Abstract

Parametric models of actual evapotranspiration (AET) based on precipitation (P) and potential evapotranspiration (PET) are region-specific and purely climate-induced and limited to represent the hydrological water balances. Basin-averaged model parameters considering P, AET, and runoff (R) using a machine learning algorithm, ensemble regression model, is proposed. Hydrologically calibrated model parameters allowed the study of AET under alterations of water use for current and for future scenarios under climate change. The effect of climate, water, and land use changes on AET was studied for the post-change period of 2004–2014 compared to pre-change period of 1965–2003 over Krishna river basin (KRB), India. The AET has increased under climate and water use changes while there is both increase and decreases of AET under land use changes for post-change period compared to pre-change period over the basin. Severe water shortages were estimated under pronounced increase of temperature (1.29 °C) compared to precipitation increase (2.19%) based on Coordinated Regional Downscaling Experiment (CORDEX) projections for the period 2021–2060. Hydrologically induced AET changes were more pronounced than climate for current climate; whereas climate-induced AET changes were found to be more prominent for projected climate signals over the basin.

INTRODUCTION

At regional scales, evapotranspiration (ET) flux is a complex process influenced by the regional climate, land use changes due to human interventions in the landscape, water withdrawals from the rivers for agricultural practices, etc. (Boucher et al. 2004; Rehana & Mujumdar 2012, 2013). Several parametric models have been developed to estimate actual evapotranspiration (AET) flux, based on the assumption that AET is limited by the water availability in terms of precipitation (P) under very dry conditions and energy availability in terms of potential evapotranspiration (PET) under very wet conditions (e.g., Turc 1954; Budyko 1958; Fu 1981). Such empirical models have evolved based on various climate, soil, and vegetation conditions and serve as a basis for deriving long-term mean annual water balances (Sivapalan et al. 2011; Thompson et al. 2011). These parametric models are region-specific and are based on various hydro-climatic conditions which necessitate calibration in the hydrological partitioning of water-energy variables (Asokan et al. 2010). AET estimated from such region-specific parametric models can be calibrated hydrologically to understand hydrologically induced AET accounting for P, PET along with closure of water balance with runoff. Various catchment processes can be conceptualized by introducing model parameters whose values can be determined through calibration (Mianabadi et al. 2017). In this context, application of model parameters accounting for various processes of net radiation (Choudhury 1999), plant available water (Zhang et al. 2004), vegetation dynamics (Donohue et al. 2007; Destouni et al. 2013), water balance equations (Jarsjö et al. 2008; Liu et al. 2017; Shibuo et al. 2007) became widely applicable. To study the long-term hydro-climatic changes of ET, basin-averaged time-invariant model parameters were introduced with the consideration of closure of the water balance by Jarsjö et al. (2008) and Asokan et al. (2010). However, use of such time-invariant model parameters estimated over a specified period in the hydrological partitioning of the river basin may limit the temporal variability of water-energy balance variables. Also, given the changes of global ET under increasing temperatures and changes in precipitation patterns due to anthropogenic climate change (Jung et al. 2010; Murray et al. 2012), implementation of such constant model parameters may not include the hydro-climatological variability of water balances at catchment scales. Therefore, the present study proposed data-driven algorithms to estimate the model parameters dynamically accounting for the temporal variability of annual P, AET, and runoff (R). The obtained relationship can be further used with projected P, AET, and R under climate change signals to estimate water-energy balance variables for future scenarios under climate change.

The main emphasis of the study is to (i) analyze the climate-induced and hydrologically calibrated AET and its predictability at catchment scale and (ii) analyze the changes in hydro-climatological ET for current and climate change signals under regional circulation model (RCM) outputs.

MATERIALS AND METHODS

Basin description

The Krishna river basin (KRB), 73°17′–81°9′E and 13°10′–19°22′N, joins the Bay of Bengal at Hamasaladeevi in Andhra Pradesh on the east coast of India and is one of the major sources of irrigation for the four states of Maharashtra, Karnataka, Telangana, and Andhra Pradesh. Krishna River is the fifth largest river system in central India with a total catchment area of 258,948 km2 (Figure 1). The river, originating in the Western Ghats, has heavy precipitation with decreasing precipitation towards the upper and lower parts of the basin, and finally reaches the Bay of Bengal, which joins the Indian Ocean. The river travels about 1,400 km across the states of Karnataka, Maharashtra, Andhra Pradesh, and Telangana before joining the Bay of Bengal. Nearly 44% lies in Karnataka, 26% of the basin falls in Maharashtra, about 15% in Telangana, and another 15% in Andhra Pradesh. Most of the KRB is covered by an arid climate with annual average precipitation in the basin being 784 mm, of which approximately 90% occurs during the South-West Monsoon from June to October (http://india-wris.nrsc.gov.in/wrpinfo/?title=Krishna).

Figure 1

Map of the Krishna River Basin (KRB). Location of the catchment in India showing rainfall grids and basin outlet discharge gauge station at Vijayawada and elevation map superimposed on the basin.

Figure 1

Map of the Krishna River Basin (KRB). Location of the catchment in India showing rainfall grids and basin outlet discharge gauge station at Vijayawada and elevation map superimposed on the basin.

The KRB is a semi-arid region with aridity index (P/PET) of 0.44, with annual basin-averaged precipitation 778 mm and PET 1,773 mm for the period of 1951–2015. The precipitation is unevenly distributed over the basin, with heavy precipitation over the Western Ghats (around 2,500 mm of annual average) and moderate to less rainfall (around 500 mm of annual average) distribution over the districts of Maharashtra and Telangana. The water use of the basin is mostly dominated by irrigation (61.9 billion cubic meters (BCM)/year) with modest domestic (1.6 BCM/year) and industrial (3.2 BCM/year) uses (Van Rooijen et al. 2009).

