}^2}\sqrt{{\sum }_{j=1}^N{\left(S_{ij}-\overline{S_i}\right)}^2}}}$	Measures the linear association between observed and satellite-derived climatic variables. A value of 1 indicates perfect correlation.
RMSE	$RMSE = \sqrt{{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{j=1}^N}\left(S_{ij}-O_{ij}\right)}^2}$	Quantifies the average difference between observed and satellite-derived climatic variables. Zero indicates no systematic error.
ME	$ME={\displaystyle \frac{1}{N}}{\displaystyle \sum _{j=1}^N}\left(S_{ij}-O_{ij}\right)$	Measures the magnitude of differences between observed and satellite-derived data. Lower values indicate better agreement.
Bias	$B = {\displaystyle \frac{{\sum }_{j=1}^N{S}_{ij}}{{\sum }_{j=1}^N{O}_{ij}}}$	Evaluates how well the mean values of observed and satellite-derived variables align. A value of 1 indicates perfect agreement.

Notes: ${\overline{O}}_i$ = mean climatic variables measured at meteorological station in the ith year; $\overline{O_{ij}}$ = climatic variables measured at meteorological in ith year and jth month; $S_{ij}$ = climatic variables extracted from satellites products in ith year and jth month; $\overline{S_i}$ = mean of climatic variables extracted from satellites products in ith year; j = number of months (1 to 12) in ith year; N = total number of months considered for correlation analysis.

, were applied to evaluate the relationship between satellite-derived climatic variables and ground-based observed data [42,43,44,45,46]. Identified biases in the satellite-derived climatic variables were subsequently corrected using the linear scaling (LS) technique.

2.4. Linear Scaling Method of Bias Correction

In this study, the linear scaling method was employed to perform monthly-scale bias correction of satellite-derived meteorological variables. This approach was selected for its methodological simplicity, low computational requirements, and demonstrated effectiveness in correcting systematic mean biases while preserving the temporal structure of the original data [47,48,49,50,51,52]. Unlike more complex techniques such as quantile mapping or distribution mapping, which require detailed statistical information and extensive observational datasets, LS relies on minimal input, making it particularly suitable for data-scarce regions like Samastipur. Furthermore, for hydrological applications focused on monthly or seasonal means, it has been shown to produce results comparable to those of more sophisticated methods, making it a practical and efficient choice for large-scale or long-term studies. The LS method, which considers the mean of long-term observed and extracted climatic variables to correct the climatic variables, is expressed as follows:

$${SCV}_{ij} = {{SCV}^{\ast }}_{ij}\times {\displaystyle \frac{{\overline{O}}_{ij}}{{\overline{S}}_{ij}}}$$

(1)

where ${SCV}_{ij}$ = bias free satellite based climatic variables in jth months of ith year; ${{SCV}^{\ast }}_{ij}$ = satellite based climatic variable in jth months of ith year; ${\overline{O}}_{ij}$ = long term mean of observed climatic variable, in ith year and jth month; ${\overline{S}}_{ij}$ = long term climatic variables extracted from satellite products in ith year and jth month.

2.5. Land Use Land Cover (LULC) Classification and Accuracy Assessment

The LULC analysis was undertaken to delineate the spatial distribution of different land use features and to examine their potential influence on hydrological dynamics and watershed-scale processes. For this purpose, LULC classification was conducted for the year 2019 utilizing Landsat-8 data. A robust, object-oriented hybrid classification framework was employed, wherein the satellite imagery was first segmented into spectrally and spatially homogeneous objects. Subsequently, supervised classification was implemented using the Maximum Likelihood Classifier (MLC) [53]. The classification scheme identified five dominant LULC categories, namely agricultural land, barren land, forest land, settlements, and water bodies.

Accuracy assessment of the classification results was conducted using both visual and statistical methods. For visual validation, the classified map was compared with high-resolution imagery from Google Earth, enabling qualitative assessment of classification accuracy through direct feature comparison. For statistical evaluation, an error matrix (confusion matrix) was constructed using 90 randomly selected validation samples, stratified across all LULC classes. Reference data were derived from field surveys and existing high-resolution ancillary sources. Accuracy metrics such as overall accuracy, producer’s and user’s accuracy, and the Kappa coefficient were computed.

The kappa coefficient (K) was used to quantify the agreement between classified data and reference data while accounting for the possibility of random agreement. It is calculated using the following formula:

$$\mathrm{K}={\displaystyle \frac{\mathrm{N}{\sum }_{\mathrm{i}=1}^{\mathrm{r}}{\mathrm{x}}_{\mathrm{i}\mathrm{i}}-{\sum }_{\mathrm{i}=1}^{\mathrm{r}}\left({\mathrm{x}}_{\mathrm{i}+}\times {\mathrm{x}}_{+\mathrm{i}}\right)}{{\mathrm{N}}^2-{\sum }_{\mathrm{i}=1}^{\mathrm{r}}\left({\mathrm{x}}_{\mathrm{i}+}\times {\mathrm{x}}_{+\mathrm{i}}\right)}}$$

(2)

where r = number of rows in the error matrix; x_ii = number of observations in i th row and column i th (on the major diagonal); x_i+ = total number of observations in rows i (shown as marginal total to right of the matrix); x_+i = total number of observations in column i (shown as marginal total at bottom of the matrix); N = total number of observations included in matrix. Kappa is a true dimensionless number ranging from 0 to 1, with a value close to 1 indicating best acceptance and a value of −1 indicating absolute disagreement (

Table 4. Interpretation of K value.

K-Value	Rating	Agreement
≥0.81	Excellent	Almost perfect agreement
0.80–0.61	Good	Substantial agreement
0.60–0.41	Moderate	Moderate agreement
0.40–0.21	Poor	Fair agreement
0.1–0.20	Bad	Slight agreement
0.0	Very bad	Less than chance agreement

).

2.6. Thornthwaite–Mather Water Balance Model

The Thornthwaite–Mather water balance model [54,55] was applied to estimate monthly water balance components such as actual evapotranspiration (AET), soil moisture storage, water deficit, and surplus. The model considers a limited capacity of soil to hold water and tracks changes based on the difference between precipitation and potential evapotranspiration (PET). When rainfall is greater than PET, soil moisture is restored until the storage capacity is full, and any extra water is treated as runoff or deep percolation. On the other hand, when PET is higher than rainfall, water is drawn from the soil store, leading to a deficit [56,57,58,59].

2.6.1. Assessment of Surplus and Deficit Water

The spatio-temporal availability of water (deficit or surplus) was determined as follows:

Water surplus = P − PET,

Water deficit = PET − AET,

where PET = monthly potential evapotranspiration (mm per month); AET = monthly actual evapotranspiration (mm per month); P = monthly rainfall.

The AET was computed on a monthly basis as follows:

AET = ∆AS + P, if ∆AS < 0

AET = PET, if ∆AS > 0

where ∆AS = change in actual storage of soil moisture (ASSM) for all the months and is calculated as

$${∆AS}_{month}={ASSM}_{month}-{ASSM}_{previous month}$$

The actual storage of soil moisture (ASSM) for each month was calculated as follows:

$$\mathrm{A}\mathrm{S}\mathrm{S}\mathrm{M}=\mathrm{A}\mathrm{W}\mathrm{C}\times {\mathrm{e}}^{{\displaystyle \frac{\mathrm{P}-\mathrm{P}\mathrm{E}\mathrm{T}}{\mathrm{A}\mathrm{W}\mathrm{C}}}}$$

(3)

where AWC = available water capacity of the soil, and P = rainfall.

