Assessing Meteorological Drought Patterns and Forecasting Accuracy with SPI and SPEI Using Machine Learning Models

Abstract

The rising frequency and severity of droughts requires accurate monitoring and forecasting to reduce the impact on water resources and communities. This study aims to investigate drought monitoring and categorization, while enhancing drought forecasting by using three machine learning models—Artificial Neural Network (ANN), Support Vector Machine (SVM), and Random Forest (RF). The models were trained on the study region’s historic precipitation and temperature data (minimum and maximum) from 1960 to 2021. The Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI) were computed for a time scale of 3, 6 and 12 months. The monthly precipitation data were used for creating lag scenarios and were used as input features for the models to improve the models’ performance and reduce overfitting. Statistical parameters like the coefficient of determination (R²), Mean Absolute Error (MAE), Root mean square error (RMSE) and Nash–Sutcliffe Efficiency (NSE) were determined to evaluate the model accuracy. For forecasting, the SPEI3, ANN and SVM models show better performance (R² > 0.9) than the RF models when the 3-month lag data were used as input features. For SPEI6 and SPEI12, the 6-month lag and 12-month lag data, respectively, were needed to increase the models’ accuracy. The models exhibited RMSE values of 0.27 for ANN, 0.28 for SVM, and 0.37 for RF for the SPEI3, indicating the superior performance of the former two. The models’ accuracy increases as the lag period increases for SPI forecasting. Overall, the ANN and SVM models outperformed the RF model for forecasting long-term drought.

1. Introduction

A drought event is an extended duration of inadequate rainfall that results in a water shortage that can majorly affect ecosystems, agriculture, water supplies, and many facets of human life. It is a natural occurrence that happens when there is an imbalance between the demand and supply of water [1]. Drought has an impact on day-to-day living because of diminished water supplies and limitations on water usage [2]. Drought prediction is crucial considering the rising global economic losses from natural disasters. Between 1980 and 2019, drought has caused a loss of USD 249.7 billion with an average loss of more than USD 9.6 billion per event [3]. Drought also indirectly affects human health, as it increases the risk of wildfire, dust, and vector-borne disease [4].

Primarily, there are four types of droughts: meteorological (related to below average rainfall), agricultural (reduction in crop production due to low precipitation events), hydrological (reduction in water storage in rivers and reservoirs), and socio-economic (disparity between supply and demand for a service or product as a result of low water supplies due to climatic conditions) [5]. These different types of droughts are interrelated and can cause impacts on each other. Therefore, effective drought management techniques should involve monitoring and addressing all aspects of droughts to decrease their effects on society, economics, and the ecosystem [6]. This highlights the urgent need for accurate drought prediction to tackle the growing economic impacts of drought. The effects of these droughts can be quantified using drought indices. Drought indices are an essential tool for tracking drought and analyzing its quantitative impact. Drought indices such as the Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), Streamflow Drought index (SDI), Palmer Drought Severity Index (PSDI) and Crop Moisture Index (CMI) are commonly used to monitor and evaluate drought. As a drought index is standardized, it becomes independent of the location because it is determined based on the average precipitation in that same area [7]. Drought indices like the SPI and SPEI are becoming increasingly popular as the SPI accounts for precipitation and the SPEI takes into consideration both rainfall and temperature variability and both of these indices are not constrained by geography [8]. These indices can be determined for various temporal scales. The SPEI is preferred when both precipitation and temperature are crucial for water availability, such as in arid or semi-arid regions where higher temperatures can significantly impact the water balance. On the other hand, the SPI is used when precipitation is the main driving factor and temperature fluctuation is not significant [9].

Drought predictions can be achieved through the utilization of physical models or data-driven models. Hydrological models provide detailed insights into the processes within a catchment, offering a deep understanding of hydrological dynamics [10]. However, these models have faced criticism for their complexity, demanding various types of data, which makes them challenging to adopt for practical forecasting [11]. In response, simpler data-driven models have gained traction as more accessible and efficient alternatives for accurate drought predictions [12]. As technology has advanced, the implementation of machine learning (ML) has become increasingly common in hydrology, allowing for the prediction of complex phenomena such as droughts [13,14,15]. ML tools have proven to be effective in saving time and delivering precise results [16].

