The performance of potential evapotranspiration (PET) methods such as pan evaporation (physical measurement), empirical formulas (Penman–Monteith (PM), Hargreaves and Thornthwaite) and satellite-derived PET (MOD16) were assessed in a semiarid region of central India. The satellite-based PET was obtained from Moderate Resolution Imaging Spectroradiometer (MODIS). The comparisons between different methods were made with observed pan evaporation (ETpan) data to identify the best method for the semiarid region. Further, the future projection of PET was carried out using RCP4.5 emission scenarios of seven CMIP5 models. Two approaches were applied for the projection of PET. In the first approach, RCP4.5 scenario data are directly used in the PM method, and in the second approach, these variables are used as a predictor in the calibrated and validated least square support vector machine (LS-SVM) model. The projection of PET was made using the best-identified model among PM and LS-SVM from the years 2006–2100. The results show that MOD16 and Hargreaves overestimate the PET; however, PM and Thornwaite underestimate the PET. PM based PET is closely related with ETpan and is a good indicator of ETpan in a semiarid region. GFDL-ESM2M is identified as the most skillful CMIP5 model, and results show that PET is projected to increase in future using the LS-SVM model.

HIGHLIGHTS

  • The PET estimation methods, namely empirical and satellite-based PET, were evaluated and compared with ground-based observed ET.

  • Satellite-based PET is closely matching with ground-based PET in wet season.

  • Satellite-based PET can be used after applying a suitable correction factor in the study area.

  • The PM method was found suitable for the semiarid region.

  • PET is projected to increase in future using CMIP5 models.

The drivers of the global water cycle are expected to be intensified by the processes of climate change. Since irrigation is the most important driver at global scale, a change in climate may change the irrigation water requirement and irrigation scheduling (Darshana et al. 2013; Kisi & Zounemat-Kermani 2014). Evapotranspiration (ET) is one of the important parameters for irrigation scheduling and regional water allocation. As ET is a key link between the atmosphere and the soil matrix within the hydrologic cycle, the assessment of ET is important to evaluate the impact of climate change on water resources. It has several dimensions such as actual evapotranspiration (AET), potential evapotranspiration (PET), reference evapotranspiration (RET) and pan evapotranspiration (ETpan). Among all, PET, which is considered as a surrogate to ETpan, has been found most important for many hydrological and agricultural applications (Chen et al. 2005; Zhang et al. 2007; Westerhoff 2015). PET is assessed through physical (i.e. evaporation pans), empirical and satellite methods. The empirical approaches of PET estimation are broadly classified into three categories, namely temperature-based (e.g. Thornthwaite 1948; Blaney & Criddle 1950; Hargreaves & Samani 1982, 1985), radiation-based (e.g. Priestley & Taylor 1972) and a combination of both (e.g. Penman 1948; Monteith 1965). The temperature-based methods use only air temperature and sometimes day length data, while radiation-based methods use net radiation and air temperature data. The combination methods use net radiation, air temperature, wind speed and relative humidity. Therefore, to calculate PET, different models use different input parameters (Chen et al. 2005; Donohue et al. 2010; Darshana et al. 2013) and the choice of an assessment method depends on the definition of PET utilization, the available input data, the purpose of calculation and surface characteristics.

Several studies have been carried out worldwide for PET estimation using empirical as well as process-based models by utilizing ground-based meteorological input parameters. The radiation-based (Priestley–Taylor) method is recommended in tropical to subtropical climates of Florida (Douglas et al. 2009) and the southeastern United States (Lu et al. 2005). The temperature-based (Thornthwaite) method is recommended in the northeastern USA (Rosenberry et al. 2007) and Iran (Tabari et al. 2013). A combination of both (Penman–Monteith (PM) method) is found superior in arid and semiarid regions of Iran (DehghaniSanij et al. 2004), China (Chen et al. 2005), Australia (Donohue et al. 2010), New Mexico, USA (Djaman et al. 2019) and southern Iran (Didari & Ahmadi 2019).

In recent decades, soft computing techniques (e.g. artificial neural networks, fuzzy and neuro-fuzzy systems, support vector machine and genetic algorithms) have been successfully applied for modeling the ecohydrological process around the world (Kisi & Tombul 2013; Lin et al. 2013; Goyal et al. 2014; Kisi & Zounemat-Kermani 2014; Duhan & Pandey 2015; Wang et al. 2017a). Goyal et al. (2014) concluded that fuzzy logic and LS-SVR approaches can be employed successfully in modeling the daily evaporation process from the available climatic data. The LS-SVM model performed better than the ANFIS and artificial neural network (ANN) models when similar meteorological input variables are used (Seifi & Riahi 2020). The multivariate adaptive regression splines (MARS) model performs better than least square support vector machine (LS-SVM) and M5Tree for the modeling of ETpan at Mediterranean sites of Turkey (Kisi 2015). Lin et al. (2013) found that the SVM based model is superior to multilayer perception models for ETpan estimation due to its accuracy, robustness and efficiency. Duhan & Pandey (2015) stated that LS-SVM is the best model among multiple linear regression (MLR), ANN and LS-SVM for the future projection of temperature in the Tons river basin in central India. The fuzzy genetic and least square support vector regression (LS-SVR) models with more input variables perform better than the MARS, M5Tree and MLR models in predicting ETpan in the Dongting Lake Basin, China (Wang et al. 2017a) and in the Yangtze River Basin, China (Wang et al. 2017b). From the literature, it can be concluded that the SVM model performs better than other models in the semiarid region.

