Drought evaluation using various evapotranspiration models over semi-arid river basins

Prediction of hydro-meteorological variables for extreme event analysis, such as droughts, is one of the key challenges in the field of hydrology and water resources due to the complex interactions between multiple non-linear physical mechanisms behind the hydrological and meteorological processes (Khandelwal et al. 2020). Due to this behavior of hydro-meteorological variables and the intrinsic complexity of climatic conditions, accurate analysis of extremes such as drought has been a challenging task in hydrological studies (Mohammadi 2023). Such hydro-meteorological variables are either estimated by empirical methods (Adesogan & Sasanya 2023) or modeled by process-based hydrological models for the study of extreme events in data-scarce regions or various hybrid Machine Learning approaches such as ANN-FA with variable efficiency or wavelet analysis are utilized as a solution to these challenges (Hinge et al. 2022; Mohammadi 2023). Droughts are one of the most weather-related natural disasters, affecting socioeconomic and environmental systems in all temperature zones with varying frequency, severity, and duration (Sheffield et al. 2012; Deo & Şahin 2015). According to earlier research, the global mean temperature from the year 2006 to 2015 was approximately 1 °C higher than the pre-industrial level, and global warming has influenced the regional and temporal distribution of dryness (Masson-Delmotte et al. 2018). Thus, for the accurate assessment of extreme drought events, the inclusion of atmospheric temperature is important along with precipitation under the changing climate scenarios (Sharma & Mujumdar 2017). The most popular temperature-based meteorological variable is Potential Evapotranspiration (PET), which accounts for the atmospheric evaporative demand and is a key element to the overall water balance and water use of a region. Hence the drought detector based on PET will be more suitable in different temperature scenarios (Vicente-Serrano 2010). The Standardized Precipitation Evapotranspiration Index (SPEI), a popular meteorological drought index based on climatic evaporative demand as difference (P-PET) between Precipitation (P) and PET developed by Vicente-Serrano (2010) is able to predict the dry as well as wet periods and is more suitable in changing climate scenarios (Vicente-Serrano 2010; Kumari et al. 2022). However, such meteorological drought indices based on precipitation and PET, do not consider the actual water availabilities, land use, soil, and vegetation in the drought severity assessment. A drought analysis based on only meteorological aspects (Precipitation and Temperature) without consideration of actual water deficits from the land in the hydrological cycle will not be able to define dryness under climate change conditions (Oloruntade et al. 2017). On the other hand, Actual Evapotranspiration (AET) is one of the important hydrological variables, depicts the transfer of water from the soil to the atmosphere in response to both atmospheric evaporative demand and available moisture supply, and thus it can be a promising variable in drought prediction (Liu et al. 2017; Rehana & Monish 2020). Moreover, Increased temperature has a significant impact on water stress in the region, particularly over longer periods. Therefore, using AET as a measure to better understand the drought is more beneficial (Homdee et al. 2016). The various complex interactions among precipitation, soil moisture, and evapotranspiration (ET) by vegetation (Parry 2007) can influence drought trends due to the changes in land use and land cover. However, this can be predictable with the inclusion of AET in drought indices such as SPAEI (Standardized Precipitation Actual Evapotranspiration Index) developed by Homdee et al. (2016). AET-based hydro-meteorological drought index, SPAEI provides more acuity toward drought assessment compared to the drought index based solely on meteorological or hydrological aspects (Rehana & Sireesha 2021). To assess the drought events accurately by various drought indices such as SPEI or SPAEI, It is necessary to predict the hydro-meteorological variables (PET and AET) precisely, There are several challenges in estimating AET and PET at fine spatial resolution, thus selecting an appropriate technique for their estimate is critical (Paul et al. 2021). Usually, distributed or physically based hydrological models are developed for the extraction of various hydro-meteorological variables useful in drought and flood assessment (Devia 2015). However, because of its complexity, it is difficult to setup a model for different terrain conditions or for a larger area scale. On the other hand, there are various empirical models (Budyko methods, Penman–Monteith, Hargreaves, etc.) for the estimation of AET and PET but these empirical methods do not account for the catchment characteristics which may underestimate the actual number of variables (Verstraeten et al. 2008). Further, satellite-based remote sensing data are accessible for the extraction of evapotranspiration (ET) values and provide global coverage and continuous observations of land surface variables affecting ET. However, satellite-based data cannot measure ET directly, and further use of remote sensing-based AET estimates provides limitations over the validation and resolutions (Cleugh et al. 2007; Bhattarai & Wagle 2021). In data-scarce regions, the most stable models are those whose findings closely match with real observations with lesser complexity of the model (Tegegne et al. 2017). The precision of results generated from the model always depends on the selection of a model and the quality of input data (Dee et al. 2011). However, in cases where the input data is of low quality and there are significant uncertainties, a simpler model may be preferable to a more complex one (Michaud & Sorooshien 1994). Several hydrological models have varied strengths in representing hydrological processes (Li et al. 2018). The recent research reveals the precision and complexity of various distributed hydrological models used in the simulation of catchment hydrological variables playing major role in the design and planning of water resources systems (Mohammadi et al. 2022). One of the most common VIC (Variable Infiltration Capacity) model, a fully distributed hydrological model was applied by Nandi & Manne (2020) for the simulation of water balance components (Shah et al. 2019) in a semi-arid climate with limited data availability. The distributed models such as VIC or SWAT are more accurate, widely applied to solve a variety of water resource problems (Singh & Saravanan 2020), and captures basin characteristics (Arnold et al. 1998) but is complex in nature and time consuming. The development and advancement of models in hydrology can enhance our comprehension of the impacts of land use and climate change on water resources (Mishra & Tiwari 2023). Whereas, there are several empirical models available that provide significant results and are easier to apply at the catchment scale (Budyko 1974; Zhang et al. 2004) can efficiently reduce our time for the analysis.