2.6.2. Determination of Available Water Capacity (AWC)

The AWC, representing the soil moisture storage potential, was estimated using the empirical approach proposed by Thornthwaite and Mather [60], which relates AWC to LULC classes, soil texture, and corresponding rooting depths. This method provides standardized AWC values for various combinations of LULC and soil texture, thereby simplifying the estimation process in data-scarce regions. Although the approach assumes uniform soil properties and rooting depths within each LULC–soil combination, such assumptions are widely adopted in large-scale hydrological modeling and are justified by the empirical foundation and established application of the Thornthwaite and Mather method.

2.6.3. Determination of PET

The Thornthwaite model [60] was used to calculate monthly PET using the monthly temperature over the grid points under the study area (Figure 2). Mean monthly temperature is derived from GLDAS LST, and the annual heat index is determined using the corrected LST as follows:

$$PET=16 C {\left(10 {\displaystyle \frac{T}{I}}\right)}^a$$

(4)

where T = mean monthly temperature (°C); I = annual heat index for the 12 months in a year; $I = {\sum }_1^{12}i$, I is the monthly heat index and can be determined as

$$i={\left({\displaystyle \frac{\mathrm{T}}{5}}\right)}^{1.514}$$

$$\mathrm{a}=6.75\times {10}^{-7}{\mathrm{I}}^3-7.71\times {10}^{-5}{\mathrm{I}}^2+1.792\times {10}^{-2}\mathrm{I}+0.49239$$

(5)

C = correction factor for each month, calculated as

$$C={\displaystyle \frac{d}{12}}\left({\displaystyle \frac{m}{30}}\right)$$

(6)

where m = number of days in a month, and d = monthly mean daily duration of bright sunshine hour.

2.6.4. Thematic Map Generation

The soil map for the study area was developed using spatial datasets obtained from the NBSS and LUP. These datasets were processed and analyzed to delineate major soil types and their relevant physical properties for hydrological assessment. The mapping of PET, AET, water surplus, and water deficit were generated by estimating water balance components at each grid point across the study area using bias-corrected climatic variables. The resulting gridded data were interpolated using the inverse distance weighted (IDW) method to produce spatially continuous thematic maps. All spatial analyses and map generation were carried out using ArcGIS Desktop version 10.8 (https://www.esri.com/en-us/arcgis/products/arcgis-desktop/overview accessed on 21 September 2021). All maps were georeferenced and standardized to a common coordinate system to ensure spatial consistency in subsequent analyses.

3. Results and Discussion

3.1. Comparison and Validation of LST

The long-term (2000–2019) SD, CV, and mean of observed air temperature were 5.63 °C, 0.226, and 24.95 °C, respectively, across the selected grid points. In comparison, the corresponding values for LST derived from GLDAS were 7.03 °C (SD), 0.271 (CV), and 25.94 °C (mean) for the same grid locations. After implementing LS on the LST derived from GLDAS, the bias-corrected LST exhibited a mean of 24.95 °C, SD of 5.68 °C, and CV of 0.228 across selected grid points (Appendix A 

Table A1. Basic Comparison statistics of observed temperature and extracted and bias-corrected LST.

Grid Points	Observed Temperature			Extracted LST (Before Bias Correction)			Extracted LST (After Bias Correction)
	CV	SD (°C)	Mean (°C)	CV	SD (°C)	Mean (°C)	CV	SD (°C)	Mean (°C)
GP-44	0.23	5.63	24.95	0.27	7.03	25.94	0.23	5.68	24.95
GP-45	0.23	5.63	24.95	0.27	7.01	25.90	0.23	5.68	24.95
GP-46	0.23	5.63	24.95	0.27	6.97	25.86	0.23	5.68	24.95
GP-47	0.23	5.63	24.95	0.27	6.94	25.82	0.23	5.68	24.95
GP-53	0.23	5.63	24.95	0.27	7.00	25.83	0.23	5.68	24.95
GP-54	0.23	5.63	24.95	0.27	6.97	25.80	0.23	5.68	24.95
GP-55	0.23	5.63	24.95	0.27	6.94	25.76	0.23	5.68	24.95
GP-56	0.23	5.63	24.95	0.27	6.90	25.73	0.23	5.68	24.95
GP-60	0.23	5.63	24.95	0.27	7.00	25.67	0.23	5.68	24.95
GP-61	0.23	5.63	24.95	0.27	6.98	25.64	0.23	5.68	24.95
GP-62	0.23	5.63	24.95	0.27	6.94	25.61	0.23	5.68	24.95
GP-63	0.23	5.63	24.95	0.27	6.89	25.59	0.23	5.68	24.95
GP-65	0.23	5.63	24.95	0.27	6.98	25.48	0.23	5.68	24.95
GP-66	0.23	5.63	24.95	0.27	6.94	25.46	0.23	5.68	24.95

).

The findings indicate that the mean observed temperature from GLDAS is slightly higher than the observed air temperature and with greater variability, as evidenced by its higher SD and CV values. This suggests that while GLDAS LST captures overall temperature trends, it exhibits inherent biases that necessitate appropriate correction techniques to enhance its accuracy for climate and environmental assessments.

The statistical comparison between observed and bias-corrected temperature is represented in Appendix A 

Table A2. Comparison statistics before and after bias correction of extracted LST.

Grid Points	Before Bias Correction of LST						After Bias Correction of LST
	PCC	RMS E (°C)	ME (°C)	Bias	Linear Regression		PCC	RMS E (°C)	ME (°C)	Bias	Linear Regression
					R2	Slope					R2	Slope
GP-44	0.94	2.74	0.99	1.04	0.89	1.18	0.98	1.00	0.00	1.00	0.96	0.99
GP-45	0.94	2.71	0.95	1.04	0.89	1.17	0.98	1.00	0.00	1.00	0.96	0.99
GP-46	0.94	2.68	0.91	1.04	0.89	1.17	0.98	1.00	0.00	1.00	0.96	0.99
GP-47	0.94	2.64	0.87	1.03	0.89	1.16	0.98	1.00	0.00	1.00	0.96	0.99
GP-53	0.94	2.67	0.88	1.04	0.89	1.17	0.98	1.00	0.00	1.00	0.96	0.99
GP-54	0.94	2.64	0.85	1.03	0.89	1.17	0.98	1.00	0.00	1.00	0.96	0.99
GP-55	0.94	2.61	0.81	1.03	0.89	1.16	0.98	1.00	0.00	1.00	0.96	0.99
GP-56	0.94	2.58	0.78	1.03	0.89	1.16	0.98	1.00	0.00	1.00	0.96	0.99
GP-60	0.94	2.61	0.72	1.03	0.89	1.17	0.98	1.00	0.00	1.00	0.96	0.99
GP-61	0.94	2.59	0.69	1.03	0.89	1.17	0.98	1.00	0.00	1.00	0.96	0.99
GP-62	0.94	2.56	0.66	1.03	0.89	1.16	0.98	1.00	0.00	1.00	0.96	0.99
GP-63	0.94	2.54	0.63	1.03	0.89	1.16	0.98	1.00	0.00	1.00	0.96	0.99
GP-65	0.94	2.54	0.53	1.02	0.89	1.17	0.98	1.00	0.00	1.00	0.96	0.99
GP-66	0.94	2.52	0.51	1.02	0.89	1.16	0.980	1.00	0.00	1.00	0.96	0.99

. LST bias correction significantly improved LST accuracy. Before correction, PCC values were around 0.94, with a bias of 1.04 and RMSE exceeding 2.7 °C (Figure 3a). Post correction, PCC increased to 0.98, bias was reduced to 1, and RMSE dropped to 1.2 °C. Linear regression results showed an improved slope of 0.98 and R² of 0.96, indicating enhanced agreement between corrected LST and observed data (Figure 3b). These improvements confirm the effectiveness of bias correction in reducing errors and increasing predictive accuracy.