Recently, different ML models such as the ANN [17,18], SVM [19,20] Extreme Learning Machine (ELM) [21,22], Genetic Programming (GP) [23,24] and RF [25,26] have been used for forecasting drought indices. Moreover, the majority of the existing research focuses on single indices or a single set of ML models, often neglecting the comparative advantages that a multi-model framework can provide, particularly when applied at local scales with varying climatic conditions [27,28,29]. This study aims to fill this gap by evaluating three widely used ML models (ANN, SVM, and RF) to predict both the SPI and SPEI at multiple temporal scales (3, 6, and 12 months), offering a systematic comparison that highlights each model’s suitability for local drought conditions. For the current study, ANN, SVM and RF models are used as these machine learning models are widely adapted for drought prediction [27]. The ANN model captures complex non-linear patterns but requires extensive data and is prone to overfitting. The SVM model works well with smaller datasets using kernels for non-linearity but struggles with extensive data. The RF model is robust against overfitting, handles small and large datasets well, and is faster and more interpretable [30,31]. By applying these models to both the SPI and SPEI across varying temporal scales, this research assesses their forecasting performance under the local climatic conditions of Sunday Creek, Ohio. The fundamental target of this research is to develop a model that predicts drought by comparing the performance of three machine learning models (ANN, SVM, and RF), which are used to forecast SPI and SPEI for various temporal scales (3, 6, and 12 months) at the local level of the study area. The main contribution of this study lies in its comprehensive approach, providing a multi-model evaluation that not only enhances understanding of model effectiveness across indices but also offers insights applicable to similar local-scale drought studies. The objective of this study is to recognize drought occurrences, their duration, and intensity based on data collected from 1960 to 2021. This study also aims to monitor drought and its categorization, develop an alternative model to predict SPI and SPEI using ANN, SVM, and RF, compare the accuracy and stability of these models, and choose the best model based on their prediction accuracy. This study hypothesized that machine learning models can be reliable and sufficiently accurate to predict drought indices. The results of this study help to validate and develop machine learning models for drought prediction at various time scales. The main contribution of this research is its comprehensive approach to drought prediction, integrating a well-structured methodology with advanced machine learning techniques. This approach has important implications for enhancing the precision and efficiency of drought monitoring systems.

2. Materials and Methods

2.1. Study Area

The study area is situated at Sunday Creek, Athens County, Ohio, USA. It covers an area of 248.32 km² and is geographically extended from a latitude of 39°29′ to 39°40′ and a longitude of −82°12′ to −81°58′. The study basin has the longest flow path of 34.4 km in length and receives an average of 40.4 inches of annual precipitation. Additionally, it has an average low temperature of 4.87 degrees Celsius and an average high temperature of 17.4 degrees Celsius. The elevation range of the study area is 190 m to 255 m. The monthly evapotranspiration and wind speed are 3.64 inches and 2.919 m/s, respectively. The study region comprises 84.7% of the basin area with forest, 7.45% with urban land, and 1.46% with water bodies. Figure 1 illustrates the different land cover classes of the Sunday Creek basin.

2.2. The Study Approach

This research adopted a structured approach utilizing machine learning techniques to assess and effectively predict drought conditions. This study focuses on integrating meteorological data and computational algorithms to develop a reliable and accurate predictive model. The following flowchart in Figure 2 illustrates the sequential steps taken from the initial data collection to the final predictive outputs, employing various algorithms to enhance the accuracy of drought predictions. Each algorithm was used to develop separate predictive models for drought conditions, allowing for comparative analysis of their effectiveness and accuracy. This approach enabled the identification of the most reliable model among them.

2.3. Data Collection

Study area datasets such as boundary of Sunday Creek basin, rainfall data, and minimum and maximum temperature data, along with SPI and SPEI calculated from R-studio were used as input parameters for the ML models. The data sets used in this study range from 1960 to 2021 AD. Sources of data used are listed in

Table 1. Data used and their sources.