MATERIALS AND METHODS

Figure 2 shows an overview of the proposed methodology to estimate AET at catchment scale including hydro-climate changes. The AET for each grid cell of the river basin was estimated in two steps: first, estimating the PET, and second, estimating AET based on the water availability in terms of P and estimated PET from the first step. In this context, we adopted empirical models which work on the assumption that AET is limited by the water availability in terms of P under very dry conditions and available energy under very wet conditions in terms of PET (Budyko 1958; Fu 1981; Zhang et al. 2004). Budyko (1958) developed a relationship between three hydro-meteorological variables, P, PET, and AET, which states that the ratio of the AET over precipitation (AET/P) is fundamentally related to the ratio of the PET over precipitation (PET/P) (Budyko 1958; Fu 1981) as follows: 
formula
(1)
Figure 2

Overview of the modeling approach to estimate hydro-climatological induced AET at catchment scale.

Figure 2

Overview of the modeling approach to estimate hydro-climatological induced AET at catchment scale.

The parameter ‘’ accounts for the effects of climate variability, basin characteristics such as soil, vegetation, terrain, etc. (Donohue et al. 2007). The original Budyko formulation (Equation (1)) has been modified by several researchers (e.g., Schreiber 1904; Turc 1954; Wu et al. 2015; Ning et al. 2018), and one of the widely used formulations is as implemented by Zhang et al. (2004) for estimating the AET, as follows: 
formula
(2)
where is the climatological induced AET, which is a function of P and PET. The original Budyko equation (Equation (1)) is a parametric formulation with parameter ‘’ to account for non-climatic influences of the catchment (Yang et al. 2007) and developed for long-term averages (>> 1 year) and large catchments (>10,000 km2) with stationary hydrological conditions as assumptions (Gunkel & Lange 2017), whereas Equation (2) is a non-parametric formulation which can differ between catchments, where long-term soil water storage changes due to groundwater recharge and storages due to geological features and human interactions such as water withdrawals are considered to be negligible (Wu et al. 2017).

The PET can be estimated based on temperature-based empirical models, such as Thornthwaite (1948) and Hargreaves & Samani (1985), etc. The present study used Thornthwaite model as one such model to quantify the PET, which considers the monthly average air temperature and geographical location of the region of interest as input variables. The study can be implemented with the Penman–Monteith model to estimate PET which requires various meteorological variables, such as temperature, wind speed, relative humidity, radiation (FAO 56 PM; Penman 1948; Allen et al. 1998). However, due to the unavailability of such operational gridded meteorological data sets for the case study, the present study is limited to use Thornthwaite model for the estimation of PET. PET is the maximum atmospheric water demand based on the energy available (Shelton 2009). AET represents the transfer of moisture from the surface to the atmosphere in response to both the energy demand and available moisture supply (Anabalón & Sharma 2017). Equation (2) represents the AET accounting for changes in P and PET for given catchment-scale properties. To understand hydrologically induced AET accounting for P, PET along with closure of water balance with runoff (R), the AET estimated from Equation (2) should be calibrated hydrologically.

Hydrologically calibrated ET flux at catchment scale using PCRaster

A distributed hydrological model, PCRaster, a GIS-based model was used for modeling of annual basin outlet runoff of KRB (Wesseling et al. 1996) http://pcraster.geo.uu.nl/pcraster/4.2.0/documentation/pcraster_manual/sphinx. The PCRaster hydrological model was found to be suitable in the estimation of hydro-climatic changes of AET at catchment scales in terms of estimation of flow accumulation accounting for the precipitation and estimated AET with empirical model following the flow direction map created based on the digital elevation model (DEM) data (Figure 2). Use of the PCRaster model allowed inclusion of precipitation and AET as input variables following the flow accumulation to simulate the basin outlet runoff by introducing hydrological dynamic model parameter. The PCRaster model works with the user-defined inputs in the flow accumulation of a river basin following the flow direction map created. The observed and modeled annual average total runoff at the basin outlet at gauging station Vijayawada (Figure 1) was estimated at catchment scale using PCRaster with water flow module of Polflow (De Wit 2001). The entire river basin was discretized with a basic hydrologic unit of 1 km × 1 km rectangular cell and assigned rainfall and estimated AET (Equation (2)) for each cell. The KRB was delineated and its local drainage network was created at a horizontal grid interval of 1 km × 1 km. The local drainage direction (ldd) was processed from DEM using ‘lddcreate’ PCRaster function. The accuthresholdflux function of PCRaster (http://pcraster.geo.uu.nl/pcraster/4.2.0/documentation/pcraster_manual/sphinx/op_accuthreshold.html) accumulates the precipitation surplus (P-AET) for each cell and transport it to the basin outlet from the upstream cells by following the elevation and local drainage map. At a grid cell, i, the precipitation surplus or residual available water, can be calculated using annual total precipitation and climate-induced AET (from Equation (2)) as follows: 
formula
(3)
where and are at annual scale in mm/year. The discharge at the basin outlet was estimated by accumulating the flow at grid cell, i, and from all upstream grid cells according to the flow direction of the river and corresponding to the area of each grid cell as follows: 
formula
(4)
is the uncalibrated total runoff from the basin outlet at steady state and it is generally not consistent with observed runoff. Here, a model parameter can be introduced, with consideration of the closure of water balance using the outputs from the hydrological model and observed runoff at the basin outlet following Jarsjö et al. (2008) and Asokan et al. (2010). Basin-averaged calibration factor, , was introduced to correct the uncalibrated AET over the river basin. By introducing a model parameter on , accounting for the closure of water balance at the catchment outlet, a hydrometeorological induced AET can be estimated. Therefore, the precipitation surplus or RAW accounting for the calibration factor, , (Figure 2) can be written as follows: 
formula
(5)
 
formula
(6)
is the calibrated total runoff from the basin outlet at steady state and should be consistent with observed runoff. Therefore, after calibration, the resulting basin outlet runoff, should be close to the observed runoff : 
formula
(7)
The model parameter (Jarsjö et al. 2008) for the entire river basin for each annual time scale can be estimated by comparing the observed and uncalibrated runoff estimated from the hydrological model at the basin outlet as follows: 
formula
(8)
 
formula
(9)
where and are the long-term annual average observed and simulated runoff at the basin outlet in m3/s, respectively, and and are the long-term accumulated annual average observed precipitation and AET (Equation (2)) over the basin in mm/year. The annual scale basin-averaged calibration factors estimated based on Equation (9) can be applied on the (Equation (2)) to study the changes of AET under hydrometeorological or water-use over the river basin. 
formula
(10)
where is hydrological AET representing the evaporative demand of the atmosphere accounting for energy available in terms of PET and water supply in terms of runoff. It can be noted that is considered to be climatological AET which is region-specific, while is computed by the water balance, in which the runoff was simulated by the distributed hydrological model, PCRaster.