3.2. Comparison and Validation of Rainfall

The long-term (2000–2019) analysis of observed monthly rainfall across all selected grid points showed a mean of 94.91 mm, with SD of 131.61 mm and CV of 1.39. In comparison, the mean monthly rainfall derived from the TRMM dataset ranged between 88.70 mm and 96.66 mm, while the corresponding SD and CV values varied from 98.41 mm to 129.58 mm and 1.10 to 1.38, respectively. Following bias correction, the mean of the bias-adjusted rainfall estimates closely matched the observed mean (94.91 mm) for all grid points except GP-44, which recorded a slightly higher mean of 95.81 mm. The SD of bias-corrected rainfall estimates was lowest at GP-47 (120.22 mm) and highest at GP-44 (123.46 mm). Similarly, CV was minimum (1.27) at GP-46, GP-47, GP-55, and GP-56, while maximum values (1.29) were observed at GP-44, GP-60, and GP-66 (Appendix A 

Table A3. Basic comparison statistics of observed, extracted, and bias-corrected rainfall estimates.

Grid Points	Observed Rainfall			Extracted Rainfall			Bias-Corrected Rainfall
	Mean (mm)	SD (mm)	CV	Mean (mm)	SD (mm)	CV	Mean (mm)	SD (mm)	CV
GP-44	94.91	131.61	1.39	89.56	118.41	1.33	95.81	123.46	1.29
GP-45	94.91	131.61	1.39	88.70	99.0	1.10	94.91	121.04	1.28
GP-46	94.91	131.61	1.39	88.94	98.41	1.38	94.91	120.53	1.27
GP-47	94.91	131.61	1.39	89.19	117.29	1.32	94.91	120.22	1.27
GP-53	94.91	131.61	1.39	90.70	120.98	1.33	94.91	121.48	1.28
GP-54	94.91	131.61	1.39	90.79	120.31	1.33	94.91	121.03	1.28
GP-55	94.91	131.61	1.39	90.96	119.87	1.32	94.91	120.60	1.27
GP-56	94.91	131.61	1.39	90.14	199.60	1.31	94.91	120.36	1.27
GP-60	94.91	131.61	1.39	90.63	125.06	1.34	94.91	121.97	1.29
GP-61	94.91	131.61	1.39	93.69	124.38	1.33	94.91	121.61	1.28
GP-62	94.91	131.61	1.39	93.81	123.83	1.32	94.91	121.26	1.28
GP-63	94.91	131.61	1.39	93.93	123.43	1.31	94.91	121.05	1.28
GP-65	94.91	131.61	1.39	96.60	129.58	1.34	94.91	123.19	1.30
GP-66	94.91	131.61	1.39	96.66	128.93	1.33	94.91	122.89	1.29

).

A comparative assessment of observed rainfall, TRMM-derived estimates, and bias-corrected values is provided in Appendix A 

Table A4. Comparison statistics between before bias correction and after bias correction of extracted rainfall estimates.

Grid Points	Before Bias Correction of Extracted Rainfall Estimates						After Bias Correction of Extracted Rainfall Estimates
	PCC	Bias	ME (mm)	RMSE (mm)	Linear Regression		PCC	Bias	ME (mm)	RMSE (mm)	Linear Regression
					R2	Slope					R2	Slope
GP-44	0.86	0.93	−6.35	68.35	0.74	0.77	0.86	1.00	0.00	23.25	0.80	0.74
GP-45	0.86	0.93	−6.22	68.03	0.74	0.76	0.87	1.00	0.00	22.82	0.79	0.75
GP-46	0.86	0.94	−5.97	68.21	0.74	0.76	0.87	1.00	0.00	24.80	0.78	0.75
GP-47	0.86	0.94	−5.73	68.71	0.73	0.76	0.86	1.00	0.00	23.14	0.78	0.75
GP-53	0.86	0.96	−4.21	68.39	0.74	0.78	0.87	1.00	0.00	20.70	0.79	0.75
GP-54	0.86	0.96	−4.13	68.15	0.74	0.78	0.87	1.00	0.00	21.33	0.79	0.75
GP-55	0.86	0.96	−3.95	68.36	0.74	0.77	0.87	1.00	0.00	25.44	0.79	0.75
GP-56	0.86	0.96	−3.78	68.89	0.73	0.77	0.86	1.00	0.00	20.90	0.78	0.75
GP-60	0.86	0.99	−1.28	70.01	0.73	0.80	0.86	1.00	0.00	23.06	0.79	0.75
GP-61	0.86	0.99	−1.22	69.91	0.73	0.80	0.86	1.00	0.00	21.92	0.79	0.75
GP-62	0.86	0.99	−1.10	70.14	0.73	0.79	0.86	1.00	0.00	19.19	0.79	0.75
GP-63	0.86	0.99	−0.99	70.61	0.72	0.79	0.86	1.00	0.00	26.73	0.78	0.74
GP-65	0.86	1.02	1.69	73.99	0.71	0.82	0.86	1.00	0.00	20.26	0.79	0.73
GP-66	0.86	1.02	1.74	74.17	0.70	0.81	0.85	1.00	0.00	23.61	0.79	0.73

. The radar plots (Figure 4) illustrate the performance of TRMM rainfall relative to ground observations, both before and after bias correction. TRMM rainfall exhibited only moderate alignment with observed data, with PCC values ranging between 0.9 and 1.0. The bias showed large variability, spanning –0.5 to 1.5, while ME values varied from –6.5 to 2.5, highlighting notable inconsistencies (Figure 4a). Following bias correction, the agreement improved markedly: PCC values stabilized between 0.8 and 1.0, the bias narrowed substantially (–0.1 to 0.2), and ME values were reduced to –0.1 to 0.1. In addition, R² consistently exceeded 0.78, underscoring the effectiveness of the correction procedure in improving the reliability of TRMM rainfall estimates (Figure 4b).

3.3. Computation of PET

The computed monthly PET for all grid points in the study area is provided in Appendix A 

Table A5. Estimated monthly PET (mm) for all the grid points in the study area.

