1. Introduction
Drought is a crucial ecological issue impacting Earth and humans. Drought refers to water scarcity, severely impacting society’s different segments, such as hydropower, agriculture, industrial, and water supply. The crucial factors for assessing the drought severity include period, location in absolute time, i.e., start and closure time points, areal coverage, and scale or force [1]. Wilhite and Glantz [2] deployed theoretical and operational expressions for describing a drought. The theoretical definition of drought is expressed generally as the shortage of precipitation causing harm to crops and harvest. The theoretical definition is vital for setting up a drought policy. The operational description aids people to determine the commencement, rigorousness, and conclusion period of the drought based on 30-year records by comparing the present situation with the historical average (recommended by the World Meteorological Organization). In general, operational droughts can be utilized for ascertaining drought frequency, rigorousness, and span for a specific return period [3]. Several drought classifications are mentioned in the literature; however, they are usually categorized into three main classes: (1) meteorological drought—a scenario where the shortage of precipitation is over 25% from the normal or average volume over an area for some time; (2) hydrological drought—a scenario where the resources of surface water and groundwater begin to exhaust from a marked level; and (3) agricultural drought—a scenario where the soil moisture and rainfall are insufficient in the growing season to boost vigorous crop growth until maturity.
The right choice of input variables [4,5] is vital for drought estimation. Understanding that a shortage of precipitation impacting streamflow, soil moisture, groundwater level, and reservoir storage led to the Standardized Precipitation Index (SPI) [6]. The SPI was constructed to calculate the precipitation deficit on various time scales and manage the impact of drought on the available water resources. For the computation of SPI long term (>30 years), precipitation data are fitted to a suitable probability distribution and then transformed into a normal distribution. In the last year, research activities were carried out on drought projection by utilizing different stochastic and artificial intelligence (hybrid or simple) models. Mishra and Desai [7] assessed the prospect of the seasonal-autoregressive integrated moving average (SARIMA) for drought projection in the Kansabati River Basin (India) by deploying multi-scalar SPI. According to available literature, all models can be deployed effectively for drought projection over varying lead times in the study area. Morid et al. [8] applied ANN (artificial neural network) for projecting meteorological drought in Tehran, Iran, province by utilizing the SPI, EDI (Effective Drought Index), and SOI (Southern Oscillation Index) as well as NAO (North Atlantic Oscillation) index. The observations indicated that the ANN could be deployed to a great extent for drought projection in the study area. Bacanli et al. [9] deployed FFNN (Feed Forward Neural Networks) and ANFIS (Adaptive Neuro-Fuzzy Inference System) for estimation of meteorological drought based on SPI-1 and SPI-12 in Turkey. Results revealed the superiority of the ANFIS models over the FFNN models. Belayneh and Adamowski [10] made a comparison of the ability of SVR (Support Vector Regression), ANN, and WNN (Wavelet Neural Networks) for projecting meteorological drought based on SPI-3 and SPI-12 in Awash River Basin, Ethiopia. The observations showed that the WNN models outperformed other models. Özger et al. [11] made a comparison of the performances of ANN, Wavelet-Fuzzy Logic (WFL), and Wavelet-ANN (WANN) models for projecting drought in Texas based on PMDI (Palmer Modified Drought Index) and ENSO (El Nino-Southern Oscillation). They noted that the WFL models performed better than other models.
Recently, several applications of Artificial Intelligence (AI)-based models have been observed for meteorological drought estimation on a global level. Deo and Şahin [12] studied ANN’s prospect for meteorological drought projection based on SPEI (standardized precipitation evapotranspiration index) at eight stations in eastern Australia 1915–2005. They noted the better utility of ANN models in projecting the SPEI over the study sites. Nguyen et al. [13] projected short- and long-term droughts by deploying ANFIS based on SPEI and SPI at CRB (Cai River basin), Vietnam. Results showed the ANFIS model’s better viability for predicting long-term SPEI (12-month) and short-term SPI (1- and 3-month) in the study basin. Djerbouai and Souag-Gamane [14] utilized WANN, ANN, SARIMA, and ARIMA models for SPI-3, SPI-6, and SPI-12 prediction Algerois basin, Algeria, and they found that the WANN model outperformed the other models. Deo et al. [15] deployed WELM (Wavelet-Extreme Learning Machine), WANN, WLSSVR (Wavelet-Least Squares Support Vector Regression), LSSVR (Least Squares Support Vector Regression), and ANN models for drought estimation based on EDI in Australia. Outcomes indicated that the WELM models had a better performance than the LSSVR, ANN, WANN, and WLSSVR models. Komasi et al. [16] evaluated the SVM (Support Vector Machine), WSVM (Wavelet-Support Vector Machine), and CS-SVM (Cuckoo Search-Support Vector Machine) for drought estimation based on SPI in Urmia Lake watershed, Iran. The performance of the WSVM model was better compared to the other models. Abbasi et al. [17] studied the meteorological drought in Urmia Lake (Iran) based on multi-scalar SPI and SPEI, and the projection was conducted by utilizing the Gene Expression Programming (GEP) model. The drought took place during 1959–1967 and 1998–2009. The observations indicated that the GEP model’s superiority increased by mounting the scale of SPI and SPEI.
With related context, Memarian et al. [18] applied the CANFIS model to forecast the drought in Birjand (Iran) with the combination of climatic signals, i.e., NINO 1 + 2, NINO 3, Multivariate Enso Index, Tropical Southern Atlantic Index, Atlantic Multi-decadal Oscillation Index, NINO 3.4, and lagged values of SPI. Results highlighted the better feasibility of the CANFIS model in drought forecasting over the study region. Rafiei-Sardooi et al. [19] employed the neuro-fuzzy (NF) and time-series, i.e., ARIMA models, to predict the meteorological drought in the Jiroft plain of Iran using 3- and 12-month SPI. The analysis of results demonstrated that the NF model outperformed the ARIMA model. Malik et al. [20] predicted meteorological drought in the Kumaon region of Uttarakhand State (India) by employing the CANFIS, MLPNN, and MLR models considering SPI-1, SPI-3, SPI-6, SPI-9, SPI-12, and SPI-24. The obtained results were evaluated based on performance measures (i.e., RMSE, NSE, COC, and WI) and revealed that the CANFIS models provided better estimates than other models and different study stations. According to our knowledge, the MLPNN, CANFIS, and MLR models’ efficacy for meteorological drought projection using the Standardized Precipitation Index (SPI) had not yet been investigated in the Garhwal region of Uttarakhand State, India. In this paper, the analysis was carried out by utilizing monthly rainfall data at Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal, and Uttarkashi stations with the three objectives: (1) to calculate the SPI at various time scales, 1-, 3-, 6-, 9-, 12-, and 24-month, by utilizing available rainfall information; (2) to formulate the MLPNN, CANFIS, and MLR models for meteorological drought projection based on nominated input by utilizing the PACF analysis of multi-scalar SPI; and (3) to standardize and corroborate the AI and regression models for prediction of multi-scalar SPI values employing visual and statistical indicators.
2. Materials and Methods 2.1. Study Area and Data Assembly
This study was executed in the Garhwal region of Uttarakhand State (India), situated in the central Himalayan zone, spanning 32,499 km2 (Figure 1) among 77°34′ E to 81°03′ E longitudes and 28°43′ N to 31°28′ N latitudes by varying altitudes of 276 m to 5046 m above mean sea level. It borders with Uttar Pradesh in the South, Himachal Pradesh in the northwest, and China and Nepal in the northeast and southeast. Uttarakhand has 13 districts divided into two administrative divisions: (1) Garhwal, which comprises seven districts (Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal, and Uttarkashi) and (2) Kumaon, which comprises six districts (Almora, Bageshwar, Champawat, Nainital, Pithoragarh, and Udham Singh Nagar). The state boasts of a temperate climate, except the plains where it is tropical. The temperature varies from sub-zero to 43 °C. The yearly rainfall falls in 260 mm and 3955 mm, where 60% to 85% occurs during the monsoon season (June to September).
For estimating meteorological drought, seven rain gauge stations were set up, as shown in Figure 1. The information regarding the longitude, latitude, altitude, and data availability are presented in Table 1. The data used in this study included monthly rainfall records that were gathered over seven stations from the India Meteorological Department (IMD), Pune.
2.2. Standardized Precipitation Index (SPI)
McKee et al. [6] formulated the SPI to describe, monitor, and examine droughts on various time scales at Colorado State University. A detailed depiction of SPI was presented by Guttman [21] and Hayes et al. [22]. The calculation of SPI for a particular time scale at any location entails long-term (≥30 years) information on monthly precipitation. In general, the SPI is computed by exploiting statistical probability distribution over the aggregated rainfall of different time scales of attention. This activity was carried out individually for every month and location in space. The SPI is calculated by transforming every probability distribution into the standardized normal distribution (Z-distribution). Many research works have been carried out on rainfall distribution by utilizing the different probability distributions [23,24].
In this research, two-parameter gamma distribution [24,25,26] was utilized for the computation process of SPI by using Equation (1) [27,28]:
Z=SPI = −t−c0 + c1t + c2 t21 + d1t + d2 t2 + d3 t3for, 0<Hx≤0.5SPI = +t−c0 + c1t + c2 t21 + d1t + d2 t2 + d3 t3for, 0.5<Hx<1.0
in whichc0, c1, c2, d1, d2, d3, and tare constants, and defined as:c0=2.515517,c1=0.802853,c2=0.010328,d1=1.432788,d2=0.189269, andd3=0.001308.Hxis the commutative probability,t=ln1Hx2for0<Hx≤0.5, andt=ln11−Hx2for0.5<Hx<1.0 [6].