In recent decades, estimating ET has been improved by advances in remote sensing, particularly in agricultural and hydrological studies. With the development of global PET products such as MOD16 (Mu et al. 2007, 2011), few researchers have compared it with ground-based PET. Chen et al. (2014) concluded that the process-based models (Priestley–Taylor type model or PT-JPL, PM-Yuan model or PM-Yuan and PM type models or PM-MOD16) are superior over the empirical models. Westerhoff (2015) reported that MOD16 satellite PET can estimate real PET better than using ground-based estimates of PET from eddy covariance. Knipper et al. (2017) stated that Moderate Resolution Imaging Spectroradiometer (MODIS)-soil moisture ET overestimates annual ET when compared with eddy covariance stations data in a semiarid region of the American Southwest. Though the satellite data provides an ample opportunity to estimate the input parameters for PET models, their utilization is limited in the Indian context. Further, the satellite-based products of PET have been rarely compared with the ground-based observation of PET and empirically derived PET from different methods in India.

Climate models are important tools that provide an understanding of future climate under different emission scenarios. The Coupled Model Intercomparison Project Phase 5 (CMIP5; Taylor et al. 2011) developed by the Intergovernmental Panel on Climate Change (IPCC 2014) supply a framework for coordinated climate change experiments that can improve our knowledge of climate and climate change. Various researches have been carried out to identify the most skillful CMIP5 model for Indian conditions. Among 20 simulation models, MPI-ESM-LR, INM-CM4 and MRI-CGCM3 best capture the spatial patterns of Indian winter monsoon (Jena et al. 2016) and for summer monsoon, BNU-ESM, MPI-ESM-LR, MIROC5 and NorESM1-M models are found better (Sharmila et al. 2015). NorESM1-M and MIROC5 models have the largest skill score in simulating the mean state of global as well as Asian–Australian monsoon (Lee & Wang 2014; Wang et al. 2014), and MPI-ESM-LR have a large skill score on intraseasonal timescales (Sperber et al. 2013). For temperature projection over India, NorESM1-M, NorESM1-ME, CCSM4, FIO-ESM and MIROC5 are the individual models that are closer to the observations (Chaturvedi et al. 2012). Ashfaq et al. (2017) found that GFDL-CM3, GFDL-ESM2M, MIROC-ESM, MIROC-ESM-CHEM and NorESM1-M have better skills in simulating the main features of the summer monsoon over the Indian subcontinent.

From the aforesaid literature and to the best of our knowledge, there is no study reported in the literature regarding the evaluation of the performance of PET methods (i.e. physical (via evaporation pans), empirical and satellite derived (MOD16)) in India and particularly in Tons river basin. The monthly correction factor developed for satellite driven PET is a new finding for the study area. This study reduces the efforts required in the collection of input data for the PM method and enhances the applicability of satellites data in PET estimation which is essentially required at regional scale. Though previous studies focused on the projections of temperature and rainfall, limited literature is available in the context of PET projection. We compared the popularly used machine learning model with the PM model for the future projection of PET which was not earlier carried out at basin scale. After that, the most skillful CMIP5 model is identified among the seven models for the future projection of PET in a semiarid region. Such evaluation of different PET estimates is important on a regional scale to improve the understanding of hydrological fluxes in a specific climatic and hydrological regime. Further, the values provided by this work through ground-based measurements would be useful in calibrating and validating global modeling and understanding. Thus, this study is valuable for integrated water resources management, crop water requirement estimation, future crop planning and management, drought monitoring, water resources managers, planner and agricultural scientist for hydrological and agricultural applications.

Looking to the aforementioned, the present study has been carried out for the Tons river basin, which is a tributary of Ganga River in central India with the following specific objectives: (1) to examine the ability of different PET estimation methods, (2) to compare ETpan with PET estimates of different methods for the identification of the best method at basin scale on a monthly basis, (3) to identify the most skillful CMIP5 model for the future projection of PET in a semiarid region and (4) the future projection of PET using the best-identified method of PET and LS-SVM model.

The Tamsa River (also known as the Tons river basin) flows through the Madhya Pradesh (MP) and Uttar Pradesh (UP) in central India. It lies between 23° 57′ N to 25° 20′ N latitudes and 80° 20′ E to 83° 25′ E longitudes (Figure 1). The total length and catchment area of the river is 320 km and 18,158 km2, respectively. The study area lies in a semiarid region, and rainfall varies from 0 to 85.4 mm/day (Table 1). The maximum amount of rainfall (about 90%) occurs in the months of June–September (monsoon season). The maximum temperature rises up to 46 °C in the months of June and minimum in the month of January (goes down up to 8.3 °C). The wheat, rice, soyabean, millets and pulses are the main crops grown in the study area. The river basin is characterized by ETpan of 0.2–20.2 mm/day (Table 1). Further, about 70% of the population's livelihood in the study area is based on the agriculture which ultimately depends on the rainfall and PET (Duhan et al. 2018). As agricultural demand is rising due to population growth, the issue of food security is coming to the fore in the region.

