Abstract

The study focused on the Godavari River basin to understand the alteration in the drought phenomenon for future scenarios. The Standardized Precipitation Evapotranspiration Index (SPEI)-3 is calculated from Climate Research Unit 4.03 precipitation, and minimum and maximum temperatures. The drought magnitude and characteristics are determined using SPEI, which considers both precipitation and temperature data as input variables. The Mann–Kendall trend analysis is performed to identify the trend associated with drought characteristics. The basin is divided into six homogeneous regions using K-means clustering algorithm. The reliability ensemble averaging method is used for ensemble averaging of regional climate models (RCMs). The drought frequency analysis is carried out using trivariate copula for reference and future time periods. Variations in the drought characteristics are observed in the future scenarios with respect to the reference period. The drought duration, severity and peak for different climate divisions showed an increasing trend in future time period, especially in the case of RCP8.5 scenarios. The return periods of future droughts based on weighted-average RCMs under the two scenarios showed the possibility of more frequent droughts in the future (2053–2099) than in the past (1971–2017).

HIGHLIGHTS

  • The Standardized Precipitation Evapotranspiration Index (SPEI) for historical and future periods is computed.

  • The SPEI is used to assess drought characteristics in the Godavari River basin.

  • The river basin is divided into six regions using K-means clustering algorithm.

  • The trend analysis is carried out using historical and future drought characteristics.

  • Future drought return periods are computed using trivariate copula.

INTRODUCTION

Drought is defined as the water deficit phenomenon for a prolonged time period, which can continue for several days, months and years, affecting the water resources, agriculture, environment and human lives. The deficiency of precipitation, soil moisture, runoff and the increased evapotranspiration is linked to the drought phenomenon. Although there are no particular definitions of drought, they can be well defined with several perspectives, like conceptual or operational droughts (Wilhite & Glantz 1985). Conceptually, it is defined based on drought regimes, namely meteorological, agricultural and hydrological drought events depending on the deficit of rainfall, lack of soil moisture and the scarcity of water in reservoirs, lakes and river streams, respectively (Mishra & Singh 2010). Another type of drought, namely socioeconomic drought is caused by a shortage of water mostly affecting the supply and demand of water for the people. Operational drought regimes can be defined as the identification of the onset, withdrawal, duration and severity of drought events.

The correct and precise formulation of drought indices must be investigated under the global warming phenomenon (Mukherjee et al. 2018). The variations in the projected climatic phenomenon and its association with the future drought events can cause more long-lasting, frequent and severe drought phenomenon (Dai 2013). Future drought projections can be helpful for the development of efficient adaptation strategies by assessing the influence of climate change impacts on water resources. The principal tools for the assessment of climate change projections of drought regimes are the global climate models (GCMs) and regional climate models (RCMs). RCMs are helpful in representing finer-scale atmospheric features and processes, which cannot be modeled by the GCMs (Torma et al. 2015). RCM outputs have been used by many authors for the quantitative and qualitative assessment of future climatic extreme events including drought regimes (Wang et al. 2011; Huang et al. 2015). So the climate change anticipated with the drought phenomenon has a massive impact on the drought characteristics in a country like India. The drought risk based on the Modified Palmer Index (MPI) is examined in the context of global warming by Mishra & Liu (2014) over India observing severe changes in the north-eastern and western India. The drought indices, like Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI) and Standardized Effective Precipitation Evapotranspiration Index, have been projected for future periods over India using RCMs (Gupta & Jain 2018). Jenkins & Warren (2015) quantified the potential climate change impact on drought regimes in countries like Ethiopia, Australia, China, Brazil, India, Portugal and the USA. Severity–Area–Frequency and Area–Probability curves were used by Burke & Brown (2010) for determining the future return period of drought events in UK. The SPEI and SPI were projected for the analysis of future return levels of drought characteristics using the multi-model RCM ensemble-averaged (Masud et al. 2017). Based on these studies, RCM models have been considered in this study for the better identification of future drought phenomenon in the Godavari River basin (GRB).

Basically, drought phenomenon is regionally concentrated and stochastic by nature and is associated with the drought characteristics like duration, peak, intensity and severity. So, drought characterization studies have been carried out by many researchers in the past for the better management of water resources (Mishra & Singh 2011; Xu et al. 2015; Mortuza et al. 2019). Consequently, the outcomes of frequency analysis may be over-estimated or under-estimated in the case of univariate analysis that provides limited evidence of the dependency of drought phenomenon. Copula functions (Sklar 1959) have the capability to model the conventional multivariate distributions by incorporating their nonlinear dependency measures of variables and hence have gained popularity for modeling the multivariate extreme event characteristics (Salvadori & De Michele 2004; Genest & Favre 2007; Ganguli & Reddy 2013; Mirabbasi et al. 2013; Dabral & Hangshing 2017; Das et al. 2020; Kim et al. 2019; Mellak & Souag-Gamane 2020). Several studies have been carried out to demonstrate the robustness of copula functions for probabilistic drought analysis (Shiau & Modarres 2009; Reddy & Ganguli 2012; Madadgar & Moradkhani 2013; Saghafian & Mehdikhani 2014; She et al. 2016). Therefore, authors have used the copula model for multivariate drought analysis.