2.3. Co-Active Neuro-Fuzzy Inference System (CANFIS)
To solve the nonlinear optimization problems, Jang et al. [29] projected the idea of the CANFIS technique. In the present time, the CANFIS model effectiveness has been found in numerous fields of sciences [20,30,31,32,33,34]. The basic structure of CANFIS involved integrating ANN and FIS (fuzzy-inference system) in one border. Figure 2 demonstrates the typical structure of the CANFIS model composed of these five layers (i.e., Layer-1: fuzzification, Layer-2: rule, Layer-3: normalization, Layer-4: defuzzification, and Layer-5: fuzzy association). Each input is passed and treated through these layers. By considering two inputs (xandy ) under the rule of Takagi–Sugeno–Kang (TSK) fuzzy system with IF-THEN rule, we can describe the CANFIS models [35,36]:
Rule 1:IF x is A1 and y is B1 THEN C1=p1x+q1y+r1
Rule 2:IF x is A2 and y is B2 THEN C2=p2x+q2y+r1
Here,A1,A2, andB1,B1are the fuzzy sets withC1andC1for the inputsxandy.p1,q1,r1andp2,q2,r2 are parameters of the consequent part (Figure 2). The functioning of every layer is defined as [37,38]:
Layer−1 fuzzification =μAix and μBiy for i = 1, 2
Layer−2 rule =wi= μAix×μBiy for i = 1, 2
Layer−3 normalization =wi¯=wiΣi wi i = 1, 2
Layer−4 defuzzification =wi¯Ci=wi¯pix+qiy+ri i = 1, 2
Layer−5 fuzzy association =wi¯Ci=∑iwi¯Ci=Σi wi CiΣi wi
In Equation (4),AiandBiare the linguistic labels andμAiandμBirepresent the membership functions (MFs) for linguistic labels. In Equation (5),wiis the weight (or firing strength) associated with inputs (xandy). In Equation (6),wi¯is the normalized firing strength. In this study, through supervised learning, the CANFIS network was designed. For input data classification, the Gaussian (Gauss) MFs were applied along with the TSK (Takagi–Sugeno–Kang) fuzzy model and hyperbolic tangent activation function (for data normalization), and DBD (delta bar delta) algorithm was found to be more potent for multi-scalar SPI prediction at seven study locations.
Climate 09 00028 g002 550
2.4. Multi-Layer Perceptron Neural Network (MLPNN)
MLPNN was first proposed by Haykin [39]. It involves layers of parallel processing elements, known as neurons. Every layer is wholly linked to the next layer through inter-links of weights (W) or strengths. A typical structure of MLPNN models is composed of three layers, Layer-1: input (i), Layer-2: hidden (j), and Layer-3: output (k) with inter-linked weights (Wij and Wjk) between these layers, as illustrated in Figure 3. We specified the number of hidden layers and neurons by the number of predictands and predictors [40].
In this research, the 2n + 1 (n represents the inputs) concept was exploited to decide the optimal number of neurons in the hidden layer [7,10]. The designed architecture of MLPNN was then applied to forecast the meteorological drought condition at various locations depending on the SPI values used as input at different lags.
2.5. Multiple Linear Regression (MLR)
The degree of association among target parameter (dependent) and two or many independent parameters was determined using MLR and written as [30,33]:
Z =β0+ β1 X1+ β2 X2+, …, + βk Xn
whereZrepresents the dependent (target) parameter,β0, β1,β2,…βkare the regression coefficient of the MLR equation, andX1, X2,…Xnare the independent parameters. Subscriptndenotes the number of independent parameters corresponding tokregression coefficient.
2.6. Input Selection and Model Development
Choosing proper inputs is a tedious task, particularly in nonlinear hydrological processes. The SPI-1, -3, -6, -9, -12, and -24 were calculated using long-term monthly rainfall information in this study. The ACF and PACF (autocorrelation function and partial-ACF) were applied for choosing the crucial inputs (lags). Both ACF and PACF were computed by utilizing the expressions below [41,42]:
ACFk=∑t=1N−kYt−Y¯ Yt+k−Y¯∑t=1NYt−Y¯
PACFk,k=ACF−∑j=1k−1PACFk−1,j ACFk−11−∑j=1k−1PACFk−1,j ACFk−1
in which k defines lag throughYtdata series,Y¯ designates the average of the whole data series, and N states the data points. Afterward, at a 5% confidence level, the computed values of PACF were tested, portraying upper and lower critical limits (UCL and LCL) by using Equation (12) [43]:
CLupper/lower=±1.96N.
2.7. Performance Indicators
The performances of AI and regression were assessed with the Nash–Sutcliffe Efficiency (NSE) [44], Root Mean Squared Error (RMSE) [45], Willmott Index (WI) [46], Coefficient of Correlation (COC) [45], and visual interpretation was by scatter plot and Taylor diagram [47]. These indices are outlined as:
RMSE=1N ∑i=1N(SPIobs, i − SPIpre,i)2 ( 0 < RMSE < ∞)
NSE=1−∑i=1N (SPIobs,i − SPIpre,i)2∑i=1N (SPIobs,i − SPIobs ¯)2 (−∞ < NSE < 1)
COC=∑i=1NSPIobs,i − SPIobs ¯ SPIpre,i − SPIpre¯ ∑i=1N (SPIobs,i − SPIobs ¯)2 ∑i=1N (SPIpre,i − SPIpre¯)2 (−1 < COC < 1)
WI=1−∑i=1N (SPIpre,i − SPIobs, i)2∑i=1N (SPIpre,i − SPIobs ¯+SPIobs,i − SPIobs ¯)2 (0 < WI ≤ 1)
whereSPIobs andSPIpre= observed (computed) and predicted multi-scalar SPI for the ith dataset, N = number of observations,SPIobs ¯andSPIpre ¯= mean of observed and predicted multi-scalar SPI.SPIpre,i − SPIobs ¯= absolute difference among predicted and observed mean andSPIobs,i − SPIobs ¯= absolute difference among the observed and their mean.
3. Results 3.1. Significant Lags’ Nomination by Using PACF Analysis
Table 2 summarizes the PACF investigation with level of significance equal to 5% carried out on SPI-1, SPI-3, SPI-6, SPI-9, SPI-12, and SPI-24 for Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal, and Uttarkashi stations, respectively. It was noted from Table 2, for Chamoli, the peaks with lags equal to 1, 9, 10, 11, and 12 (SPI-1); 1, 2, 3, 4, 7, 8, 10, and 11 (SPI-3); 1, 2, 3, 7, 11, and 12 (SPI-6); 1, 2, 8, 10, 11, and 12 (SPI-9); 1, 2, 6, 10, and 11 (SPI-12); and 1, 2, 3, 6, 11, and 12 (SPI-24); for Dehradun, the spikes with lags 1 and 4 (SPI-1); 1, 2, 3, 4, 6, and 7 (SPI-3); 1, 2, 3, 6, 7, 11, and 12 (SPI-6); 1, 4, 6, 7, 8, 9, and 10 (SPI-9); 1, 2, 3, 6, 7, 8, 9, 10, and 11 (SPI-12); and 1, 2, 3, 6, 7, 10, 11, and 12 (SPI-24); for Haridwar, the spikes with lags 1 and 4 (SPI-1); 1, 2, 3, 4, 6, and 7 (SPI-3); 1, 2, 3, 6, 7, 11, and 12 (SPI-6); 1, 4, 6, 7, 8, 9, and 10 (SPI-9); 1, 2, 3, 6, 7, 8, 9, 10, and 11 (SPI-12); and 1, 2, 3, 6, 7, 10, 11, and 12 (SPI-24); for Pauri Garhwal, the spikes with lags 1, 5, 10, 11, and 12 (SPI-1); 1, 2, 3, 4, 7, and 10 (SPI-3); 1, 2, 6, 7, 9, and 12 (SPI-6); 1, 8, 9, and 10 (SPI-9); 1, 2, 3, and 6 (SPI-12); and 1, 2, 3, 7, 8, 10, and 11 (SPI-24); for Rudraprayag, the spikes with lags 1, 5, 10, 11, and 12 (SPI-1); 1, 2, 3, 4, 5, 7, and 10, (SPI-3); 1, 2, 6, 7, and 12 (SPI-6); 1, 2, 3, 6, 7, 8, 9, and 10 (SPI-9); 1, 2, 3, and 6 (SPI-12); and 1, 2, 3, 7, 8, 10, and 11 (SPI-24); for Tehri Garhwal, the peaks with lags equal to 1 and 5 (SPI-1); 1, 2, 3, 4, and 7 (SPI-3); 1, 2, 6, 7, and 12 (SPI-6); 1, 8, 9, and 10 (SPI-9); 1, 2, 6, and 12 (SPI-12); and 1, 2, and 12 (SPI-24); and for Uttarkashi, the peaks with lags equal to 1, 2, 5, 6, and 12 (SPI-1); 1, 2, 3, and 4 (SPI-3); 1, 2, 6, and 7 (SPI-6); 1, 2, 6, 7, 9, and 10 (SPI-9); 1, 2, 3, and 6 (SPI-12); and 1, 2, 6, and 7 (SPI-24) were significant with level equal to 5% and utilized as inputs for all SPI to project meteorological drought at study sites. This information was utilized to formulate the MLPNN, CANFIS, and MLR models, as outlined in Table 3. These models were trained with 70% of the data and tested by deploying 30% data of SPI-1, 3-, 6-, 9-, 12-, and 24 at seven study sites.