Table 1

Location of stations and meteorological parameters characteristics during the years of 2000–2008

Station nameLat. (N)Long. (E)Alt., amsl (m)Range of meteorological variables
Tmax (°C)Tmin (°C)Rainfall (mm/day)ETpan (mm/day)Wind speed (km/h)Relative humidity (%)Solar radiation (MJ/m2/day)
Allahabad 25.27 81.44 98 8.3–47.1 0–34.7 0–80 0.75–20.2 0–18 24–87 8.1–15.1 
Satna 24.34 80.5 317 10.4–46.1 2–34.2 0–85.4 0.2–10.4 0–12 23–90 7.4–15.0 
Station nameLat. (N)Long. (E)Alt., amsl (m)Range of meteorological variables
Tmax (°C)Tmin (°C)Rainfall (mm/day)ETpan (mm/day)Wind speed (km/h)Relative humidity (%)Solar radiation (MJ/m2/day)
Allahabad 25.27 81.44 98 8.3–47.1 0–34.7 0–80 0.75–20.2 0–18 24–87 8.1–15.1 
Satna 24.34 80.5 317 10.4–46.1 2–34.2 0–85.4 0.2–10.4 0–12 23–90 7.4–15.0 
Figure 1

Location map of the Tons river basin with stations' locations.

Figure 1

Location map of the Tons river basin with stations' locations.

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Details of data

Meteorological data

In the study area, only two meteorological stations, i.e. Allahabad and Satna are available which is maintained by India Meteorological Department (IMD), Pune. Daily data of maximum air temperature (°C), minimum air temperature (°C), dew point temperature (°C), dry bulb temperature (°C), wet bulb temperature (°C), relative humidity (%) and wind speed (km/h at 10 m height) from January 2000 to December 2008 were procured from the IMD, Pune. Table 1 shows the location of stations and characteristics of meteorological parameters. The monthly values of each meteorological variable are obtained by averaging daily values of each calendar month. The data quality control is a necessary step before analysis of time series because erroneous outliers can seriously impact their trends. In the present study, the data series were plotted to detect the outliers. After visual detection of outliers, the suspected values were calculated using the normal ratio method. There were few missing observations in the time series of variables. These missing data were substituted with the corresponding long-term mean. In the developing countries like India, availability of data is very limited and meteorological stations are sparsely distributed. IMD is an apex body for monitoring accurate weather data and collecting the data only at district level throughout India. The Tons river basin covers only two districts, which is why two stations data are used in the present study. Although only two stations' data are available, the study is highly important because the area is rain-fed which is governed by PET. Thus, studies related to the estimation and future projection of PET may help in taking important decisions related to the climate change abetment and will help the farmers to adapt accordingly.

ETpan data

United States Weather Bureau (USWB) Class ‘A’ pan is the most widely used pan throughout the world (Allen et al. 1998). In India, IMD has also adopted USWB Class ‘A’ evaporimeter for the measurement of pan evaporation. The ETpan is procured from IMD Pune from January 2000 to December 2008. It is related with ET through pan coefficient (Kpan = 0.7), by the following equation:
formula
(1)

Satellite-based PET data

The MOD16 algorithm uses satellite data from NASA's MODIS sensor onboard the Terra and Aqua satellites. The PET value in MODIS is calculated using remote sensing or satellite derived and meteorological data. The satellite-derived parameters are land cover, albedo, leaf area index (LAI), fraction of absorbed photo synthetically active radiation and enhanced vegetation index. The meteorological data such as temperature, radiation, air humidity and pressure data are derived from the daily global meteorological reanalysis dataset from NASA's Global Modeling and Assimilation Office (GMAO). The ET algorithm in MOD16 PET (Mu et al. 2007, 2011) is based on the PM equation (Monteith 1965). Data are available in 8-daily, monthly and yearly intervals. Global PET data are made available by Numerical Terra-dynamic Simulation group (NTSG) with spatial resolution of 0.05° × 0.05° (≈5 × 5 km2) which is used in the present study. The data was downloaded from ‘ftp://ftp.ntsg.umt.edu/pub/MODIS/NTSG_products/MOD16/MOD16A2_MONTHLY.MERRA_GMAO_1kmALB/GEOTIFF_0.05degree/’ for the period of January 2000–December 2008.