Ensemble regression model (ERM) algorithm for modeling the calibration factors

To investigate the changes in the hydro-climatological induced AET under climate variability, the dependence between P, , , and for the entire river basin for the present climate was estimated. Here a data-driven model based on ensemble regression model (ERM) algorithm (Friedman 2001; Bühlmann 2004) was trained using P, , and as independent variables with model parameter, , as the response variable. The ERM is based on the principle that a diverse set of models can make better decisions in comparison to an individual model (Friedman 2001) and has gained much attention in hydrological assessments in recent years (Schapire 2003; Sajedi-Hosseini et al. 2018). Ensemble regression models help to decrease variance between the predicted and observed values and will produce a more reliable estimate than a single regression model. The ensemble regression model was used to fit a relationship between the model parameter as dependent variable (Y) and hydro-climatological variables (P, ET and R) as independent variables (X).

Consider an input training data set of ‘N’ points {X, Y} = , where is the set of predictors and is the observed predictand value at the ith timestep. Initially, all the input points (predictors) in the data set are given equal weighting coefficients and a base model to predict values of the form is trained on this data set. At every iteration, m, errors/residuals are calculated between the observed and model predictand value . Then, a base-learner (hm) is fitted to these residuals using the loss function ‘L’ in the direction of steepest gradient, i.e., weight, of point ‘i’ is increased corresponding to a higher value of errors/residual .

The model is then sequentially updated as follows 
formula
(11)
where is the optimization notation, ring to minimization of base-learner error (hm) and least squares loss function is used to update the errors/residuals . The algorithm is described in the following steps:

Initialize . is the set of observed predictand values.

For m = 1 to M where M is the total number of iterations under consideration: 
formula
(12)
Fit a base learner (hm) to these residuals using the training set  
formula
(13)
 
formula
(14)
where h is base learner added to to improvise the model (ideally after m iterations the base learner h will be estimated such that ). is the multiplier that is applied to the base learner to get the updated model. The trained ERM will be further used to predict the calibration factors for the future scenarios under projected changes of P, , and. Here, the will be the uncalibrated runoff from the hydrological model with projected P and for the future scenarios. To quantify the changes in the dependence between calibration factors and hydrological variables, coefficient of determination (R2) was selected as performance measure. Finally, the hydrological induced regional AET under climate change over the basin was estimated with projections of various RCM outputs of precipitation and temperatures and estimated and . The changes of climatological, , and hydrometeorological AET, , at river-basin scale was analyzed under climate signals with regional climate change projections.

Assessment of changes in AET under climate, water, and land use changes

To study the land use changes (i.e., vegetation) impact on AET, the present study adopted time-trend analysis, which can be applied over large catchments for after-the-fact analysis of the existing data (Bosch & Hewlett 1982; Zhang et al. 2011). The time-trend analysis method was successfully applied to study the streamflow changes on single catchments that have undergone vegetation cover change (Zhang et al. 2011). In this study, the relationship between AET and precipitation and runoff is developed and evaluated during the pre-change period using multiple linear regression analysis, and the statistical relationship is then used to estimate AET during the post-change period. Such relationships will be developed for and to study the changes in AET under climate and water use changes, respectively. To study the change in AET under land cover use (i.e., vegetation), the study used AET derived from satellite-based remote sensing data, represented as . The effect of climate, water use, and land use on AET is expressed as the difference between observed and predicted , , and during the post-change period. The generalized equations are presented here as follows: 
formula
(15)
 
formula
(16)
 
formula
(17)
where P represents annual precipitation (mm), R represents annual observed runoff (mm), AET is the annual AET which can be replaced by , , and to study the corresponding changes of AET under climate, water use, and land use changes, respectively. The indices of 1 and 2 represent the pre-change period and post-change period, respectively.

Regional climate change projections

The present study adopted a quantile-based mapping method developed by Li et al. (2010) with the comparison of cumulative distribution functions (CDFs) of observed and RCM simulated data of precipitation and temperatures for the historical and future scenarios. Here, the CDFs of RCM and observed precipitation data were compared to correct the bias present in RCM historical and future data sets (Li et al. 2010), where Gamma distribution is used to calculate the CDFs of each time series as follows: 
formula
(18)
where is the bias-corrected climate variable for current period (RCM-historical); is the biased RCM variable; is the CDF of RCM historical data; and is the CDF of observed data and is the inverse CDF of observed data which gives the observed variable at the corresponding equal CDF level.
For bias correction of future RCM data, it is generally assumed that the difference between the model and observed value during the training period also applies to the future period, for a given percentile, which means the adjustment function remains the same. However, the difference or shift between the CDFs for the future and historic periods is also taken into account: 
formula
(19)
where is the bias-corrected climate variable for future period (RCM-future); is the biased RCM future variable; is the CDF of RCM future data; is the CDF of observed data; is the inverse CDF of observed data which gives the observed variable at the corresponding equal CDF level; and is the CDF of RCM historical data and is the inverse CDF of RCM data which gives the RCM variable at the corresponding equal CDF level.

This ensures that the RCM data are standardized and can perform water-energy simulations with higher accuracy for models trained with observed data. This is based on the stationarity assumption that the climate variables' distributions do not change over time. The RCM data sets which are at a resolution of 0.44° × 0.44° were brought to the observed precipitation data resolution of 0.25° × 0.25° using the inverse distance weighting method after bias correction.