Drought indices associated with specific timescales are useful tools for monitoring and management of drought. Many studies on droughts have been conducted to develop several drought indices (Palmer 1965; Vicente-Serrano et al. 2010; Tsakiris 2017; Abbasi et al. 2019). The SPI developed by McKee et al. (1993) is simple and easy to compute the deficit in the amount of precipitation for multiple time scales. Drought index based on precipitation data only may not be adequate to monitor droughts, since temperature and evapotranspiration also play vital roles in the availability of moisture that directly or indirectly impact the drought phenomenon. Therefore, SPEI is selected which combines the sensitivity nature of PDSI due to change in evapotranspiration based on temperature changes and the multitemporal behavior of SPI (Gupta & Jain 2018). The overall aim is to obtain a comprehensive evaluation of historical and future droughts in the GRB by incorporating the potential associations of drought characteristics. The precise goals involve (i) historical drought assessment using SPEI, (ii) weightage averaging of RCMs using the reliability ensemble averaging (REA) method, (iii) identification of homogenous regions using K-means clustering algorithm, (iii) trend analysis of drought characteristics for historical as well as the future periods using the MK test, (iv) multivariate drought return period using copula functions and (v) assessment of changes in the future droughts using RCMs under RCP4.5 and RCP8.5 scenarios for the understanding of the impact of future climatic variability on drought characteristics.

MATERIALS AND METHODS

Study area

The study undertaken here is for the GRB lying in southern Indian peninsular India. The GRB flows for a length of 1,465 km toward east, draining the states of Maharashtra (48.6%), Karnataka (1.6%), Telangana (18.8%), Andhra Pradesh (4.5%), Chhattisgarh (10.9%) and Odisha (5.7%), eventually emptying into the Bay of Bengal. Covering a drainage area of 312,812 km2, it is one of the main river basins of India. The basin, shown in Figure 1, lies in the Deccan Plateau between longitudes 73̊24′ and 83̊40′E and latitudes 16̊19′ and 22̊34′N and is mainly dominated by the south-west monsoon, which is generally erratic with wide temporal and spatial variation in rainfall. The south-west monsoon sets by July and withdraws by September, and the major portion of its annual rainfall occurs during this period of time. The average annual rainfall of the basin is about 1,100 mm. The economy is directly and indirectly related to agricultural practices. South-west monsoon has a direct influence on agriculture, which is more vulnerable to extreme weather events. Hence, irrigation, amounting to approximately 95% of the water use, has high priority in this basin (Palanisami et al. 2014). Of late, rapid urbanization in this basin is leading to increase in domestic water demand. The extreme events in this basin are associated with the anthropogenic activities, which bring extra pressure on the water resources. So, a comprehensive drought assessment for future must be carried out to identify the future drought variability with respect to the changing climate.

Data used

The present study focuses on estimating the drought characteristics and the future drought frequency analysis using trivariate copula. Prediction of the drought and its frequency analysis are helpful to investigate the potential impacts on the river basin.

Climate Research Unit Time Series (CRU TS) is a monthly climate anomaly 0.5° × 0.5° gridded dataset, which was derived based on the angular distance weighting (ADW) method over all the land domain in the world except Antarctica. ADW was used for improving the gridded dataset and to assess the geographical variations of data over the world. CRU dataset can also capture the local scale of climate variability like river, catchments and agronomy. The observation stations that are used for creating the CRU TS datasets are obtained from the US National Oceanographic and Atmospheric Administration (NOAA) and presented in Figure 1. The details regarding Version 4 of the CRU TS monthly high-resolution gridded datasets are given in Harris et al. (2020). CRU T 4.03 (Climate Research Unit T 4.03) data were used by Harris et al. (2014) for the temperature-based derivation of potential evapotranspiration (PET). Many hydro-climatological studies have been conducted by using CRU data in different parts of the world (Zarch et al. 2015; Lawal et al. 2019). So, monthly precipitation data, minimum and maximum temperature data for 106 grid points (0.5 × 0.5 grid) for the period of 1970–2017 were obtained from CRU TS 4.03 datasets (https://data.ceda.ac.uk/badc/cru/data/cru_ts/cru_ts_4.03). The climate data were extracted and regridded by using the bilinear interpolation method to GRB scale.

Figure 1

Study area map of the GRB.

Figure 1

Study area map of the GRB.

Finer-scale atmospheric processes and features can be better represented by the RCMs (Gao et al. 2012; Torma et al. 2015). The comparison of seven RCMs, namely CERFACS-CNRM-CM5-RegCM4, CCCma-Can-ESM2-RegCM4, GFDL-ESM2M-RegCM4, HadGEM2-RCA4, MIROC5-RCA4, ESM-LR-REMO2009 and ESM-MR-RegCM4 was carried out for simulating the precipitation and temperature (Gupta & Jain 2018). The four GCMs like CAN-ESM2, CMCC-CMS, MPI-ESM-MR and CSIR are used to project precipitation for RCP4.5 and RCP8.5 in Bihar, India (Kumar et al. 2020). CNRM-CM5.0 and GFDL-CM3.0 models were used by Padhiary et al. (2020) to estimate the hydrological fluxes of Baitarani basin. So, for this study, the daily precipitation, minimum and maximum temperature projections from 2053 to 2099 are obtained from Centre for Climate Change Research (CCCR), Indian Institute of Tropical Meteorology (IITM), Pune, India (https://cccr.tropmet.res.in/home/cordexsa_datasets.jsp) database. Five RCMs, namely ACCESS 1-0, GFDL-ESM2G, MPI-ESM-LR, CCSM4 and CNRM-CM5 for RCPs 4.5 and 8.5 with a spatial resolution of 0.44° are downloaded from the above-mentioned site. Therefore, all the RCM datasets are regriddd to CRU grids under the same spatial and temporal resolution for analyzing the future dry and wet spells.

SPEI and identification of drought characteristics

PET in monthly scale is computed in the present study by using the Hargreaves method (Equation (1)). The output from this method is comparable with the Penman–Monteith formula with fewer climate data (Subburayan et al. 2011).
formula
(1)
where , and are the monthly mean, maximum and minimum air temperatures, respectively, in °C, and is represented as the extra-terrestrial radiation (MJ m−2 d−1).