3.2. Application of AI and Regression Models for Multi-Scalar SPI Prediction
Projection of drought situation was carried out by determining the appropriateness of the MLPNN, CANFIS, and MLR deployed on all SPI values for seven study sites. All models were trained using 70% from the data set, and the remaining 30% were utilized to test the model. The performances of the MLPNN, CANFIS, and MLR were assessed by utilizing NSE, RMSE, COC, and WI during the testing, as stated in Table 4, Table 5 and Table 6, for Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag Tehri Garhwal, and Uttarkashi stations, respectively. As noted from Table 4, the CANFIS performance was observed to be the best with 2 Gaussian (Gauss) membership functions for SPI-12 at Chamoli (RMSE = 0.158, NSE = 0.980, COC = 0.994, WI = 0.995), Dehradun (RMSE = 0.117, NSE = 0.977, COC = 0.995, WI = 0.994), Rudraprayag (RMSE = 0.089, NSE = 0.992, COC = 0.997, WI = 0.998), and Tehri Garhwal (RMSE = 0.177, NSE = 0.965, COC = 0.991, WI = 0.990); SPI-9 at Haridwar (RMSE = 0.240, NSE = 0.943, COC = 0.980, WI = 0.983) and Uttarkashi (RMSE = 0.344, NSE = 0.868, COC = 0.966, WI = 0.957); and SPI-6 at Pauri Garhwal (RMSE = 0.261, NSE = 0.957, COC = 0.996, WI = 0.987) during the testing span for projection of drought condition.
Table 5 outlines that the MLPNN models produced better estimates for SPI-12 at Chamoli (5-11-1: RMSE = 0.181, NSE = 0.974, COC = 0.991, WI = 0.993), Dehradun (4-8-1: RMSE = 0.145, NSE = 0.964, COC = 0.988, WI = 0.990), Haridwar (9-19-1: RMSE = 0.177, NSE = 0.969, COC = 0.986, WI = 0.992), Pauri Garhwal (4-6-1: RMSE = 0.225, NSE = 0.970, COC = 0.994, WI = 0.994), Rudraprayag (4-7-1: RMSE = 0.082, NSE = 0.994, COC = 0.997, WI = 0.998), and Tehri Garhwal (4-8-1: RMSE = 0.208, NSE = 0.952, COC = 0.984, WI = 0.986); and SPI-6 at Uttarkashi (4-7-1: RMSE = 0.356, NSE = 0.875, COC = 0.964, WI = 0.960) in the testing period.
Similarly, Table 6 summarizes that the best performance of MLR models was for projecting the SPI-12 at Chamoli (RMSE = 0.298, NSE = 0.931, COC = 0.965, WI = 0.982), Dehradun (RMSE = 0.302, NSE = 0.845, COC = 0.928, WI = 0.959), Haridwar (RMSE = 0.390, NSE = 0.847, COC = 0.921, WI = 0.958), Pauri Garhwal (RMSE = 0.319, NSE = 0.940, COC = 0.970, WI = 0.984), and Rudraprayag (RMSE = 0.275, NSE = 0.926, COC = 0.964, WI = 0.980); and SPI-24 at Tehri Garhwal (RMSE = 0.238, NSE = 0.935, COC = 0.968, WI = 0.983) and Uttarkashi (RMSE = 0.143, NSE = 0.975, COC = 0.988, WI = 0.994) in the testing period.
3.3. Performance Assessment by Using Scatter Plots and Taylor Diagram
The temporal disparity between the projected and computed (calculated) values for all SPI scales by the MLPNN, CANFIS, and MLR models during the testing span at Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag Tehri Garhwal, and Uttarkashi stations are presented in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10. As clearly seen from these figures, line of regression of CANFIS was quite near the best-fit line (highlighted by red color) for SPI-1, SPI-3, SPI-6, SPI-9, and SPI-12 at Chamoli and Tehri Garhwal; SPI-3, SPI-6, SPI-9, and SPI-12 at Dehradun; SPI-1, SPI-3, SPI-6, and SPI-9 at Haridwar and Pauri Garhwal; SPI-1, SPI-3, and SPI-6 at Rudraprayag; and SPI-3 at Uttarkashi. The MLPNN the regression line was close to the best-fit line on Chamoli and Tehri Garhwal for SPI-24; Dehradun for SPI-1 and SPI-24; Haridwar SPI-12 and SPI-24; Pauri Garhwal for SPI-12; Rudraprayag for SPI-9, SPI-12, and SPI-24; and Uttarkashi for SPI-1 and SPI-6. Likewise, for MLR models, these lines were close at Pauri Garhwal on SPI-24 and Uttarkashi on SPI-9, SPI-12, and SPI-24.
Accordingly, the spatial design of projected and calculated (observed) values of multi-scalar SPI for the MLPNN, CANFIS, and MLR models was also assessed by utilizing the Taylor diagram (TD) as a polar plot for attaining a graphical judgment of model performance based on SD, COC, and RMSE. Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17 show the TD of MLPNN, CANFIS, and MLR models at Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal, and Uttarkashi, respectively, for the testing span. Consequently, Figure 11a–f shows that the CANFIS with chosen lags can be utilized for SPI projection at 1-, 3-, 6-, 9- and 12-month time spans, and MLPNN for the 24 months at Chamoli. Figure 12a–f displays that the CANFIS model with chosen lags can be utilized for SPI projection at 3-, 6-, 9- and 12-month time scales, and MLPNN for 1- and 24-month time spans at Dehradun. Figure 13a–f illustrates that the CANFIS model with certain lags can be utilized for SPI projection at 1-, 3-, 6-, and 9-month periods. The MLPNN model for 12-and 24-month time scales at Haridwar. Figure 14a–f demonstrates that the CANFIS model with certain lags was deployed for SPI projection at 1-, 3-, 6-, and 9-month time scales, MLPNN for the 12 months, and MLR the 24-month time scale at Pauri Garhwal. Figure 15a–f reveals that the CANFIS model with certain lags can be deployed for SPI projection at 1-, 3-, 6-month time scales and the MLPNN model for 9-, 12-, 24-month time spans at Rudraprayag. Figure 16a–f exposes that the CANFIS with certain lags can be utilized for SPI projection at 1-, 3-, 6-, 9-, and 12-month periods. The MLPNN model for 24 months at Tehri Garhwal. Figure 17a–f discloses that the CANFIS with certain lags can be utilized for SPI projection at 3-month time scales, MLR for 9-, 12-, 24-month duration, and MLPNN for 1- and 6-month duration at Uttarkashi.
4. Discussion
Table 4, Table 5 and Table 6 show that for a short time scale, i.e., SPI-1, both the AI and regression models yielded higher values of RMSE and lower values of NSE, COC, and WI. It means their unsatisfactory performance at a short time scale SPI. Apart from this, a comparison among AI performance (i.e., CANFIS and MLPNN) and regression (i.e., MLR) models is shown in Table 7, which reveals that the CANFIS gained the highest-ranking followed by the MLPNN at all study sites except the Uttarkashi. Overall, the MLR model received a lower ranking at Chamoli, Dehradun, Haridwar, Pauri Garhwal, Rudraprayag, Tehri Garhwal stations, and the highest Uttarkashi station.
To make the results more concrete, this research’s findings were compared with the recent investigations conducted in different parts of the world on meteorological droughts’ prediction using stochastic and AI models. Mokhtarzad et al. [48] applied SVM, ANFIS, and ANN techniques to forecast the meteorological drought in Tehran based on SPI. According to the results, the SVM model provided more precise estimates than the ANFIS and ANN models. Nguyen et al. [49] conducted a study on the ANFIS model potential concerning meteorological drought prediction using SPEI and SPI at Khanhhoa Province, Vietnam. The investigation revealed the superior performance of the ANFIS model for SPEI and SPI in the study area. Zhang et al. [50] predicted the drought condition by employing the SVR, WANN, ANN, and ARIMA models that used 3 and 6 months of SPI values in Haihe River Basin, China. The estimated outcomes of SPI-6 and SPI-3 showed that the WANN model exhibited superior performance to other models. Liu et al. [51] used the Self-Adaptive Evolutionary-Extreme Learning Machine (SADE-ELM), Online Sequential-ELM (OS-ELM), and ELM for meteorological drought prediction based on SPEI and SPI in Khanhhoa Province, Vietnam. They found that the performance of the SADE-ELM models was superior to the other models. Mouatadid et al. [52] exploited the LSSVR, MLR, ANN, and ELM to forecast drought through various-scalar SPEI and SPI in eastern Australia. The results showed the better performance of ANN and ELM models than the LSSVR and MLR models. Özger et al. [53] applied standalone and hybrid use of ANFIS, SVM, and M5 models coupled with empirical mode decomposition (EMD-ANFIS, EMD-SVM, EMD-M5) and wavelet decomposition (i.e., WD-ANFIS, WD-SVM, WD-M5) for self-calibrated Palmer Drought Severity Index (SC-PDSI) prediction in the southern part of Turkey. The obtained results indicated the improved performance of hybrid WD-ANFIS, WD-SVM, and WD-M5 models over the other models. Considering the excellent performance of AI models, i.e., CANFIS and MLPNN, applied in this study, it might be insightful to compare these two models’ performances with other future studies models. In this regard, more recent meteorological data may be considered. Comparing two models applied in this study with other models for drought prediction to consider different climate projections would also be an essential task to be carried out in future studies to assist water managers in better long-term planning of water resources’ exploitation.