Grid Points	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
GP-1	4.8	18.4	62.3	124.9	156.5	134.2	91.3	88.4	83.0	79.7	32.6	6.7
GP-2	4.8	18.6	62.7	125.0	155.5	133.2	90.6	87.9	83.1	80.7	32.8	6.6
GP-3	4.9	18.5	61.3	123.5	154.9	133.6	91.2	88.4	83.3	80.7	32.9	6.7
GP-4	4.9	18.5	61.5	123.4	154.1	132.8	90.6	88.0	83.4	81.6	33.1	6.7
GP-5	4.8	18.6	61.8	123.2	153.0	131.7	89.9	87.4	83.4	82.4	33.3	6.7
GP-6	4.8	18.8	62.1	123.1	151.8	130.4	89.0	86.6	83.1	83.1	33.4	6.7
GP-7	5.0	18.6	60.6	122.1	152.6	132.3	90.6	88.1	83.9	82.8	33.4	6.8
GP-8	4.9	18.6	60.7	121.8	151.7	131.4	90.0	87.7	83.9	83.5	33.6	6.7
GP-9	4.9	18.7	60.9	121.5	150.6	130.2	89.1	87.0	83.7	84.1	33.7	6.8
GP-10	4.9	18.9	61.1	121.2	149.2	128.8	88.2	86.1	83.2	84.4	33.8	6.8
GP-11	4.9	19.0	61.2	120.8	147.8	127.4	87.2	85.2	82.8	84.8	33.9	6.8
GP-12	5.1	19.5	61.4	119.4	144.0	123.3	85.2	83.5	81.6	84.7	33.8	6.8
GP-13	5.0	18.7	60.0	120.6	150.3	131.0	90.0	87.9	84.5	84.9	33.9	6.8
GP-14	5.0	18.7	60.0	120.3	149.4	130.0	89.3	87.3	84.4	85.5	34.1	6.8
GP-15	5.0	18.8	60.0	119.8	148.1	128.7	88.4	86.6	83.9	85.8	34.2	6.8
GP-16	5.0	18.9	60.0	119.3	146.6	127.1	87.3	85.5	83.3	85.8	34.2	6.8
GP-17	4.9	18.6	58.6	116.0	141.7	122.7	84.2	82.5	80.7	83.8	33.5	6.7
GP-18	5.1	19.1	60.1	118.2	143.5	124.0	85.2	83.6	82.0	85.8	34.3	6.9
GP-19	5.2	19.4	60.1	117.4	141.4	121.6	84.4	83.0	81.5	85.5	34.2	7.0
GP-20	5.4	19.8	60.0	115.8	137.2	117.1	82.7	81.8	80.4	85.0	33.9	7.1
GP-21	5.5	20.0	60.1	115.3	135.1	115.0	82.2	81.7	80.3	84.9	33.9	7.1
GP-22	5.6	20.2	60.3	114.8	133.0	112.9	81.8	81.6	80.3	84.8	33.9	7.2
GP-23	5.2	18.9	59.1	118.5	146.7	128.2	88.7	86.8	84.0	85.4	34.1	6.9
GP-24	5.2	19.0	59.0	118.0	145.5	126.9	87.8	86.1	83.5	85.6	34.2	6.9
GP-25	5.2	19.1	59.0	117.5	144.0	125.4	86.8	85.1	82.9	85.4	34.2	6.9
GP-26	5.2	19.2	59.1	117.0	142.6	123.8	85.8	84.2	82.2	85.2	34.2	7.0
GP-27	5.3	19.3	59.1	116.5	141.0	122.1	84.8	83.3	81.6	85.0	34.2	7.0
GP-28	5.4	19.5	59.2	115.8	138.8	119.7	84.0	82.8	81.1	84.7	34.1	7.1
GP-29	5.5	19.8	59.3	115.1	136.6	117.4	83.3	82.3	80.6	84.4	33.9	7.2
GP-30	5.6	20.0	59.4	114.4	134.4	115.1	82.5	81.8	80.1	84.1	33.8	7.2
GP-31	5.7	20.2	59.6	113.8	132.2	113.0	82.1	81.7	80.0	83.9	33.8	7.3
GP-32	5.8	20.5	59.9	113.3	129.9	110.9	81.7	81.7	80.0	83.8	33.8	7.4
GP-33	5.9	20.7	60.1	112.9	127.8	108.8	81.3	81.7	79.9	83.8	33.7	7.4
GP-34	5.4	19.2	58.1	116.7	144.0	126.4	88.1	86.3	83.3	84.8	34.0	7.0
GP-35	5.4	19.2	58.0	116.3	142.9	125.1	87.3	85.7	83.0	84.9	34.1	7.0
GP-36	5.4	18.5	55.7	111.0	135.5	118.4	82.7	81.2	78.9	81.0	32.6	6.8
GP-37	5.5	19.4	58.2	115.4	140.1	122.0	85.4	83.9	81.7	84.2	34.0	7.1
GP-38	5.5	19.5	58.3	114.9	138.5	120.3	84.6	83.2	81.1	83.9	34.0	7.2
GP-39	5.6	19.8	58.5	114.3	136.2	117.8	83.8	82.7	80.6	83.4	33.9	7.2
GP-40	5.8	20.0	58.7	113.7	133.9	115.4	83.1	82.3	80.1	83.0	33.7	7.3
GP-41	5.9	20.3	59.0	113.0	131.6	113.0	82.4	81.8	79.7	82.6	33.6	7.4
GP-42	6.0	20.6	59.3	112.5	129.2	110.9	82.0	81.8	79.5	82.4	33.5	7.5
GP-43	6.1	20.9	59.7	112.0	126.9	108.8	81.7	81.8	79.4	82.3	33.5	7.5
GP-44	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-45	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-46	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-47	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-48	5.8	19.7	57.4	113.4	136.1	118.5	84.3	83.0	80.6	82.7	33.8	7.3
GP-49	5.9	20.0	57.8	112.8	133.7	116.0	83.6	82.6	80.1	82.2	33.7	7.4
GP-50	6.0	20.3	58.2	112.3	131.2	113.5	83.0	82.2	79.7	81.7	33.5	7.5
GP-51	6.2	20.6	58.6	111.7	128.9	111.0	82.3	81.8	79.2	81.2	33.3	7.6
GP-52	6.3	20.9	59.0	111.1	126.3	108.8	81.9	81.8	79.0	81.0	33.3	7.6
GP-53	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-54	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-55	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-56	5.3	17.8	51.4	103.1	125.3	110.4	78.8	77.4	74.4	75.2	33.1	6.6
GP-57	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-58	6.1	20.1	56.9	110.8	130.5	113.6	83.0	82.0	79.0	80.2	33.0	7.4
GP-59	6.2	20.4	57.3	110.0	127.8	110.8	82.2	81.5	78.4	79.5	32.8	7.5
GP-60	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-61	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-62	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-63	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-64	6.0	19.6	55.6	109.5	130.3	113.9	83.1	81.7	78.3	78.4	32.4	7.3
GP-65	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-66	5.7	19.3	55.7	111.6	135.7	119.5	85.3	83.8	80.5	81.4	33.1	7.1
GP-67	5.6	18.2	51.5	102.2	122.2	107.5	78.7	77.3	73.5	72.9	30.0	6.8
Mean	5.5	19.4	58.5	115.2	139.1	120.7	85.3	83.1	81.7	82.7	33.5	7.1

. The mean monthly PET estimates from January to December were 5.5 mm, 19.4 mm, 58.5 mm, 115.2 mm, 139.1 mm, 120.7 mm, 85.3 mm, 83.9 mm, 81.1 mm, 82.7 mm, 33.5 mm, and 7.1 mm, respectively. The highest PET value, 156.5 mm, was recorded in May at grid point GP-1, while the lowest value, 4.8 mm, occurred in January across grid points GP-1 to GP-6, covering the southeastern part of the district. PET increased steadily from January to May, declining gradually from June to December (Appendix A Table A5). From April to June, PET peaked significantly. This elevation in PET coincides with the pre-monsoon warming and increased insolation, which enhance evapotranspiration rates. This seasonal rise is realistic given that PET typically culminates in early summer or pre-monsoon months over India, as supported by national trends showing maximum monthly PET between April and June [57].