Data	Sources
Precipitation	TerraClimate from Climate Engine “https://www.climateengine.org/ (accessed on 26 December 2023)”
Boundary Shapefile	Streamstats “https://streamstats.usgs.gov/ss/ (accessed on 14 December 2023)”
Minimum and Maximum temperature	TerraClimate from Climate Engine “https://www.climateengine.org/ (accessed on 26 December 2023)”

. Precipitation data were extracted from the Climate Engine website, and the Terra Climate dataset was used at a 4-km resolution on a monthly time scale. The same dataset with the same resolution was also used for acquiring temperature data.

2.4. Standardized Precipitation Index (SPI)

SPI is an aid to assess drought that was developed by McKee, Doesken, and Leist in 1993. It is widely used because of its simplicity and versatility. Unlike other indices, such as the Palmer Index and the Crop Moisture Index, the SPI focuses only on precipitation, which makes it easy to evaluate [7]. To calculate the SPI, a probability distribution is fitted to monthly precipitation data over distinct time scales, and then normalized to yield a standardized index [17]. The precipitation data, after undergoing transformation, are utilized for calculating dimensionless SPI values using the Equation (1) [32]. This index is used to assign values that delineate the drought category characterizing each location and time scale. SPI values can be categorized according to classes as extreme drought (≤−2.00), severe drought (−1.50 to −1.99), and moderate drought (−1.00 to −1.49) [33].

$$\mathrm{SPI}={\displaystyle \frac{p-p^{\mathrm{*}}}{{\sigma }_p}}$$

(1)

Here,

p = observed monthly precipitation,

p* = mean of monthly precipitation and

${\sigma }_p$ = standard deviation of observed precipitation.

2.5. Standardized Precipitation Evapotranspiration Index (SPEI)

SPEI is a drought index developed in 2010 by Vicente-Serrano, Beguería, and López-Moreno. It is a multi-scalar index that measures drought based on meteorological data [34]. The SPEI considers the imbalance between rainfall and potential evapotranspiration. Unlike the SPI, which only considers rainfall for drought tracking, the SPEI considers both rainfall and temperature [35]. This is why the SPEI has gained popularity among researchers in recent times. It is widely used to determine drought over different time scales of interest.

To determine the SPEI, monthly water balance (Di) is calculated from the imbalance between monthly precipitation (Pi) and monthly potential evapotranspiration (PETi). There are several formulas for the calculation of PET and for this study the formula from Hargreaves and Samani (1985) is employed [36]. Monthly water balance is then accumulated at the required time scales of interest as in the following Equations (2) and (3)

$${\mathrm{D}}_{\mathrm{i}}={\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}\mathrm{E}\mathrm{T}}_{\mathrm{i}}$$

(2)

$${\mathrm{D}}_n^{\mathrm{m}}={\sum }_{\mathrm{i}=0}^{\mathrm{m}-1}({\mathrm{P}}_{n-1}-{\mathrm{P}\mathrm{E}\mathrm{T}}_{n-\mathrm{i}}),n\ge \mathrm{m}$$

(3)

where m = 12 for SPEI-12 is the accumulation temporal interval and n is the calculation month of SPEI. A log-logistic probability distribution function with three parameters is represented by the following Equation (4).

$$f\left(x\right)={[1+{\left({\displaystyle \frac{\lambda }{x-\phi }}\right)}^{\varphi }]}^{-1}$$

(4)

Here, $\lambda$, $\varphi ,$ and $\phi$ are the scale, shape, and location domain, respectively.

Ultimately, using the approximation method from Milton Abramowitz and Irene A. Stegun [37], SPEI is evaluated by computing the standardized value of F(x).

$$SPEI=W-{\displaystyle \frac{c_o+c_{1}W+c_2{W}^2}{1+d_{1}W+d_2{W}^2+d_3{W}^3}}$$

(5)

Here, $W=\sqrt{-2\mathrm{l}\mathrm{n}\left(P\right)}$ for p ≤ 0.5 and P is the probability of exceedance of a certain threshold value Di. If p > 0.5, non-exceedance probability (1 − P) is used and sign of the SPEI is inverted. The following constants are used in the Equation: c_o = 2.515517, c₁ = 0.802853, c₂ = 0.010328, d₁ = 1.432788, d₂ = 0.189269, and d₃ = 0.001308. It can be evaluated in different temporal intervals of 1–48 months. It can also be categorized using different classes: extremely dry (<−2.00), severely dry (−1.5 to −1.99), moderately dry (−1.0 to −1.49), and mild drought (−0.99 to 0.99) [38].