Accordingly, this study confirmed the superiority of AI models such as MLPNN and CANFIS in predicting meteorological droughts of various durations at the selected study stations. 5. Conclusions This study analyzed the feasibility of AI and regression models that can be applied to predict the meteorological drought based on multi-scalar SPI at Pauri Garhwal, Chamoli, Rudraprayag, Dehradun, Haridwar, Uttarkashi, and Tehri Garhwal stations. Partial Autocorrelation Function (PACF) was utilized to choose the optimal input parameters (lags) for MLPNN, CANFIS, and MLR models at 5% significance level on SPI-24, SPI-12, SPI-9, SPI-6, SPI-3, and SPI-1 data series. The estimates yielded by the MLPNN, CANFIS, and MLR models were compared with the calculated (observed) values of multi-scalar SPI that applies statistical indicators, such as NSE, RMSE, WI, COC, and visual basis through Taylor diagram and scatter plot for study stations. Appraisal of results revealed that the applied AI models (i.e., CANFIS and MLPNN) significantly enhanced the modeling performance by improving the WI, COC, and NSE and decreasing the RMSE measurements in the study stations. Also, the executions of MLR at study stations were the poorest, except SPI-24 at Pauri Garhwal and SPI-9, SPI-12, and SPI-24 at Uttarkashi to predict meteorological drought. This study will help develop a reliable and standard intelligent system that can be used for the considered rainfall stations. It will be precious for policymakers and water resources managers to frame the study regions’ drought mitigation strategies.
Enlarge this image.Figure 3. Three-layer multi-layer perceptron neural network (MLPNN) model configuration.
Enlarge this image.Figure 4.(a-f) Scatter plots of calculated and predicted multi-scalar SPI values by CANFIS, MLPNN, and MLR models during the testing period at Chamoli station.
Enlarge this image.Figure 5.(a-f) Scatter plots of calculated and predicted multi-scalar SPI values by CANFIS, MLPNN, and MLR models during the testing period at Dehradun station.
Enlarge this image.Figure 6.(a-f) Scatter plots of calculated and predicted multi-scalar SPI values by CANFIS, MLPNN, and MLR models during the testing period at Haridwar station.
Enlarge this image.Figure 7.(a-f) Scatter plots of calculated and predicted multi-scalar SPI values by CANFIS, MLPNN, and MLR models during the testing period Pauri Garhwal station.
Enlarge this image.Figure 8.(a-f) Scatter plots of calculated and predicted multi-scalar SPI values by CANFIS, MLPNN, and MLR models during the testing period at Rudraprayag station.
Enlarge this image.Figure 9.(a-f) Scatter plots of calculated and predicted multi-scalar SPI values by CANFIS, MLPNN, and MLR models during the Tehri Garhwal station's testing period.
Enlarge this image.Figure 10.(a-f) Scatter plots of calculated and predicted multi-scalar SPI values by CANFIS, MLPNN, and MLR models during the testing period at Uttarkashi station.
Enlarge this image.Figure 11.(a-f) Taylor diagram of predicted and calculated multi-scalar SPI at Chamoli station.
Enlarge this image.Figure 12.(a-f) Taylor diagram of predicted and calculated multi-scalar SPI at Dehradun station.
Enlarge this image.Figure 13.(a-f) Taylor diagram of predicted and calculated multi-scalar SPI at Haridwar station.
Enlarge this image.Figure 14.(a-f) Taylor diagram of predicted and calculated multi-scalar SPI at Pauri Garhwal station.
Enlarge this image.Figure 15.(a-f) Taylor diagram of predicted and calculated multi-scalar SPI at Rudraprayag station.
Enlarge this image.Figure 16.(a-f) Taylor diagram of predicted and calculated multi-scalar SPI at Tehri Garhwal station.
Enlarge this image.Figure 17.(a-f) Taylor diagram of predicted and calculated multi-scalar SPI at Uttarkashi station.
| Meteorological Station | Latitude (N) | Longitude (E) | Altitude (m) | Rainfall Data (Year) |
|---|---|---|---|---|
| Chamoli | 30°46′30″ | 79°37′41″ | 5046 | 1901–2015 |
| Dehradun | 30°27′32″ | 77°53′28″ | 728 | 1901–2015 |
| Haridwar | 29°55′26″ | 78°03′04″ | 276 | 1901–2015 |
| Pauri Garhwal | 29°50′28″ | 78°43′44″ | 1134 | 1901–2015 |
| Rudraprayag | 30°36′07″ | 79°05′53″ | 2117 | 1901–2015 |
| Tehri Garhwal | 30°26′53″ | 78°32′42″ | 1996 | 1955–2015 |
| Uttarkashi | 31°00′47″ | 78°24′29″ | 3366 | 1951–2015 |
| Station | Index | Lag | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
| Chamoli | SPI-1 | 0.213 * | 0.048 | 0.021 | 0.031 | 0.043 | 0.045 | 0.041 | 0.038 | 0.063 * | 0.081 * | 0.074 * | 0.135 * |
| SPI-3 | 0.725 * | −0.180 * | −0.150 * | 0.236 * | 0.000 | −0.041 | 0.146 * | 0.058 * | 0.040 | 0.129 * | 0.055 * | 0.050 | |
| SPI-6 | 0.881 * | −0.172 * | −0.071 * | −0.042 | −0.018 | −0.024 | 0.416 * | −0.002 | 0.036 | −0.016 | −0.073 * | −0.072 * | |
| SPI-9 | 0.934 * | −0.112 * | −0.025 | 0.015 | −0.038 | −0.015 | 0.011 | −0.055 * | −0.031 | 0.390 * | −0.073 * | −0.062 * | |
| SPI-12 | 0.963 * | −0.150 * | −0.001 | 0.016 | −0.048 | −0.054 * | −0.037 | −0.020 | −0.038 | −0.083 * | −0.075 * | 0.011 | |
| SPI-24 | 0.949 * | 0.342 * | 0.149 * | 0.025 | −0.027 | −0.060 * | 0.040 | 0.020 | −0.003 | −0.047 | −0.110 * | −0.068 * | |
| UCL/LCL | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | |
| Dehradun | SPI-1 | 0.134 * | 0.019 | −0.053 | −0.059 * | 0.033 | −0.031 | 0.001 | −0.005 | −0.026 | 0.031 | 0.078 * | 0.056 * |
| SPI-3 | 0.659 * | −0.176 * | −0.209 * | 0.167 * | 0.001 | −0.095 * | 0.072 * | 0.017 | 0.032 | 0.047 | 0.047 | 0.020 | |
| SPI-6 | 0.818 * | −0.149 * | −0.059 * | −0.009 | −0.044 | −0.111 * | 0.250 * | 0.014 | 0.037 | 0.034 | 0.002 | −0.089 * | |
| SPI-9 | 0.875 * | −0.054 * | 0.072 * | 0.018 | −0.002 | −0.046 | −0.044 | −0.099 * | −0.135 * | 0.279 * | 0.044 | 0.008 | |
| SPI-12 | 0.951 * | −0.169 * | −0.057 * | −0.001 | −0.020 | −0.050 | −0.030 | −0.048 | −0.047 | −0.083 * | −0.049 | −0.022 | |
| SPI-24 | 0.932 * | 0.289 * | 0.084 * | 0.018 | 0.003 | 0.028 | 0.146 * | 0.074 * | −0.008 | −0.085 * | −0.093 * | −0.061 * | |
