2.1 Study Area
The Anandapur catchment of Baitarani River Basin is situated between 85º0′0″ to 86º30′0″ E longitude and 21º0′0″ to 22º30′0″N latitude. This catchment is selected as the study area due to the availability of its data and is not studied before. It can be located in the Keonjhar district of Odisha state, India (Fig. 1). The catchment area is 8645 km2 with topographic elevation ranging from 32 to 1181 m above mean sea level (MSL). The basin experiences an undulated topography with an average slope varying between 0–2%. The average rainfall in the basin is 1628 mm with a sub-humid tropical climate predominating over the complete basin. As per the information of the India Meteorological Department, the basin experiences four climatic seasons in a year, i.e., winter (January and February), pre-monsoon (March-May), monsoon (June–September) and post-monsoon (October–December). About 80% of rainfall occurs during the monsoon spanning between June and September. Temperature in the catchment vary between 30 and 36 ºC during the summer and 16–17 ºC during winter. Two land-use types, i.e. forest and farmland are predominant in the catchment. Being an agriculture dominant basin, rice, maize, green gram, wheat, groundnut and vegetable are cultivated throughout the year.
Two climate model such as the National Centre for Meteorological Research-Climate Model Version 5.0 (CNRM-CM5.0) and Geophysical Fluid Dynamics Laboratory- Climate Model Version 3.0 (GFDL-CM3.0) models have been used under the Coordinated Regional Downscaling Experiment (CORDEX) for South Asia (http://cccr.tropmet.res.in/cordex/). These two models were selected based on the model evaluation works of Sperber et al. (2013) and Hasson et al. (2014). They found that CNRM-CM5.0 and GFDL-CM3.0 models simulate the June–September rainfall climatology more accurately over the Indian monsoon region. Hence, the CNRM-CM5.0 and GFDL-CM3.0 models of CMIP5 versions have been selected for this study.
2.2 Streamflow calibration and validation
The SWAT-CUP interface is coupled with SWAT model for the calibration and validation (Abbaspour et al., 2007) of daily discharge data. The Sequential Uncertainty Fitting (SUFI-2) algorithm is adopted for investigating the sensitivity and uncertainty in streamflow prediction. SWAT is calibrated and validated for monthly streamflow by comparing the results with the observed streamflow at the Anandapur outlet. Three years (1980–1982) are considered for the warm-up of the model, and subsequently, the period 1983–2003 and 2004–2012 are selected as calibration and validation periods, respectively.
Performance of the model is evaluated by checking the reliability of its output through various statistical indicators (Moriasi et al., 2007). In this study, the Nash–Sutcliffe efficiency (NSE) (Eq. 2), coefficient of determination (R2) (Eq. 3) and percent bias (PBIAS) (Eq. 4) statistical indicators are used in the model performance evaluation. Performance of the model is good when the PBIAS is within ± 15%, NSE is above 0.75 (Moriasi et al., 2007) and R2 is close to one. The following equations are used for evaluation of the statistical indicators:
$$NSE=1- \frac{\sum _{i=1}^{N}{({O}_{i}-{S}_{i})}^{2}}{\sum _{i=1}^{N}{({O}_{i}-\stackrel{-}{O})}^{2}}$$
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$${R}^{2}={\left\{\frac{\sum _{i=1}^{N}({O}_{i}-\stackrel{-}{O})({P}_{i}-\stackrel{-}{P})}{{\left[\sum _{i=1}^{N}{({O}_{i}-\stackrel{-}{O})}^{2}\right]}^{0.5}{\left[\sum _{i=1}^{N}{({P}_{i}-\stackrel{-}{P})}^{2}\right]}^{0.5}}\right\}}^{2}$$
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\(PBIAS=100*\frac{\sum _{i=1}^{t}{({O}_{i}-{S}_{i})}_{i}}{\sum _{i=1}^{t}{O}_{i}}\) (3)
where \({O}_{i}\) is the ith observed data, \({S}_{i}\) the ith predicted value, \({P}_{i}\) the ith predicted data, \(\stackrel{-}{O}\) the mean of measured data, \(\stackrel{-}{P}\) the mean of model estimated values, and N the total number of simulation periods.
Correlation analysis is commonly used to know the relationship between two variables (Ichii et al., 2002). Correlation between drought indices and decomposed crop yields are assessed using the Pearson correlation coefficient, which is calculated as follows:
$${r}_{X,Y}=\frac{\sum \left(X-\stackrel{-}{X}\right)\left(Y-\stackrel{-}{Y}\right)}{\sqrt{\sum {\left(X-\stackrel{-}{X}\right)}^{2}\sum {\left(Y-\stackrel{-}{Y}\right)}^{2}}}$$
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where X and Y are the time series of two variables, \(\stackrel{-}{X}\) and \(\stackrel{-}{Y}\) are the mean values of the two series. The correlation coefficient \({r}_{X,Y}\)ranges from − 1 to + 1, with − 1 indicating that the two variables are perfectly negatively correlated and + 1 indicating a perfect positive correlation.
