Spatiotemporal trends and evapotranspiration estimation using an improvised SEBAL convergence method for the semi-arid region of Western Rajasthan, India

Calculating actual evapotranspiration (ET) is crucial as it regulates how much water and thermal energy is exchanged between the atmosphere and the ground surface. ET significantly affects the ecosystem of any region, and its assessment at a high spatial and temporal resolution plays a crucial role in the integrated management and planning of agricultural water supplies. Therefore, many mathematical models and algorithms have been planned to assess quantitative values of evapotranspiration. Calculation methods either use the inputs available from meteorological stations or other mediums such as gridded and reanalysis data where there is a lack of data from meteorological stations.

In canal-based irrigation commands, the irrigation schedule is either done based on the farmer's demand or on the calendar days passed since the last irrigation. Compared to the rotational water distribution system, canal water supply based on actual crop water demand is of great importance. ‘The National Commission on Integrated Water Resources Development (NCIWRD-1999) had projected the efficiency of India's surface irrigation systems as forty, fifty, and sixty per cent in the years 2010, 2025, and 2050, respectively’ (Amarasinghe et al. 2007). Ground-based flux measurement methods like the Bowen Ratio (BR) method (Bowen 1926), Eddy covariance (EC) method (Wilson et al. 2002), and the recent Surface Renewal (SR) alpha calibration method (Shapland et al. 2014) can furnish ET measurements with high temporal scales such as half-hourly to daily. However, these methods cannot capture diversification within the plantation fields due to their low spatial trace. Furthermore, these methods need expensive equipment for data collection, and their maintenance demands intensive labor.

The objective of the present study is to evaluate the feasibility of the application of the SEBAL model in the region to estimate the actual evapotranspiration. Optimization in irrigation scheduling would facilitate the decision-makers and will reduce losses, improve irrigation efficiency and maintain the crop yield. With recent advancements, the radiative energy interchange among the Sun, Earth, and space can be evaluated more precisely utilizing new satellite technologies. The plant's growth stage or level of maturity, solar radiation, wind speed, temperature, relative humidity, and percentage of soil cover are some of the key factors that affect evapotranspiration. A standard measurement of ET at a spatially large variation is quite complex. Therefore, remote sensing and Geographic Information System (GIS) approaches were applied to evaluate ET from available satellite and meteorological data to estimate ET over such a large spatial extent accurately.

In the past five decades, numerous methods have been developed to calculate according to climatic conditions and available metrological data. To improve the performance of the evaluation, the United Nation's (UN) body – the Food and Agriculture Organization (FAO) – has propounded four methods, including the modified Penman method, radiation method, pan evaporation method, and Blaney–Criddle method. However, these methods often give varying results among different locations and have large deviations (Pereira et al. 2015). Among various methods, Priestly-Taylor and Hargreave's methods show results with high accuracy in the arid and semi-arid regions (Gao et al. 2017). In recent decades, with increasingly available free satellite observations from multiple sensors, various methods have been implemented across the world (Elkatoury et al. 2020). Shamloo et al. (2021) estimated ET and crop coefficient of corn in the Mediterranean region of Adana province in Turkey using the SEBAL algorithm. Aryalekshmi et al. (2021) reviewed various surface energy balance (SEB) models for ET estimation using remote sensing data. Wu et al. (2010) applied SEBAL and Markov models for simulating future streamflow. Empirical algorithms have been built and demonstrated that connect ET with vegetation indices obtained from satellite observations and meteorological data (Johnson & Trout 2012). Studies suggest, ‘These models perform well in areas where they are calibrated, but uncertainty increases when applied to other areas.’ However, the Hargreaves method, calibrated with weather measurements of arid and semi-arid regions, has shown optimistic results for assessing ET integrated with remote sensing (Shamloo et al. 2021).

Three substantially important forms of ET can be expressed as actual evapotranspiration ⁠, potential evapotranspiration ⁠, and reference evapotranspiration ⁠. ‘ is the water loss which would occur when sufficient moisture is available in the soil such that stomata are fully open and resistance to water vapor transport from bare soil to the atmosphere is at a minimum’ (Beaumont Blake & Wagstaff 2016). is defined by a theoretical surface with no restrictions on the availability of soil moisture as the reference evapotranspiration rate (Allen et al. 1998). is the disappearance of water through a surface under vegetation with prevailing soil moisture conditions. can significantly vary on a daily timescale. However, several studies have reported spatially very consistent at the regional scale unless where there are significant topographical slopes (Zhang et al. 2019).