In the current global warming situation, the effect of temperature and evapotranspiration must be considered for estimating the meteorological drought. Therefore, the widely used SPEI is computed in the present study for future drought assessment (Vicente-Serrano et al. 2010). It is computed based on the resulting water balance (P-PET) from precipitation (P) and evapotranspiration (PET). In this study, SPEI is estimated to investigate the effects of climate change on drought in the context of global warming. For more details regarding SPEI computation, see Vicente-Serrano et al. (2010).

The run analysis method suggested by Yevjevich (1967) is the most commonly used method in drought studies. Several past studies have showed the effective application of run analysis for the estimation of drought characteristics (Shiau 2006; Ganguli & Reddy 2012; Saghafian & Mehdikhani 2014). Hence, this approach is employed for the identification of different drought characteristics like duration, peak and severity. A run can be represented as a negative or positive based on the part of a drought time series, in which all values remain below or above the chosen truncation level. The drought severity is defined as the deficit volume under the threshold level, duration is the time period between initiation and termination of drought and peak is the highest value of deficit volume. In this study, −1 is considered as the threshold value for identifying drought characteristics for observed and future time periods.

Detection of monotonic trend in SPEI time series

In the present study, positive and negative trends associated with the drought characteristics are investigated using the nonparametric Mann–Kendall (MK) trend test and Sen's slope estimator for both historical and future periods. The S-statistics are used in the MK test as suggested by Mann (1945) and Kendall (1975). If there exists any positive difference between data points, then the S-statistics increase by 1 and vice versa, while zero difference represents that S-statistic is constant. The S-statistic is given by the following equation:
formula
(2)
where and are data points in the time series linked with the Sgn is outlined in the following equation:
formula
(3)

The positive S-statistic values indicate an upward trend, whereas the negative values indicate a downward trend.

The Z-statistic, as given in Equation (4), is generally used to test the statistical significance of the detected trends in the data points (Golian et al. 2015; Byakatonda et al. 2018).
formula
(4)
where n represents the total sample associated with the study, r represents the number of tied groups in the datasets and tm is the number of data points in the mth tied groups. The outcome of the MK test gives the hypothesis, H = 1, which says that if there exists a statistically significant trend, the null hypothesis is rejected when |Z − stat| > 1.96. Throughout the study, the value of 1.96 is taken as a threshold value obtained from the standard normal table at the confidence level of 95%. The MK statistic is the identification of the direction associated with the detected trends. The magnitude of the trend can be determined using Sen's slope estimator (Sen 1968). More details regarding Sen's slope estimator can be obtained from Gocic & Trajkovic (2013).

Regionalization of drought characteristics

The GRB is the second largest river basin in India covering an area of about 312,812 km2. The river basin is divided into sub-regions based on the homogeneous drought characteristics. Since drought is considered as a regional phenomenon, the drought studies must be carried out in a regional perspective (Gupta & Jain 2018). Many studies have been carried out in the past for delineating homogeneous regions using various approaches such as hierarchical clustering (Raziei et al. 2008), fuzzy C-means clustering (Shamshirband et al. 2015), combination of wavelet and self-organzing map clustering (Agarwal et al. 2016), k-means clustering (Zhang et al. 2012) and entropy-based method (Ridolfi et al. 2016). K-means clustering algorithm developed by MacQueen (1967) is used to achieve the best combination of subregions with each cluster being represented by its centroid. The attributes selected for the present study are latitude, longitude and drought characteristics to segregate the homogeneous regions. The mathematical form of K-means clustering is given by the following equation:
formula
(5)
is the square of Euclidean distance between the nth data points and mth cluster centers, V is the total number of data points and U is the total number of clusters. k-means is an iterative clustering algorithm technique that aims to obtain the well-segregated clusters given below:
  1. Initially, the data points are divided randomly among k-clusters, and then each data point is allocated to its nearest cluster centers.

  2. Cluster centers are computed based on the averaging of the coordinates for specific clusters, and each point is reassigned to the closest cluster centroid to obtain new clusters.

  3. This algorithm must be repeated till the best result is obtained, as the final result shows sensitivity to initial cluster centers.

  4. Two validation criteria, namely silhouette coefficient (SC) and Dunn index (DI) were implemented to justify the total number of clusters as a consequence of k-means algorithm for obtaining the homogeneous climate regions (Roushangar & Alizadeh 2018).

Linear scaling bias correction

The RCMs have systematic biases of climate model simulations relative to observations, and hence, RCM model outputs cannot be used directly in impact assessment studies. Therefore, bias correction techniques have been used widely for post-processing the climate model output prior to application for impact studies (Wood et al. 2004; Ashfaq et al. 2010; Piani et al. 2010; Ngai et al. 2017). The linear scaling bias correction method is implemented to adjust the RCM mean values (Fang et al. 2014; Shrestha et al. 2017). The monthly correction of RCM data is on the basis of the differences between observed and RCM data.

For precipitation, correction is given by the following equation:
formula
(6)
For temperature, correction is given by the following equation:
formula
(7)
where Pcorr and Tcorr are the corrected precipitation and temperature, PRCM and TRCM are the RCM precipitation and temperature data, and Pobs and Tobs represent the observed precipitation and temperature data.

Reliability ensemble averaging

The uncertainty generated from multiple RCMs is addressed by REA developed by Giorgi & Mearns (2003), Das et al. (2018), and Das & Umamahesh (2018). The weights assigned to the climate models can be derived using an iterative algorithm called as REA by considering the deviation of RCMs from CRU precipitation, maximum and minimum temperatures. The algorithm for the proposed approach is as follows.