The spatio-temporal distribution of monthly normal PET estimates from January to December is presented in Figure 5. In January, normal PET ranged from 5.0 mm to 6.3 mm, and in February, it ranged from 18.0 mm to 21.0 mm. The lowest PET values were observed in the southern part of the region, while the highest values were concentrated in the northeast and eastern parts in January and February, respectively. From March to September, the highest PET values (62.2 mm to 155.4 mm) were found in the southern part, while the minimum values (51.4 mm to 103.1 mm) were located in the northeastern region. In October, the maximum PET value was 85.8 mm, concentrated in the northern part, while the minimum was 75.2 mm, observed in the middle to southern part of the region. In November and December, the highest PET values of 34.3 mm and 8 mm were observed in the middle and eastern parts, respectively, with the minimum values located in the northern and southern parts.

The PET patterns identified in this study are consistent with previous research. Verma et al. [61] and Sonali et al. [62] found that PET increases from winter, peaks in May, and decreases during the monsoon and post-monsoon months. Goroshi et al. [63] reported similar behavior using satellite data, with higher pre-monsoon evapotranspiration and a decline afterwards, along with regional variability.

3.4. LULC Analysis

The five classified land use features, namely agricultural land, barren land, forest land, settlement, and water body (Figure 6), occupy an area of 1869 km², 111 km², 258 km², 626 km², and 36 km², respectively, in the region. The percentage aerial coverage of agricultural land (64.46%) was found to be highest in the study area, followed by settlement (21%) and forest land (8.89%). The minimum area of water bodies (1.23%) in the region was observed (

Table 5. Areal distribution of land use features in the study area in the year of 2019.

Land Use	Area (km2)	Percentage Area
Agriculture land	1869	64.46
Barren land	111	3.89
Forest land	258	8.89
Settlement	626	21.59
Water bodies	36	1.23
Total	2900	100

).

An error matrix (also called a confusion matrix) is a statistical tool commonly used in remote sensing and machine learning image classification to evaluate the accuracy of a classification or prediction by comparing it with reference or observed data. The error matrix of LULC classification was computed and is presented in

Table 6. Error matrix of LULC classification for the year 2019.

Feature Classes	Water Bodies	Agricultural Land	Barren Land	Forest Land	Settlement	Total
Water Bodies	15	2	0	0	0	17
Agricultural Land	0	28	0	0	0	28
Barren Land	3	0	9	0	0	12
Forest land	0	0	0	15	0	15
Settlement	0	3	0	0	15	18
Total	18	33	9	15	15	90

.

The classified LULC map achieved an overall accuracy of 91.11%, with a kappa coefficient of 0.88. This value shows that the classification of the land use feature map is in almost-perfect agreement and rated as excellent, and hence, the classified image is therefore found to be valid for further analysis.

3.5. Determination Soil Textural Class

The validated soil map of the study area is presented in Figure 7, and details of the soil mapping units, including their USDA classifications and corresponding local names, are presented in Appendix A 

Table A6. Soil mapping units used in the study area, represented by alphanumeric codes along with their USDA soil classifications and corresponding local names. These units were delineated and classified based on soil survey data prepared by the NBSS and LUP.

Soil Code	USDA Soil Classification	Local Soil Name
BH11	Coarse-loamy, mixed, hyperthermic, Typic Endoaquepts	Moti Domat Mitti
BH17	Coarse-loamy, mixed, hyperthermic, Typic Endoaquepts	Moti Domat Mitti
BH18	Fine-loamy, mixed (calcareous), hyperthermic, Aeric Fluvaquents	Bhangar Mitti
BH19	Fine-loamy, mixed, hyperthermic, Fluventic Haplustepts	Barik Domat Mitti
BH33	Fine-loamy, mixed, hyperthermic, Typic Haplustepts	Barik Domat Mitti
BH34	Fine-silty, mixed, hyperthermic, Typic Ustifluvents	Kewal Mitti / Retili Mitti
BH35	Fine-loamy, mixed, hyperthermic, Typic Haplustepts	Barik Domat Mitti
BH36	Fine-loamy, mixed (calcareous), hyperthermic, Typic Ustorthents	Bhangar Mitti
BH38	Fine-loamy, mixed (calcareous), hyperthermic, Aeric Fluvaquents	Bhangar Mitti
BH39	Very fine, mixed, hyperthermic, Vertic Haplustepts	Barik Chikni Kali Mitti
BH42	Mixed, hyperthermic, Aquic Ustipsammaents	Baluahi Mitti
BH43	Fine-loamy, mixed, hyperthermic, Aeric Endoaquepts	Barik Domat Mitti
BH44	Fine-loamy, mixed, hyperthermic, Aeric Endoaquepts	Barik Domat Mitti
BH176	Mixed (calcareous), hyperthermic, Typic Psammaquents	Baluahi Mitti
BH177	Fine-loamy, mixed, hyperthermic, Aeric Endoaquents	Barik Domat Mitti

. Soil map analysis of the study area revealed three major soil textural classes, namely, silt loam, clay loam, and clay.

3.6. Computation of Available Water Capacity (AWC)

The rooting depth and corresponding AWC values of each land use feature were decided by considering land use features and type of soil in the study area following established guidelines [55,60]. The results are summarized in the

Table 7. Computation of AWC in the root zone for various soil textures and land use features [60].

Land Use	Soil Texture	AWC (%)	Rooting Depth (m)	AWC in Root Zone (mm)
Agricultural land	Silt loam	20	0.62	124
	Clay loam	25	0.40	100
	Clay	30	0.25	75
Settlement	Silt loam	15	0.35	52.5
	Clay loam	20	0.30	60
Barren land	Silt loam	18	0.35	63
	Clay loam	20	0.30	60
Forest area	Clay loam	25	1.50	375
water body	Silt loam	15	0.40	60

.

3.7. Computation of AET

The estimated monthly AET for all the grid points in the study area are presented in Appendix A 

Table A7. Estimated monthly AET (mm) for all the grid points in the study area.