The main objective of this study is to include and analyze the sensitivity of various approaches for the estimation of hydro-meteorological variables required in extreme event drought modeling. The process-based distributed hydrological model such as SWAT is more precise compared to any empirical model since it accounts for various catchment characteristics as well but it is complex to setup and requires time and data. However, there are many uncertainties associated with each model in the simulation of hydro-meteorological variables hence this study observed the results of drought prediction by each model, and tried to find out the effect of ET calculated in different ways on SPEI and SPAEI, i.e., using distributed model (SWAT), empirical and remote sensing to provide an ease in the drought assessment with SPEI and SPAEI index. The present methodology was tested on a dry-sub-humid river catchment of India, the Tunga-Bhadra River catchment.

The SWAT model was used to simulate monthly PET and AET. This model uses climate data along with three types of spatial data in hydrological modeling to simulate water budget (i) digital elevation model (DEM) data,(ii) land use/land cover (LULC) data and (iii) soil data. The climate data used in this model consisted of daily time series of precipitation, temperature, wind speed, relative humidity, and solar radiation for the past time slices (i.e. 1986–2013). The historical daily gauge precipitation data for the period 1986–2013 were obtained from the Advanced Centre for Integrated Water Resources Management (ACIWRM). However, the daily maximum and minimum temperatures, wind speed, relative humidity and solar radiation datasets were downloaded from readily available Climate Forecast System Reanalysis (CFSR) datasets (globalweather.tamu.edu) for the hydrological model input. We used the historical streamflow data of five gauge stations for the period 2005–2013 during the stages of calibration (2005–2009) and validation (2010–2013) of the SWAT model (Kumari et al. 2023). Further PET and AET of the model was validated at catchment scale and performance of the model was evaluated against water balanced-based ET and empirical equation-based ET. The SWAT simulated streamflow and ET estimates were used in the previous study by Kumari et al. (2023) for the drought assessment.

For the empirical models, the available gauge datasets with the daily maximum and minimum temperature were obtained from ACIWRM for the period 2000–2012, and used as observed data to estimate the PET/AET of the catchment, wind speed, relative humidity, and solar radiation data were taken from CFSR datasets, required in various empirical equation for PET/AET estimates for the period of 2000–2012.

Since, for the empirical models gauge data were available for the time period of 2000–2012, we further consider the analysis for the time frame of 2000–2012 only.

Furthermore, remote sensing PET and AET data were downloaded from MODIS data sets from the climate engine (https://climateengine.com) website and considered as ground-truth data in this study. Table 1 shows the details of the data sets used in this research work.

The estimation of hydro-meteorological variables using empirical equations and its simulation by SWAT, drought index formulation, and analysis over the period 2000–2012 are explained in the following section, along with the comparative analysis of various model results.

