Assessment of basin-wise future agricultural drought status across India under changing climate

Most of the existing studies on meteorological drought suggest more intense and frequent drought events due to changing climate. However, basin-scale assessment of future agricultural drought is lacking due to many reasons. In this study, the intensity and frequency of future agricultural drought (characterized by the Standardized Soil Moisture Index, SSMI) for 226 sub-basins across India are analyzed, and vulnerable basins are identified. The prediction of the future agricultural drought status is achieved using the wavelet-based drought temporal consequence modeling of meteorological drought with the best performing bias-corrected Coordinated Regional Downscaling Experiment (CORDEX) simulations, selected by Multi-Criteria Decision-Making frameworks. This study reveals a geographically contrasting change in future agricultural drought that indicates more intense agricultural drought in north, north-east, and central India as compared with south India. The area under drought is also expected to increase, and about 20 and 50% of the Indian mainland is expected to suffer from extreme (SSMI 2) and moderate (SSMI 1) agricultural drought conditions by the end of this century. Sub-basins lying in north and central India are expected to have a longer time under drought conditions. Thus, the findings of this study will be useful for future planning and preparedness against agricultural productivity.


GRAPHICAL ABSTRACT INTRODUCTION
Agricultural drought is defined as a prolonged period of soil moisture deficit, which affects agricultural production. For a country like India, which is heavily dependent on agricultural economy (constituting 16% of the gross domestic product according to the Ministry of Finance, India ()), agricultural droughts have a significant impact on its socioeconomic well-being. Hence, monitoring, assessment, and prediction of agricultural drought are of immense importance. With prior knowledge of vulnerable regions in terms of drought propensity, policies/plans can be developed to mitigate the adverse effects of agricultural drought.
Previous studies suggest that, in general, drought risk has increased globally (Dai et  For instance, according to Burke & Brown (), the intensity and frequency of droughts may increase over the entire UK with regional variation, but it is difficult to ascertain whether these changes will result from natural variability or from the effect of the changing climate. According to Chen & Sun (), the drought severity, frequency, and duration are expected to increase in the future in eastern China. Similarly, the severity and frequency of droughts in Europe are expected to increase with spatio-temporal variations due to the changing climate (Spinoni et al. ). Hence, the spatio-temporal distribution of drought and risk, thereof, are nonuniform with local variations under changing climate, which, if understood well, can help in managing/mitigating the future droughts (Thomas et al. ; Xu et al. ).
In the Indian context, the characterization of drought has been attempted in multiple studies (Mishra &  an analysis of the spatial extent of concurrent meteorological droughts and heatwaves by Sharma & Mujumdar () using observed data suggested that, along with an increase in drought severity and frequency across India in the past, droughts are also becoming more regional in nature. According to them, the most affected regions are coastal south India, central Maharashtra, and the Indo-Gangetic plain, all being major agricultural areas. Zhang et al. () suggested an increase in drought severity over the wheat-growing areas of India and estimated its impact on wheat production. Bisht et al. () analyzed future meteorological drought and reported that despite a long-term increase in drought severity and intensity across the Indian mainland, regional variations in these drought characteristics are expected.
Most of the above-mentioned studies analyzed meteorological drought using indices, such as the SPI, the Standardized Precipitation Evapotranspiration Index (SPEI), and the Palmer Drought Severity Index (PDSI), using coarse resolution data (usually from General Circulation Models (GCMs)) in the future. A pan-India, basin-wise assessment of future agricultural drought across all basins is lacking. To address this issue, the use of finer resolution is necessary to reveal a local variation in drought condition(s) in a better way from many perspectives. Additionally, the fine-resolution analysis of soil moisture deficit may help in assessing other climatic variables, as the soil moisture is expected to have a feedback to many climatic variables/ phenomena, such as heatwave (Hirabayashi et  The rest of the article is organized as follows. In the next section, details of the study area, showing the river basins and sub-basins across India, and data used are presented. In the section 'Methodology', details of the methodological approach are outlined. In the subsequent 'Results and discussion' section, the major findings of this study are presented.
Finally, the conclusions are provided in the last section.