Stationary actual evapotranspiration estimation methods have multiple drawbacks when the spatial extents are very large (10 hectares or more). Major drawbacks include issues such as measurement of point data for a specific region, maintenance problems, estimation of the hydrological process that is of a complex nature, and the need for expert workers. To resolve these prominent issues, a method such as the ‘Surface Energy Balance Algorithm for Land’ (SEBAL) model, which is based on remotely sensed images, can be utilized. When compared to other SEB models, SEBAL has performed well for ET studies at regional scales for diverse climatic conditions and scarce meteorological data (Li et al. 2009; Wanniarachchi & Sarukkalige 2022). Presently available remote sensing-based ET and reanalysis datasets with global gamut comprise the 1 km – Moderate Resolution Imaging Spectroradiometer (MODIS) data products (Rahimi et al. 2015) and reanalysis records such as MERRA-2 (Lv et al. 2021) having 8-day and 1-month temporal resolutions, respectively, which are considered coarse for various regional-level hydrological applications. Using the FAO Penman–Monteith (FAO-PM) and Hargreaves Method as a benchmark, we evaluated the accuracy of daily ET generated from remote sensing data vs. ET derived from observation/station data using the FAO-PM and Hargreaves Method. We compared which method performs best in arid and semi-arid regions and investigated the dominant drivers of ET spatial and temporal variation in Western Rajasthan. Therefore, a semi-automated code using Google Earth Engine (GEE) was developed, enabling the assessment of ET for the study region (arid and semi-arid). Following the development of the algorithm, a thorough assessment of the large Western Rajasthan region's major crops and spatiotemporal cropping patterns with growth stages was identified using various studies (Jangid et al. 2018) and data available from the Department of Economics & Statistics under the Department of Planning (Agricultural Statistics 2020) and the Department of Agriculture, Government of Rajasthan (Crop Wise Sowing Area Report 2020).

The primary objectives of the present research are (a) to generate a spatiotemporal distribution of evapotranspiration of the western region of Rajasthan, India, and (b) to develop a remote sensing-based semi-automated evapotranspiration modeling framework.

The study area encompasses regions of IGNP in Sri Ganganagar, Hanumangarh, and Churu in the north-western parts of Rajasthan, Bikaner, Jaisalmer, and Barmer in the west, and Jodhpur and Nagaur in the central-west districts of Rajasthan, stretching a terrestrial extent of 1,72,050 km². The mean elevation is 211 m above sea level. The climatic characteristics of arid regions are low and erratic precipitation compared to high atmospheric demands. This region gets annual rainfall in the range of 100 to 500 mm with high rates of atmospheric water demand, i.e., evapotranspiration (Moharana et al. 2016). The IGNP command area map with Stage I and Stage II canal flow areas was acquired from the Department of Water Resources (WRD), Govt. of Rajasthan (Physical Progress 2020). Moharana et al. have comprehensively discussed the major landforms and desertification status of Western Rajasthan (Moharana et al. 2016).

Three sources of remotely sensed datasets were used in this study for the years 2019 and 2020. The United States Geological Survey (USGS) provided Landsat 8 surface reflectance observations that had been atmospherically rectified utilizing the ‘Land Surface Reflectance Code (LaSRC) algorithm’. The ‘Shuttle Radar Topography Mission (SRTM) digital elevation (Data Version 4)’ dataset was used to assess the topography of the region. The MODIS Terra Land Surface Temperature (LST) and emissivity inputs with a spatiotemporal resolution of 8-day Global 1 km from the USGS were used to obtain LST values. Landsat 8 with two thermal bands—10 and 11—is sufficient for obtaining LST and emissivity values (Jiménez-Muñoz et al. 2014), but to avoid temporal gaps in final results, MODIS Terra LST product was used in this study. Many studies have demonstrated the satisfactory application of Landsat-MODIS-based fusion models for ET estimation integrated with SEB methods (Bhattarai et al. 2015). The remote sensing data were accessed within the GEE framework.