Climate projection scenario data for future PET prediction

The Intergovernmental Panel on Climate Change (IPCC 2014) develops Representative Concentration Pathways (RCPs) scenarios in its fifth Assessment Report under the CMIP5. RCPs give us four possible future climate scenarios, namely RCP2.6, RCP4.5, RCP6.0 and RCP8.5 based on pathways of radiative forcing of possible greenhouse gases that are emitted in the years to come. These are named based on possible range of radiative forcing values of +2.6, +4.5, +6.0 and +8.5 W/m2, respectively, in the year 2100 relative to pre-industrial values (Weyant et al. 2009). These scenarios are developed based on stabilization, mitigation and baseline emission scenarios. The naming convention reflects socioeconomic pathways that reach a specific radiative forcing by the year 2100. Among the RCP scenarios, RCP 4.5 is also called a stabilized scenario in which the total radiative forcing will rise to a peak value of 4.5 W/m2 by the year 2070 and stabilizes afterwards by applying a range of technologies and strategies for reducing greenhouse gas emissions. The monthly climatic data of RCP4.5 emission scenario (i.e. maximum temperature, minimum temperature, wind speed, relative humidity, longwave and shortwave radiation) of nine grid points whose latitude ranges from 20.41° N to 27.83° N and longitude ranges from 78.75° E to 86.25° E for the period of January 2006–December 2100 are downloaded from https://esgf-node.llnl.gov/search/cmip5/ (Table 2). In the present study, only the RCP4.5 emission scenario was used because it is a medium range radiation forcing level scenario and is said to be in good coherence with the observed climate of the Indian subcontinent (Chaturvedi et al. 2012). Based on previous studies conducted in the Indian region by various researchers (i.e. Chaturvedi et al. 2012; Sperber et al. 2013; Sharmila et al. 2015; Ashfaq et al. 2017; Jena et al. 2016), the seven CMIP5 models, namely CanESM2, GFDL-ESM2G, CNRM-CM5, MPI-ESM-LR, MPI-ESM-MR, HadGEM2-ES and MIROC5 (Table 3) are selected for the future projection of PET in this study. The nine grid points of the spatial domain for climatic variables are chosen as suggested by Wilby & Wigley (2000). The weighted average of RCP data for each station is calculated using the inverse square weighted interpolation method (Willmott et al. 1985).

Table 2

Monthly predictors selected from CMIP5 models at near surface during 2006–2100

Variable nameIPCC variable nameUnits
Maximum Air Temperature at Near-Surface tasmax 
Minimum Air Temperature at Near-Surface tasmin 
Relative humidity at Near-Surface hurs 
Surface Upwelling Longwave Radiation rlus W/m2 
Surface Downwelling Longwave Radiation rsus W/m2 
Surface Downwelling Shortwave Radiation rsds W/m2 
Surface Upwelling Shortwave Radiation rlds W/m2 
Near-Surface Wind Speed sfcWind m/s 
Variable nameIPCC variable nameUnits
Maximum Air Temperature at Near-Surface tasmax 
Minimum Air Temperature at Near-Surface tasmin 
Relative humidity at Near-Surface hurs 
Surface Upwelling Longwave Radiation rlus W/m2 
Surface Downwelling Longwave Radiation rsus W/m2 
Surface Downwelling Shortwave Radiation rsds W/m2 
Surface Upwelling Shortwave Radiation rlds W/m2 
Near-Surface Wind Speed sfcWind m/s 

Source: https://esgf-node.llnl.gov/search/cmip5/.

Table 3

Details of CMIP5 models used in the present study

Models nameGroup acronymsInstitution/OrganizationResolution (longitude × latitude)
CanESM2 CCCMA Canadian Centre for Climate Modelling and Analysis, Canada 2.80° × 2.80° 
GFDL-ESM2G NOAA GFDL NOAA Geophysical Fluid Dynamics Laboratory, USA 2.00° × 2.50° 
CNRM-CM5 CNRM National Centre for Meteorological Research, France 1.40° × 1.40° 
MPI-ESM-LR MPI-M Max Planck Institute for Meteorology, Germany 1.87° × 1.88° 
MPI-ESM-MR MPI-M Max Planck Institute for Meteorology, Germany 1.87° × 1.88° 
HadGEM2-ES MOHC Met Office Hadley Centre, UK 1.25° × 1.87° 
MIROC5 MIROC University of Tokyo, National Institute for Environmental Studies and Japan Agency for Marine–Earth Science and Technology, Japan 1.40° × 1.40° 
Models nameGroup acronymsInstitution/OrganizationResolution (longitude × latitude)
CanESM2 CCCMA Canadian Centre for Climate Modelling and Analysis, Canada 2.80° × 2.80° 
GFDL-ESM2G NOAA GFDL NOAA Geophysical Fluid Dynamics Laboratory, USA 2.00° × 2.50° 
CNRM-CM5 CNRM National Centre for Meteorological Research, France 1.40° × 1.40° 
MPI-ESM-LR MPI-M Max Planck Institute for Meteorology, Germany 1.87° × 1.88° 
MPI-ESM-MR MPI-M Max Planck Institute for Meteorology, Germany 1.87° × 1.88° 
HadGEM2-ES MOHC Met Office Hadley Centre, UK 1.25° × 1.87° 
MIROC5 MIROC University of Tokyo, National Institute for Environmental Studies and Japan Agency for Marine–Earth Science and Technology, Japan 1.40° × 1.40° 