STUDY AREA AND DATA USED
A total of 226 contiguous sub-basins that cover the entire Indian mainland are selected as individual study areas.
These sub-basins are from 21 groups, including major river basins, as shown in Figure 1. The area of these sub-basins ranges from 111 to 91,268 km 2 , with the circularity ratio ranging from 0.068 to 0.642. Most of the subbasins receive the maximum amount of rainfall during the monsoon months (June-September); however, the climatology of these sub-basins is diverse. The daily precipitation, maximum and minimum air temperature, and total soil moisture content obtained from six CORDEX models (Table 1)

METHODOLOGY
The methodological overview is shown in Figure 2. The methodology can be divided into five modules: (i) bias-correction of precipitation, temperature, and soil moisture obtained from CORDEX simulation and estimation of Figure 1 | Sub-basins and major basins (and other groups of sub-basins) of India. In the legend, the major basin name is provided along with the number of sub-basins falling inside the major basin (right column). Some coastal groups of sub-basins like 8, 9, and others (marked as --) are not part of any major basin as they directly flow into the sea in the form of multiple small channels.  the variable(s) with many zero values (such as precipitation) to other variables, such as air temperature and soil moisture, that do not have any specific repetitive value. Hence, a suitable bias-correction approach should be utilized depending upon the variable being bias-corrected.
In the case of precipitation, a copula-based bias-correc- using the corresponding calibrated distribution. The bias correction is then carried out by using this reduced variate against the calibrated distribution of the observed data.
Hence, the bias-corrected value (S) for a simulated variable (say S) using QM is expressed as follows: For the application of these MCDM methods, multiple performance statistics are calculated for historical CORDEX simulations by comparing them with the observed data.
The MCDM methods utilize these performance statistics for making decisions.

Compromise programming
CP ranks different CORDEX simulations based on the distance of their performance statistics from the best possible values of performance statistics. The distance measure for a CORDEX simulation is defined as follows: where subscript i ∈ {1, 2, . . . , s} and s is the total number of performance statistics. The f Ã i and w i are the best value and weight of ith performance statistics, respectively; f i (m) and L p (m) are the values of ith performance statistics and the distance measure for mth CORDEX simulation with parameter p. In this study, p ¼ 2, and hence, L 2 distance measure (or the weighted Euclidean distance) has been used. The weight for performance statistics is estimated using the entropy method, as discussed in the subsequent section.
Preference Ranking Organization METHod of Enrichment Evaluation-2 PROMETHEE-2 ranks different alternatives (CORDEX simulations in this study) based on the preference/criterion function. It has been employed to rank GCMs (Raju & Kumar ). The preference function (denoted by P i (m j , m k )) utilizes the pairwise difference in the ith performance measure (denoted by d i (m j , m k )) between two CORDEX simulations (denoted by m j and m k ). There are six types of preference functions, namely, (i) usual criterion, (ii) quasi criterion, (iii) linear preference with no indifferent area, (iv) linear preference with indifferent area, (v) level criterion, and (vi) Gaussian criterion. In this study, the usual criterion function is utilized to rank the CORDEX simulation. Using the usual criterion function, the preference function for different performance measures and pairs of CORDEX models are expressed as follows: The preference functions for different performance measures are weighted-averaged to obtain the multicriteria preference index for a pair of CORDEX models, I(m j , m k ), where w i is the weight for the ith performance measure, and s is the number of performance measures used. The weight for different performance measures can be estimated using their entropy, as discussed in the next section. It should be noted that the model m j is better than m k pairwise if In the case of multiple CORDEX models, the mean net difference of I(m j , m k ) and I(m k , m j ), known as the outranking index (denoted by ϕ(m j ) for the jth model), is used for ranking.
where N is the total number of CORDEX simulations being compared. The CORDEX simulation having the highest ϕ(m j ) is considered to be the best among the options.

Entropy method for weighting performance statistics
In the MCDM methods for ranking CORDEX simulation, the relative weights for different performance measures are calculated by the entropy of performance measures (i.e., the amount of information present in the performance measures). Before calculating the entropy, the performance measures are normalized using their sum to reduce the effect of scale, if any. If f ij denotes the value of the ith performance measure for the jth model, then the normalized performance measure for the model is expressed as follows: where N is the number of CORDEX simulations.
where Using the normalized performance measures, the entropy of the ith performance measure (denoted as E i ) is calculated as (notations explained earlier): For a performance measure with high entropy, the uncertainty is also high, and it should have less weightage. The degree of diversification of the information provided by the ith performance measure (D i ) is calculated as (1 À E i ).
Hence, for a performance measure with high entropy, the degree of diversification of information will be low. The weight of the ith performance measure is expressed as: where s is the total number of performance measures used.
High weightage, as calculated above, means low relative uncertainty, and hence, higher importance (as compared with others) for the performance measure.
Drought characterization using bias-corrected CORDEX where T max , T min , and T avg are the maximum, minimum, and average daily air temperature, respectively in C; R a is extraterrestrial radiation (radiation received on the top of the atmosphere) expressed in mm/day. R a at a location with latitude l (in radian) is estimated as follows: The symbols f and g represent Multiple Linear Regression (MLR) and inverse wavelet functions, respectively. T2 ¼ T1 þ 1; T1 ¼ 2 l , where l is highest MRSWT level (i.e., 2 in this study).