| UCL/LCL | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | |
| Haridwar | SPI-1 | 0.101 * | 0.008 | −0.037 | −0.081 * | 0.029 | −0.015 | −0.020 | −0.003 | −0.044 | 0.032 | 0.010 | 0.039 |
| SPI-3 | 0.639 * | −0.141 * | −0.246 * | 0.165 * | 0.000 | −0.101 * | 0.078 * | −0.013 | −0.022 | 0.001 | −0.008 | 0.005 | |
| SPI-6 | 0.796 * | −0.109 * | −0.079 * | −0.032 | −0.042 | −0.192 * | 0.237 * | −0.021 | −0.022 | −0.014 | −0.056 * | −0.074 * | |
| SPI-9 | 0.857 * | 0.030 | −0.035 | −0.060 * | −0.047 | −0.072 * | −0.068 * | −0.116 * | −0.208 * | 0.288 * | 0.012 | 0.026 | |
| SPI-12 | 0.924 * | −0.143 * | −0.079 * | −0.033 | −0.029 | −0.065 * | −0.064 * | −0.054 * | −0.100 * | −0.110 * | −0.100 * | −0.044 | |
| SPI-24 | 0.870 * | 0.287 * | 0.073 * | −0.007 | −0.018 | 0.068 * | 0.112 * | 0.052 | −0.033 | −0.103 * | −0.103 * | −0.058 * | |
| UCL/LCL | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | |
| Pauri Garhwal | SPI-1 | 0.210 * | 0.033 | 0.013 | −0.041 | 0.058 * | 0.002 | 0.005 | 0.016 | −0.019 | 0.057 * | 0.073 * | 0.084 * |
| SPI-3 | 0.696 * | −0.145 * | −0.140 * | 0.181 * | 0.017 | −0.047 | 0.058 * | 0.005 | 0.051 | 0.075 * | 0.051 | 0.047 | |
| SPI-6 | 0.857 * | −0.103 * | −0.042 | −0.043 | −0.001 | −0.109 * | 0.243 * | 0.003 | 0.066 * | 0.052 | −0.023 | −0.062 * | |
| SPI-9 | 0.898 * | −0.013 | 0.039 | −0.008 | 0.024 | −0.049 | −0.038 | −0.068 * | −0.116 * | 0.281 * | 0.045 | 0.031 | |
| SPI-12 | 0.959 * | −0.100 * | −0.100 * | −0.033 | 0.001 | −0.074 * | −0.050 | 0.001 | −0.038 | −0.035 | −0.018 | −0.036 | |
| SPI-24 | 0.944 * | 0.314 * | 0.079 * | 0.005 | 0.014 | 0.025 | 0.104 * | 0.082 * | −0.007 | −0.073 * | −0.078 * | −0.041 | |
| UCL/LCL | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | |
| Rudraprayag | SPI-1 | 0.197 * | 0.014 | 0.002 | −0.003 | 0.075 * | 0.049 | 0.038 | 0.030 | 0.007 | 0.055 * | 0.068 * | 0.084 * |
| SPI-3 | 0.697 * | −0.172 * | −0.100 * | 0.224 * | 0.054 * | −0.051 | 0.081 * | 0.048 | 0.024 | 0.084 * | 0.045 | 0.017 | |
| SPI-6 | 0.866 * | −0.099 * | 0.015 | −0.027 | −0.039 | −0.083 * | 0.265 * | 0.015 | 0.042 | 0.038 | −0.026 | −0.102 * | |
| SPI-9 | 0.916 * | −0.060 * | 0.063 * | 0.009 | 0.025 | −0.067 * | −0.057 * | −0.105 * | −0.096 * | 0.311 * | 0.033 | −0.013 | |
| SPI-12 | 0.965 * | −0.165 * | −0.058 * | −0.033 | −0.011 | −0.063 * | −0.035 | −0.008 | −0.036 | −0.049 | −0.035 | −0.009 | |
| SPI-24 | 0.949 * | 0.320 * | 0.098 * | −0.005 | −0.011 | 0.025 | 0.076 * | 0.127 * | −0.025 | −0.120 * | −0.130 * | −0.010 | |
| UCL/LCL | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | ±0.053 | |
| Tehri Garhwal | SPI-1 | 0.157 * | 0.050 | −0.020 | 0.049 | 0.076 * | 0.010 | 0.007 | 0.040 | 0.006 | 0.054 | 0.064 | 0.008 |
| SPI-3 | 0.692 * | −0.125 * | −0.162 * | 0.282 * | −0.009 | −0.064 | 0.088 * | 0.011 | 0.052 | 0.021 | 0.039 | −0.001 | |
| SPI-6 | 0.851 * | −0.093 * | 0.001 | −0.025 | −0.055 | −0.119 * | 0.287 * | −0.026 | 0.035 | 0.016 | −0.040 | −0.079 * | |
| SPI-9 | 0.904 * | −0.009 | 0.010 | −0.017 | −0.020 | −0.051 | −0.070 | −0.082 * | −0.126 * | 0.344 * | 0.020 | −0.045 | |
| SPI-12 | 0.948 * | −0.085 * | −0.036 | −0.023 | −0.031 | −0.087 * | −0.054 | −0.004 | −0.048 | −0.062 | −0.066 | −0.082 * | |
| SPI-24 | 0.976 * | −0.137 * | −0.055 | −0.002 | −0.030 | −0.070 | −0.022 | 0.019 | −0.017 | −0.037 | −0.029 | −0.075 * | |
| UCL/LCL | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | ±0.073 | |
| Uttarkashi | SPI-1 | 0.276 * | 0.116 * | 0.069 | 0.041 | 0.130 * | 0.104 * | 0.015 | 0.012 | 0.055 | 0.029 | 0.045 | 0.072 * |
| SPI-3 | 0.773 * | −0.114 * | −0.081 * | 0.273 * | 0.036 | −0.019 | 0.050 | 0.008 | 0.055 | 0.050 | 0.041 | 0.017 | |
| SPI-6 | 0.911 * | −0.151 * | −0.020 | −0.022 | −0.004 | −0.082 * | 0.264 * | −0.031 | 0.038 | −0.001 | −0.039 | −0.040 | |
| SPI-9 | 0.947 * | −0.144 * | −0.021 | 0.020 | −0.030 | −0.085 * | −0.076 * | −0.040 | −0.072 * | 0.316 * | −0.036 | 0.055 | |
| SPI-12 | 0.972 * | −0.255 * | −0.095 * | 0.007 | −0.020 | −0.095 * | −0.063 | 0.015 | 0.004 | −0.034 | 0.028 | 0.058 | |
| SPI-24 | 0.991 * | −0.196 * | −0.025 | −0.007 | 0.004 | −0.105 * | −0.102 * | −0.014 | −0.015 | −0.039 | −0.050 | 0.029 | |
| UCL/LCL | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | ±0.071 | |
Note: * statistically significant PACF at 5% confidence limit.
| Station | Output | Input Variables |
|---|---|---|
| Chamoli | SPI-1 | SPI-1t-1, SPI-1t-9, SPI-1t-10, SPI-1t-11, SPI-1t-12 |
| SPI-3 | SPI-3t-1, SPI-3t-2, SPI-3t-3, SPI-3t-4, SPI-3t-7, SPI-3t-8, SPI-3t-10, SPI-3t-11 | |
| SPI-6 | SPI-6t-1, SPI-6t-2, SPI-6t-3, SPI-6t-7, SPI-6t-11, SPI-6t-12 | |
| SPI-9 | SPI-9t-1, SPI-9t-2, SPI-9t-8, SPI-9t-10, SPI-9t-11, SPI-9t-12 | |
| SPI-12 | SPI-12t-1, SPI-12t-2, SPI-12t-6, SPI-12t-10, SPI-12t-11 | |
| SPI-24 | SPI-24t-1, SPI-24t-2, SPI-24t-3, SPI-24t-6, SPI-24t-11, SPI-24t-12 | |
| Dehradun | SPI-1 | SPI-1t-1, SPI-1t-4, SPI-1t-11, SPI-1t-12 |
| SPI-3 | SPI-3t-1, SPI-3t-2, SPI-3t-3, SPI-3t-4, SPI-3t-6, SPI-3t-7 | |
| SPI-6 | SPI-6t-1, SPI-6t-2, SPI-6t-3, SPI-6t-6, SPI-6t-7, SPI-6t-12 | |
| SPI-9 | SPI-9t-1, SPI-9t-2, SPI-9t-3, SPI-9t-8, SPI-9t-9, SPI-9t-10 | |
| SPI-12 | SPI-12t-1, SPI-12t-2, SPI-12t-3, SPI-12t-10 | |
| SPI-24 | SPI-24t-1, SPI-24t-2, SPI-24t-3, SPI-24t-7, SPI-24t-8, SPI-24t-10, SPI-24t-11, SPI-24t-12 | |
| Haridwar | SPI-1 | SPI-1t-1, SPI-1t-4 |
| SPI-3 | SPI-3t-1, SPI-3t-2, SPI-3t-3, SPI-3t-4, SPI-3t-6, SPI-3t-7 | |
| SPI-6 | SPI-6t-1, SPI-6t-2, SPI-6t-3, SPI-6t-6, SPI-6t-7, SPI-6t-11, SPI-6t-12 | |
| SPI-9 | SPI-9t-1, SPI-9t-4, SPI-9t-6, SPI-9t-7, SPI-9t-8, SPI-9t-9, SPI-9t-10 | |
| SPI-12 | SPI-12t-1, SPI-12t-2, SPI-12t-3, SPI-12t-6, SPI-12t-7, SPI-12t-8, SPI-12t-9, SPI-12t-10, SPI-12t-11 | |
| SPI-24 | SPI-24t-1, SPI-24t-2, SPI-24t-3, SPI-24t-6, SPI-24t-7, SPI-24t-10, SPI-24t-11, SPI-24t-12 | |
| Pauri Garhwal | SPI-1 | SPI-1t-1, SPI-1t-5, SPI-1t-10, SPI-1t-11, SPI-1t-12 |