The very first step in the development of the modeling framework is to estimate both PET and AET using various empirical models. There are several models for the formulation of PET among all FAO-56 Penman–Monteith, which was adopted as the standard procedure for PET by the International Commission of Irrigation and Drainage (ICID), the Food and Agriculture Organization of the United Nations (FAO), and the American Society of Civil Engineers (ASCE), and Hargreaves Method, which is chosen to formulate PET and their comparative analysis due to its minimum data requirement. AET was also estimated using the Budyko, and Turc frameworks. The SWAT model was used to simulate PET and AET in the second approach, and in the third approach, these were retrieved from remote sensing-based satellite data sources (MODIS). This study made an effort to cover a range of methods for estimating PET and AET, which are crucial in drought assessment. However, each selected approach has some strengths and limitations as shown in Table 2. Further, the empirical equations and SWAT model setup are explained in Section 2.2.1.1.

For model setup, QSWAT of version 1.9 (QSWAT tool, a plugin for the Quantum Geographic Information System (QGIS) software) with SWAT Editor 2012 was used to model the hydro-meteorological variables PET, AET, and discharge of the Tunga-Bhadra river catchment. SRTM DEM was used to generate the stream networks (Goyal et al. 2014) and to delineate the catchment area in the QSWAT. Precipitation, atmospheric temperature, wind speed, solar radiation, and relative humidity data were used as model input. We used SWAT- Calibration and Uncertainty Program (SWAT-CUP) for calibration, uncertainty, or sensitivity analysis of the model as proposed by Abbaspour et al. (2018). Using Sequential Uncertainty Fitting (SUFI-2) algorithm in SWAT-CUP, model was calibrated and validated at multiple-gauge locations against the observed discharge data (Kumari et al. 2023) and its performance was evaluated based on two objective functions: Nash–Sutcliffe Efficiency (Nash & Sutcliffe 1970) and Coefficient of determination, R². Model performance was found to be more adequate during the monthly time step calibration and validation processes, as results at all selected gauge locations were found to be satisfactory, with R² ranging from 0.57 to 0.92 and NSE ranging from 0.55 to 0.87 in the calibration period (2005–2009), and with R² ranging from 0.57 to 0.93 and NSE ranging from 0.53 to 0.92 in the validation period (2010–2013). The setup of SWAT Model includes various steps., (i) Collection of data sets (climatic and spatial data sets such as Land Use and Land Cover Map, DEM, and Soil Map of the area. (ii) Catchment Delineation (iii) Creation of HRUs (Hdydrological Response Units, (iii) Model run and visualization for desired time step. (iv) Model calibration and validation using observed data. The Step-wise model development procedure is described and used in the earlier study (Kumari et al. 2023). The SWAT model was setup for the period of 1986–2013 with starting two years as a warm-up period. The model warm-up is an adjustment process for the model to reach an optimal state, wherein the internal stores(e.g., soil moisture) move from an estimated initial condition to an optimal state. The response of the hydrological model during this process may show a drift and could be unrealistic. When the model reached an ‘optimal’ state, the response of the model becomes realistic (or stable), and the simulated hydrologic variables are better matched to the observations (Cosgrove et al. 2003; Kim et al. 2018).This model based ET estimates were used in the earlier study for the development of novel drought index SPAEI-Agro (Kumari et al. 2023). However, in this present study, we have utilized the model data from 2000 to 2012 only for the analysis of drought due to unavailability of other model (empirical) estimates for entire time frame.

Further, these SWAT simulated hydro-meteorological variables are compared with the calculated values by empirical model and the satellite datasets of PET and AET. Standardized drought indices are computed for the drought studies with the use of hydro-meteorological variables extracted by various approaches are discussed in the following section.

The meteorological drought index, SPEI takes both precipitation and temperature into account, it combines the response of drought to ET. The SPEI is calculated based on the monthly differences between precipitation and potential evapotranspiration (P-PET)series (Vicente-Serrano 2010). However, the SPAEI is based on the accumulated residual water balance (P-AET) series (Rehana & Sireesha 2021; Kumari et al. 2023). In the warming global climate, there is a need for better consideration of temperature and evaporative demand on drought estimation (Stagge et al. 2017). In this context, as with evaporation and ET-based indicators, SPEI has been found as the best indicator (Wable et al. 2023). The three-parameter log-logistic distribution has performed very well in the (P-PET or P-AET) series for all time scales (Vicente-Serrano 2010; Vicente-Serrano et al. 2015; Monish & Rehana 2019). This distribution accommodates negative values and can take on various forms to describe the frequencies of the P-PET series in various time periods. Following this, the present study adopted a three-parameter log-logistic distribution for fitting the P-PET and P-AET series. Various lags that might be considered for the SPEI calculation can be related to different drought types in a region. whereas water resources in a region with reservoirs are mostly related to longer time scales (Beguería et al. 2010). The SPEI/SPAEI is particularly suited for detecting, monitoring, and assessing the effects of global warming on drought conditions. Hence a 12-month time scale is used for both the SPEI and SPAEI calculation to represent the annual accumulations of atmospheric evaporative demand representing the annual water availability of a given basin. The procedure for the calculation of SPEI and SPAEI are as follows.