Step 1: The cumulative distribution function (CDF) deviations of RCMs from CRU datasets are computed using root-mean-square error (RMSE) for the entire GRB covered with CRU grid points. The initial weights are computed by the following equation:
formula
(8)
where n is the number of RCMs, and Wk is represented as the initial weight of kth RCMs.
Step 2: The weighted-mean CDF of RCMs is computed by the following equation:
formula
(9)
where is represented as the RCM-weighted mean, is the future CDF of kth RCM under a particular RCP scenario.

Step 3: Inverse RMSE is computed and new weights are assigned, and this procedure is repeated till the converged weights are generated.

Multivariate copula analysis of drought properties

Univariate analysis of drought characteristics is not capable of determining the drought frequencies, as it is based on the assumption that drought variables are interdependent of each other. Therefore, the trivariate drought analysis is incorporated using copula functions for the assessment of the dependence structure among the drought characteristics. Copula can join the marginal distributions of variables to find a uniquely single joint distribution based on their dependence status (Shiau 2006). In this study, peak (P), duration (D) and severity (S) are considered as dependent random variables to obtain the multivariate dependence structure. FD, FP and FS are the marginal distributions of D, P and S. denote the CDF of the trivariate distribution with marginal CDFs as . Sklar explained that there exists a unique copula c for all real P, D and S as shown in the following (Sklar 1959):
formula
(10)
where are the probability density functions (PDF) of the dependent variables P, D and S, respectively, linked to the density function C as expressed in the following equation.
formula
(11)
where are the CDF of P, D and S with values varying between 0 and 1. Gumbel, Clayton and Frank copulas are used to obtain the joint probability distribution of variables based on their dependency phenomenon. The dependency status between the interrelated drought variables is represented by the respective copula parameter. The maximum pseudo-likelihood (MPL) estimation method is used for estimating the copula parameters that imitate the dependence structure among the correlated drought characteristics. The best-fitted copula is then estimated based on the goodness-of-fit (GoF) measures, namely, Kolmogorov–Smirnov (KS) and Cramér–von Misses (CVM) tests (Genest & Favre 2007). Akaike information criteria (AIC) and the maximum likelihood function are also used to justify the best-fitted copula model. More details regarding a different copula construction and its mathematical description are available in Nelsen (2007) and Sadegh et al. (2017).

RESULTS

Performances of RCM models and uncertainty analysis

For future drought analysis, five linearly bias-corrected RCMs are considered. Although RCMs are widely utilized for the assessment of extreme events with respect to climate change, there are uncertainties associated with the RCM-simulated variables. The sources of uncertainty in climate models are associated with (i) their spatial and temporal scales, and (ii) scenario uncertainties are associated with anthropogenic activities and GHG emissions (Ghosh & Mujumdar 2007).

The individual model and ensemble mean quantile plots for precipitation, maximum and minimum temperature are presented in Figure 2 for a single grid. For the RCP4.5 scenario, the precipitation obtained from the ensemble mean is performed well when compared to the other RCM models. The extreme and low precipitation events are clearly modeled by the ensemble model. The ensemble model for the RCP8.5 scenario shows a satisfactory performance for the precipitation series, although heavy uncertainty is exhibited by the series under RCP8.5 scenarios in the GRB. The precipitation comparison shows that the least performed models are CNRM-CM5 and CCSM4 for RCP4.5. For RCP8.5, the least performed models are ACCESS 1-0 and CCSM4. From Figure 2, the ensemble maximum and minimum temperature are showing better performance under both scenarios. For maximum temperature, the least performed models are CNRM-CM5 and CCSM4 for RCP4.5. ACCESS 1-0 and GFDL-ESM2G showed the least performance for RCP8.5 scenarios. The bias-adjusted RCMs individually are under- and over-estimating the climate parameters. So, the consideration of individual models will increase the uncertainty in modeling the drought phenomenon. The REA approach provides a remedy to this problem by accounting for the uncertainty caused by RCMs.

Figure 2

Comparison of historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5 using quantile-quantile plots: (a) comparison of precipitation for RCP4.5, (b) comparison of precipitation for RCP8.5, (c) comparison of maximum temperature for RCP4.5, (d) comparison of maximum temperature for RCP8.5, (e) comparison of minimum temperature for RCP4.5 and (f) comparison of minimum temperature for RCP8.5.

Figure 2

Comparison of historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5 using quantile-quantile plots: (a) comparison of precipitation for RCP4.5, (b) comparison of precipitation for RCP8.5, (c) comparison of maximum temperature for RCP4.5, (d) comparison of maximum temperature for RCP8.5, (e) comparison of minimum temperature for RCP4.5 and (f) comparison of minimum temperature for RCP8.5.

Spatial variation of reference and future climate parameters

Spatial maps are presented in this section for a better understanding of variability experienced due to annual precipitation, dry days, fluctuations in minimum and maximum temperatures, and increased intensity of heatwaves. Figure 3 shows the spatial distribution of mean annual precipitation. The MPI-ESM-LR and ensemble model in RCP4.5 captured the highest annual precipitation. Similarly, for RCP8.5, ACCESS1-0, MPI-ESM and ensemble model captured the highest amount of annual precipitation in the north-east part of the GRB. Furthermore, for the mean annual precipitation, the ensemble model gives the uncertainty in each grid cell. The time period of 2053–2099 showed a decrease in precipitation in the western part of the GRB and an increase in the other lower part of the basin. The mountains present in the western part of the GRB generally create a rain shadow region. The winds blowing from the Arabian Sea strike perpendicularly to the Western Ghats causing lower rainfall that affects the south-west summer monsoon. Moreover, significant variations in annual precipitation are more pronounced under RCP8.5. From Figure 4, except CCSM4, the maximum temperature hot spots are visible in the middle part of the basin for all climate models. The average annual minimum temperature has a significant increasing trend in RCP8.5. The minimum temperature hot spots are more prominent in RCP8.5 scenarios, indicating an average increase in the minimum temperature in the future scenarios (Figure 5). The intensification in projected maximum and minimum temperatures will directly increase the evapotranspiration. So from observation, increase in evapotranspiration, variation in precipitation and the increase in the dry spells for future time period will further accelerate the drought phenomenon in the GRB under global warming.