Data used

The study used gridded daily precipitation data from India Meteorological Department (IMD) available for the period of 1901–2015 at 0.25° × 0.25° resolution (Rajeevan & Bhate 2009). The gridded daily average temperature data all over India at a resolution of 1° × 1° resolution for the period of 1951–2014 from IMD was cropped to the basin (Srivastava et al. 2009). The temperature was interpolated to 0.25° × 0.25° resolution using the inverse distance weighting method from 1° × 1° resolution. The DEM data with a resolution of 30-arc second (approximately 1 km) were collected from Global 30 Arc-Second Elevation (GTOPO30) data set provided by USGS (US Geological Survey). Using raster extraction in Quantum Geographic Information System (QGIS) the KRB basin was delineated using the DEM data. The discharge data were obtained from Krishna & Godavari Basin Organisation (KGBO), Central Water Commission (CWC), Hyderabad, Government of India (http://www.kgbo-cwc.ap.nic.in) for about 25 discharge locations for the period of 1966–2015.

In the present study, satellite-based land surface global AET product derived from the Numerical Terradynamic Simulation Group (http://files.ntsg.umt.edu/data/ET_global_monthly_ORIG/Global_HalfDegResolution), from 1983 to 2006 at 0.5° × 0.5° resolution was adopted (Zhang et al. 2010). The continuous satellite-derived global land surface AET was developed based on Moderate Resolution Imaging Spectroradiometer (MODIS) data, meteorological observations, and satellite-based vegetation parameters. The AET data account for the canopy transpiration and soil evaporation with modified Penman–Monteith approach, biome-specific canopy conductance from Normalized Difference Vegetation Index (NDVI) and open water evaporation from Priestley–Taylor approach (Zhang et al. 2010), and the AET data were found to be in general agreement with most of the global basins (Liu et al. 2016). The original land surface satellite-based AET data were at 0.5° × 0.5° resolution which was rescaled to 0.25° × 0.25° resolution by bilinear spatial interpolation method.

The ET data based on remote sensing can account for the soil properties, spatial vegetation, and land cover fractions (Dimiceli et al. 2015). Therefore, the study adopted Global Land Evaporation Amsterdam Model (GLEAM) satellite-based ET data which provide the land evaporation data considering the evaporation from land, soil, plant surfaces, open-water, and transpiration from vegetation along with dynamic land cover information (https://www.gleam.eu/). Also, GLEAM-based ET estimates have shown high skill scores for most of the land-cover types (Yang et al. 2017). Due to the availability of long time series ET data sets of GLEAM for the period 1980–2018 compared to MODIS data (1983–2006), the present study used GLEAM data to study the change of AET due to change in land use (i.e., vegetation changes) over KRB.

The Coordinated Regional Downscaling Experiment (CORDEX) is mainly associated with general circulation model (GCM) projections from Coupled Model Intercomparison Project (CMIP5, http://cmip-pcmdi.llnl.gov/cmip5/) and were downscaled with the RCMs run by various research institutes. CORDEX data sets are available for 14 domains covering the entire globe, and the present study selected the South-Asian domain of the CORDEX project from Centre for Climate Change Research, Indian Institute of Tropical Meteorology, Pune, India (http://cccr.tropmet.res.in/home/index.jsp). Daily precipitation and temperature data simulated by three RCMs, driven by various GCMs, were obtained from CORDEX (www.cordex.org). Three CORDEX experiments used in the study are: (1) RegCM4(LMDZ), the Abdus Salam International Centre for Theoretical Physics (ICTP) Regional Climatic Model version 4 (RegCM4; Giorgi et al. 2012), with deriving GCM as IPSL LMDZ4, from Centre for Climate Change Research (CCCR), Indian Institute of Tropical Meteorology (IITM), India; (2) CCLM4(MPI), COnsortium for Small-scale MOdelling (COSMO) model in CLimate Mode version 4.8 (CCLM; Dobler & Ahrens 2008), with deriving GCM as Max Planck Institute for Meteorology, Germany, Earth System Model (MPI-ESM-LR; Giorgetta et al. 2013), from Institute for Atmospheric and Environmental Sciences (IAES), Goethe University, Frankfurt am Main (GUF), Germany; and (3) REMO2009(MPI) regional model, with deriving GCM as MPI-ESM-LR (Giorgetta et al. 2013), from Climate Service Center, Hamburg, Germany. The projections for the period of 2006–2060 were analyzed under the representative concentration pathway (RCP) 4.5 representing atmospheric radiation at 4.5 Wm−2 at the end of 2100.

RESULTS AND DISCUSSION

Analysis of predictability of ET flux at catchment scale

To study the hydro-climatic changes of ET flux at catchment scale, a hydrological model was applied to estimate the water budget and required calibration factors to be applied on the simulated runoff. The PCRaster model was applied for 348 cells of the KRB basin at 0.25° × 0.25° resolution at annual scale to estimate the uncalibrated basin outlet runoff at Vijayawada (Equation (6)) using the drainage map created based on the elevation map. The precipitation surplus (P-AET) was estimated for each cell from 1965 to 2014 using P and . The precipitation surplus is converted to runoff accounting for the area of each grid cell, which is considered as uncalibrated runoff, . Then, the uncalibrated runoff , P, and were used to estimate the calibration factors (Equation (6)) using ensemble regression model. The ensemble regression model was trained with annual P, AET, , and , for a period from 1966 to 2003 (correlation coefficient of 0.95) and validated with the 2004–2014 period (correlation coefficient of 0.59) (Figure 3(a)). Hydrologically induced was estimated by applying the calibration factors modeled to study the changes in ET flux over the basin under current and climate signals.

Figure 3

Comparison of (a) calibration factors obtained from closure of water balance and ensemble regression, (b) observed runoff, uncalibrated runoff obtained from PCRaster, calibrated runoff with calibration factors obtained from ensemble regression.