| SPI-3 | SPI-3t-1, SPI-3t-2, SPI-3t-3, SPI-3t-4, SPI-3t-7, SPI-3t-10 | |
| SPI-6 | SPI-6t-1, SPI-6t-2, SPI-6t-6, SPI-6t-7, SPI-6t-9, SPI-6t-12 | |
| SPI-9 | SPI-9t-1, SPI-9t-8, SPI-9t-9, SPI-9t-10 | |
| SPI-12 | SPI-12t-1, SPI-12t-2, SPI-12t-3, SPI-12t-6 | |
| SPI-24 | SPI-24t-1, SPI-24t-2, SPI-24t-3, SPI-24t-7, SPI-24t-8, SPI-24t-10, SPI-24t-11 | |
| Rudraprayag | SPI-1 | SPI-1t-1, SPI-1t-5, SPI-1t-10, SPI-1t-11, SPI-1t-12 |
| SPI-3 | SPI-3t-1, SPI-3t-2, SPI-3t-3, SPI-3t-4, SPI-3t-5, SPI-3t-7, SPI-3t-10 | |
| SPI-6 | SPI-6t-1, SPI-6t-2, SPI-6t-6, SPI-6t-7, SPI-6t-12 | |
| SPI-9 | SPI-9t-1, SPI-9t-2, SPI-9t-3, SPI-9t-6, SPI-9t-7, SPI-9t-8, SPI-9t-9, SPI-9t-10 | |
| SPI-12 | SPI-12t-1, SPI-12t-2, SPI-12t-3, SPI-12t-6 | |
| SPI-24 | SPI-24t-1, SPI-24t-2, SPI-24t-3, SPI-24t-7, SPI-24t-8, SPI-24t-10, SPI-24t-11 | |
| Tehri Garhwal | SPI-1 | SPI-1t-1, SPI-1t-5 |
| SPI-3 | SPI-3t-1, SPI-3t-2, SPI-3t-3, SPI-3t-4, SPI-3t-7 | |
| SPI-6 | SPI-6t-1, SPI-6t-2, SPI-6t-6, SPI-6t-7, SPI-6t-12 | |
| SPI-9 | SPI-9t-1, SPI-9t-8, SPI-9t-9, SPI-9t-10 | |
| SPI-12 | SPI-12t-1, SPI-12t-2, SPI-12t-6, SPI-12t-12 | |
| SPI-24 | SPI-24t-1, SPI-24t-2, SPI-24t-12 | |
| Uttarkashi | SPI-1 | SPI-1t-1, SPI-1t-2, SPI-1t-5, SPI-1t-6, SPI-1t-12 |
| SPI-3 | SPI-3t-1, SPI-3t-2, SPI-3t-3, SPI-3t-4 | |
| SPI-6 | SPI-6t-1, SPI-6t-2, SPI-6t-6, SPI-6t-7 | |
| SPI-9 | SPI-9t-1, SPI-9t-2, SPI-9t-6, SPI-9t-7, SPI-9t-9, SPI-9t-10 | |
| SPI-12 | SPI-12t-1, SPI-12t-2, SPI-12t-3, SPI-12t-6 | |
| SPI-24 | SPI-24t-1, SPI-24t-2, SPI-24t-6, SPI-24t-7 |
| Station | Index | Model Structure | Testing Period | |||
|---|---|---|---|---|---|---|
| RMSE | NSE | COC | WI | |||
| Chamoli | SPI-1 | Gauss-2 | 0.818 | 0.308 | 0.658 | 0.564 |
| SPI-3 | Gauss-2 | 0.467 | 0.820 | 0.966 | 0.931 | |
| SPI-6 | Gauss-2 | 0.242 | 0.956 | 0.988 | 0.987 | |
| SPI-9 | Gauss-2 | 0.213 | 0.965 | 0.988 | 0.990 | |
| SPI-12 | Gauss-2 | 0.158 | 0.980 | 0.994 | 0.995 | |
| SPI-24 | Gauss-2 | 0.209 | 0.959 | 0.981 | 0.989 | |
| Dehradun | SPI-1 | Gauss-2 | 0.877 | 0.192 | 0.668 | 0.399 |
| SPI-3 | Gauss-2 | 0.421 | 0.807 | 0.937 | 0.932 | |
| SPI-6 | Gauss-2 | 0.226 | 0.933 | 0.991 | 0.980 | |
| SPI-9 | Gauss-2 | 0.225 | 0.924 | 0.979 | 0.977 | |
| SPI-12 | Gauss-2 | 0.117 | 0.977 | 0.995 | 0.994 | |
| SPI-24 | Gauss-2 | 0.192 | 0.898 | 0.953 | 0.971 | |
| Haridwar | SPI-1 | Gauss-3 | 0.842 | 0.140 | 0.578 | 0.307 |
| SPI-3 | Gauss-2 | 0.441 | 0.809 | 0.934 | 0.931 | |
| SPI-6 | Gauss-2 | 0.251 | 0.940 | 0.994 | 0.981 | |
| SPI-9 | Gauss-2 | 0.240 | 0.943 | 0.980 | 0.983 | |
| SPI-12 | Gauss-2 | 0.301 | 0.909 | 0.962 | 0.937 | |
| SPI-24 | Gauss-2 | 0.286 | 0.909 | 0.962 | 0.937 | |
| Pauri Garhwal | SPI-1 | Gauss-2 | 0.890 | 0.273 | 0.707 | 0.500 |
| SPI-3 | Gauss-2 | 0.477 | 0.836 | 0.964 | 0.939 | |
| SPI-6 | Gauss-2 | 0.261 | 0.957 | 0.996 | 0.987 | |
| SPI-9 | Gauss-2 | 0.418 | 0.898 | 0.974 | 0.967 | |
| SPI-12 | Gauss-2 | 0.275 | 0.956 | 0.993 | 0.987 | |
| SPI-24 | Gauss-2 | 0.512 | 0.857 | 0.977 | 0.951 | |
| Rudraprayag | SPI-1 | Gauss-2 | 0.854 | 0.285 | 0.793 | 0.533 |
| SPI-3 | Gauss-2 | 0.421 | 0.840 | 0.971 | 0.943 | |
| SPI-6 | Gauss-2 | 0.183 | 0.969 | 0.993 | 0.991 | |
| SPI-9 | Gauss-2 | 0.266 | 0.933 | 0.977 | 0.981 | |
| SPI-12 | Gauss-2 | 0.089 | 0.992 | 0.997 | 0.998 | |
| SPI-24 | Gauss-2 | 0.231 | 0.944 | 0.976 | 0.984 | |
| Tehri Garhwal | SPI-1 | Gauss-2 | 0.895 | 0.267 | 0.898 | 0.573 |
| SPI-3 | Gauss-2 | 0.545 | 0.756 | 0.904 | 0.912 | |
| SPI-6 | Gauss-2 | 0.227 | 0.953 | 0.992 | 0.986 | |
| SPI-9 | Gauss-2 | 0.235 | 0.930 | 0.971 | 0.980 | |
| SPI-12 | Gauss-2 | 0.177 | 0.965 | 0.991 | 0.990 | |
| SPI-24 | Gauss-2 | 0.229 | 0.940 | 0.985 | 0.982 | |
| Uttarkashi | SPI-1 | Gauss-2 | 0.869 | 0.264 | 0.646 | 0.563 |
| SPI-3 | Gauss-2 | 0.380 | 0.857 | 0.968 | 0.953 | |
| SPI-6 | Gauss-2 | 0.372 | 0.864 | 0.962 | 0.956 | |
| SPI-9 | Gauss-2 | 0.344 | 0.868 | 0.966 | 0.957 | |
| SPI-12 | Gauss-2 | 0.400 | 0.812 | 0.951 | 0.936 | |
| SPI-24 | Gauss-2 | 0.504 | 0.695 | 0.951 | 0.884 | |
| Station | Index | Model Structure | Testing Period | |||
|---|---|---|---|---|---|---|
| RMSE | NSE | COC | WI | |||
| Chamoli | SPI-1 | 5-11-1 | 0.826 | 0.294 | 0.626 | 0.553 |
| SPI-3 | 8-13-1 | 0.474 | 0.815 | 0.916 | 0.938 | |
| SPI-6 | 6-13-1 | 0.252 | 0.951 | 0.982 | 0.986 | |
| SPI-9 | 6-13-1 | 0.233 | 0.958 | 0.983 | 0.988 | |
| SPI-12 | 5-11-1 | 0.181 | 0.974 | 0.991 | 0.993 | |
| SPI-24 | 6-13-1 | 0.178 | 0.970 | 0.987 | 0.992 | |
| Dehradun | SPI-1 | 4-6-1 | 0.861 | 0.222 | 0.700 | 0.429 |
| SPI-3 | 6-12-2 | 0.446 | 0.783 | 0.913 | 0.924 | |
| SPI-6 | 6-13-1 | 0.270 | 0.905 | 0.978 | 0.970 | |
| SPI-9 | 6-12-1 | 0.277 | 0.885 | 0.960 | 0.965 | |
| SPI-12 | 4-8-1 | 0.145 | 0.964 | 0.988 | 0.990 | |
| SPI-24 | 8-9-1 | 0.140 | 0.946 | 0.978 | 0.985 | |
| Haridwar | SPI-1 | 2-5-1 | 0.856 | 0.112 | 0.472 | 0.298 |
| SPI-3 | 6-12-1 | 0.468 | 0.785 | 0.911 | 0.923 | |
| SPI-6 | 7-17-1 | 0.253 | 0.940 | 0.986 | 0.981 | |
| SPI-9 | 7-17-1 | 0.275 | 0.925 | 0.967 | 0.979 | |
| SPI-12 | 9-19-1 | 0.177 | 0.969 | 0.986 | 0.992 | |
| SPI-24 | 8-9-1 | 0.265 | 0.922 | 0.965 | 0.978 | |
| Pauri Garhwal | SPI-1 | 5-7-1 | 0.904 | 0.250 | 0.639 | 0.483 |
| SPI-3 | 6-9-1 | 0.558 | 0.774 | 0.927 | 0.913 | |
| SPI-6 | 6-11-1 | 0.377 | 0.911 | 0.986 | 0.970 | |
| SPI-9 | 4-9-1 | 0.422 | 0.896 | 0.971 | 0.966 | |
| SPI-12 | 4-6-1 | 0.225 | 0.970 | 0.994 | 0.991 | |
| SPI-24 | 7-15-1 | 0.447 | 0.891 | 0.980 | 0.964 | |
| Rudraprayag | SPI-1 | 5-9-1 | 0.885 | 0.232 | 0.625 | 0.504 |
| SPI-3 | 7-10-1 | 0.490 | 0.784 | 0.912 | 0.926 | |
| SPI-6 | 5-10-1 | 0.226 | 0.953 | 0.987 | 0.986 | |
| SPI-9 | 8-16-1 | 0.201 | 0.962 | 0.984 | 0.990 | |
| SPI-12 | 4-7-1 | 0.082 | 0.994 | 0.997 | 0.998 | |
| SPI-24 | 7-10-1 | 0.169 | 0.970 | 0.987 | 0.992 | |
| Tehri Garhwal | SPI-1 | 2-4-1 | 0.906 | 0.250 | 0.876 | 0.482 |
| SPI-3 | 5-9-1 | 0.552 | 0.750 | 0.902 | 0.910 | |
| SPI-6 | 5-7-1 | 0.281 | 0.928 | 0.985 | 0.978 | |
| SPI-9 | 4-7-1 | 0.275 | 0.917 | 0.961 | 0.976 | |