Figure 3

Spatial variation of annual mean precipitation for reference period (1971–2017) and the future time period (2053–2099).

Figure 3

Spatial variation of annual mean precipitation for reference period (1971–2017) and the future time period (2053–2099).

Figure 4

Spatial variation of annual mean maximum temperature for reference period (1971–2017) and the future time period (2053–2099).

Figure 4

Spatial variation of annual mean maximum temperature for reference period (1971–2017) and the future time period (2053–2099).

Figure 5

Spatial variation of annual mean minimum temperature for reference period (1971–2017) and the future time period (2053–2099).

Figure 5

Spatial variation of annual mean minimum temperature for reference period (1971–2017) and the future time period (2053–2099).

Identification of homogeneous drought regions

All the meteorological stations located in various climatological regions of the GRB are used in this study. Some of these stations have been facing extremely vulnerable drought conditions in each season because of the significant variability of rainfall among seasons. There are also variations in climatic variables based on their topographic existence. So, K-means clustering is used to identify the homogeneous drought regions. The division of the total study area into homogeneous climate divisions (clusters) is advantageous in reducing the unwanted noise resulting from the grid-wise frequency analysis (Masud et al. 2017). After the successful application of this algorithm, the entire dataset is divided into k-clusters. For each cluster, the nearest data point to the respective cluster head is chosen to represent the data point to obtain the results. The cluster validation indices based on k-means techniques for the historical period are given in Table 1. It could be concluded from Table 1 that for k-means algorithm, the clustering numbers equal to 6 captured homogenous areas better in comparison to other cluster numbers, as the values of SC and DI are more when compared to other cluster numbers. From Figure 6, the number of grids in each climate division was as follows: a total of 21 grids in climate division I, 5 grids in climate division II, 4 grids in climate division III, 25 grids in climate division IV, 29 grids in climate division V and 22 grids in climate division VI. The homogeneous regions using the drought features provide a clear foundation for further drought analyses.

Table 1

Validation of clustering models based on historical dataset

Number of clusters
Validity index345678910
DI 2.85 3.08 4.52 8.1 0.15 3.11 0.29 
SC 0.377 0.454 0.33 0.511 −0.214 0.389 0.211 0.178 
Number of clusters
Validity index345678910
DI 2.85 3.08 4.52 8.1 0.15 3.11 0.29 
SC 0.377 0.454 0.33 0.511 −0.214 0.389 0.211 0.178 
Figure 6

Cluster map of SPEI-3 drought characteristics.

Figure 6

Cluster map of SPEI-3 drought characteristics.

Comparison between historical and future drought

Water resources are sensitive to droughts, and their demand is mostly met by the amount of precipitation. Due to high spatial and temporal variations, India is facing major issues for managing the water resources (Kumar & Jayakumar 2020). The prolonged droughts associated with an increase in water demand under climate change will lead to further stress on water shortage. Pathak & Dodamani (2019) stated that the 3-month time scales have a shorter duration and create a greater number of drought events. On the other hand, the 12-month time scale indicates fewer drought events with a high number of durations. This study considered SPEI-3 for estimating the meteorological drought events. The drought characteristics for each grid cell have been extracted using the observed and future SPEI series based on the run approach for further return period analysis.

Drought events are directly related to high temperature and evapotranspiration. The study was carried out to determine how precipitation and evapotranspiration affect the future SPEI in the six climate divisions. The temporal changes of SPEI are represented in Figure 7(a)–7(f). Significant differences exist in signals between the SPEI time series generated using RCM outputs and the observed climatic data for all the six climate divisions. Higher peaks in signals are detected in RCP8.5 when compared with RCP4.5 series and the reference period. The number of dry months is significant in the case of RCP8.5 and RCP4.5. The SPEI for RCP8.5 and RCP4.5 captured an early onset of drought. The projected SPEI signals exhibited more severe and persistent drought events. Due to the future increase in CO2 and greenhouse gas concentration, the temperature and precipitation exhibit high fluctuations, which have a great influence on the behavior of drought indices. SPEI time series of projected periods and reference periods differ from each other for different climate divisions, showing an intensification of dry spells for future periods.

Figure 7

Comparison of SPEI time series for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5.

Figure 7

Comparison of SPEI time series for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5.

In this section, projected changes of drought characteristics are evaluated as the differences between future period and reference period. The projected characteristics are presented as density plots and box plots for different climate divisions in Figures 813. Significant changes in the density of drought characteristics are noticed between historical, RCP4.5 and RCP8.5 for different climate divisions. For climate divisions I, III, V and VI, higher densities are observed during the reference period compared to the future scenarios, whereas the magnitude of projected drought duration for RCP8.5 displayed higher density in the case of climate division IV. RCP4.5 showed higher densities in projected drought duration for climate division II. Prominent deviations are also exhibited in the historical and future peak densities (Figure 9) for different climate divisions. The higher peak densities are observed for RCP8.5 in the case of climate divisions I and IV (Figure 10). It is observed from the figures that RCP4.5 series showed higher peak densities for climate division II. In the case of climate divisions III and V, the reference time series showed high densities in peak. The density plots for severities (Figure 11) for all climate divisions reveal the change in the probability densities for historical and future scenarios. Larger differences in the projected drought severities are observed for all the time periods in the climate divisions. Higher densities in the case of severities are observed for climate divisions I, III, V and VI during the reference period (1971–2017), whereas RCP8.5 and RCP4.5 showed higher densities in the case of climate divisions IV and II, respectively. Hengade et al. (2018) stated that spatial and temporal variations of rainfall are observed in the GRB under climate change scenarios, whereas the evapotranspiration of the basin showed a huge increment due to increasing temperature in most parts of the basin. He also observed that there are huge variations in the climatic phenomenon of the GRB under RCP8.5 than RCP4.5. So, the evapotranspiration can intensify the drought phenomenon when the temperature is higher for this river basin. Also, deficit precipitation and more evapotranspiration in future can impact the future drought phenomenon.