2.3 Bias Correction and Downscaling
The bias correction of GCM output is essential due to the associated systematic and random model errors (Teutschbein and Seibert, 2013; Fiseha et al., 2014). The parametric and non-parametric bias correction techniques are generally used for reducing the bias from GCM output. But non-parametric bias correction technique has used in this study for efficient reduction of bias from GCM outputs (Gudmundsson et al., 2012). The non-parametric quantile mapping bias correction method is based on following Equation.
$${P}_{obs}={F}_{obs}^{-1}\left({F}_{wet}\right({P}_{wet}\left)\right)$$
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where, \({P}_{obs}\) and \({P}_{wet}\) are the observed and weighted precipitation, \({F}_{wet}\) the CDF of \({P}_{wet}\) and \({F}_{obs}^{-1}\) the inverse CDF corresponding to \({P}_{obs}\).
A multi-GCM ensemble approach is used in this study because a single GCM output is not reliable enough in evaluating future climate change impacts. A weighted ensemble average approach is used to ensemble the two GCMs (CNRM-CM5.0 and GFDL-CM3.0).
2.4 Estimation of Drought Indices
2.4.1 Standardized Precipitation Index (SPI)
The SPI method was proposed by Mckee et al. (1993, 1995) to assess and analyse the meteorological drought. The SPI can be used to identify the drought conditions for different time scales (3-, 6-, 12-, 24- and 48-month time scales); therefore, it is used to compare drought conditions among different time periods and regions with different climatic conditions. In the SPI computation, only normally or log-normally distributed input data can be used. But precipitation data distribution is not normally distributed, rather it follows the gamma distribution. Hence, the data must be transformed to normal distribution before they can be used for computation of the SPI. The SPI computation is a probability transformation of observed precipitation series to the standard normal distribution having standard deviation one and mean zero (Mckee et al. 1993). A Positive SPI values indicate wet periods, while negative values indicate drought periods (Dash et al. 2021). The computation of SPI consists of the following steps:
1) For the computation of SPI gamma distribution is fitted to the observed precipitation data. The gamma probability distribution function is expressed as:
$$g \left(x\right)=\frac{1}{{\beta }^{\alpha }\varGamma \left(\alpha \right)}{x}^{\alpha -1}{e}^{-x/\beta }$$
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where α > 0 is a shape parameter, β > 0 is a scale parameter, and x > 0 is the amount ofprecipitation. Γ(α) is the gamma function, which is defined as:
$$\varGamma \left(\alpha \right)=\underset{0}{\overset{\infty }{\int }}{y}^{\alpha -1}{e}^{-y}dy$$
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Fitting the distribution to the data requires estimation of α and β. These parameters can be estimated as follows:
\(\alpha =\frac{1}{4A}\left(1+\sqrt{1+\frac{4A}{3}}\right)\),\(\beta =\frac{\stackrel{-}{x}}{\alpha }\), with \(A=\text{ln}\stackrel{-}{x}-\frac{\sum \text{ln}\left(x\right)}{n}\) (8)
where n is number of observed precipitations and x refers to the mean of the sample data.
Integrating the probability density function with respect to x yields the following expression G(x) for the cumulative probability:
$$G\left(x\right)=\underset{0}{\overset{x}{\int }}g\left(x\right)dx=\frac{1}{{\beta }^{\alpha }\varGamma \left(\alpha \right)}\underset{0}{\overset{x}{\int }}{x}^{\alpha -1}{e}^{-x/\beta }dx$$
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The gamma distribution is undefined for x = 0; however, it is possible to have several zero values in a sample set. Therefore, in order to account for zero value probability, the cumulative probability function for gamma distribution is modified as:
$$H\left(x\right)=q+\left(1-q\right)G\left(x\right)$$
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where q is the probability of zero precipitation.
2) The cumulative probability distribution is transformed into the standard normal distribution and the transformed probability distribution is considered as SPI (Abramowitz and Stegun 1964).
\(SPI=-\left(t-\frac{{c}_{0}+{c}_{1}t+{c}_{2}{t}^{2}}{1+{d}_{1}t+{d}_{2}{t}^{2}+{d}_{3}{t}^{3}}\right)\), \(t=\sqrt{\text{ln}\frac{1}{{\left(H\left(x\right)\right)}^{2}}}\) (11)
For\(0<H\left(x\right)<0.5\)
\(SPI=+\left(t-\frac{{c}_{0}+{c}_{1}t+{c}_{2}{t}^{2}}{1+{d}_{1}t+{d}_{2}{t}^{2}+{d}_{3}{t}^{3}}\right)\), \(t=\sqrt{\text{ln}\left(\frac{1}{{\left(1.0-H\left(x\right)\right)}^{2}}\right)}\) (12)
2.4.2 Standardized Precipitation Evapotranspiration Index (SPEI)
The Standardized Precipitation Evapotranspiration Index (SPEI) is an extension of the conventional SPI, which is used for assessing the temperature-induced moisture stress (Chitsaz and Hosseini-Moghari, 2018). The drought classification of SPEI is almost similar to the SPI based drought classification system given by McKee et al. 1993. The steps for estimation of SPEI could be adopted from the method given by Vicente-Serrano et al., 2010.