2.6. Artificial Neural Network

An ANN is a machine learning algorithm that can adapt to changes based on internal or external information during the training phase. Neural networks are statistical modelling tools that are capable of modelling complex relationships between outputs and inputs or identifying patterns in data. They are non-linear and can be used in a variety of applications [39]. An ANN can model any relationship between inputs and output with enough data and complexity [40]. The ANN model does not require intermediary relationships between inputs and outputs to be fully declared [41]. In this research, a feedforward neural network is applied, which helps information travel unidirectionally from the initial input layer, traversing through one or multiple hidden layers, and reaching the final output layer. The neural network architecture defined in the code consists of an input layer, a hidden layer with an activation function, another hidden layer with another activation function, and an output layer for regression. A neuron calculates its output response by adding up the weighted inputs using an activation function. A simple graphical representation of feed-forward ANN architecture is demonstrated in Figure 3 [42].

In this study, 80% of data were allocated for training the model and 20% of the data in chronological order were reserved for testing of the model. For this study, the number of hidden layers, the number of neurons per layer, and the batch size were tested across a range of values. The final architecture consisted of two hidden layers with 64 and 32 neurons, respectively, and the batch size was set to 32. The learning rate for the Adam optimizer was set to its default value based on the best performance observed during validation. The sigmoid function was adopted as simulation metric as it serves as a non-linear function for feed-forward neural networks. It is continuous function that exists for actual or true input values and has favorable derivatives across its entire range with a specified degree of smoothness. It is commonly used in the output layer of deep learning models and plays a crucial role in predicting outputs based on probabilities [43]. Its mathematical representation is presented in Equation (6).

$$f\left(x\right)=\left({\displaystyle \frac{1}{1+{exp}^{-x}}}\right)$$

(6)

2.7. Support Vector Machine

SVM is an algorithmic learning model introduced by Boser, Guyon, and Vapnik [44]. SVM models are typically divided into two categories: classification and regression models. The classification model is used when the data are categorized into distinct categories, while the regression model is used for predictive analysis. In regression analysis, a hyperplane is established through regression on fitted data [45]. The distance of a specific point from the hyperplane represents the error of that point. While the least-squares method is frequently adopted for linear regression, it may not be effective if there are outliers, which can lead to suboptimal performance. To address this issue, it is important to develop a resilient estimator that is less responsive to minor changes in the algorithm and ensures better performance. The Radial Basis Function (RBF) kernel was utilized as it can model non-linear interrelationships between inputs and outputs. The RBF kernel is a popular and versatile kernel type that closely resembles the Gaussian distribution. For this study, the penalty parameter C and the RBF kernel coefficient γ were optimized using grid search. The values tested for C ranged from 0.1 to 100, and for γ from 0.01 to 1. The best model was selected based on the highest R² score during the validation phase. It measures the similarity between two points, x₁ and x₂, to indicate how closely they are related [46]. The RBF kernel function can be presented numerically as seen in Equation (7).

$$K\left(x_1,x_2\right)=\mathit{exp}\left(-{\displaystyle \frac{{\left|\left|x_1-x_2\right|\right|}^2}{2{\sigma }^2}}\right)$$

(7)

Here,

‘σ’ represent the variance and hyperparameter and ||x₁ − x₂|| represents the distance between x₁ and x₂ in Euclidean space. SVM can also detect the data patterns and transform the original data from input space to new space using kernel function. Figure 4 demonstrates the basic architecture of SVM model [47].