Figure 8

Comparison of probability density of duration for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 8

Comparison of probability density of duration for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 9

Comparison of probability density of peak for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 9

Comparison of probability density of peak for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 10

Comparison of probability density for severity for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 10

Comparison of probability density for severity for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 11

Comparison of drought duration using box plots for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 11

Comparison of drought duration using box plots for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 12

Comparison of drought peak using box plots for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 12

Comparison of drought peak using box plots for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 13

Comparison of drought severity using box plots for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

Figure 13

Comparison of drought severity using box plots for historical period (1971–2017) and future time period (2053–2099) under RCP4.5 and RCP8.5: (a) represents for climate division I; (b) represents for climate division II; (c) represents for climate division III; (d) represents for climate division IV; (e) represents for climate division V and (f) represents for climate division VI.

The variations of the drought characteristics are identified using box plots shown in Figures 1113 for the six climate divisions. The historical and RCM-simulated weightage-averaged drought durations are shown in Figure 11. Relative variances are observed between historical and future durations for different climate divisions. Climate divisions II and III showed higher durations in the case of the reference period, whereas for RCP4.5, climate divisions I, IV, V and VI showed higher drought durations. Significant variations are also noticed in the drought severity and peak between historical and future periods for the different climate divisions. High peaks are noticed in the case of future periods. RCP4.5 displayed high peaks in climate divisions I, IV and VI, whereas the RCP8.5 exhibited higher peaks in other climate divisions II, III and V. Climate division II showed severe drought in the case of historical period. RCMs tend to produce relatively more severe droughts when compared to historical drought. The drought severity shows high values in the case of climate divisions VI for RCP4.5. Similarly, RCP8.5 shows high values for climate divisions I, II, IV and V. Hence, it can be concluded that the changes in severities are more prominent in the case of RCP4.5 and RCP8.5.

The river basin shows extreme drought conditions due to the lower rainfall in the Western Ghats. Deficient rainfall causes extreme drought condition in the GRB (Masroor et al. 2020). In the summer season, the temperature increases which can accelerate the drought condition. From spatial observation in Figures 35, RCMs under RCP 4.5 and RCP8.5 projected a change in drought pattern during 2053–2099, as there would be an increase in dry spells in the GRB. The drought severity, peak and duration will increase in the future due to the effect of climate change for most of the climate divisions. The south-west monsoon is significant for agricultural water management in the river basin. So, future drought analysis will be helpful for water managers to understand the drought behavior considering the variable climatic phenomenon.

MK test of drought characteristics

For the six climate divisions, the MK test and Sen's slope estimator were used for trend analysis. For determining the upward or downward trend of drought characteristics, the parameters of the MK test, such as Kendall's , S and Z statistics, were calculated at 95% confidence level. Supplementary Material, Tables S1, S2 and S3 show the trend of drought duration, peak and severity for historical and future periods for the different climate divisions, respectively. Increasing trends in duration are observed in the case of climate divisions I, II and VI for reference periods, whereas the decreasing trends are observed in the case of climate divisions III, IV and V. However, decreasing trends detected for duration are not significant for the reference period. The results of the MK test for future periods under two scenarios showed significant positive trends for durations in four climate divisions (I, II, IV and VI) for RCP4.5 and four climate divisions (III, IV, V and VI) for RCP8.5. Furthermore, negative trends are observed for future periods in the case of climate divisions III and V for RCP4.5, and climate divisions I and II for RCP8.5. The MK test for peak revealed positive trends in climate divisions I, III, VI and VI, while negative trends are detected in climate divisions II and V for the reference period. Significant increasing trends in peaks are observed throughout the future period in the case of climate divisions I, II, III, IV and VI and climate divisions II, III, VI, V and VI under RCP4.5 and RCP8.5, respectively. Downward trends are noticed in the case of climate division V for RCP4.5 and climate division I for RCP8.5. For reference period, climate divisions I, II, III, IV and VI showed positive Z values for the severity, indicating increasing trends. Negative Z value of climate division V indicate decreasing trends. Climate divisions IV and VI showed significant positive trends, whereas the negative trends are no longer significant for reference period. Positive Z values are observed for climate divisions II, IV, V and VI for RCP4.5. Similarly, positive Z values in climate divisions II, III, IV, V and VI show increasing trend for RCP8.5. Decreasing trends in drought severities are also observed in climate divisions I and III for RCP4.5 and climate division I for RCP8.5.

Trivariate copula models

Exponential and Gamma distributions are used in many drought characterization studies to obtain the marginal distributions of drought properties (She & Xia 2018). Gumbel, Gamma, log-normal, Weibull and exponential distributions have been fitted to drought characteristics for evaluating the marginal distributions. Different statistical measures like AIC and log-likelihood functions are used for obtaining the best-fitted distribution. The variations in drought characteristics could significantly affect the future drought phenomenon. Hence, trivariate copula analyses are carried out for reference as well as future periods by combining the dependency of drought characteristics to obtain copula parameters. The copula models, namely Clayton, Gumbel and Frank are selected for modeling the trivariate drought characteristics. The copula parameters are estimated using the MPL estimation method. CVM and KS statistics are used for testing the GoF for comparing the performance of different copula models based on their dependency between drought characteristics. The maximum p-values of statistics CVM and KS for 5,000 sample runs, copula parameters and corresponding log-likelihood function values, and the best-fitted copulas for a 3-month duration for six climate divisions are given in Supplementary Material, Tables S4, S5 and S6 for reference and future time periods. From the Supplementary tables, the drought characterization can be conducted using Frank, Clayton and Gumbel copulas that are verified at 5% significance level. Here, the copula with the highest p-value is selected to find the dependence structure among drought characteristics. Overall, Frank and Gumbel copulas performed well when compared to other copulas. The best-fitted parameters are used further to compute the joint return period.