Methodology

The following methodology has been adopted in the present study: (1) estimation/extraction of PET using various methods such as PM, Hargreaves, Thornthwaite and satellite-based PET (MOD16); (2) comparisons of these methods with observed ETpan and identification of the best method for the study area; (3) bias correction in a satellite-based PET with ETpan; (4) identification of the most skillful climatic model for the study area; (5) development of the LS-SVM model for the future projection of PET and (6) future projection of PET with the best-identified PET model and LS-SVM model using simulated data of RCP emission scenario. The flow chart of the adopted methodology is shown in Figure 2. The detailed description of PM (Allen et al. 1998), Hargreaves (Hargreaves et al. 1985) and Thornthwaite (Thornthwaite 1948) methods may be found in previous works (Abdelhadi et al. 2000; Kite & Droogers 2000; Goyal 2004; Gavilán & Castillo-Llanque 2009; Jhajharia et al. 2012; Darshana et al. 2013). The performance of PET estimates was carried out using root mean square error (RMSE), coefficient of determination (R2), mean bias error (MBE) and percentage error of estimate (PE) which is explained in previous works (Duhan & Pandey 2015). The detailed description of the LS-SVM model may be found in work done by Duhan & Pandey (2015). Bias correction in projected PET is carried out based on the procedure explained by Wood et al. (2007) using observed ETpan data which is explained in the previous work (Duhan & Pandey 2015).

Figure 2

Flow chart for adopted methodology in the study area.

Figure 2

Flow chart for adopted methodology in the study area.

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LS-SVM model development

The choice of appropriate predictors is one of the important steps in model development. The selection of predictors differs from region to region, predictand to predictand and the characteristics of the large-scale atmospheric circulation (Hewitson & Crane 1996). The best predictor is whether a good relationship exists between the predictor and the predictand (Wetterhall et al. 2005). In the present study, the input variable of the PM method, i.e. maximum air temperature (°C), minimum air temperature (°C), net radiation (MJ/m2/day), relative humidity (%) and wind speed (m/s) (which is identified as the best method for the estimation of PET by various researchers and in the present study also) are used as predictors. The predictor's data are divided into two datasets, i.e. one for calibration (training) and the other for validation (testing) of model. About 70% of data are randomly chosen for training, and the remaining 30% of data are used for testing the model. The data from 2000 to 2005 (around 70%) are used for calibration of the model and from 2006 to 2008 are used for validation of the model at both the stations (Allahabad and Satna). The development of LS-SVM models requires the ‘gam’ and the squared kernel parameters, whose values are obtained using RBF kernel types and grid search optimization algorithms which are identified as the best kernel and optimization algorithms by Duhan & Pandey (2015). The model development with RBF kernel involves the selection of RBF kernel width (sig2) and parameter gam. The obtained optimal values using RBF kernel with grid search procedure for sig2 are 91.985 and 90.405 for Allahabad and Satna stations, respectively. Further, the optimal value of gam is 193.13 and 810.64 for Allahabad and Satna stations, respectively. The training of LS-SVM models gave the values of alpha and beta, which are used to simulate the training values. Then, RCP4.5 emission scenario data of these variables (Table 2) are used in the calibrated and validated LS-SVM model for the future projection of PET.

Projection of PET using RCP 4.5 emission scenario data

For the future projection of PET, the predictors (Table 2) of RCP4.5 emission scenario of seven CMIP5 models are used. Two approaches are applied for the future projection of PET. In the first approach, RCP derived variables are directly used in the PM method as input variables for the estimation of PET. In the second approach, these variables are used as a predictor in a calibrated and validated LS-SVM model. The root mean square error (RMSE), coefficient of correlation (R2), MBE and PE between ETpan and projected PET of seven CMIP5 models were calculated to identify the most skillful climatic model for the study area.

Monthly variation in ETpan with PET estimates

Figures 3 and 4 show the variations in monthly PET estimated using different methods at Allahabad and Satna stations, respectively, for the years 2000–2008. For Allahabad station (Figure 3), when ETpan is compared with other methods, it is found that MOD16 and Hargreaves methods overestimate the PET; however, PM and Thornwaite methods underestimate the PET. Further, PM based PET is closely related with ETpan. Among all methods, MOD16 gives higher PET than other methods. Similar results are reported in previous research (Westerhoff 2015). This may be because the MOD16 PET approach takes vegetation transpiration into account, where the other methods do not. Further, it is expected that MOD16 will overestimate the PET compared to ETpan because of (a) the scale of the measurement and (b) different meteorological conditions and parameters in a 5 × 5 km grid (MOD16 PET) and a point scale (station data). Surprisingly, it is also found that the Hargreaves method, which takes only temperature and solar radiation as input data for the calculation of PET, estimates approximately close to the MOD16 PET on a monthly basis in the study area.

Figure 3

Comparison of monthly ETpan and PET estimates at Allahabad station for the years 2000–2008.

Figure 3

Comparison of monthly ETpan and PET estimates at Allahabad station for the years 2000–2008.

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Figure 4

Comparison of monthly ETpan and PET estimates at Satna station for the years 2000–2008.

Figure 4

Comparison of monthly ETpan and PET estimates at Satna station for the years 2000–2008.