The local weather parameters required for the SEBAL model were acquired from the Indian Meteorological Department (IMD) station installed in Jodhpur City at 26.2578° N and 72.9952° E. The meteorological data obtained have a daily temporal resolution and include various parameters, as shown in Table 1. Daily values of are measured utilizing the meteorological data using the FAO-PM and Hargreaves equations integrated with crop coefficient values ⁠.

In the present study, the SEBAL algorithm-based model was applied for the assessment of ET over the study region. SEBAL utilizes digital images produced by sensors such as Landsat that can capture radiation throughout the visible, near-infrared, and thermal infrared bands. Developed by Bastiaanssen et al. (1998), the SEBAL model has become a valuable tool in various fields, such as agriculture, hydrology, and environmental studies. It operates on the basic principle of energy balance at the land surface. The general equation of SEBAL Equation (1) considers various components of the energy balance equation, including incoming solar radiation, outgoing radiation, sensible heat flux, soil heat flux, and latent heat flux. The SEBAL model relies on accurate meteorological input data and the availability of high-quality satellite imagery. Additional data requirements include LST and surface albedo. For this study, the median composite was generated using the power of the gigantic computation resources within a cloud-computing environment by analyzing more than 40 petabytes of geospatial data provided within the GEE framework (Gorelick et al. 2017). A simple linear regression–based fusion model was utilized to integrate Landsat and MODIS data (Bhattarai et al. 2015). The combination of remote sensing and GEE capabilities helps in achieving new levels of remote sensing modeling studies. This semi-automated code is particularly proposed in this study to evaluate ET obtained on a regional scale using an improvised SEBAL iterative convergence method, which is particularly useful during the computation of the sensible heat flux (H) when the measured wind speeds are low. The results obtained were validated using location-specific meteorological data. Also, as the study region is mostly flat in topography, the terrain influence is minimal.

As pioneered by Bastiaanssen, in Equation (8) can be approximately estimated as a relatively simple linear function of (Bastiaanssen 2000). Using a digital elevation model (DEM), each pixel (surface temperature) is assigned to a common elevation data, and a and b are further determined. The two coefficients need the sampling of two anchor pixels, designated as the hot and cold pixels, which reflect the near-extreme circumstances of temperature and relative humidity. The cold pixel is identified as a fully covered, well-irrigated crop surface. is supposed to be zero for the dry, barren farming represented by the hot pixel. These two anchor pixels are used to calculate all other pixels between them.

The SEBAL model is improvised as the measured meteorological data show relatively low wind speeds across the year, which results in difficulty in quantifying the value of aerodynamic resistance and the various components that are computed indirectly. Errors in affect the concluding value of H and dT, which are calculated using Equation (7). Using the modified iterative procedure of the SEBAL as proposed by Dhungel et al. (2016), the convergence of Monin–Obukhov stability correction was expedited. The method of improvisation in the convergence mechanism for the iterative process suggested by Dhungel et al. states that ‘The first iteration generates the set of data for the next iterations by averaging the u* from the current time-step and the previous time-step ⁠, which is stored for each iteration in a nested loop’ (Dhungel et al. 2016). The pixel was unable to achieve convergence from the previous method and either needed a large number of iterations or resulted in divergence in various instances.

The non-convergence would either result in over-estimating or under-estimating ⁠, which influences the final values of dT, H, and latent heat flux. After the averaging modification, convergence was achieved in a few iterations (less than 10), and the oscillation behavior was eliminated in this study. It has been demonstrated by Dhungel et al. (2016) that for higher wind speeds, the convergence behavior was similar before and after the modifications. This modification decreased the uncertainty in flux calculations caused by non-convergence, enhancing the precision of SEB parameters, which is particularly relevant in arid and semi-arid climates (Dhungel et al. 2016). The results of this study confirm that averaging the components present in the nested loop helped expedite the process and achieve convergence in low wind speed conditions.