Drought risks assessment

The multivariate analyses of drought characteristics help in the risk assessment of extreme events like floods and droughts (Shiau & Modarres 2009; Ganguli & Reddy 2013; Saghafian & Mehdikhani 2014). So, the trivariate copula model is implemented to obtain the multivariate drought return periods for different climate divisions of the GRB. The return period of a particular event can be used for designing the hydrologic projects, which gives a qualitative and quantitative measure of risk associated with extreme events. The joint return period analysis is carried out by using the two probability cases, primary return periods ‘TAND’ and ‘TOR’ for the drought variables. Further details regarding concepts of return periods are given in Salvadori & De Michele (2004). The joint occurrence probabilities of drought severity (S), peak (P) and duration (D) exceed a definite threshold level (i.e. S > s, P > p, D > d) related to the trivariate return for ‘TAND’ and ‘TOR’, which are shown in the following equations:
formula
(12)
formula
(13)
where, FP(p), FD(d) and FS(s) are the marginal CDF of peak, drought, and severity, respectively. Here, is expressed as the ratio of the total number of years (N) to the number of drought events (n) for the estimation of drought return period (Ganguli & Reddy 2013). denotes the joint return period of Pp, Dd and Ss, and denotes the joint return period of Pp, Dd or Ss.

The trivariate return levels for different return periods using the ‘AND’ and ‘OR’ criteria are presented in Tables 2 and 3, respectively. The tables show that large uncertainties are present in future return periods for different climate divisions and the uncertainties will increase with the variation in return periods. These uncertainties of trivariate return period are because of the future variations in projected climatic parameters like precipitation, evapotranspiration, minimum and maximum temperatures based on the increment in GHG and CO2 under the two RCP scenarios. Comparable differences in the return periods between reference and future are also noticed. Furthermore, it can be seen from the tables that the joint return period of ‘AND’ case is more than the ‘OR’ case. In the case of reference period, the return period is less in climate division II compared to other climate divisions. It can, hence, be concluded that climate division II shows more frequent drought events. Similarly, the drought events are more frequent in climate divisions I, III, IV and V under RCP8.5, whereas climate division VI showed more frequent drought under the RCP4.5 scenario for the period 2053–2099. Climate division VI will be more vulnerable with the increase in the number of dry days and changing future climate conditions. Overall, the return period analysis revealed that for a certain drought event, future drought return periods are lower than the reference period specifying the probable increase in drought occurrences than those detected in the past periods. Under the two RCP scenarios, the frequency of dry periods will increase during 2053–2099. This indicates that more severe and long-lasting droughts can be anticipated in the future in the GRB. Overall, the frequency, duration, severity and peak of droughts will increase in the future. The trivariate copula analysis can be beneficial for a better management and planning of the water resources considering the extreme events.

Table 2

TAND for drought characteristics of SPEI computed based on trivariate copula models

Historical return period (T)Climate division I
TAND
Climate division II
TAND
Climate division III
 TAND
Climate division IV
 TAND
Climate division V
TAND
Climate division VI
TAND
18.01 10.7 15.66 12.91 10.88 8.15 
10 41.33 17.63 37.14 23.54 27.41 14.21 
20 86.63 36.97 61.28 53.14 81.12 51.11 
50 454.32 184.13 334.72 310.57 213.54 198.53 
RCP4.5 return period (T)Climate division I
TAND
Climate division II
 TAND
Climate division III
 TAND
Climate division IV
 TAND
Climate division V
 TAND
Climate division VI
 TAND
9.98 11.35 10.8 9.78 6.61 5.6 
10 17.15 20.48 18.07 14.65 15.35 12.31 
20 45.46 37.31 32.33 29.38 28.91 21.84 
50 86.52 191.28 164.05 89.05 84.66 84.13 
RCP8.5 return period (T)Climate division I
TAND
Climate division II
 TAND
Climate division III
 TAND
Climate division IV
 TAND
Climate division V
 TAND
Climate division VI
 TAND
8.15 14.14 8.96 8.67 6.2 7.11 
10 15.19 31.03 13.46 12.51 14.26 17.82 
20 37.68 78.85 31.34 26.35 24.15 39.11 
50 79.69 302.37 125.57 72.13 77.31 96.42 
Historical return period (T)Climate division I
TAND
Climate division II
TAND
Climate division III
 TAND
Climate division IV
 TAND
Climate division V
TAND
Climate division VI
TAND
18.01 10.7 15.66 12.91 10.88 8.15 
10 41.33 17.63 37.14 23.54 27.41 14.21 
20 86.63 36.97 61.28 53.14 81.12 51.11 
50 454.32 184.13 334.72 310.57 213.54 198.53 
RCP4.5 return period (T)Climate division I
TAND
Climate division II
 TAND
Climate division III
 TAND
Climate division IV
 TAND
Climate division V
 TAND
Climate division VI
 TAND
9.98 11.35 10.8 9.78 6.61 5.6 
10 17.15 20.48 18.07 14.65 15.35 12.31 
20 45.46 37.31 32.33 29.38 28.91 21.84 
50 86.52 191.28 164.05 89.05 84.66 84.13 
RCP8.5 return period (T)Climate division I
TAND
Climate division II
 TAND
Climate division III
 TAND
Climate division IV
 TAND
Climate division V
 TAND
Climate division VI
 TAND
8.15 14.14 8.96 8.67 6.2 7.11 
10 15.19 31.03 13.46 12.51 14.26 17.82 
20 37.68 78.85 31.34 26.35 24.15 39.11 
50 79.69 302.37 125.57 72.13 77.31 96.42 
Table 3