2.8. Random Forest

The RF model was introduced by Leo Breiman and Adele Cutler [48], and it relies on collection of decision trees to effectively manage variance. The utilization of this model extends to both regression and classification tasks. RF regression is a unique form of resampling aggregate, which involves constructing probabilistic binary trees using subsets of observations obtained through bootstrapping. Bootstrapping is the process of randomly sampling a portion of the training data from the original dataset, which contributes to the development of the model [31]. Random forest models are a type of additive model that utilizes a combination of base models to produce predictions. Mathematically, this class of models is expressed as the sum of individual base models, where each base model is a simple decision tree. The final model is the sum of all the base models as shown in Equation (8). This approach, known as model ensembling, improves predictive performance.

g(x) = f0(x) + f1(x) + f2(x) + …

(8)

In RF algorithm, all the base models are designed by applying unique subsamples of the data. Figure 5 demonstrates the structure of a random forest model [49]. In this study, the number of trees (n_estimators) was set to 100. The maximum depth of the trees and the minimum samples required for splitting were optimized using cross-validation. The grid search tested values for the maximum depth from 10 to 50, and for the minimum samples per split from 2 to 10. It shows different trees that run in parallel to each other without interaction between them. It functions by building numerous decision trees during training period and generating outputs as the means of the classes of all the forecasting from all trees.

2.9. Evaluation Parameters of the Models

This study adopts various measures to assess the precision of the model. These measures comprised the coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe Efficiency (NSE) [50]. The R² value ranges from 0 to 1, and a higher value represents less variance in error. An R² and NSE values greater than 0.5 is usually deemed satisfactory [51]. Furthermore, the RMSE and MAE values indicate errors, where a smaller value is indicative of fewer errors in modelling [52].

3. Results and Discussion

This section provides the research findings, focusing on four main aspects. Firstly, it reveals the drought conditions of the creek from 1960 to 2021. Secondly, it shows the correlation between both drought indices. Thirdly, it provides the results of the drought categorization based on the SPI and SPEI. Finally, it evaluates the performance of the drought prediction models using ANN, SVM, and RF. The aim is to identify the most reliable model for forecasting drought in the study region.

3.1. Drought Condition Monitoring

Both drought indices (SPI and SPEI) were calculated for 3-, 6-, and 12-month time scales using precipitation and temperature data from 1960 to 2021. Figure 6 shows the variability of the SPI and SPEI during this period across the various time scales. While the indices exhibit similar patterns, there are notable differences in the severity and characteristics of the drought conditions across the different time scales. The SPI and SPEI show monthly variations that reflect changes in dry and wet conditions in the study area, with blue representing wetter periods and red indicating drier season.

At the 3-month time scale (Figure 6a,d), the indices are sensitive to short-term precipitation anomalies, reflecting immediate impacts on crop production. These short-term fluctuations show a higher variability and highlight periods of intense but brief drought conditions. The severity of these short-term droughts can be more pronounced due to the immediate response to sudden changes in rainfall, such as during the early 1970s and 1990s, which had significant agricultural impacts [53,54].

On the 6-month time scale (Figure 6b,e), the indices capture medium-term trends, which integrate precipitation and temperature anomalies over a longer period. This time scale reveals droughts that may not appear as severe as in the 3-month scale but show more persistence, impacting water resources and ecosystems. While the variability is reduced, the severity of droughts at this scale, such as those in the late 1980s, remains significant, particularly in terms of water resource management. The National Integrated Drought Information system (https://www.drought.gov/) also corroborates this result for Perry County, where the study area lies.

For the 12-month time scale (Figure 6c,f), the indices smooth out short-term variability and emphasize long-term drought trends. However, this does not imply that the differences diminish. In fact, droughts at this scale, such as those observed from 1962 to 1972 and 1981 to 1989, exhibit considerable severity due to the cumulative effect of sustained precipitation deficits over time. These long-term droughts have a pronounced impact on hydrological systems, including groundwater depletion and reduced streamflow [8].

In recent years the study regions have shown reduced drought events, which is also supported by the increasing precipitation trend in the study region as shown in Figure 7. Thus, while shorter time scales show more immediate and extreme variability, the longer time scales reveal the sustained severity of droughts over extended periods. The extent of the impact and severity differs significantly between short-term and long-term droughts, and these differences are critical for understanding the full scope of drought dynamics in the study area.