| SPI-12 | 4-8-1 | 0.208 | 0.952 | 0.984 | 0.986 | |
| SPI-24 | 3-5-1 | 0.225 | 0.942 | 0.985 | 0.983 | |
| Uttarkashi | SPI-1 | 5-11-1 | 0.782 | 0.389 | 0.797 | 0.690 |
| SPI-3 | 4-9-1 | 0.462 | 0.789 | 0.939 | 0.925 | |
| SPI-6 | 4-7-1 | 0.356 | 0.875 | 0.964 | 0.960 | |
| SPI-9 | 6-13-1 | 0.482 | 0.741 | 0.919 | 0.909 | |
| SPI-12 | 4-7-1 | 0.346 | 0.859 | 0.960 | 0.954 | |
| SPI-24 | 4-7-1 | 0.515 | 0.682 | 0943 | 0.879 | |
| Station | Index | Testing Period | |||
|---|---|---|---|---|---|
| RMSE | NSE | COC | WI | ||
| Chamoli | SPI-1 | 0.934 | 0.096 | 0.313 | 0.387 |
| SPI-3 | 0.715 | 0.578 | 0.761 | 0.856 | |
| SPI-6 | 0.544 | 0.778 | 0.882 | 0.935 | |
| SPI-9 | 0.422 | 0.866 | 0.929 | 0.963 | |
| SPI-12 | 0.298 | 0.931 | 0.965 | 0.982 | |
| SPI-24 | 0.344 | 0.889 | 0.943 | 0.970 | |
| Dehradun | SPI-1 | 0.972 | 0.008 | 0.156 | 0.261 |
| SPI-3 | 0.720 | 0.434 | 0.675 | 0.791 | |
| SPI-6 | 0.535 | 0.625 | 0.806 | 0.884 | |
| SPI-9 | 0.428 | 0.725 | 0.865 | 0.920 | |
| SPI-12 | 0.302 | 0.845 | 0.928 | 0.959 | |
| SPI-24 | 0.294 | 0.762 | 0.881 | 0.932 | |
| Haridwar | SPI-1 | 0.903 | 0.012 | 0.131 | 0.188 |
| SPI-3 | 0.732 | 0.473 | 0.688 | 0.799 | |
| SPI-6 | 0.633 | 0.621 | 0.791 | 0.882 | |
| SPI-9 | 0.492 | 0.761 | 0.873 | 0.931 | |
| SPI-12 | 0.390 | 0.847 | 0.921 | 0.958 | |
| SPI-24 | 0.463 | 0.761 | 0.873 | 0.930 | |
| Pauri Garhwal | SPI-1 | 0.999 | 0.086 | 0.336 | 0.320 |
| SPI-3 | 0.770 | 0.571 | 0.762 | 0.836 | |
| SPI-6 | 0.603 | 0.772 | 0.879 | 0.932 | |
| SPI-9 | 0.515 | 0.845 | 0.919 | 0.956 | |
| SPI-12 | 0.319 | 0.940 | 0.970 | 0.984 | |
| SPI-24 | 0.395 | 0.915 | 0.956 | 0.977 | |
| Rudraprayag | SPI-1 | 0.987 | 0.045 | 0.288 | 0.321 |
| SPI-3 | 0.741 | 0.505 | 0.720 | 0.821 | |
| SPI-6 | 0.539 | 0.374 | 0.863 | 0.920 | |
| SPI-9 | 0.403 | 0.846 | 0.923 | 0.957 | |
| SPI-12 | 0.275 | 0.926 | 0.964 | 0.980 | |
| SPI-24 | 0.322 | 0.891 | 0.946 | 0.971 | |
| Tehri Garhwal | SPI-1 | 1.052 | -0.011 | 0.195 | 0.279 |
| SPI-3 | 0.771 | 0.512 | 0.725 | 0.818 | |
| SPI-6 | 0.558 | 0.719 | 0.852 | 0.916 | |
| SPI-9 | 0.416 | 0.811 | 0.902 | 0.947 | |
| SPI-12 | 0.335 | 0.876 | 0.938 | 0.966 | |
| SPI-24 | 0.238 | 0.935 | 0.968 | 0.983 | |
| Uttarkashi | SPI-1 | 0.965 | 0.069 | 0.343 | 0.433 |
| SPI-3 | 0.649 | 0.584 | 0.784 | 0.859 | |
| SPI-6 | 0.436 | 0.814 | 0.907 | 0.947 | |
| SPI-9 | 0.338 | 0.873 | 0.938 | 0.965 | |
| SPI-12 | 0.251 | 0.926 | 0.965 | 0.980 | |
| SPI-24 | 0.143 | 0.975 | 0.988 | 0.994 | |
| Station | Index | |||||
|---|---|---|---|---|---|---|
| SPI-1 | SPI-3 | SPI-6 | SPI-9 | SPI-12 | SPI-24 | |
| Chamoli | CANFIS | CANFIS | CANFIS | CANFIS | CANFIS | MLPNN |
| Dehradun | MLPNN | CANFIS | CANFIS | CANFIS | CANFIS | MLPNN |
| Haridwar | CANFIS | CANFIS | CANFIS | CANFIS | MLPNN | MLPNN |
| Pauri Garhwal | CANFIS | CANFIS | CANFIS | CANFIS | MLPNN | MLR |
| Rudraprayag | CANFIS | CANFIS | CANFIS | MLPNN | MLPNN | MLPNN |
| Tehri Garhwal | CANFIS | CANFIS | CANFIS | CANFIS | CANFIS | MLPNN |
| Uttarkashi | MLPNN | CANFIS | MLPNN | MLR | MLR | MLR |
Author Contributions
Conceptualization, A.M. and A.K. (Anil Kumar); methodology, A.M.; software, A.M.; validation, A.M., A.K. (Anil Kumar), and A.K. (Alban Kuriqi); formal analysis, A.M.; investigation, A.M., A.K. (Anil Kumar), P.R., and A.K. (Alban Kuriqi); writing-Original draft preparation, A.M., A.K. (Anil Kumar), P.R., and A.K. (Alban Kuriqi); writing-Review and editing, A.M., A.K. (Anil Kumar), P.R., and A.K. (Alban Kuriqi); visualization, A.M., A.K. (Anil Kumar), P.R., and A.K. (Alban Kuriqi); supervision, A.K. (Anil Kumar) and A.K. (Alban Kuriqi); project administration, A.K. (Alban Kuriqi); funding acquisition, A.K. (Alban Kuriqi). All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Acknowledgments
The authors would like to thank the Indian Meteorological Department, Pune, and Directorate of Research, G.B. Pant University of Agriculture and Technology, Pantnagar, for providing the monthly rainfall time series data of Uttarakhand State for this study. The authors would also like to thank the anonymous reviewers for their valuable comments and suggestions to further improve this manuscript. Alban Kuriqi was supported by a Ph.D. scholarship granted by Fundação para a Ciência e a Tecnologia, I.P.P (FCT), Portugal, the Ph.D. Program FLUVIO-River Restoration and Management, grant number: PD/BD/114558/2016.
Conflicts of Interest
The authors declare no conflict of interest.
1. Dracup, J.A.; Lee, K.S.; Paulson, E.G. On the statistical characteristics of drought events. Water Resour. Res. 1980, 16, 289-296.
2. Wilhite, D.A.; Glantz, M.H. Understanding the drought phenomenon: The role of definitions. Water Int. 1985, 10, 111-120.
3. Mishra, A.K.; Singh, V.P. Analysis of drought severity-area-frequency curves using a general circulation model and scenario uncertainty. J. Geophys. Res. 2009, 114, D06120.
4. Mishra, A.K.; Singh, V.P. A review of drought concepts. J. Hydrol. 2010, 391, 202-216.
5. Mishra, A.K.; Singh, V.P. Drought modeling-A review. J. Hydrol. 2011, 403, 157-175.
6. McKee, T.B.; Doesken, N.J.; Kleist, J. The relationship of drought frequency and duration to time scales. In Proceedings of the Eighth Conference on Applied Climatology, Anaheim, CA, USA, 17-22 January 1993.
7. Mishra, A.K.; Desai, V.R. Drought forecasting using feed-forward recursive neural network. Ecol. Modell. 2006, 198, 127-138.
8. Morid, S.; Smakhtin, V.; Bagherzadeh, K. Drought forecasting using artificial neural networks and time series of drought indices. Int. J. Climatol. 2007, 27, 2103-2111.
9. Bacanli, U.G.; Firat, M.; Dikbas, F. Adaptive Neuro-Fuzzy Inference System for drought forecasting. Stoch. Environ. Res. Risk Assess. 2009, 23, 1143-1154.
10. Belayneh, A.; Adamowski, J. Standard Precipitation Index Drought Forecasting Using Neural Networks, Wavelet Neural Networks, and Support Vector Regression. Appl. Comput. Intell. Soft Comput. 2012, 2012, 1-13.