For example, obtaining a 12-month SPEI time series is constructed by the sum of D values from 11 months, i.e., before to the current month.

The constants are: C0 = 2.515517, C1 = 0.802853, C2 = 0.010328, d1 = 1.432788, d2 = 0.189269, and d3 = 0.001308.

Positive SPEI/SPAEI values indicate average humidity conditions, while negative values indicate drier conditions. A drought is defined when the SPEI/SPAEI value is less than or equal to −1 in a given time. The drought categories according to SPEI/SPAEI values are given in Table 3.

Table 5 shows the comparative analysis of drought indices SPEI and SPAEI against the reference method, where satellite-based PET and AETs were used in the drought indices estimation. Overall, Hargreaves (NSE: 0.95, R²: 0.95) and Penman–Monteith (NSE: 0.93, R²: 0.93)-based SPEI indices are more synchronized with satellite-based PET-induced SPEI compared with SWAT (NSE: 0.85, R²: 0.91)-induced PET-based SPEI. Similarly, Budyko (NSE: 0.75, R²:0.77) and Turc (NSE: 0.74, R²: 0.76)-based SPAEI indices are more synchronized with satellite-based AET-induced SPAEI compared with SWAT (NSE: 0.71, R²: 0.75)-induced AET-based SPAEI. Overall, empirical-based PET and AET-induced drought indicators are more convincing with satellite-based PET and AET-induced drought indices compared with the process-based PET and AET-induced drought indicators as it shows comparetively high statistical indicator values (Table 5)

The total number of drought events that occurred with PET estimates using Penman–Monteith, Hargreaves, SWAT, and remote sensing are 11, 9, 13, and 7, respectively from Jan 2000 to Dec 2012. Major drought events occurred using Penman–Monteith from June 2001 to August 2004 with a severity value of −46.93. Using Hargreaves, a major event occurred from July 2001 to August 2004 with a severity value of −45.60. Using SWAT, a major event occurred from May 2001 to November 2005 with a severity value of −62.89. Using remote sensing, the major event occurred from June 2001 to August 2004 with a severity value of −43.22. Overall, the drought severity resulting from empirical-based PET estimates is more convincing with satellite-based drought severities compared to process-based PET-induced drought severity.

Similarly, the total number of drought events using Budyko, Turc, SWAT, and remote sensing AET estimates are noted as 8, 8, 13, and 12, respectively from Jan 2000 to Dec 2012. Major drought events occurred using Budyko from July 2001 to August 2004 with a severity value of −46.53. Using Turc, a major event occurred from July 2001 to August 2004 with a severity value of −46.48. Using SWAT, the major event occurred from June 2001 to July 2004 with a severity value of −51.64. Using remote sensing, the major event occurred from May 2002 to July 2004 with a severity value of −39.48. Overall, remote sensing-based AET estimates lead to less drought severities compared to empirical-based and process-based AET estimates.