Figure 3

Comparison of (a) calibration factors obtained from closure of water balance and ensemble regression, (b) observed runoff, uncalibrated runoff obtained from PCRaster, calibrated runoff with calibration factors obtained from ensemble regression.

Further, the observed discharge at the basin outlet was compared with the climate-induced and hydrologically induced discharges resulting water balances of (P-AET) and (P-), respectively (Figure 3(b)). The comparison of observed runoff with uncalibrated and calibrated runoff at annual scale resulted in root mean square error (RMSE) (R-square) values of 444 (0.4) and 312 (0.6), respectively (Figure 3(b)). The use of hydrologically calibrated AET has significantly improved the runoff prediction and can be considered as the more reliable term in the long-term annual water balance studies.

The modeled ET estimates must be validated by assessing the strength of predictability with the observed data. The present study used a parametric formulation of Budyko hypothesis to estimate evapotranspiration, , which works at annual scale with a reasonable assumption as storage changes can be considered as constant (Gentine et al. 2012). It should be noted that, if the water balances were estimated at monthly scale, then the assumption of constant storage changes is no longer valid (Wang & Tang 2014). Further, as the Budyko model adopted is parametric (w = 0.5), it is essential to test the applicability of such empirical model for the river basin. Therefore, to validate the applicability of Budyko hypothesis and the predictability of the proposed hydrologically calibrated AET at annual scale, the observed ET, which can be estimated with catchment scale water-balance equation, AET-WB = P − R, was used for the comparison (Figure 4). The AET estimated with Budyko hypothesis and the proposed hydrologically calibrated AET at annual scale were compared with the AET estimated based on water balance, AET-WB = P − R, where R is considered at the basin outlet, Vijayawada, from 1965 to 2003 as shown in Figure 4. The annual basin averaged hydrologically calibrated estimates were comparable with the water budget-based AET-WB as shown in Figure 4 in comparison with the .

Figure 4

Comparison of basin-averaged annual AET estimates based on climate-induced, , hydrologically calibrated, , and water balance-based observed AET-WB (P − R) at catchment scale.

Figure 4

Comparison of basin-averaged annual AET estimates based on climate-induced, , hydrologically calibrated, , and water balance-based observed AET-WB (P − R) at catchment scale.

The study compared both climatological and hydrological AET estimates with remote sensing-based MODIS ET estimates. The correlation coefficients between MODIS-based ET data, which account for the energy budget, canopy transpiration, soil evaporation, and open water evaporation of a region (Zhang et al. 2010), and , estimates were analyzed (Figure 5). The climate-induced AET and hydrologically induced AET were observed to be reasonably comparable with MODIS-based ET data with higher correlation coefficients ranging from 0.3 to 0.7, respectively, for most of the KRB. Specifically, estimates were observed to be more comparable with the remote sensing-based ET estimates with higher correlation coefficients for most of the basin compared to climate-induced AET estimates. More than 80% of the basin has shown positive correlations between MODIS-based ET data and , whereas has shown about 85% of the basin with positive correlations. Furthermore, estimates have shown better predictability for regions with higher temperatures and low to moderate precipitation, i.e., regions where arid climate prevails (Asokan et al. 2010). Therefore, the estimates were observed to be more reliable for arid climate and a convincing measure in the estimation of long-term water balances at catchment scales. Further, it should be noted that the correlation between remotely sensed ET data and modeled hydrologically induced AET depends on the variability of land-cover type on both spatial and temporal scales (Yang et al. 2017).

Figure 5

Correlation coefficients between remote sensing-based data (MODIS) and Thornthwaite model (PET), Budyko hypothesis , hydrologically calibrated for the period of 1983–2006 over KRB.

Figure 5

Correlation coefficients between remote sensing-based data (MODIS) and Thornthwaite model (PET), Budyko hypothesis , hydrologically calibrated for the period of 1983–2006 over KRB.

Changes in hydro-climatological evapotranspiration: current scenario

The basin-averaged annual average precipitation and temperatures have shown increasing trends over KRB for the periods of 1965–2014 (Figure 6). Further, to assess the period from where significant changes have occurred in precipitation and temperatures, Pettitt's test (Pettitt 1979) has been performed on the basin-averaged annual time series data from 1965 to 2014. The spatially averaged precipitation has shown an increasing trend at a rate of 28 mm/decade (Figure 6(a)) with Pettit change point detection year as 2003.

Figure 6

Precipitation (a) temporal trends of basin-averaged conditions, (b) spatial distribution of changes of average conditions from 1965–2003 to 2004–2014. Temperature (c) temporal trends of basin-averaged conditions, (d) spatial distribution of changes of average conditions from 1965–2003 to 2004–2014.

Figure 6

Precipitation (a) temporal trends of basin-averaged conditions, (b) spatial distribution of changes of average conditions from 1965–2003 to 2004–2014. Temperature (c) temporal trends of basin-averaged conditions, (d) spatial distribution of changes of average conditions from 1965–2003 to 2004–2014.

Increasing use of water from the basin for irrigation and hydropower generation from 2001 onwards has resulted in changes in water balance variables over KRB (Bouwer et al. 2003). Such variation of hydrological variables has resulted in decrease in runoff and continuous drought years during 2001, 2002, and 2003 (Bouwer et al. 2003). Therefore, to illustrate the changes in spatial distribution of water balance variables over KRB, two time intervals of 1965–2003 and 2004–2014 were selected as before and after the change point of precipitation year of 2003 (Figure 6). Regarding the spatial variation of precipitation, the upper and lower basins of Krishna river have shown increase of precipitation from 1965–2003 to 2004–2014 (Figure 6(b)), with central and north-east parts of the basin decreasing in precipitation. Here, it can be noted that the temporal variation of basin-averaged temperature over KRB also has shown an increasing trend of 0.1 °C/decade (Figure 6(c)) with Pettit change point detection year as 1992. Here, positive change of annual average temperature from 1965–2003 to 2004–2014 was identified over the entire KRB with the highest increase of about 0.3 °C over a few districts of Telangana (Figure 6(d)).