11. Özger, M.; Mishra, A.K.; Singh, V.P. Long Lead Time Drought Forecasting Using a Wavelet and Fuzzy Logic Combination Model: A Case Study in Texas. J. Hydrometeorol. 2012, 13, 284-297.
12. Deo, R.C.; Şahin, M. Application of the Artificial Neural Network model for prediction of monthly Standardized Precipitation and Evapotranspiration Index using hydrometeorological parameters and climate indices in eastern Australia. Atmos. Res. 2015, 161-162, 65-81.
13. Nguyen, L.B.; Li, Q.F.; Ngoc, T.A.; Hiramatsu, K. Adaptive Neuro-Fuzzy Inference System for drought forecasting in the Cai River basin in Vietnam. J. Fac. Agric. Kyushu Univ. 2015, 60, 405-415.
14. Djerbouai, S.; Souag-Gamane, D. Drought Forecasting Using Neural Networks, Wavelet Neural Networks, and Stochastic Models: Case of the Algerois Basin in North Algeria. Water Resour. Manag. 2016, 30, 2445-2464.
15. Deo, R.C.; Tiwari, M.K.; Adamowski, J.F.; Quilty, J.M. Forecasting effective drought index using a wavelet extreme learning machine (W-ELM) model. Stoch. Environ. Res. Risk Assess. 2017, 31, 1211-1240.
16. Komasi, M.; Sharghi, S.; Safavi, H.R. Wavelet and cuckoo search-support vector machine conjugation for drought forecasting using Standardized Precipitation Index (case study: Urmia Lake, Iran). J. Hydroinf. 2018, 20, 975-988.
17. Abbasi, A.; Khalili, K.; Behmanesh, J.; Shirzad, A. Drought monitoring and prediction using SPEI index and gene expression programming model in the west of Urmia Lake. Theor. Appl. Climatol. 2019, 138, 553-567.
18. Memarian, H.; Pourreza Bilondi, M.; Rezaei, M. Drought prediction using co-active neuro-fuzzy inference system, validation, and uncertainty analysis (case study: Birjand, Iran). Theor. Appl. Climatol. 2016, 125, 541-554.
19. Rafiei-Sardooi, E.; Mohseni-Saravi, M.; Barkhori, S.; Azareh, A.; Choubin, B.; Jafari-Shalamzar, M. Drought modeling: A comparative study between time series and neuro-fuzzy approaches. Arab. J. Geosci. 2018, 11, 1-9.
20. Malik, A.; Kumar, A.; Salih, S.Q.; Kim, S.; Kim, N.W.; Yaseen, Z.M.; Singh, V.P. Drought index prediction using advanced fuzzy logic model: Regional case study over Kumaon in India. PLoS ONE 2020, 15, e0233280.
21. Guttman, N.B. Comparing the palmer drought index and the standardized precipitation index. J. Am. Water Resour. Assoc. 1998, 34, 113-121.
22. Hayes, M.J.; Svoboda, M.D.; Wilhite, D.A.; Vanyarkho, O.V. Monitoring the 1996 Drought Using the Standardized Precipitation Index. Bull. Am. Meteorol. Soc. 1999, 80, 429-438.
23. Angelidis, P.; Maris, F.; Kotsovinos, N.; Hrissanthou, V. Computation of Drought Index SPI with Alternative Distribution Functions. Water Resour. Manag. 2012, 26, 2453-2473.
24. Yacoub, E.; Tayfur, G. Evaluation and Assessment of Meteorological Drought by Different Methods in Trarza Region, Mauritania. Water Resour. Manag. 2017, 31, 825-845.
25. Lloyd-Hughes, B.; Saunders, M.A. A drought climatology for Europe. Int. J. Climatol. 2002, 22, 1571-1592.
26. Mishra, A.K.; Desai, V.R. Spatial and temporal drought analysis in the Kansabati river basin, India. Int. J. River Basin Manag. 2005, 3, 31-41.
27. Abramowitz, M.; Stegun, A. Handbook of Mathematical Formulas, Graphs, and Mathematical Tables; Dover Publishing: New York, NY, USA, 1965; p. 470.
28. Edwards, D.C.; McKee, T.B. Characteristics of 20th Century drought in the United States at multiple time scales. Atmos. Sci. Pap. 1997.
29. Jang, J.-S.R.; Sun, C.-T.; Mizutani, E. Neuro-Fuzzy and Soft Computing A Computational Approach to Learning and Machine Intelligence; Prentice Hall: Upper Saddle River, NJ, USA, 1997; ISBN 0132610663.
30. Malik, A.; Kumar, A. Pan Evaporation Simulation Based on Daily Meteorological Data Using Soft Computing Techniques and Multiple Linear Regression. Water Resour. Manag. 2015, 29, 1859-1872.
31. Malik, A.; Kumar, A. Meteorological drought prediction using heuristic approaches based on effective drought index: A case study in Uttarakhand. Arab. J. Geosci. 2020, 13, 1-17.
32. Malik, A.; Kumar, A.; Piri, J. Daily suspended sediment concentration simulation using hydrological data of Pranhita River Basin, India. Comput. Electron. Agric. 2017, 138, 20-28.
33. Malik, A.; Kumar, A.; Kisi, O. Monthly pan-evaporation estimation in Indian central Himalayas using different heuristic approaches and climate based models. Comput. Electron. Agric. 2017, 143, 302-313.
34. Singh, A.; Malik, A.; Kumar, A.; Kisi, O. Rainfall-runoff modeling in hilly watershed using heuristic approaches with gamma test. Arab. J. Geosci. 2018, 11, 1-12.
35. Sugeno, M.; Kang, G. Structure identification of fuzzy model. Fuzzy Sets Syst. 1988, 28, 15-33.
36. Takagi, T.; Sugeno, M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man. Cybern. 1985, SMC-15, 116-132.
37. Aytek, A. Co-active neurofuzzy inference system for evapotranspiration modeling. Soft Comput. 2009, 13, 691-700.
38. Tabari, H.; Talaee, P.H.; Abghari, H. Utility of coactive neuro-fuzzy inference system for pan evaporation modeling in comparison with multilayer perceptron. Meteorol. Atmos. Phys. 2012, 116, 147-154.
39. Haykin, S. Neural Networks-A Comprehensive Foundation, 2nd ed.; Prentice-Hall International, Inc.: Upper Saddle River, NJ, USA, 1999; pp. 26-32.
40. Dawson, C.W.; Wilby, R.L. Hydrological modelling using artificial neural networks. Prog. Phys. Geogr. Earth Environ. 2001, 25, 80-108.
41. Landeras, G.; Ortiz-Barredo, A.; López, J.J. Forecasting Weekly Evapotranspiration with ARIMA and Artificial Neural Network Models. J. Irrig. Drain. Eng. 2009, 135, 323-334.
42. Deo, R.C.; Kisi, O.; Singh, V.P. Drought forecasting in eastern Australia using multivariate adaptive regression spline, least square support vector machine and M5Tree model. Atmos. Res. 2017, 184, 149-175.
43. Douglas, E.M.; Vogel, R.M.; Kroll, C.N. Trends in floods and low flows in the United States: Impact of spatial correlation. J. Hydrol. 2000, 240, 90-105.
44. Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I-A discussion of principles. J. Hydrol. 1970, 10, 282-290.
45. Moriasi, D.N.; Gitau, M.W.; Pai, N.; Daggupati, P. Hydrologic and Water Quality Models: Performance Measures and Evaluation Criteria. Trans. ASABE 2015, 58, 1763-1785.
46. Willmott, C.J. On the validation of models. Phys. Geogr. 1981, 2, 184-194.
47. Taylor, K.E. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos. 2001, 106, 7183-7192.
48. Mokhtarzad, M.; Eskandari, F.; Jamshidi Vanjani, N.; Arabasadi, A. Drought forecasting by ANN, ANFIS, and SVM and comparison of the models. Environ. Earth Sci. 2017, 76, 729.
49. Nguyen, V.; Li, Q.; Nguyen, L. Drought forecasting using ANFIS- a case study in drought prone area of Vietnam. Paddy Water Environ. 2017, 15, 605-616.
50. Zhang, Y.; Li, W.; Chen, Q.; Pu, X.; Xiang, L. Multi-models for SPI drought forecasting in the north of Haihe River Basin, China. Stoch. Environ. Res. Risk Assess. 2017, 31, 2471-2481.
51. Liu, Z.; Li, Q.; Nguyen, L.; Xu, G. Comparing Machine-Learning Models for Drought Forecasting in Vietnam's Cai River Basin. Pol. J. Environ. Stud. 2018, 27, 2633-2646.
52. Mouatadid, S.; Raj, N.; Deo, R.C.; Adamowski, J.F. Input selection and data-driven model performance optimization to predict the Standardized Precipitation and Evaporation Index in a drought-prone region. Atmos. Res. 2018, 212, 130-149.
53. Özger, M.; Başakın, E.E.; Ekmekcioğlu, Ö.; Hacısüleyman, V. Comparison of wavelet and empirical mode decomposition hybrid models in drought prediction. Comput. Electron. Agric. 2020, 179, 105851.
Anurag Malik
1,2,*,
Anil Kumar
1,
Priya Rai
1 and
Alban Kuriqi
3
1Department of Soil and Water Conservation Engineering, College of Technology, G.B. Pant University of Agriculture & Technology, Pantnagar 263145, Uttarakhand, India
2Regional Research Station, Bathinda, Punjab Agricultural University, Punjab 151001, India
3CERIS, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
*Author to whom correspondence should be addressed.
© 2021. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.