2.4.3 Streamflow Drought Index (SDI)
The SDI was proposed by Nalbantis (2008) for analysis of hydrological drought characteristics at different time scales. The calculation steps include: (1) Accumulation of the monthly simulated streamflow data, (2) Fitting Gamma probability distribution to these accumulated streamflow time series, (3) Estimation of cumulative density function of observed cumulative streamflow data, and finally, (4) The cumulative probability is transformed to a normal distribution with mean zero and standard deviation one. The SDI is evaluated based on the monthly standard normal flow (Nalbantis and Tsakiris 2009). The calculation procedure is similar to SPI except that discharge monthly series were used instead of rainfall data as the input in SDI. The cumulative streamflow volume could be obtained as given below:
$${V}_{i,k}=\sum _{j=1}^{3k}{Q}_{i,j}i=1, 2, 3\dots .;j=1, 2, \dots .,12;k=1, 2, 3, 4$$
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where \({V}_{i,k}\)is the cumulative streamflow value of ith hydrological year and the kth reference period,\({Q}_{i,j}\)is the monthly streamflow, j denotes the month within the hydrological year.
The SDI is defined as by:
$${SDI}_{i,k}=\frac{{V}_{i.k}-{\stackrel{-}{V}}_{k}}{{s}_{k}}$$
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where,\({\stackrel{-}{V}}_{k}\) and \({s}_{k}\) are respectively the mean and standard deviation of cumulative streamflow volumes of reference period k.
Usually, Gamma and log-normal distributions are used for representing streamflow. However, in case of log-normal distribution, the normalization is relatively easier. The SDI is defined as:
\({SDI}_{i,k}=\frac{{y}_{i,k}-{\stackrel{-}{y}}_{k}}{{s}_{y,k}}\), \(i=1, 2, \dots ;k=1, 2, 3, 4\) (15)
\({y}_{k}=\text{ln}\left({V}_{i,k}\right)\), \(i=1, 2, \dots ;k=1, 2, 3, 4\) (16)
where, \({y}_{k}\) is the natural logarithm of cumulative streamflow with mean \({\stackrel{-}{y}}_{k}\) and the standard deviation\({s}_{y,k}\). SDI also has same drought-severity classes as those for SPI and SPEI.
2.4.4 Agricultural Standardized Precipitation Evapotranspiration Index (aSPEI)
In the aSPEI, effective precipitation is used instead of the total precipitation of the conventional SPEI. Though SPEI is found to be good for agricultural drought characterization (Fu et al., 2019), the use of effective precipitation leads to giving more promising results. Effective precipitation is evaluated to analyze agricultural drought characteristics for the concerned time scale. The term effective precipitation (Pe) has several definitions in different research fields (i.e., reservoir management, groundwater management, agricultural applications). In reservoir management, Pe is the amount of water from the total precipitation entering into the reservoir. In groundwater management, Pe is the portion of precipitation that contributes to groundwater recharge. Similarly, for agricultural applications, Pe is the percentage of precipitation that used by plant root for plat development. Here Pe is used in term water that contributes to the plant for consumptive use. In this study \({P}_{e}\) is estimated using the CROPWAT model and the monthly total precipitation is used as the input variable (Smith, 1992), as given by:
\({P}_{e}=P\times (125-0.2\times P)/125\) For P ≤ 250mm (17)
\({P}_{e}=0.1\times P+125\) For P > 250mm (18)
2.5 Selection of Appropriate Reference Period
Selection of the base periods for calculation of the agricultural drought index is based on the crop development time. For assessment of agricultural drought, the month of seeding is considered as the reference period. The reference period corresponding to various critical development stages of the plants is to know the early drought warning time. Short reference periods are more suitable for soil moisture condition, while long reference periods are appropriate for arid or semi-arid regions due to high percentage of zero precipitation values in the time series (Quiring and Ganesh 2010; Mallya et al. 2013). Generally, the crop development pattern follows seasonal weather variability. Therefore, the reference period should be selected according to crop development stages. For hydrological drought monitoring, the reference period starts from the first month of the hydrological year, while the first month of crop production is considered as starting of reference period for agricultural drought monitoring (Nalbantis and Tsakiris 2009).
The backward stepwise selection is performed to investigate the combined influence of climate, catchment variables on hydrological drought duration. The proposed backward stepwise selection model was evaluated based on the Akaike Information Criterion (AIC).
Backward stepwise selection (or backward elimination) is a variable selection method which:
i. Begins with a model that contains all variables under consideration (called the Full Model)
ii. Then starts removing the least significant variables one after the other
iii. The removal should continue until a pre-specified stopping rule is reached or no variable is left in the model
The least significant variable is treated as a variable that:
i. Has the highest p-value in the model, or
ii. Its elimination from the model causes the lowest drop in R2, or
iii. Its elimination from the model causes the lowest increase in RSS (Residuals Sum of Squares) compared to other predictors
Finally the stopping rule criteria is defined in order to stop the algorithm. The stopping rule is satisfied when all remaining variables in the model have a p-value smaller than some pre-specified threshold. When that state is reached, backward elimination will terminate and return the current step’s model. The threshold is determined by using Akaike Information Criterion (AIC) (Akaike, 1974).