3.2. Correlation Analysis Between SPI and SPEI

This study utilized Pearson Correlation analysis to demonstrate the strength and direction of the relationship between the drought indices because of the standardized nature of the SPI and SPEI. The drought index Pearson correlation matrix is shown in

Table 2. Correlation coefficient matrix of SPI and SPEI at different time scales.

INDEX	SPEI3	SPEI6	SPEI12	SPI3	SPI6	SPI12
SPEI3	1.00	0.72	0.54	0.81	0.38	0.42
SPEI6		1.00	0.74	0.71	0.84	0.64
SPEI12			1.00	0.53	0.71	0.91
SPI3				1.00	0.72	0.56
SPI6					1.00	0.74
SPI12						1.00

. When the correlation coefficient is equal to or higher than 0.8, a significant positive link is assumed [8]. When the correlation matrix was analyzed, a higher correlation was observed for the same time scales between SPI and SPEI. The maximum correlation coefficient between SPI12 and SPI12 was found (0.91), whereas the minimum correlation between SPI6 and SPEI3 was (0.38). At higher time scale, correlation coefficients tend to increase for the same time scale of SPI and SPEI. Calculating correlations at different time scales is significant for several reasons. Each time scale captures unique hydrological impacts; for example, shorter time scales (e.g., 3 months) are more sensitive to meteorological drought, while longer time scales (e.g., 12 months) are associated with hydrological or agricultural drought. The strength of correlation at each time scale indicates the consistency between SPI, which only accounts for precipitation, and SPEI, which considers both precipitation and evapotranspiration. A higher correlation at longer time scales suggests that precipitation alone becomes a more dominant factor in capturing drought conditions, whereas, at shorter time scales, evapotranspiration plays a greater role, resulting in a weaker correlation between SPI and SPEI [8,55].

3.3. Drought Severity Categorization

This study quantified and classified drought events into three categories: moderate, severe, and extreme. The bar graph in Figure 8 displays the total number of drought events calculated each year for both the SPI and SPEI. Moderate droughts were found to be the most frequent, followed by severe and then extreme droughts, across all time scales. This indicates that moderate droughts are common in the study region. During the study period, the SPEI3 had the highest number of drought events with 128 events, while the SPI12 had the lowest with 108 events, as shown in Figure 8a and Figure 8c, respectively. For both the SPI and SPEI, the total number of drought events is slightly higher for the shorter time scales (3 and 6 months) compared to the 12-month scale. This suggests that there are more frequent changes in drought conditions over shorter time scales. This study also found that the SPEI generally indicates more moderate droughts than the SPI, especially at the 3-month scale. This might suggest that temperature factors and precipitation deficits are essential in the onset of drought conditions, particularly in the short term. At longer time scales (12 months), the difference in the total number of drought events between the SPEI and SPI narrows, indicating that long-term precipitation patterns are crucial in determining annual drought conditions.

3.4. Drought Prediction

In this study, three distinct predictive algorithms were used: Random Forest (RF), Support Vector Machine (SVM), and Artificial Neural Networks (ANNs). Evaluating the accuracy of machine learning models is a critical aspect of the development process as it helps in assessing the models’ predictive capabilities. This study assessed the effectiveness of these models using different metrics such as MAE, RMSE, and R². For training the models, 80% of the overall data were used and the remaining 20% of the data were used for the testing of the model. Among the different time scales of the SPI and SPEI, the 3-, 6-, and 12-month temporal scales were used to predict the drought indices. Furthermore, three different lag periods were created for enhancing feature selection for the models. For the 3-month lag time, the precipitation data from the previous 3 months were used as input features. For the 6-month lag time, the data from the past 6 months were used, and for the 12-month lag time, the data from the previous 12 months were used. The maximum and minimum temperatures were also used as input features for the SPEI prediction.

For example, to predict the SPEI6 for x month with the 3-month precipitation lag data, the input features P (x), P (x − 1), P (x − 2), P (x − 3), Tmax, and Tmin were utilized.