Grid Points	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
GP-1	4.8	18.4	52.6	72.3	79.2	97.2	91.3	88.4	83.0	78.1	26.1	5.3
GP-2	4.8	18.6	52.7	72.2	80.8	130.1	90.6	87.9	83.1	79.3	26.3	5.3
GP-3	4.9	18.5	50.0	64.8	73.2	129.6	91.2	88.4	83.3	78.2	24.2	5.0
GP-4	4.9	18.5	47.0	55.6	68.9	130.2	90.6	88.0	83.4	78.5	22.3	4.7
GP-5	4.8	18.6	52.0	72.3	83.0	131.0	89.9	87.4	83.4	80.6	26.2	5.3
GP-6	4.8	18.8	52.1	72.2	84.3	26.5	89.0	86.6	83.1	81.5	26.6	5.3
GP-7	5.0	18.6	46.5	55.4	69.1	131.1	90.6	88.1	83.9	78.8	21.5	4.6
GP-8	4.9	18.6	49.4	65.1	77.6	131.4	90.0	87.7	83.9	80.7	24.2	5.0
GP-9	4.9	18.7	49.4	65.3	79.4	130.2	89.1	87.0	83.7	81.5	24.6	5.0
GP-10	4.9	18.8	49.4	65.5	80.8	128.8	88.2	86.1	83.2	82.1	25.1	5.0
GP-11	4.9	19.0	49.5	65.6	82.2	127.4	87.2	85.2	82.8	82.7	25.5	5.0
GP-12	5.1	19.4	49.5	65.9	86.5	123.3	85.2	83.5	81.6	84.3	28.5	5.5
GP-13	5.0	18.7	49.0	64.7	77.6	131.0	90.0	87.9	84.5	81.1	23.5	5.0
GP-14	5.0	18.7	48.9	65.1	79.9	130.0	89.3	87.3	84.4	82.1	23.9	5.0
GP-15	5.0	18.8	48.8	65.5	81.7	128.7	88.4	86.6	83.9	82.7	24.4	5.0
GP-16	5.0	18.9	48.8	65.8	83.1	127.1	87.3	85.5	83.3	83.0	24.9	5.0
GP-17	4.9	18.5	44.5	55.5	77.9	122.7	84.2	82.5	80.7	80.9	22.6	4.5
GP-18	5.1	19.1	48.7	66.4	86.0	124.0	85.2	83.6	82.0	83.9	26.2	5.1
GP-19	5.2	19.3	48.7	66.5	88.7	121.6	84.4	83.0	81.5	85.0	28.4	5.5
GP-20	5.4	19.7	48.8	66.7	94.0	117.1	82.7	81.8	80.4	85.0	31.0	6.1
GP-21	5.5	19.9	49.1	67.0	95.6	115.0	82.2	81.7	80.3	84.9	31.0	6.1
GP-22	5.6	20.2	50.6	70.1	85.8	112.9	81.8	81.6	80.3	82.2	25.5	5.6
GP-23	5.2	18.9	50.2	72.1	88.2	128.2	88.7	86.8	84.0	82.7	25.5	5.4
GP-24	5.2	19.0	50.1	72.4	89.9	126.9	87.8	86.1	83.5	83.1	25.9	5.4
GP-25	5.2	19.0	48.2	66.2	86.2	125.4	86.8	85.1	82.9	82.8	24.8	5.1
GP-26	5.2	19.1	48.2	66.6	87.6	123.8	85.8	84.2	82.2	82.9	25.3	5.1
GP-27	5.3	19.2	48.1	66.9	89.3	122.1	84.8	83.3	81.6	83.3	26.1	5.2
GP-28	5.4	19.5	48.2	66.9	92.0	119.7	84.0	82.8	81.1	84.2	28.3	5.6
GP-29	5.5	19.7	48.3	67.0	94.7	117.4	83.3	82.3	80.6	84.4	30.6	6.0
GP-30	5.6	19.7	39.1	45.9	88.9	115.1	82.5	81.8	80.1	84.1	27.8	5.2
GP-31	5.7	20.1	50.6	73.3	101.9	113.0	82.1	81.7	80.0	83.9	31.4	6.4
GP-32	5.8	20.3	49.1	67.6	99.7	110.9	81.7	81.7	80.0	83.8	30.9	6.2
GP-33	5.9	20.5	49.5	67.9	100.8	108.8	81.3	81.7	79.9	83.8	30.9	6.3
GP-34	5.4	19.1	47.9	65.8	85.8	126.4	88.1	86.3	83.3	81.7	24.0	5.3
GP-35	5.4	19.2	47.7	66.2	87.8	125.1	87.3	85.7	83.0	82.2	24.4	5.2
GP-36	5.4	18.4	41.7	52.3	81.5	118.4	82.7	81.2	78.9	78.3	20.7	4.5
GP-37	5.5	19.3	47.6	66.9	91.0	122.0	85.4	83.9	81.7	82.2	25.3	5.3
GP-38	5.5	19.4	47.6	67.2	92.8	120.3	84.6	83.2	81.1	82.4	26.0	5.4
GP-39	5.6	19.7	47.8	67.2	95.6	117.8	83.8	82.7	80.6	83.1	28.3	5.8
GP-40	5.8	19.9	48.0	67.2	98.2	115.4	83.1	82.3	80.1	83.0	30.4	6.1
GP-41	5.9	20.2	50.0	73.1	103.8	113.0	82.4	81.8	79.7	82.6	31.1	6.5
GP-42	6.0	20.4	50.3	73.3	104.5	110.9	82.0	81.8	79.5	82.4	31.1	6.5
GP-43	6.1	20.6	51.2	71.8	126.9	108.8	81.7	81.8	79.4	82.3	32.9	7.5
GP-44	5.7	19.2	46.0	67.5	100.7	119.5	85.3	83.8	80.5	80.8	26.5	5.7
GP-45	5.7	19.1	44.1	61.3	97.5	119.5	85.3	83.8	80.5	80.6	25.2	5.4
GP-46	5.7	19.1	44.1	61.3	97.5	119.5	85.3	83.8	80.5	80.6	25.2	5.4
GP-47	5.7	19.2	46.0	67.5	100.7	119.5	85.3	83.8	80.5	80.8	26.5	5.7
GP-48	5.8	19.6	47.3	67.5	98.0	118.5	84.3	83.0	80.6	82.7	30.8	6.2
GP-49	5.9	19.9	47.1	66.9	99.9	116.0	83.6	82.6	80.1	81.5	26.7	5.8
GP-50	6.0	20.3	48.7	71.8	79.7	113.5	83.0	82.2	79.7	74.2	20.6	4.4
GP-51	6.2	20.6	48.7	71.8	80.7	111.0	82.3	81.8	79.2	74.1	20.8	4.5
GP-52	6.3	20.8	43.5	58.3	72.0	108.8	81.9	81.8	79.0	70.6	15.5	3.3
GP-53	5.7	19.2	45.2	68.3	80.7	119.5	85.3	83.8	80.5	73.4	18.7	3.8
GP-54	5.7	19.2	52.8	95.7	120.9	119.5	85.3	83.8	80.5	81.2	31.1	6.7
GP-55	5.7	19.2	46.0	67.5	100.7	119.5	85.3	83.8	80.5	80.8	26.5	5.7
GP-56	5.3	17.7	43.8	66.8	100.0	110.4	78.8	77.4	74.4	75.0	28.0	5.5
GP-57	5.7	19.2	39.6	53.9	73.6	119.5	85.3	83.8	80.5	68.9	12.9	2.7
GP-58	6.1	20.0	47.3	72.7	87.6	113.6	83.0	82.0	79.0	74.0	21.2	4.5
GP-59	6.2	20.3	47.3	72.6	88.4	110.8	82.2	81.5	78.4	73.8	21.3	4.6
GP-60	5.7	19.2	46.5	74.4	91.7	119.5	85.3	83.8	80.5	75.5	21.3	4.3
GP-61	5.7	19.2	47.7	73.2	104.1	119.5	85.3	83.8	80.5	80.9	27.7	5.9
GP-62	5.7	19.2	46.3	74.2	94.9	119.5	85.3	83.8	80.5	75.5	21.4	4.4
GP-63	5.7	19.2	46.1	74.5	96.3	119.5	85.3	83.8	80.5	75.9	21.6	4.4
GP-64	6.0	19.5	45.9	74.0	96.6	113.9	83.1	81.7	78.3	74.0	21.9	4.6
GP-65	5.7	19.2	47.7	73.2	104.1	119.5	85.3	83.8	80.5	80.9	27.7	5.9
GP-66	5.7	19.2	47.7	73.2	104.1	119.5	85.3	83.8	80.5	80.9	27.7	5.9
GP-67	5.6	16.8	45.7	71.9	100.0	107.5	78.7	77.3	73.5	72.9	26.3	6.2
Mean	5.5	19.3	47.9	67.6	90.3	118.4	85.3	83.9	81.1	80.4	25.6	5.3