Highest annual PET estimates and positive changes from 1965–2003 to 2004–2014 were observed over the north and north-east region of KRB (Figure 7(b)). The temporal variability of PET was assessed in terms of increasing trend of basin-averaged annual simulated PET at 13 mm/decade for the period 1966–2014. The has shown an increasing trend for the entire basin at a rate of 14 mm/decade for the period of 1966–2014 (Figure 7(b)). The has shown positive changes varying from 36 mm to 689 mm with a few cells scattered with negative changes from 1965–2003 to 2004–2014. Similarly, the which is hydrologically calibrated AET with surface water balances of P, PET, and runoff (R) has shown an increasing trend of about 72 mm/decade for the period of 1965–2014 (Figure 7(c)). The spatial variability of has also shown positive changes varying from 37 mm to 610 mm. Both and have followed similar spatial and temporal patterns with higher magnitudes for as it accounted for the water use from the river basin along with water (P) and energy (PET) variability.

Figure 7

Temporal trends of basin-averaged conditions of (a) PET, (c) AET-clim, (e) AET-hydro. Spatial distribution of changes of average conditions from 1965–2003 to 2004–2014 of (b) PET, (d) AET-clim, (f) AET-hydro.

Figure 7

Temporal trends of basin-averaged conditions of (a) PET, (c) AET-clim, (e) AET-hydro. Spatial distribution of changes of average conditions from 1965–2003 to 2004–2014 of (b) PET, (d) AET-clim, (f) AET-hydro.

Basin-averaged hydro-meteorological variables of precipitation, climate-induced AET , hydrologically induced AET , and R for the periods 1965–2003 and 2004–2014 are summarized in Table 1. Overall, the precipitation has been increased by 22% from 1965–2003 to 2004–2014 over KRB. An increase of and by 12% and 39%, respectively, was noted over KRB for the current climate scenario. That is, hydrologically induced AET change is more pronounced than climate-induced AET change over the basin, which encapsulates that AET has been affected more due to water use compared to climate-induced AET. It can be noted that the increase in and can be related to the increase of temperature over KRB ranging from 0.1 to 0.3 °C. Such increase in water use-induced AET may also be due to the severe irrigation expansion practices over the river basin (Biggs et al. 2007). In addition to the increase of ET fluxes over the basin, a decrease in observed runoff was also noted as around 39% from 1966–2003 to 2004–2014 at basin-averaged annual scale over KRB. Although precipitation has shown an increasing trend over KRB, the increase in temperatures and consequent increase of ET flux under climate and water use has resulted in a decrease in streamflows. It can be noted that the streamflow station under consideration is controlled/regulated, which can be affected by water abstractions or withdrawals. Overall, the KRB has suffered a severe decrease in water availability from 1966–2003 to 2004–2014 for the current climate scenario with pronounced increased temperature and ET flux over KRB compared to the increase of precipitation. Particularly, the period 2004–2014 has suffered huge water shortages for the years 2002, 2003, 2009, and 2014. These years were also reported as drought years over KRB with significant increasing trends of droughts for the period of 1948–2012 (Mishra et al. 2014; Shah & Mishra 2016).

Table 1

Summary of spatial average annual water-energy variables for current (1966–2003, 2004–2014) and future period (2021–2040, 2041–2060) for KRB