Here,

P (x) = precipitation of x month

Tmax = maximum temperature of x month

Tmin = minimum temperature of x month

Table 3. Performance metrics or forecasting SPI at different time lags.

R2
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPI3	0.71	0.72	0.67	0.73	0.73	0.69	0.74	0.77	0.68
SPI6	0.36	0.54	0.43	0.64	0.75	0.66	0.63	0.80	0.74
SPI12	0.11	0.35	0.27	0.43	0.57	0.47	0.69	0.92	0.94
MAE
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPI3	0.46	0.48	0.47	0.44	0.46	0.46	0.44	0.42	0.47
SPI6	0.66	0.55	0.62	0.49	0.43	0.48	0.50	0.38	0.41
SPI12	0.78	0.66	0.69	0.62	0.53	0.57	0.46	0.22	0.18
RMSE
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPI3	0.57	0.56	0.61	0.55	0.55	0.59	0.54	0.51	0.60
SPI6	0.84	0.71	0.79	0.63	0.52	0.61	0.63	0.38	0.53
SPI12	0.95	0.81	0.86	0.76	0.66	0.73	0.56	0.28	0.26
NSE
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPI3	0.72	0.75	0.69	0.73	0.74	0.71	0.79	0.79	0.69
SPI6	0.46	0.58	0.53	0.64	0.79	0.69	0.69	0.85	0.76
SPI12	0.31	0.39	0.37	0.43	0.67	0.49	0.71	0.94	0.95

shows the statistical metrics of the drought index used to predict the SPI and

Table 4. Performance metrices for forecasting SPEI at different time lags.

R2
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPEI3	0.88	0.93	0.93	0.86	0.93	0.90	0.84	0.93	0.87
SPEI6	0.55	0.69	0.67	0.69	0.89	0.85	0.67	0.91	0.86
SPEI12	0.31	0.45	0.40	0.44	0.60	0.52	0.67	0.89	0.91
MAE
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPEI3	0.29	0.22	0.23	0.31	0.22	0.25	0.33	0.23	0.31
SPEI6	0.61	0.49	0.50	0.48	0.28	0.33	0.50	0.26	0.34
SPEI12	0.71	0.63	0.65	0.62	0.53	0.57	0.50	0.27	0.24
RMSE
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPEI3	0.37	0.28	0.28	0.39	0.27	0.33	0.42	0.29	0.39
SPEI6	0.72	0.60	0.61	0.60	0.35	0.42	0.62	0.33	0.40
SPEI12	0.86	0.77	0.80	0.78	0.66	0.72	0.60	0.34	0.41
NSE
	3 months of lag data			6 months of lag data			12 months of lag data
	RF	ANN	SVM	RF	ANN	SVM	RF	ANN	SVM
SPEI3	0.47	0.32	0.34	0.43	0.33	0.45	0.42	0.33	0.43
SPEI6	0.75	0.62	0.65	0.65	0.39	0.49	0.62	0.35	0.51
SPEI12	0.89	0.79	0.80	0.79	0.71	0.75	0.60	0.39	0.53

shows the parameters of the SPEI in the study region. The accuracy of the predictions was measured for precipitation time lags of 3 months, 6 months, and 12 months for both the SPI and SPEI indices. For the prediction of SPI3, the ANN model showed the most impressive performances, particularly at the 12-month precipitation lag, where it achieved R² values as high as 0.77, indicating a robust predictive capability. The SVM and RF models were relatively less effective for SPI3 prediction during the same lag period. In terms of its error metrics, the ANN model consistently demonstrated lower MAE and RMSE values, indicating more accurate predictions. For forecasting SPI6 and SPI12, both the ANN and SVM models performed satisfactorily when higher lag periods were created, whereas the RF model could not provide a better result even with higher lag months. In contrast, when forecasting SPEI12, the models showed different strengths. The SVM model showed a significant performance in SPEI predictions at the 12-month lag period, where it achieved an R² of 0.91, surpassing both the RF and ANN models, which had R² values of 0.67 and 0.89, respectively. This suggests that the SVM model’s sensitivity to temperature and evapotranspiration contributed to its accuracy in SPEI predictions. Table 3 and Table 4 represents the statistical parameter values of the testing datasets. In short-term forecasts, fewer features or less interactions between variables were sufficient, allowing simpler models like RF to perform well. In long-term forecasting, capturing dependencies between multiple features and accounting for the cumulative effects of the climate over time were required, and this is where the ANN and SVM models shows better performances [56]. The NSE values also show a similar pattern with the R² value showing the efficacy of the machine learning used in the study [57].