The study aimed to characterize the drought by incorporating PET as well AET, which influences highly in the drought indices in its characterization, along with precipitation at catchment scales to represent meteorological and hydrological aspects. However, hydro-meteorological data such as PET and AET is difficult to formulate for a larger area, therefore, vital to conclude the more precise ways to estimate these for the formulation of drought indices. To check the amount of variability for accurate drought characterization we have considered various methods to estimate PET and AET variables., Empirical models, Process-based hydrological model (SWAT), and Satellite data products. The empirical formulae used in the formulation of PET are FAO-56 Penman–Monteith, which is considered as the best equation in the formulation of PET-based drought index (Wang et al. 2022). However, this equation demands a large amount of input data, making it less practical for the data-sparse region., Whereas,the Hargreaves equation (Hargreaves & Samani 1982, 1985) is also widely used in the estimation of PET for the large area and catchment scale and requires minimum data for its estimation which makes it more simpler. Similarly, for the estimation of AET, the present study selected the Budyko and Turc models. However, it is difficult to estimate both PET and AET accurately due to a lack of gauged data. With the limited availability of meteorological variables for ungauged basins, the estimation of ET at different spatiotemporal scales for efficient hydro-meteorological extremes study is becoming a challenging task. Moreover, there are a variety of satellite-based remote sensing observations for AET and PET, available at various spatial and temporal resolutions. The study has chosen the MODIS-based PET and AET estimates for drought index formulation. The remote sensing method is considered a standard method as it is satellite-based data and these data products partially solve the problem by providing information in a fast and cost-effective way. However, satellite-based remote sensing techniques such as MODIS-based ET estimates, are highly underestimated with a periodic shift that may be attributed to the cloud cover and leaf shadowing effects (Srivastava et al. 2017). Whereas, ET estimates by process-based hydrological model generated satisfactory results and are widely used to solve a variety of water resource problems and several objective functions are available which can be used to calibrate a model (Singh & Saravanan 2020).

SWAT, widely used for hydrologic studies and climate change studies, divides the catchment of interest into sub-catchments and then further into hydrologic response units (HRUs) depending on land use, management, and soils in order to represent hydrologic processes. SWAT estimates all hydro-meteorologic variables for each HRU separately, and then the total value for the entire catchment. Since this catchment has a limited guage stations and lack of datasets can lead to inaccuracy in the results, for this purpose, the study developed a hydrological model SWAT for the catchment to generate hydro-meteorological variables for drought impact assessment at catchment scales. Although the adopted hydrological model has simulated major hydrological variables, P, PET, and AET which have been used in the drought assessment, implementation of any other hydrological model can equally provide insights to such analysis. The main emphasis of the present study is to integrate major hydrological simulations and to study the sensitivity of PET and AET estimates in the drought characterization, which can be implemented for large area scale and data-scarce regions. The SWAT model developed in this study is limited to the simulation of hydro-meteorological variables for previous years only (1988–2013) and the drought assessment were for the period 2000–2012 due to the unavailability of complete data sets required by various models to estimate PET/AET and to compare with remote-sensing PET/AET data, which was available from the year 2000 onwards. However, it can be extended up to the present period using the recent year's input datasets. Further, the model is developed based on input datasets such as DEM, LULC, soil, and weather data in this study; one can extend such a hydrological model by adding reservoir and channel information for a better simulation of high flows, which is crucial in terms of hydrological drought. In this study efforts were made to show the variations in PET and AET estimates that can have significant implications on drought severities, making them a critical aspect of drought study. Both PET and AET are essential components in understanding the water balance of the river basin and assessing the drought conditions.Howerver, hydrological model simulated PET and AET are parameter specific and requires huge efforts toward validation. To study the effect of different ET over drought severity, the present study has considered the modeled datasets for drought indices formulation and analyzed the comparative results of empirically, remote sensing, and hydrologically modeled PET and AET-based drought index of SPEI and SPAEI, respectively. In this study we have chosen the longer time scale drought index estimation such as SPEI/SPAEI-12 for the drought assessment to provide the annual water balance status of the catchment. While the shorter time scale drought index such as SPEI-3 represents short-term seasonal fluctuations (Gond et al. 2023). Our study was more focused on variations in PET and AET estimates of the catchment and both PET and AET are essential components in understanding the water balance of the river basin and assessing the drought conditions. So we used SPEI/SPAEI at 12 months of time scale.’The results of SPEI and SPAEI were found similar for the catchment where the SPEI was also found to be more intense compared to the AET-based drought index by Rehana & Sireesha Naidu (2021). The data extracted from remote sensing and modeling has been considered more practical and alluring for researchers (Khorrami & Gündüz 2022). This study has considered the remote sensing data product as standard and ground-truth data products as these data products partially solve the problem by providing information in a fast and cost-effective way and can be used to continuously monitor the processes of and changes in drought across both time and space (Hao et al. 2015). The remote sensing data sets have been made available and have become an important data source for large-scale drought assessment (Rhee et al. 2010), however due to its limitation discussed by Srivastava et al. (2017) one can select the other data products as a standard sets for their analysis. Further, in order to show the potential of drought indices estimated by using different PETs and AETs this research work has presented the comparative analysis over a large catchment area, i.e., Tunga-Bhadra River of India. Overall, the empirical equations-based drought indices SPEI/SPAEI were more synchronized with satellite-based drought indices (Table 5). However, considering the results of drought severity computed by different PETs and AETs one can opt for empirical equations or process-based hydrological models to simulate PET and AET for drought indices depending on the availabilities of dataset in the interest of the region. Since the drought indices value are nearly same despite of variations in PETs and AETs estimate. The reasons behind this consistency could be human activities and land use changes in the catchment that stabilizes the water balance, could contribute to the observed small variation in SPEI/SPAEI. Further, It is important to conduct research and analysis specific to the region in question to understand the interplay of these factors and determine the main reasons for the variations in PET/AET and consistency in SPEI/SPAEI values.