. The mean monthly AET of grid points from January to December were found to be 5.5 mm, 19.3 mm, 47.9 mm, 67.6 mm, 90.3 mm, 118.4 mm, 85.3 mm, 83.9 mm, 81.1 mm, 80.4 mm, 25.6 mm, and 5.3 mm, respectively. The maximum value (118.4 mm) of AET was observed for the month of May and the minimum (5.3 mm) for the month of January. The mean monthly AET was found to be progressively increasing from January to June and thereafter there was gradually declining from July to December (Appendix A Table A7).

The spatio-temporal distribution of monthly normal AET estimates (January to December) is shown in Figure 8. In January and February, AET ranged from 4.8 mm to 6.3 mm and 17.7 mm to 20.8 mm, with higher values in the eastern region and lower values in the south. In March, the maximum AET (52.80 mm) was in the southern and eastern parts, while the minimum (39.1 mm) was in the north. For April and May, maximum AET values (95.6 mm and 120.8 mm) were observed in the north and minimum values (46.0 mm and 68.9 mm) in the southwest. From June to September, maximum AET (131.4 mm to 84.4 mm) was in the south, and minimum values (74.4 mm to 77.6 mm) were in the east. The maximum values of normal AET estimates in the months October to December, 85.0 mm, 31.4 mm, and 6.7 mm, respectively, were found to be distributed in extreme southern part of the region, while the minimum values of 69.0 mm, 13.0 mm, and 2.7 mm were observed to be distributed in eastern part of the region. These variations are influenced by climatic factors, land use, soil texture, and moisture storage. The changes in the spatial distribution of estimated monthly AET were attributed to variations in atmospheric demand, primarily influenced by climatic variables such as temperature and mean daily sunshine hours as well as by land use features, soil texture, AWC, and actual moisture storage at each grid point across the study area.

The monthly variation of AET across the study area shows a pronounced seasonal trend, beginning with low values during winter, rising gradually through the pre-monsoon months and reaching peak in May. Thereafter, AET declined consistently during the monsoon and post-monsoon periods. This trend is largely controlled by temperature and solar radiation, where the initial increase reflects enhanced, atmospheric demand driven by higher temperatures and longer sunshine hours, while the subsequent decline corresponds to cooler conditions and reduced radiation. The PET followed a similar seasonal course, with maximum values recorded in the pre-monsoon months and a substantial decrease during the wet and cooler seasons. Spatial patterns indicated relatively higher AET in the southern and eastern zones during warmer months, whereas the northern and southwestern regions exhibited lower values due to cooler temperatures or soil moisture limitations. These spatio-temporal variations highlight the combined influence of climatic drivers, land use, soil properties, and water storage capacity.

3.8. Determination of Surplus and Deficit Water

The region receives the minimum amount of rainfall in the month of December (2.5 mm), followed by November (5.1 mm) and January (9.3 mm), and the maximum amount of rainfall is observed in the month of July (276.0 mm), followed by August (256.3 mm) and September (210.6 mm). The monthly average PET over the area was found to be minimum in the range of January (5.5 mm) and December (7.1 mm) and maximum in the month of May (139.1 mm) and June (120.7 mm). However, the monthly average AET was observed to be in the month of December (5.3 mm), followed by January (5.5 mm), and it was maximum over the region in the month of June (118.4 mm), followed by May (90.3 mm) (

Table 8. Monthly average rainfall, PET, AET, and deficit and surplus water available in for all grid points over the study area.

Months	P (mm)	PET (mm)	AET (mm)	Deficit (mm)	Surplus (mm)
Jan	9.3	5.5	5.5	0.0	3.8
Feb	15.5	19.4	19.3	0.1	0.0
Mar	11.8	58.5	47.9	10.6	0.0
Apr	32.8	115.2	67.6	47.6	0.0
May	77.9	139.1	90.3	48.7	0.0
Jun	197.2	120.7	118.4	0.0	27.4
Jul	276.0	85.3	85.3	0.0	190.7
Aug	256.3	83.9	83.9	0.0	172.6
Sept	210.6	81.1	81.1	0.0	126.8
Oct	139.1	82.7	80.4	0.0	2.5
Nov	5.1	33.5	25.6	7.8	0.0
Dec	2.5	7.1	5.3	0.0	0.02
Total	1234.1	832.0	710.6	121.2	523.8

).

The monthly average deficit of water was depicted to be maximum in the district in the month of May (48.7 mm), followed by April (47.6 mm) and March (10.6 mm). Meanwhile, the monthly average availability of surplus water was estimated to be maximum in the month of July (190.7 mm), followed by August (172.6 mm) and September (126.8 mm). In the region, an annual water deficit of 121.2 mm and annual water surplus of 523.8 mm were depicted.

The value of AET was observed to be equal to that of PET for the months January, February, July, August, and September, while the value of AET was found to be lesser than that of PET for the months of February, March, April, May, June, October, November, and December (Figure 9).

The temporal variation in water deficit and surplus across the study area is primarily governed by the relationship between precipitation, PET, and AET. During the pre-monsoon months (March to May), PET values are substantially higher than the precipitation, resulting in marked water deficits due to insufficient moisture availability to meet atmospheric evaporative demand. For instance, in May, PET reaches 139.1 mm, while precipitation is only 77.9 mm, leading to a deficit of 48.7 mm. In contrast, during the monsoon season (June to September), precipitation exceeds PET by a significant margin, allowing AET to approach or equal PET and generating a considerable water surplus. For example, in July, precipitation is 276.0 mm compared to a PET of 85.3 mm, resulting in a surplus of 190.7 mm. These seasonal dynamics reflect the dominant hydrological processes in the region, where surplus is driven by high rainfall during the monsoon, and deficit arises due to increased evaporative demand under limited precipitation in the dry season.