TOR return periods for drought characteristics of SPEI computed based on trivariate copula models

Historical return period (T)Climate division I TORClimate division II
TOR
Climate division III
TOR
Climate division IV
TOR
Climate division V
TOR
Climate division VI
TOR
3.99 3.04 4.79 4.03 4.79 3.14 
10 7.54 5.96 8.51 651 6.51 5.08 
20 15.87 12.08 16.89 20.33 13.89 15.99 
50 35.41 24.33 41.22 45.4 35.22 38.77 
RCP4.5 return period (T)Climate division I
TOR
Climate division II
 TOR
Climate division III
TOR
Climate division IV
TOR
Climate division V
TOR
Climate division VI
TOR
3.02 3.2 3.51 5.88 4.27 2.39 
10 6.56 6.77 6.86 9.47 9.33 5.04 
20 11.38 13.54 15.09 18.12 18.25 10.52 
50 25.6 29.91 33.83 39..66 34.12 23.78 
RCP8.5 return period (T)Climate division I
TOR
Climate division II
TOR
Climate division III
TOR
Climate division IV
 TOR
Climate division V
 TOR
Climate division VI
 TOR
2.91 4.01 3.12 3.25 2.84 3.13 
10 6.16 7.87 5.1 8.49 6.14 5.82 
20 13.08 15.04 14.15 16.07 12.65 12.04 
50 28.17 31.44 26.83 43.91 29.16 25.47 
Historical return period (T)Climate division I TORClimate division II
TOR
Climate division III
TOR
Climate division IV
TOR
Climate division V
TOR
Climate division VI
TOR
3.99 3.04 4.79 4.03 4.79 3.14 
10 7.54 5.96 8.51 651 6.51 5.08 
20 15.87 12.08 16.89 20.33 13.89 15.99 
50 35.41 24.33 41.22 45.4 35.22 38.77 
RCP4.5 return period (T)Climate division I
TOR
Climate division II
 TOR
Climate division III
TOR
Climate division IV
TOR
Climate division V
TOR
Climate division VI
TOR
3.02 3.2 3.51 5.88 4.27 2.39 
10 6.56 6.77 6.86 9.47 9.33 5.04 
20 11.38 13.54 15.09 18.12 18.25 10.52 
50 25.6 29.91 33.83 39..66 34.12 23.78 
RCP8.5 return period (T)Climate division I
TOR
Climate division II
TOR
Climate division III
TOR
Climate division IV
 TOR
Climate division V
 TOR
Climate division VI
 TOR
2.91 4.01 3.12 3.25 2.84 3.13 
10 6.16 7.87 5.1 8.49 6.14 5.82 
20 13.08 15.04 14.15 16.07 12.65 12.04 
50 28.17 31.44 26.83 43.91 29.16 25.47 

DISCUSSION AND CONCLUSION

In this study, 3-month SPEI is derived by utilizing the precipitation and the evapotranspiration data for the reference and future periods in the GRB. The bias-adjusted RCMs individually showed large uncertainties in climate parameters. Hence, the REA method is implemented to reduce the uncertainties caused by individual RCMs. A comprehensive assessment of drought frequency is carried out using trivariate regional frequency analysis considering the inherent dependence between the drought characteristics. From the study, the main conclusions are as follows.

The temporal distribution of projected drought characteristics showed an increase in drought duration peak, and severity in future periods under the two RCPs in different climate divisions. The mean duration, severity and peak for climate divisions V and VI showed an increasing pattern having a longer duration, higher severity and peak than the other climate divisions.

The statistical homogeneity of the six climate divisions is tested by validation indices: SI and DI which identify most of the regions as homogenous.

Based on the drought characteristics, the nonparametric MK test is applied to assess the variability and pattern of drought characteristics. Most of the climate divisions showed significant changes in the trend of drought characteristics for future time period for two RCPs. It can be concluded that these changes will agree with the dry and severe climate condition alleviating the drought phenomenon.

The trivariate copula analysis showed that Gumbel and Frank copulas performed well for most of the climate divisions using CVM and KS tests. After analyzing the trivariate return period for TAND and TOR cases, climate division V showed longer and severe drought events in comparison with other divisions. Frequent drought events are also observed in the case of climate divisions II, V and VI. It can be suggested that appropriate water resource planning and management activities should be implemented for climate divisions II, V and VI by considering the long-lasting behavior and high-severity characteristics of the drought events. The future return periods for different scenarios showed lower values of return periods than those shown in the past for climate division VI in the case of RCP 4.5, indicating more frequent drought events in the future periods. The risk of future droughts will become intensified with the changes of precipitation and evapotranspiration that are considered using SPEI-based drought index.

On the regional scale, the derived conclusions will be helpful for a precise and systematic understanding for managing the drought phenomenon. The identification of the drought-prone areas will be useful for water managers for the planning and management of drought mitigation strategies. For a better management of drought, return period analysis is carried out for reference and future periods.

DATA AVAILABILITY STATEMENT

All relevant data are available from an online repository or repositories (https://data.ceda.ac.uk/badc/cru/data/cru_ts/cru_ts_4.03 and https://cccr.tropmet.res.in/home/ cordexsa_datasets.jsp).

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