Two methods were used in this study to estimate ⁠, FAO-PM (Equation (12) and Hargreaves method (Droogers & Allen no date) (Equation (13)), and was also correlated with the pan evaporation data obtained from the weather station. To estimate as per standard conditions for the median image, crop coefficients were identified, as shown in Table 2.

The evapotranspiration was evaluated by the SEBAL algorithm for the IGNP region. Furthermore, to validate the ET results obtained from the SEBAL model, various statistical parameters such as determination coefficient, root-mean-square, and mean bias error (MBE) of the values computed from SEBAL with the values obtained from the calculation using the Excel sheet were evaluated, as shown in Figure 7.

The SEBAL model was used to calculate daily and seasonal actual evapotranspiration for the years 2019 and 2020 using Landsat 8 and MODIS Terra images integrated with meteorological data collected from a weather station. To validate the actual evapotranspiration calculated by SEBAL, FAO-PM and Hargreaves methods were used. Major crop coefficients for various seasons were estimated using statistical methods from the studies and data obtained from Rao & Poonia (2011), Shahrokhnia & Sepaskhah (2013), and Crop Wise Sowing Area Report (2020).

The seasonal variations in LST and NDVI (Supplementary Material, Figure S10) for 2 years are demonstrated. During the pre-monsoon period (April to mid-June), LST is high in Western Rajasthan, ranging from 23 to 45 °C. Low temperatures correspond to agricultural lands in the northern part. Moderate to high LST is recorded over the arid western sections of the region, which is a major part of the Thar Desert. The monsoon season (July to mid-September) shows a reduction in LST mainly due to rainfall and cloudy weather. It also becomes difficult to obtain cloud-free images during this season, but with the abilities of GEE, it is possible to develop a representative median image without much complexity. This is also the period of highest precipitation. However, the observed LST is lower than in the pre-monsoon season. The LST during the post-monsoon season (October–November) ranges from 12 to 37 °C. In this season, the Kharif crops (the local name for summer crops) are harvested, and the LST observed over the fallow agricultural lands is higher when compared to vegetated areas. The winter season (December–February) is the crop-growing Rabi (local name for winter crops) season. The winter LST ranges from 5 to 26 °C, with low LST in the study area's northern and middle regions and comparatively high LST in the non-vegetated barren areas.

The NDVI index of the pre-monsoon period ranges between −0.2 and 0.45 in different time periods. Most of the region consists of barren land and fallow agricultural areas, as this is the season when the winter crops have already been harvested, showing low NDVI. Zaid crops (local name for crops between winter crops and summer crops) are grown in some of the northern and eastern regions of the study, which demonstrates relatively higher NDVI. The locations that have a low NDVI also correspond to the locations that have a high LST.

A representative pixel of the ET of the agricultural fields in proximity to the weather station was chosen to assess the execution results. The parameters obtained in the northern regions were examined afterward, and the final ET product was evaluated. Table 3 displays the statistics of the representative pixel for the years 2019 and 2020.

Table 3

Statistics of the important components acquired from the SEBAL model for the selected/representative pixel for years 2019 and 2020

Median image (season-wise) .	NDVI .	Albedo .	LST (°C) .	Rn (W/m2) .	H (W/m2) .	G (W/m2) .	ETSEBAL (mm/day) .	(mm/day) .	(mm/day) .
Pre-monsoon (2019)	0.16	0.34	45.95	668.47	163.53	168.12	4.98	6.33	4.38
Monsoon (2019)	0.61	0.30	28.53	656.62	−16.3	84.98	6.20	7.90	5.58
Post-monsoon (2019)	0.73	0.26	35.61	693.59	42.97	90.66	4.97	7.82	4.67
Winter (2019)	0.71	0.22	23.72	638.92	178.38	55.8	3.73	3.95	3.74
Pre-monsoon (2020)	0.17	0.32	45.71	652.17	235.24	160.86	4.56	7.30	4.54
Monsoon (2020)	0.63	0.29	29.29	646.89	−20.2	95.91	6.28	7.41	5.51
Post-monsoon (2020)	0.62	0.28	38.72	674.76	62.59	97.42	4.75	4.70	4.45
Winter (2020)	0.78	0.23	22.64	629.47	154.21	44.53	3.82	3.98	3.81