Hydrological variableRCM nameCurrent period
Future period
1966–20032004–20142021–20402041–2060
Average annual precipitation (mm) Observed 733.12 894.47 – – 
COSMO 757.91 698.27 762.82 (−0.85) 807.52 (4.96) 
REMO 755.36 841.84 864.29 (12.34) 850.7 (10.58) 
SMHI 773.33 834.73 834.73 (8.50) 869.82 (13.06) 
Annual temperature (°C) Observed 26.6 26.7 – – 
COSMO 26.53 27.05 27.71 (4.09) 28 (5.17) 
REMO 26.54 26.71 27.81 (4.46) 28.09 (5.51) 
SMHI 26.56 27.1 27.74 (4.19) 28.22 (6.00) 
Annual PET (mm) Observed 1,801.39 1,816 – – 
COSMO 1,772.65 1,910.99 2,109.07 (16.87) 2,197.44 (21.76) 
REMO 1,778.28 1,823.63 2,142.09 (18.7) 2,226.67 (23.38) 
SMHI 1,782.09 1,896.53 2,093.21 (15.99) 2,254.23 (24.91) 
Total modeled AET – Budyko (mm) Observed 644.21 724.35 – – 
COSMO 652.27 618.26 665.25 (0.46) 710.56 (7.30) 
REMO 681.4 728.65 762.95 (15.21) 763.76 (15.34) 
SMHI 667.81 719.39 699.04 (5.56) 766.9 (15.81) 
Total hydrologically calibrated AET (mm) Observed 383.53 533.01 – – 
COSMO 356.02 430.68 383.95 (−7.94) 428.82 (2.81) 
REMO 414.97 362.16 470.97 (12.92) 537.77 (28.93) 
SMHI 423.29 373.62 516.46 (23.83) 480.97 (15.32) 
Average observed runoff at Vijayawada (m3/s) Observed 509.73 307.59 – – 
Average modeled runoff at Vijayawada (m3/s) Uncalibrated 149.84 187.79   
COSMO 154.83 156.61 98.39 (−37.87) 106.95 (−32.46) 
REMO 161.75 180.17 120.47 (−23.93) 143.49 (−9.39) 
SMHI 178.27 149.29 153.03 (−3.37) 131.85 (−16.74) 
Average calibrated runoff at Vijayawada (m3/s) Calibrated 359.57 361.47 – – 
COSMO 401.89 267.59 378.9 (5.25) 378.7 (5.20) 
REMO 340.4 479.68 393.32 (9.26) 312.94 (−13.07) 
SMHI 350.04 461.11 266 (−26.11) 388.86 (8.02) 
Hydrological variableRCM nameCurrent period
Future period
1966–20032004–20142021–20402041–2060
Average annual precipitation (mm) Observed 733.12 894.47 – – 
COSMO 757.91 698.27 762.82 (−0.85) 807.52 (4.96) 
REMO 755.36 841.84 864.29 (12.34) 850.7 (10.58) 
SMHI 773.33 834.73 834.73 (8.50) 869.82 (13.06) 
Annual temperature (°C) Observed 26.6 26.7 – – 
COSMO 26.53 27.05 27.71 (4.09) 28 (5.17) 
REMO 26.54 26.71 27.81 (4.46) 28.09 (5.51) 
SMHI 26.56 27.1 27.74 (4.19) 28.22 (6.00) 
Annual PET (mm) Observed 1,801.39 1,816 – – 
COSMO 1,772.65 1,910.99 2,109.07 (16.87) 2,197.44 (21.76) 
REMO 1,778.28 1,823.63 2,142.09 (18.7) 2,226.67 (23.38) 
SMHI 1,782.09 1,896.53 2,093.21 (15.99) 2,254.23 (24.91) 
Total modeled AET – Budyko (mm) Observed 644.21 724.35 – – 
COSMO 652.27 618.26 665.25 (0.46) 710.56 (7.30) 
REMO 681.4 728.65 762.95 (15.21) 763.76 (15.34) 
SMHI 667.81 719.39 699.04 (5.56) 766.9 (15.81) 
Total hydrologically calibrated AET (mm) Observed 383.53 533.01 – – 
COSMO 356.02 430.68 383.95 (−7.94) 428.82 (2.81) 
REMO 414.97 362.16 470.97 (12.92) 537.77 (28.93) 
SMHI 423.29 373.62 516.46 (23.83) 480.97 (15.32) 
Average observed runoff at Vijayawada (m3/s) Observed 509.73 307.59 – – 
Average modeled runoff at Vijayawada (m3/s) Uncalibrated 149.84 187.79   
COSMO 154.83 156.61 98.39 (−37.87) 106.95 (−32.46) 
REMO 161.75 180.17 120.47 (−23.93) 143.49 (−9.39) 
SMHI 178.27 149.29 153.03 (−3.37) 131.85 (−16.74) 
Average calibrated runoff at Vijayawada (m3/s) Calibrated 359.57 361.47 – – 
COSMO 401.89 267.59 378.9 (5.25) 378.7 (5.20) 
REMO 340.4 479.68 393.32 (9.26) 312.94 (−13.07) 
SMHI 350.04 461.11 266 (−26.11) 388.86 (8.02) 

Values in the brackets are percentage changes with respect to observed values.

Changes in AET under climate, water-use and land-use changes

The period 1965–2003 was considered as pre-change period and 2004–2014 was considered as post-change period in the time-trend analysis method to study the impact of changes of climate, water use, and land use on AET independently. That is, the annual change in the AET for the post-change period of 2004–2014 was estimated under changes of climate , hydrological , and land use changes . Figure 8 shows the annual changes in AET due to change in climate , hydrological , and land use changes over KRB for the period of 2004–2014 as post-change period compared to pre-change period of 1965–2003. The change in AET with respect to change in climate, hydrological, and land use was estimated as the differences between observed and predicted , , and , respectively, for the testing (post-change) period. Both climate and water use changes have shown positive change of AET over the KRB for the period of 2004–2014. However, the land use change has shown positive changes of AET of about 226 mm for the year of 2005 due to construction of dams and rapid irrigation expansion (Biggs et al. 2007). The average positive change of AET due to land use for the remaining years was estimated as 22 mm over the basin. Overall, the study observed that climate and hydrology has a positive effect, whereas land use change has a positive effect of about 56% and a negative effect of about 40% on AET of the basin. Further, there is strong evidence of an increase in ET at a rate of 4.97 mm/year over the basin based on the study by Teluguntla et al. (2013) for the period of 1983–2001 with advanced very high resolution on radiometer (AVHRR)-based ET estimates due to the expansion of irrigation over the basin. The same study also revealed that construction of dams and irrigation expansion resulted in a decrease in annual discharge (Teluguntla et al. 2013).

Figure 8

Annual changes in AET due to change in climate (AET-clim), hydrological (AET-hydro), and land use changes (AET-land use) over Krishna river basin for the period of 2004–2014 as post-change period compared to pre-change period of 1965–2003.

Figure 8

Annual changes in AET due to change in climate (AET-clim), hydrological (AET-hydro), and land use changes (AET-land use) over Krishna river basin for the period of 2004–2014 as post-change period compared to pre-change period of 1965–2003.