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Further, considering two seasons in a year, one is the wet season (June, July, August, September, October and November) and the other is the dry season (December, January, February, March, April and May), it is found that satellite-based PET is lower than Hargreaves PET in the wet season and vice versa in the dry season. In the dry season (Figure 3), high difference between ETpan and estimated PET from different methods may be due to high radiation and temperature which increase the PET estimates. Another reason for the same may be intense cropping patterns of wheat grown in the study area which creates more transpiration surface in the form of high LAI, contributes high transpiration along with high evaporation due to enough moisture availability. However, in the wet season, less PET difference may be due to low radiation. Similar results have been observed for the Satna station for the years 2000–2008 (Figure 4).

Performance evaluation of observed ETpan with PET estimates

The performance evaluation of PET estimates was carried out using RMSE, R2, MBE and PE. The method which gives the highest R2 and lowest RMSE, PE and MBE is considered as the best method which gives the closest value of PET to ETpan. Table 4 shows the results of the statistical performance of the PET estimates versus ETpan on a monthly basis during 2000–2008 at Allahabad and Satna stations. At Allahabad station, R2 varied between 0.58 (MOD16) and 0.82 (PM method), and for Satna station, it varied from 0.5 (MOD16) to 0.70 (PM method). The RMSE ranged between 1.05 mm/day (PM method) and 2.91 mm/day (MOD16) at Allahabad station and from 1.06 mm/day (PM method) to 5 mm/day (MOD16) for Satna station. For Allahabad station, the minimum MBE of 0.02% was obtained with the PM method and the maximum of 2.55% with the Hargreaves method. For Satna station, the minimum MBE of −0.03% was found with the Thornthwaite method and the maximum MBE of 1.83% with the Hargreaves method. Further, the lowest PE of 32 and 16% was found with the PM method at Allahabad and Satna stations, respectively. Overall results from the analysis indicate that the PM method gives the best performance (R2 = 0.82 and 0.70, RMSE = 1.05 and 1.06 mm/day, and PE = 32 and 16%) with ETpan among all methods, followed by the Thornthwaite, Hargreaves and MOD16 at both the stations. Further, Figures 5 and 6 show the plots between ETpan and PET estimates of different methods on a monthly basis during the study period of 2000–2008 for Allahabad and Satna stations, respectively. ETpan is highly correlated with the PM method (R2 = 0.82 and 0.70) followed by Hargreaves (R2 = 0.80 and 0.64), Thornthwaite (R2 = 0.62 for each station) and satellite-based PET (R2 = 0.59 and 0.51) for Allahabad and Satna stations. The results suggest that the PM method is a good indicator of ETpan in arid and semiarid regions. Similar results are reported by Chen et al. (2005), (2014); Donohue et al. (2010); Westerhoff (2015) and Wang et al. (2017b) in arid and semiarid regions. The reasons for differences in model performance may be due to input parameters used for the calculation of PET because each variable plays a different role in estimating PET. The models with full weather data (solar radiation, air temperature, sunshine durations, relative humidity and wind speed) have the better accuracy in the semiarid region (Darshana et al. 2013; Wang et al. 2017c).

Table 4

Statistical performance of the PET estimates versus ETpan on a monthly basis during the study period (2000–2008) at Allahabad and Satna stations

Station nameStatistical performance indicators
Method nameR2RMSEMBEPE (%)
Allahabad PM 0.82 1.05 0.02 32 
Hargreaves 0.80 2.71 2.55 68 
Thornthwaite 0.62 1.57 0.68 56 
Satellite-based PET 0.58 2.91 2.51 104 
Satna PM 0.70 1.06 − 0.52 16 
Hargreaves 0.64 2.15 1.83 52 
Thornthwaite 0.62 1.09 − 0.03 31 
Satellite-based PET 0.50 3.5 1.82 79 
Station nameStatistical performance indicators
Method nameR2RMSEMBEPE (%)
Allahabad PM 0.82 1.05 0.02 32 
Hargreaves 0.80 2.71 2.55 68 
Thornthwaite 0.62 1.57 0.68 56 
Satellite-based PET 0.58 2.91 2.51 104 
Satna PM 0.70 1.06 − 0.52 16 
Hargreaves 0.64 2.15 1.83 52 
Thornthwaite 0.62 1.09 − 0.03 31 
Satellite-based PET 0.50 3.5 1.82 79 
Figure 5

Relationship of ETpan with PET estimates on a monthly basis at Allahabad station during the years 2000–2008.

Figure 5

Relationship of ETpan with PET estimates on a monthly basis at Allahabad station during the years 2000–2008.

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Figure 6

Relationship of ETpan with PET estimates on a monthly basis at Satna station during the years 2000–2008.

Figure 6

Relationship of ETpan with PET estimates on a monthly basis at Satna station during the years 2000–2008.

Close modal
Figure 7

Monthly variation in ETpan and corrected satellite PET at (a) Allahabad and (b) Satna station during the year 2000–2008.

Figure 7

Monthly variation in ETpan and corrected satellite PET at (a) Allahabad and (b) Satna station during the year 2000–2008.