Median image (season-wise) .	NDVI .	Albedo .	LST (°C) .	Rn (W/m2) .	H (W/m2) .	G (W/m2) .	ETSEBAL (mm/day) .	(mm/day) .	(mm/day) .
Pre-monsoon (2019)	0.16	0.34	45.95	668.47	163.53	168.12	4.98	6.33	4.38
Monsoon (2019)	0.61	0.30	28.53	656.62	−16.3	84.98	6.20	7.90	5.58
Post-monsoon (2019)	0.73	0.26	35.61	693.59	42.97	90.66	4.97	7.82	4.67
Winter (2019)	0.71	0.22	23.72	638.92	178.38	55.8	3.73	3.95	3.74
Pre-monsoon (2020)	0.17	0.32	45.71	652.17	235.24	160.86	4.56	7.30	4.54
Monsoon (2020)	0.63	0.29	29.29	646.89	−20.2	95.91	6.28	7.41	5.51
Post-monsoon (2020)	0.62	0.28	38.72	674.76	62.59	97.42	4.75	4.70	4.45
Winter (2020)	0.78	0.23	22.64	629.47	154.21	44.53	3.82	3.98	3.81

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The representative pixel was chosen on the basis of regional knowledge of agricultural patterns followed in various seasons. It was based on the density of vegetative coverage of the major crops of the season. The presence of moisture in vegetation results in higher sensible heat flux for timescales, corresponding to higher NDVI. The values of G are proportional to the values of Rn, and when Rn is high, soil heat flux (G) is also high.

The NDVI for the monsoon ranges between −0.15 and 0.84. The maximum NDVI values are recorded in the northern sections of farmlands, while the lowest NDVI values are observed over arid and agricultural fallow. Following the monsoon season, the NDVI ranges from −0.18 to 0.89 in the post-monsoon season. The development of vegetation caused by the monsoon season resulted in a higher NDVI during the post-monsoon period. The wintertime NDVI ranges from −0.42 to 0.83. Over the northern and central portions of the study area, which consist of agricultural fields, a high NDVI is found.

The NDVI demonstrates greater values when the observed LST is low. Many studies have also demonstrated such an inverse linear relationship between NDVI and LST (Kalluri et al. 1998; Kumar & Shekhar 2015; Tran et al. 2017; Kundu et al. 2018). NDVI is higher in vegetated lands, and after crop harvest, NDVI decreases. The direct surface heating is restrained as the higher leaf area index (LAI) captures the incident solar radiation. Furthermore, it alters the energy flux at the surface because of the constant cooling and evapotranspiration from the surface (Babatunde 2012).

In the pre-monsoon season, the northern and mid-eastern parts show high ET, which consists of agricultural areas. The western region is mostly barren and, hence, shows negligible ET. As the winter crops are harvested in this season, low ET is observed when correlated to the monsoon season. The monsoon season shows elevated ET values in the agricultural fields (northern and mid-eastern regions) for various reasons, such as higher availability of surface water (from rainfall) combined with high air temperatures. Also, Kharif crops (summer crops) are grown during this season, exhibiting high transpiration rates. However, the surface temperature values observed are lower than in the pre-monsoon season because of the cooling effects of overcast skies and rainfall during this season.

Low ET is detected over the farmlands in the northern and mid-eastern regions in the post-monsoon season, which are mainly fallow lands as the summer crops are harvested during the months of October to November. High evapotranspiration is observed in agricultural areas in the winter period as this is the Rabi crop's (winter crop) growth phase. Rabi crops are mainly grown in canal-irrigated areas and regions with available access to groundwater of desired quality. Across all seasons, it is observed that NDVI varies with ET, as demonstrated in Figures 3 and 4. The crop calendar for major crops is depicted in Supplementary material, Table S1.

As demonstrated in Figure 7, the determination coefficient across SEBAL-estimated ET and estimates by the FAO-PM and Hargreaves techniques has an acceptable value of 0.84 for the Hargreaves method but shows a slight decrease of 0.60 for the FAO-PM method. Moreover, the RMSE value for the FAO-PM was computed as 3.99 mm day⁻¹ and 0.05 mm day⁻¹ for the Hargreaves method. Thus, these outcomes demonstrate the efficacy of the SEBAL model in calculating ET for the Western Rajasthan IGNP command region. It can be observed that bias was higher for the pre-monsoon season. This is due to the fact that the winter crops have been harvested, and most of the fields are fallow.