Changes in hydro-climatological evapotranspiration: climate change signals

The bias-corrected monthly precipitation and temperatures from each CORDEX RCM model compared well with the observed IMD data for the period of 1966–2014. The normalized RMSE (R-square) values estimated between observed precipitation and each RCM model outputs of COSMO, REMO, SMHI was estimated as 0.10 (0.2), 0.09 (0.23), 0.10 (0.15), respectively, for the period of 1966–2014, whereas the normalized RMSE (R-square) values estimated between observed temperature and each RCM model outputs of COSMO, REMO, SMHI was estimated as 0.07 (0.6), 0.06 (0.7), 0.07 (0.52), respectively, for the period of 1966–2014. Among the three selected RCMs, the REMO CORDEX model has shown the best performance for simulating precipitation and temperatures over KRB. Precipitation has been predicted to be increasing under climate change signals with all three RCM models for the future periods of 2021–2060 over KRB (Table 1) (Figure 9(a)). The SMHI model predicted the highest increase of precipitation as 101.6 mm and 136.7 mm for the future time periods of 2021–2040 and 2041–2060, respectively, compared to the current climate period of 1966–2003 over KRB. Lowest precipitation projections, about 29.7 mm and 74.4 mm of increase for the period of 2021–2014 and 2041–2060, respectively, compared to the observed period of 1966–2003, were noted with COSMO RCM model outputs. Overall, the projected increase of precipitation under climate signals was predicted to be from 74.4 to 136.7 mm over KRB for the future time period of 2041–2060 compared to the observed period of 1966–2003. About 1.06 °C and 1.35 °C of increase in temperature was predicted for the periods of 2021–2040 and 2041–2060, respectively, compared to the observed period of 1966–2014 over KRB (Figure 9(b)) (Table 1). Both and have been predicted to increase for the future scenarios for KRB under climate change. The predicted increase in was observed from 21.04 mm (COSMO) to 118.71 mm (REMO) and 66.35 mm (COSMO) to 122.7 mm (SMHI) for the periods of 2021–2040 and 2041–2060, respectively, compared to observed period of 1966–2003. Similarly, was predicted to increase with lower magnitudes compared to from 45.29 mm (COSMO) to 154.24 mm (REMO) for the period of 2041–2060 compared to 1966–2003. The lower magnitudes of were the resulting effect of decreasing projections of runoff over KRB under climate change signals. The runoff resulting from water balance has predicted a higher decrease in runoff ranging from 366.24 m3/s (REMO) to 402.78 m3/s (COSMO) for the period of 2041–2060 compared to the observed period of 1966–2003. The runoff resulting from hydrologically calibrated water balance has predicted a lower decrease in runoff ranging from 120.87 m3/s (SMHI) to 196.79 m3/s (REMO) for the period of 2041–2060 compared to the observed period of 1966–2003.

Figure 9

Basin-averaged annual observed and projected (a) precipitation and (b) temperatures for the periods of 1966–2003, 2004–2014, 2021–2040, and 2041–2060 over KRB with various RCM model outputs.

Figure 9

Basin-averaged annual observed and projected (a) precipitation and (b) temperatures for the periods of 1966–2003, 2004–2014, 2021–2040, and 2041–2060 over KRB with various RCM model outputs.

Here it can be noted that various CORDEX model outputs have disparity and limitations to simulate spatiotemporal variations across India (Singh et al. 2017). Further, RCMs are limited in simulating all the patterns of observed data due to the shortcomings and errors in their parameterization of convection and boundary layer schemes (Fowler et al. 2007; Diasso & Abiodun 2017). Also, RCMs are limited in improving the simulation of changed climate, as projected by parent GCMs involved (Feser et al. 2011). However, in general, the performance of CORDEX in simulating the water balance variables at regional scales as presented in this study was noted to be encouraging. This implies that use of CORDEX data sets at regional scales can prove to be valuable after checking for the performance of model simulations with observed data (Ehret 2012; Singh et al. 2017; Das & Umamahesh 2018).

CONCLUSIONS

A modeling framework was proposed to estimate catchment-scale ET with consideration of closure of water balance accounting for water use along with water supply and energy, which was identified as a more reliable measure in the estimation of long-term water-energy balances. Instead of constant model parameters for the entire basin, the study proposed a modeling framework to estimate the model parameters dynamically accounting for the temporal variability of precipitation, potential evapotranspiration, and runoff. Such calibration factors can be applied on the empirical region-specific actual evapotranspiration models with consideration of closure of water balance to estimate hydrologically calibrated actual evapotranspiration estimates at catchment scales. The ensemble regression model was used to find the basin-averaged annual hydrological calibration factors for current climate by considering precipitation, actual evapotranspiration, and runoff as independent variables. The trained and tested ensemble regression model was further used with projected precipitation and runoff under climate change signals to estimate such model parameters for future scenarios to estimate the hydrologically calibrated actual evapotranspiration. The study tested how a hydrologically calibrated evapotranspiration estimate accounting for various major water-energy balance variables is appropriate for predicting current water availabilities at regional (or catchment) scale by comparing with satellite-based land surface evapotranspiration estimates. The proposed modeling framework of actual evapotranspiration estimation can be implemented with any region-specific empirical actual evapotranspiration models to study climate and hydrologically induced changes of evapotranspiration.

The KRB basin has suffered a severe decrease in water availability from 1966–2003 to 2004–2014 with increase in precipitation, temperature, evapotranspiration and decrease in runoff. Climate and water use changes have shown a positive effect on actual evapotranspiration for the post-change period of 2004–2014 compared to pre-change period of 1965–2003. Overall, the study observed that climate and hydrology changes have shown positive contributions over actual evapotranspiration over the basin for the post-change period compared with the pre-change period, whereas land use change has shown a positive change of about 56% and about 40% as a negative change of actual evapotranspiration for the post-change period compared with the pre-change period over the basin.

Overall, the projected increase of precipitation under climate signals was predicted to be from 74.4 to 136.7 mm over KRB for the future time period of 2041–2060 based on regional climate model outputs compared to the observed periods of 1966–2003. About 1.06 °C and 1.35 °C of increase in temperatures was predicted for the periods of 2021–2040 and 2041–2060, respectively, compared to the observed period of 1966–2014 over KRB. The actual evapotranspiration estimates based on climatological (precipitation and potential evapotranspiration) and hydrological (precipitation, potential evapotranspiration, and runoff) have been predicted to increase over the basin with lower magnitudes of hydrologically calibrated actual evapotranspiration due to decreasing projections of basin outlet runoff. Irrigation water use is another dominant factor which results in a decrease in runoff and enhanced evapotranspiration. Furthermore, the water-energy variable projections are expected to vary with various regional circulation model outputs with different representative concentration pathways, various empirical actual evapotranspiration and hydrological models which accumulate climate and model uncertainty in the impact assessment. Implementation of multimodal-weighted mean water-energy variables to study the possible range of uncertainty bounds accumulating from various stages of decision-making and cascading of uncertainties can be potential future research (Rehana & Mujumdar 2014).

ACKNOWLEDGEMENTS

The research work presented in the paper is funded by Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India through Start-up Grant for Young Scientists (YSS) Project no. YSS/2015/002111.

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