Close modal

Bias correction in satellite-based PET with respect to ETpan

Table 5 shows the monthly bias correction factor (Δ) for accurate estimation of ETpan from MOD16 PET (ETpan = MOD16 PET – Δ). It can be seen from Table 4 that Δ is very small in the wet season as compared with the dry season. It indicates that satellite data can predict better in the wet season compared to the dry season. Further, intercomparison between Allahabad and Satna stations shows that the monthly Δ values are lower in Satna station in comparison to Allahabad station. The possible reason for the same may be the additive effect of vegetation transpiration in MOD16 PET at Allahabad station because the cropping intensity is higher at Allahabad station than Satna station.

Table 5

Monthly bias correction factor (Δ) for conversion of MODIS data to ETpan (mm/day)

Station nameMonths
JanFebMarchAprilMayJuneJulyAugSeptOctNovDec
Allahabad 3.01 3.08 3.79 3.29 2.92 1.28 1.20 0.95 0.31 1.74 2.51 2.82 
Satna 2.53 3.00 3.12 3.83 2.86 0.79 − 0.43 0.02 − 0.10 0.67 1.42 1.93 
Station nameMonths
JanFebMarchAprilMayJuneJulyAugSeptOctNovDec
Allahabad 3.01 3.08 3.79 3.29 2.92 1.28 1.20 0.95 0.31 1.74 2.51 2.82 
Satna 2.53 3.00 3.12 3.83 2.86 0.79 − 0.43 0.02 − 0.10 0.67 1.42 1.93 

Further, monthly variation of ETpan with corrected MOD16 PET at Allahabad and Satna stations (Figure 7(a) and 7(b), respectively) during the years 2000–2008 show that satellite-based monthly PET is matching with ETpan. For Allahabad station, a very good correlation of R2 = 0.82 was obtained in corrected MOD16 PET and ETpan (Figure 8(a)) which is equal to the best-identified method of PET (PM method) instead of the original MOD16 PET (R2 = 0.58; Figure 5). Further, for Satna station (Figure 8(b)), the good statistical performance indices were observed (R2 = 0.70, RMSE = 1.00, MBE = 0.18 and PE = 25%) between corrected MOD16 PET and ETpan. It is concluded from the results that after applying the monthly correction factor, MOD16 PET may be a better option to estimate monthly PET in the study area even when the weather stations do not have full datasets.

Figure 8

Relationship of ETpan with corrected MODIS 16 PET on a monthly basis at (a) Allahabad and (b) Satna stations during the years 2000–2008.

Figure 8

Relationship of ETpan with corrected MODIS 16 PET on a monthly basis at (a) Allahabad and (b) Satna stations during the years 2000–2008.

Close modal

Projection of PET using RCP 4.5 emission scenario

Seven CMIP5 models, namely CanESM2, GFDL-ESM2G, CNRM-CM5, MPI-ESM-LR, MPI-ESM-MR, HadGEM2-ES and MIROC5 are used to identify the most skillful model for the study area. The correlation coefficient, RMSE, PE and MBE between ETpan and CMIP5 models PET (Table 6) show that GFDL-ESM2M is the most skillful model followed by CNRM-CM5, MPI-ESM-LR, MPI-ESM-MR, MIROC5 HadGEM2-ES and CanESM2 models for a semiarid region in central India. For the future projection of PET, two approaches are applied. In the first approach, RCP derived variables of the GFDL-ESM2M model are directly used in the PM method as an input, and in the second approach, these variables are used as a predictor in the calibrated and validated LS-SVM model. Figure 9(a) and 9(b) shows the comparison in estimated PET using the PM method, LS-SVM and ETpan for the years 2006–2008 at Allahabad and Satna stations, respectively. LS-SVM based projected PET is nearer to ETpan than PM based projected PET. It can be concluded that LS-SVM is a better model in comparison to the PM method for the future projection of PET in the study area. Therefore, results of projected PET with LS-SVM are shown here. The monthly ETpan and simulated PET using the LS-SVM model during calibration and validation are shown in Figure 10(a) and 10(b) for Allahabad and Satna stations, respectively. It is inferred that the observed values of PET are quite close to those of simulated data at both the stations.

Table 6

Correlation coefficient between observed ET and the CMIP5 models ET

Station nameStatistical performance indicatorsCMIP5 models name
CanESM2GFDL-ESM2GCNRM-CM5MPI-ESM-LRMPI-ESM-MRHadGEM2-ESMIROC5
Allahabad R2 0.46 0.71 0.69 0.71 0.70 0.55 0.72 
RMSE 4.72 1.92 2.30 2.82 2.94 2.37 3.22 
MBE 4.34 1.16 1.63 2.31 2.43 1.52 2.80 
PE (%) 52 29 34 37 38 35 42 
Satna R2 0.32 0.70 0.62 0.70 0.69 0.50 0.71 
RMSE 4.82 1.96 2.40 2.90 2.32 2.39 2.80 
MBE 4.75 1.23 1.77 2.27 2.78 1.55 2.33 
PE (%) 55 30 32 35 37 37 38 
Station nameStatistical performance indicatorsCMIP5 models name
CanESM2GFDL-ESM2GCNRM-CM5MPI-ESM-LRMPI-ESM-MRHadGEM2-ESMIROC5
Allahabad R2 0.46 0.71 0.69 0.71 0.70 0.55 0.72 
RMSE 4.72 1.92 2.30 2.82 2.94 2.37 3.22 
MBE 4.34 1.16 1.63 2.31 2.43 1.52 2.80 
PE (%) 52 29 34 37 38 35 42 
Satna R2 0.32 0.70 0.62 0.70 0.69 0.50 0.71 
RMSE 4.82 1.96 2.40 2.90 2.32 2.39 2.80 
MBE 4.75 1.23 1.77 2.27 2.78 1.55 2.33 
PE (%) 55 30 32 35 37 37 38 

The bold values indicate the best model among the selected models.