Evapotranspiration plays a major role in optimizing the irrigation management system and water balance. Sufficient information is scarce on the spatial distribution of ET. As per our knowledge, there is a huge lack of observed data on actual ET for the broad Western Rajasthan region, which is publicly available. Low ET is witnessed in the fallow lands during the pre-monsoon season as all the crops are harvested, whereas the monsoon and winter seasons demonstrate high values of ET as these are the crop-growing seasons in the region. In every season, water bodies exhibit extremely high ET. After the crop harvest, low ET is seen in fallow farmlands. The measured data by the meteorological station is scarce, and the estimation is valid just for the installed location. On the other hand, the SEBAL-based ET outputs are successful in covering a large spatial extent with satisfactory accuracy. As per our knowledge, there is a significant lack of publically available observed data on actual ET for the broad Western Rajasthan region. Low ET is witnessed in the fallow lands during the pre-monsoon season as all the crops are harvested, whereas the monsoon and winter seasons demonstrate high values of ET as these are the crop-growing seasons in the region. In every season, water bodies exhibit extremely high ET. After the crop harvest, low ET is seen in fallow farmlands. The measured data by the meteorological station is scarce, and the estimation is valid just for the installed location. On the other hand, the SEBAL-based ET outputs are successful in covering a large spatial extent with satisfactory accuracy.

In comparison to places with low or medium fractional vegetation cover, vegetated agricultural areas have a higher fractional vegetation cover, which leads to higher transpiration in the northern regions. Over agricultural regions, soil moisture also contributes to higher ET, whereas rocky surface areas and desert regions are mostly barren, exhibiting high surface temperatures and high sensible heat movement, which results in small ET. The SEBAL-generated ET and the Hargreaves technique of daily ET estimation have not been shown to differ significantly.

The model developed is a semi-automated, flexible, user-friendly ET retrieval system with high spatial resolution. The main features of this model include spatial coverage over a large extent, such as the IGNP region, estimation of various vegetation indices, emissivity, LST, and actual ET, specifically in arid and semi-arid regions experiencing low wind speeds with readily available Landsat-8 and MODIS images, which would have required huge computational resources if applied using the conventional methods. The advantage of employing such a model is to acquire the desired ET data with its high resolution and spatiotemporal variations, particularly in regions having scarce weather and soil moisture data. The valuable facts and data will assist in optimizing water management at any scale for the IGNP command region. The results can be used for irrigation management by identifying the areas and seasons with high ET rates, indicating higher water demand. Temporal patterns of ET can be used for drought monitoring. A sudden decrease in ET might indicate water stress in vegetation. Monitoring these patterns over time can help anticipate and manage drought conditions effectively. Changes in spatiotemporal ET patterns can be indicative of climate change impacts. Monitoring these changes over the years can contribute to climate change impact assessments, helping communities adapt to new conditions for sustainable development. The present study assesses the remodeling of the deserted region into agriculturally and socioeconomically productive land, which fits well with the ‘Sustainable Development Goals’ (SDG) and the targets anticipated by the UN for the year 2030. The SEBAL-based model was calibrated and authenticated for the different seasons with an accuracy of more than 96% compared to the suggested Hargreaves method. The overall trend analyzed from the available weather data (pan evaporation) shows a downward trend in the rate of evapotranspiration (2010–2020). In summary, the spatial and temporal patterns of evapotranspiration are valuable for making informed decisions regarding water management, land use planning, and adapting to changing environmental conditions. These insights contribute to more sustainable and efficient water use in a region. The future scope of this study can be used to generate new climate parameters as a result of altering other SEBAL characteristics. Alternative climatic and land use change scenarios, as well as seasonal fluctuation in land use changes, might be taken into account as potential future scenarios. Agricultural lands differ in crop cover, which results in varying rates of actual ET values and can serve as a future research topic.

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

The authors declare there is no conflict.