The minimum and maximum annual water deficit was observed at grid points GP-54 (36.1 mm) and GP-4 (186.1 mm), respectively, while the minimum and maximum annual surplus water was observed at grid points GP-2 (445.4 mm) and GP-64 (609.2 mm), respectively (

Table 9. Annual availability of water for all grid points over the Samastipur District of Bihar.

Grid Points	Annual Available Water			Grid Points	Annual Available Water
	Deficit (mm)	Surplus (mm)	Available Water (mm)		Deficit (mm)	Surplus (mm)	Available Water (mm)
GP-1	186.0	445.9	259.9	GP-34	134.2	492.8	358.6
GP-2	149.9	445.4	295.5	GP-35	129.7	495.1	365.4
GP-3	168.5	453.7	285.2	GP-36	143.6	515.9	372.3
GP-4	186.1	450.5	264.4	GP-37	120.8	504.9	384.1
GP-5	141.7	451.0	309.3	GP-38	115.3	509.3	394
GP-6	172.1	454.8	212.7	GP-39	105.9	511.9	406
GP-7	183.7	457.1	273.4	GP-40	97.5	514.8	417.3
GP-8	156.1	455.3	299.2	GP-41	80.3	526.2	445.9
GP-9	152.2	458.4	306.2	GP-42	76.5	531.5	455
GP-10	148.5	464.9	316.4	GP-43	49.4	578.9	529.5
GP-11	144.8	471.4	326.6	GP-44	97.5	535.7	438.2
GP-12	130.0	482.2	352.2	GP-45	110.6	535.7	425.1
GP-13	155.6	462.2	306.6	GP-46	110.6	535.7	425.1
GP-14	151.1	462.8	311.7	GP-47	97.5	535.7	438.2
GP-15	146.7	466.7	320	GP-48	98.3	507.4	409.1
GP-16	142.3	473.9	331.6	GP-49	99.8	542.3	442.5
GP-17	154.5	490.1	335.6	GP-50	125.1	565.5	440.4
GP-18	132.6	487.1	354.5	GP-51	120.8	567.2	446.4
GP-19	122.7	489.5	366.8	GP-52	155.3	568.9	413.6
GP-20	107.6	502.4	394.8	GP-53	134.6	551.0	416.4
GP-21	102.8	509.6	406.8	GP-54	36.1	535.7	499.6
GP-22	114.3	507.7	393.4	GP-55	97.5	535.7	438.2
GP-23	126.6	477.0	350.4	GP-56	75.7	564.3	488.6
GP-24	122.4	480.3	357.9	GP-57	173.0	580.1	407.1
GP-25	133.9	486.5	352.6	GP-58	111.7	588.9	477.2
GP-26	129.5	492.7	363.2	GP-59	106.9	591.6	484.7
GP-27	124.0	498.1	374.1	GP-60	110.9	574.1	463.2
GP-28	114.4	500.3	385.9	GP-61	85.2	535.7	450.5
GP-29	105.6	502.4	396.8	GP-62	108.0	602.4	494.4
GP-30	142.7	513.1	370.4	GP-63	105.9	599.9	494
GP-31	83.4	519.4	436	GP-64	96.7	609.2	512.5
GP-32	90.9	524.8	433.9	GP-65	85.2	535.7	450.5
GP-33	86.7	530.2	443.5	GP-66	85.2	535.7	450.5
GP-34	134.2	492.8	358.6	GP-67	64.0	546.8	482.8

).

The spatio-temporal distribution of surplus and deficit water from January to December is shown in Figure 10. Water availability in January, July, August, and September was entirely in surplus, with values ranging from 2.5 mm to 5.6 mm in January, 179.0 mm to 209.5 mm in July, and 161.4 mm to 185.0 mm in August. Water deficits occurred in February, March, April, May, and November, with values ranging from 0.01 mm to 0.4 mm in February, 3.0 mm to 20.4 mm in March, 16.0 mm to 68.4 mm in April, 15.0 mm to 85.2 mm in May, and 2.0 mm to 20.1 mm in November. In June, October, and December, some regions experienced both surplus and deficit.

The maximum surplus values were 5.6 mm (January), 209.5 mm (July), 185.0 mm (August), and 129.5 mm (September), primarily distributed in the northern region, with the exception of August, where the surplus was in the middle part. Minimum surplus values were 2.5 mm (January), 179.0 mm (July), 161.4 mm (August), and 102.7 mm (September), observed in the southern region, except for January, which had surplus in the middle part. Maximum deficit values were observed in the eastern part during February and March and the southern part during April, May, and November. Minimum deficits occurred in the southern part in February, the northern part in March–May, and the eastern part in November. The distribution patterns of water surplus and deficit varied monthly due to changes PET, AET, and ΔAS across the study area.

4. Limitations and Future Directions

This study has certain limitations that should be addressed in future research. The reliance on a single ground station (RPCAU, Pusa) may introduce errors, as spatial variability in rainfall and temperature across the study area cannot be fully captured. Limited ground-based observations may therefore affect the accuracy of bias correction. In addition, the use of monthly data restricted the detection of short-term climate variability and extreme events. Frequent cloud cover in satellite imagery, particularly during the monsoon season, can further reduce the reliability of rainfall and temperature estimates. The application of a single linear scaling method may not adequately correct complex, non-linear biases present in satellite data. Furthermore, the Thornthwaite–Mather model simplifies hydrological processes and does not account for groundwater flow or dynamic land cover changes. Future research should incorporate high-resolution, cloud-resilient datasets (e.g., IMERG and ERA5), adopt advanced correction techniques such as quantile mapping or machine learning approaches, and employ physically based distributed models like the soil and water assessment tool (SWAT) and the variable infiltration capacity (VIC) model. Including dynamic land use, groundwater interactions, and climate change scenarios will improve the robustness and applicability of hydrological assessments for sustainable water resource planning.

5. Conclusions

Satellite-derived rainfall products have become essential tools in hydrological studies, offering broad spatial coverage and high temporal resolution. Nonetheless, their indirect estimation methods often introduce systematic biases when compared to ground-based measurements. In this study, a comprehensive assessment of water resources was conducted using satellite-derived climatic variables over the Samastipur District in Bihar, India, with particular emphasis on the application of bias correction techniques to enhance the quality of satellite data for improved hydrological modeling.

The use of linear scaling as a bias correction method improved the consistency of satellite-derived climate data with observed meteorological records, enabling more accurate estimation of seasonal AET and PET in the study area. Analysis of the water balance showed peak surpluses during the monsoon months, with values of 190.7 mm in July, 172.6 mm in August, and 126.8 mm in September. Conversely, notable water deficits were recorded in the pre-monsoon season, reaching 48.7 mm in May, 47.6 mm in April, and 10.6 mm in March. These deficits were mainly the result of increased evapotranspiration demand under limited rainfall conditions.

These findings carry critical implications for regional water resource management, particularly in supporting irrigation planning, flood risk mitigation, and drought preparedness. The integration of bias-corrected remote sensing data offers a scientifically robust foundation for the development of sustainable and climate-resilient water management strategies. Future research should incorporate advanced machine learning approaches and finer-resolution climatic datasets to further enhance predictive capabilities and inform evidence-based policy decisions. Overall, this study highlights the vital role of remote sensing, GIS, and bias correction techniques in advancing hydrological assessments, particularly in regions with limited in situ data availability.