Figure 9

Comparison of monthly ETpan and PET simulated using LS-SVM and PM methods at (a) Allahabad and (b) Satna stations during the years 2006–2008.

Figure 9

Comparison of monthly ETpan and PET simulated using LS-SVM and PM methods at (a) Allahabad and (b) Satna stations during the years 2006–2008.

Close modal
Figure 10

The monthly ETpan and simulated PET using LS-SVM model during calibration and validation at (a) Allahabad station and (b) Satna station.

Figure 10

The monthly ETpan and simulated PET using LS-SVM model during calibration and validation at (a) Allahabad station and (b) Satna station.

Close modal

Figure 11(a) and 11(b) shows the monthly predicted PET (mm/day) of the GFDL-ESM2M model for the years 2006–2100 at Allahabad and Satna stations, respectively. It can also be seen that the maximum value of PET was observed in the month of May at both the stations. Further, the maximum PET of around 12 mm/day was observed in the month of June for the year 2064 for both the stations. The box plots of 10-year time slices (2006–2015, 2016–2025, 2026–2035, 2036–2045, 2046–2055, 2056–2065, 2066–2075, 2076–2085, 2086–2095 and 2096–2100) are used to determine decadal patterns in projected PET. The box plots of projected PET of seven CMIP5 models by employing LS-SVM are shown in Figure 12(a) and 12(b) at Allahabad and Satna stations, respectively. The middle line of the box shows the median values, whereas the upper and lower edges give 75 and 25 percentiles of the dataset, respectively. The box plots show that there is no significant change in the median value of future PET for RCP4.5 scenario at both the stations. Further, future PET is higher than observed average mean of 2006–2008. The results show that PET is projected to increase in future by employing the LS-SVM model which ultimately increases the irrigation water requirement of crops in the study area.

Figure 11

Monthly future PET (mm/day) during 2006–2100 at (a) Allahabad and (b) Satna stations.

Figure 11

Monthly future PET (mm/day) during 2006–2100 at (a) Allahabad and (b) Satna stations.

Close modal
Figure 12

Box plot depicts the decadal changes in future predicted PET (mm/day) of different CMIP5 models using the LS-SVM model from 2006 to 2100 at (a) Allahabad and (b) Satna stations. The horizontal red line in the box denotes the median value. The black square represents the mean value of simulated PET.

Figure 12

Box plot depicts the decadal changes in future predicted PET (mm/day) of different CMIP5 models using the LS-SVM model from 2006 to 2100 at (a) Allahabad and (b) Satna stations. The horizontal red line in the box denotes the median value. The black square represents the mean value of simulated PET.

Close modal

In the present study, the performance of various PET methods (i.e. pans evaporation (physical measurement), empirical and satellite derived (MOD16)) were assessed at two stations (i.e. Allahabad and Satna) in the Tons river basin in central India during January 2000–December 2008. Three empirical PET methods such as PM, Hargreaves and Thornthwaite were used to estimate PET and satellite-based PET (MOD16 PET) were obtained from MODIS on a monthly timescale. The comparisons of above methods were carried out with ETpan, and the best method was identified for a semiarid region of central India. For the future projection of PET, two approaches were applied. In the first approach, simulated data of RCP4.5 scenario are used in PM methods directly for the PET estimation, and in the second approach, these variables are used as predictors in calibrated and validated LS-SVM models. Then, the monthly future projection of PET was carried out with the developed LS-SVM model using simulated data of RCP4.5 scenario.

Comparisons between different methods show that the MOD16 and Hargreaves methods overestimate the PET; however, the PM and Thornwaite methods underestimate the PET in comparison to ETpan in the study area. Further, PM based PET is closely related with ETpan, and the results suggest that the PM method is a good indicator of ETpan. After applying bias correction factors in satellite-based PET, it can be a better option to estimate PET in the study area even when the weather stations do not have full datasets or ground-based measurements are not available. Further, GFDL-ESM2M is identified as the most skillful climatic model for the prediction of monthly PET for a semiarid region in central India. Among the two approaches, it is found that LS-SVM is a better model than the PM method for the future projection of PET. The results show that PET is projected to increase in future using the LS-SVM model which will ultimately increase the irrigation water requirement of crops in the study area. The output of this study will be helpful for water resource managers, planners and agricultural scientists. Looking for the broader perspective of our study, we have gone through regional and global research papers on this topic, which are most of time based on generalized modeling and satellite-based estimation. We hope that region-specific values provided by our work through ground-based measurements would be useful in calibrating and validating global modeling and understanding.

All relevant data are included in the paper or its Supplementary Information.

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