RESULTS AND DISCUSSION
Bias-correction of CORDEX simulation and their skillbased selection As stated earlier, the daily precipitation, being a zeroinflated variable, is bias-corrected using the copula-based bias-correction scheme (Maity et al. ). Other variables, i.e., maximum daily temperature, diurnal temperature range, and daily total soil moisture are bias-corrected using Despite the differences in ranking from these methodologies, RegCM4 RCM driven by MPI-ESM-LR and CSIRO-Mk3.6.0 GCMs is found to be the best models for simulating the monthly precipitation in most of the sub-

Modeling of the temporal consequence of drought
Using the bias-corrected values of monthly precipitation and monthly soil moisture, the SPI and SSMI are calculated at the 3-month running mean of the respective variables. Similarly, the SPEI is calculated using the 3-month running mean of the monthly climatic water balance series (the difference of monthly precipitation and PET series). Wavelet-based models 1-3, as shown in Table 1 Figure 6 for the case when the SPI is used for characterizing metrological drought. From Figure 6, the performance of model 2 is found to be the best among all of the models as evident by the high values of R 2 , Dr, NSE and low values of the uRMSE for sub-basins across India. The performance of model 2 is found to be slightly better for the sub-basins in north India on an average as compared with that for the subbasins in south India. The better performance of models using the past values of the SSMI series (models 2 and 3) as compared with model 1 (which does not use any information from the SSMI series) indicates the high innate memory of soil moisture throughout the sub-basins across India.
The models are also run using the SPEI. Model 2 is found to work marginally better in the case when the SPI is used as input rather than SPEI. This might be due to Hence, the SPEI-based prediction of the SSMI is more desirable for a future period. The performance of model 2 for both validation schemes during the testing period is shown in Figure 7 for the case when the SPI is used for characterizing meteorological drought.
Comparing Figures 6 and 7 A trend analysis of the SSMI series in the future (obtained from the SPEI-based models for validation scheme II; Figure 8) carried out using the Mann-Kendall Test at a 5% level of significance suggests that most of the sub-basins in south India show a more wetting (an increasing trend in the SSMI series) condition. However, most of

CONCLUSIONS
This study investigates the future status of agricultural drought in 226 sub-basins across India. The translation of meteorological droughts to agricultural droughts is modeled using a recently developed wavelet-based approach. At first, the CORDEX simulation of precipitation, air temperature and others are bias-corrected, and the best performing CORDEX model for simulating precipitation is selected for each sub-basin. Based on the data from the selected CORDEX model, the temporal consequence of predecessor drought to a successor one is modeled. In this study, agricultural drought (characterized by the SSMI) is considered as a successor drought.
The temporal consequence modeling is found to perform satisfactorily across India despite varying climatology.
Given that the models are not over-or under-fitting, the models are then utilized to estimate the future state of agricultural drought in different sub-basins across India.
The major findings regarding the state of future agricultural drought across India are as follows: (i) The study has identified a geographically contrasting change in the spatial pattern of future agricultural drought over south and north India. Agricultural drought shows an increasing trend in most of the sub-basins in the Indian mainland, except for some of the sub-basins that are situated in south India.
(ii) Sub-basins in north and central India are expected to be vulnerable to frequent agricultural droughts, with the sub-basins in central India expected to be comparatively more vulnerable. However, the vulnerability of subbasins in south India is found to be comparatively less.
(iii) In general, the percentage area of the Indian mainland under extreme or moderate drought conditions is expected to increase by the end of this century. On average, more than 20% area of the Indian mainland is expected to suffer from extreme agricultural drought conditions (SSMI À2). Moderate drought conditions (SSMI À1) will be experienced as much as 50% of the area.
(iv) The percentage time under extreme drought conditions is found to be higher for many sub-basins in north India. It is also noticed that most of the subbasins in the Gangetic plain exhibit high vulnerability to extreme drought conditions in future. This may have an adverse effect on food production in this region.
Overall, the analysis has identified vulnerable basins across India considering future agricultural drought. It also underlines the geographically contrasting agricultural drought between north and south India. These findings are expected to be highly useful for policymakers for future planning and preparedness in terms of agricultural productivity. Utilizing the temporal consequence of meteorological drought to analyze agricultural drought leads to a reduction in the uncertainty associated with simulated soil moisture; however, simulated precipitation also has uncertainty (though less than a secondary variable like soil moisture). As a way forward, it should be noted that this study is carried out with CORDEX simulations driven