This study aimed to characterize drought using different PET and AET models for the Tunga-Bhadra catchment, India, from 2000 to 2012. PET is estimated using the empirical methods of Penman–Monteith and Hargreaves. AET is estimated using the empirical methods of Budyko and Turc. The hydrological model SWAT is used to estimate both PET and AET. Remote sensing (MODIS) data for PET and AET is cropped from the climate engine website. There is a significant variation in the lowest value of PET estimated by Hargreaves equations and remote sensing-based PET compared to SWAT and Penman–Monteith PET. However, the maximum monthly value estimated by the Hargreaves equation has shown a large deviation with remote sensing and SWAT-modeled PET. After estimating both PET and AET, drought is estimated using SPEI and SPAEI. The drought indices values estimated based on empirical and process-based induced PET and AETs are compared with remote sensing PET and AET data-induced drought indices.

For the study area, a continual drop in precipitation was observed between the years 2000–2004, with the falling profile of streamflow in the same year, which specifies major drought events that occurred in those years. The study compared various drought characteristics, such as drought severity, frequency, and duration corresponding from 2000 to 2012. Results show that despite variations observed in PET and AET estimates, drought indices values are nearly identical regardless of the method. It is observed that the average value of drought indices formulated based on PET and AET by various methods are nearly the same with the values of −1.20 (SPEI) and −1.22 (SPAEI) for the major drought event period 2002–2004. Although all methods correlated better with each other, Hargreaves for SPEI and Budyko for SPAEI performed relatively better with NSE and R² values of 0.95, 0.95, and 0.75, 0.77, respectively. The total number of drought events that occurred for PET estimates using Penman, Hargreaves, SWAT, and remote sensing are 11, 9, 13, and 7, respectively. Long duration of drought using PET is captured by SWAT with a severity value of −62.89 from May 2001 to November 2005. All other three methods generated similar severity values.

Similarly, for AET total number of drought events using Budyko, Turc, SWAT, and remote sensing are 8, 8, 13, and 12, respectively. The long duration of drought using AET is captured by SWAT with a severity value of −51.64 from June 2001 to July 2004. Budyko and Turc's approach predicts the onset and end of the drought similarly.The SPEI was able to capture more number of drought events as well captures the more severe drought events than SPAEI. Also the Performance of statistical indicator for SPEI values by various methods against remote sensing is comparatively better than of SPAEI. It is recommend to use PET-based SPEI over SPAEI.

The following are some major concluding remarks of the present study:

• It is recommended to use PET instead of AET when estimating drought indices as SPEI values performed relatively better than SPAEI. Although PET and AET estimates vary with different models, drought indices SPEI and SPAEI do not differ much.

• Hargreaves and Penman–Monteith performed better results compared to the reference method in SPEI calculations. And for SPAEI Budyko and Turc performed better results.

• The drought severity resulting from empirical-based PET estimates are more convincing with satellite-based drought severities compared to process-based PET-induced drought severity.

• Remote sensing-based AET estimates lead to less drought severities compared to empirical-based and process-based AET estimates.

• Overall, the present study concludes that empirical models of PET and AET are correlated better with the remote sensing data (MODIS).

The authors sincerely thank Dr P. Somasekhar Rao, Technical Director, at the Advanced Centre for Integrated Water Resources Management (ACIWRM), Bengaluru, Karnataka, India, for providing Tunga-Bhadra basin data.

The research presented in this study was funded by Council of Scientific & Industrial Research (CSIR), Human Resource Development Group (HRDG), under A Special Call for Research Grants for Women Scientists (ASPIRE), CSIR-HRDG-EMR-II, with Project no. 22WS (0035)/2023-24/EMR-II/ASPIRE to Dr. Shaik Rehana.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.