For the short-term SPEI3 and SPEI6, the ANN (3-months lag and 6-months lag, respectively, was sufficient for the models to perform satisfactorily. The SVM and ANN models both had an R² greater than 0.8 for forecasting the SPEI3 and SPEI6 with a lag period of 6 months, indicating a solid fit for short-term and intermediate drought conditions. The error analysis in the SPEI predictions showed that the ANN consistently maintained a lower MAE as the lag period increased. This improvement in accuracy may be attributed to the model’s ability to capture longer-term precipitation trends and seasonal patterns, which become more pronounced with extended lag periods. As the lag time increases, the model can better incorporate accumulated precipitation data, leading to more accurate predictions. The SVM and ANN models performed similarly with a slight edge to the ANN models, whereas the RF models did not provide consistent accuracy and the errors from the RF model were concerning.

Overall, the ANN model emerged as the most consistent and accurate model across both SPI and SPEI indices for various timeframes, making it a reliable choice for drought modelling. The SVM model distinguished itself in long-term SPEI predictions, potentially making it the preferred model for long-range forecasting in areas where evapotranspiration is a significant factor. Despite its broader applicability, the RF model lagged slightly behind for both indices, suggesting a need for more nuanced tuning when it is used for drought prediction. The choice of the SPI or SPEI for prediction models should be based on regional climatic specifics and the need to incorporate temperature and evapotranspiration data into drought assessments [8]. Figure 9 presents the best models for the prediction of different time scales of both the SPI and SPEI. The observed and predicted values of SPI and SPEI are plotted with the respective R² values of each model. Figure 9a–c shows the SPI values with the 3-, 6-, and 12-month time scales, respectively, and Figure 9d–f shows the SPEI values with the 3-, 6-, and 12-month time scales, respectively.

4. Conclusions

Drought is a harsh natural calamity that significantly impacts communities across diverse climates. Thus, it is imperative to investigate drought and develop effective forecasting techniques using drought indices. This study endeavors to evaluate the drought condition of the study area and forecast the drought indices using three distinct machine learning models. The outcome of this study indicates that the region was subjected to prolonged drought during the 1960s and 1980s. The research utilized two meteorological drought indices (SPI and SPEI) to analyze the drought events in the area. The SPEI accounted for higher numbers of moderate drought events than the SPI, as the SPEI considers both precipitation and evapotranspiration for its drought analysis. This indicates the importance of considering multiple features in a drought analysis to obtain a more precise understanding of drought phenomena. The higher correlation coefficients between the SPI and SPEI suggest the linear relationship between the indices. For forecasting the droughts, the ANN provided the most reliable and accurate model at different time scales with an R² value as high as 0.93. The SVM algorithm also performed well, especially for higher time scales with an R² value of 0.94. However, the RF model fell slightly behind both the ANN and SVM models. Based on the performance metrics of the models, ANN and SVM can be suggested as the most reliable models for drought forecasting in humid regions like Sunday Creek basin. For future research, exploring the integration of additional climatic features and developing hybrid models combining the strengths of the ANN, SVM, and RF models may enhance their predictive accuracy. Applying these models in different geographical climatic conditions would also provide valuable insights into their adaptability and effectiveness. In conclusion, this study provides a thorough understanding of drought dynamics and forecasting techniques. It highlights the importance of adaptable, accurate, and region-specific approaches in managing droughts. The insights gained from this study could help in advancing drought prediction methodologies, which can contribute significantly to environmental management and sustainable planning in the face of changing global climate conditions.