Enhanced hydrological drought prediction in the Gediz Basin: integrating meteorological drought via hybrid wavelet-machine learning-random oversampling models using

The hydrological cycle of water, which is vital for living things on Earth, is directly related to meteorological, hydrological variables, and anthropogenic effects. Unfortunately, due to human interventions such as excessive carbon dioxide emissions, deforestation, and industrialization, the quantity and quality of water is damaged and climate changes due to global warming occur. This situation leads to global disasters such as increasing storms, increasing floods and droughts, melting glaciers, rising sea levels, desertification, decrease in biodiversity, soil, water, and air pollution (Özcan 2017; Büyükşahin 2018; Kale 2021). Among these disasters, drought is frequently encountered in Turkey (Çoban et al. 2023; Gul et al. 2023; Kara & Orhan 2023; Khorrami et al. 2023). According to the 2023 Climate Assessment Report prepared by the General Directorate of Meteorology in Turkey, the average temperature between 1991 and 2020 increased from 13.9 to 15.1 °C, an increase of 1.2 °C. Between 1991 and 2020, the areal annual mean precipitation across Turkey was 573.4 mm, and in 2023, it was 641.5 mm, an increase of 11.9% compared with mean (CA 2023). Drought, which can be defined as a decrease in precipitation over an extended period, affects surface and groundwater resources, leading to a reduction in water quality, quantity, and agricultural productivity, resulting in economic losses (Riebsame et al. 1991; Mishra & Singh 2010).

Following meteorological drought, which is characterized by a drop in precipitation and an increase in evapotranspiration, hydrological drought happens as surface and groundwater resources are decreased. Subsequently, agricultural drought arises with reduced soil moisture (Choi et al. 2013; Dabanlı et al. 2017). Finally, socio-economic drought in which water supply cannot meet water demand occurs (Rajsekhar et al. 2013; Şen & Almazroui 2021).

The standardized precipitation evapotranspiration index (SPEI), one of the monitoring methods for meteorological drought, was proposed by Vicente-Serrano et al. (2010,). Unlike the standardized precipitation index (SPI), SPEI uses precipitation and air temperature data to examine the impact of air temperature on drought (McKee et al. 1993). SPEI calculates the difference between precipitation and potential evapotranspiration (PET) at different time scales using air temperature data, allowing for a more sensitive assessment of climate change (Beguería et al. 2014). Many researchers have used SPEI in drought studies (Stagge et al. 2015; Um et al. 2017; Tirivarombo et al. 2018; Manzano et al. 2019; Li et al. 2020; Liu et al. 2021; Ojha et al. 2021). Stagge et al. (2014) compared SPI and SPEI using five different PET formulas in their European drought analysis. Ogunrinde et al. (2020) conducted a hydrological drought analysis in Nigeria for other agricultural areas using PET values calculated with Hargreaves, Penman–Monteith, and Thornthwaite methods, stating that Hargreaves and Penman–Monteith outperformed Thornthwaite. Öney & Anlı (2023) used the SPEI in their meteorological drought analysis in the Gediz Basin. Kumanlioglu (2020) preferred SPI and SPEI for meteorological drought and standardized runoff index (SRI) for hydrological drought.

The SRI is one of the preferred methods for assessing hydrological drought (Shukla & Wood 2008; Salimian et al. 2021). Like the SPI proposed by McKee et al. (1993), SRI expresses the standard deviation of accumulated surface runoff for a given period. Mercado et al. (2016) preferred SRI to determine the temporal and spatial distribution of hydrological drought in southeastern Mexico. Wu et al. (2018) used non-parametric SRI to examine the temporal changes in hydrological drought in 17 basins on the Loess Plateau. Gan et al. (2023) used non-parametric SRI to calculate hydrological drought in the Shaying River Basin from 1956 to 2023, stating an increasing trend in drought.

For the purpose of predicting droughts, researchers have recently begun to use machine learning (ML) systems. The abundance of measured data for hydrological parameters has made ML an inevitable tool in this field (Brunton et al. 2020; Shen 2018). ML algorithms, such as support vector machine (SVM), artificial neural network (ANN), and k-nearest neighbor (kNN), have been used to develop drought prediction models for different regions (Mohamadi et al. 2020; Mokhtar et al. 2021). Khan et al. (2020) attempted to develop drought prediction models for Pakistan using SVM, ANN, and kNN. Mohamadi et al. (2020) used adaptive neural-based fuzzy inference system (ANFIS), multi-layer perceptron (MLP), radial basis function neural network (RBFNN), and SVM models to predict meteorological drought in Iran from 1980 to 2014. Mokhtar et al. (2021) used random forest (RF), extreme gradient boost (XGB), convolutional neural network (CNN), and long-term short memory (LSTM) algorithms for drought prediction in Tibet, stating that XGB and RF models outperformed others in different scenarios. However, researchers have used deep learning methods such as LSTM as ensemble and hybrid models in hydrology to improve the prediction accuracy of ML algorithms. Widiasari et al. (2018) used an LSTM-based deep learning model for the streamflow prediction of the East Canal River in Semarang Province, Indonesia, and achieved good success with a mean absolute percentage error of 3.6%. Yuan et al. (2018) used LSTM parameters to model the monthly streamflow of the Astor River by calibrating them with ant lion optimization (ALO). Fu et al. (2020) used an LSTM-based deep learning model to predict the streamflow of the Kelantan River in northeastern Malaysia. They compared the performance of the model with classical backpropagation (BP). They stated that LSTM had better success than BP in both dry and wet periods. Adnan et al. (2021) used a novel hybrid adaptive neuro-fuzzy inference system (ANFIS-WCAMFO) calibrated with moth-flame optimization algorithm (MFO) and water cycle optimization algorithm (WCA) to predict reference evapotranspiration for Dhaka and Mymensing stations in Bangladesh. They stated that this algorithm, a new hybrid neuro-fuzzy method, was very successful. Adnan et al. (2022) used the SVM method improved by a hybrid firefly algorithm–particle swarm optimization (FFAPSO) method to model dissolved oxygen concentration values for station number 07106000 selected for the Fountain Creek basin in Colorado. They stated that the SVM-FFAPSO method achieved good success with an R² value of 0.8234. Adnan et al. (2023a) similarly proposed extreme learning machine (ELM) methods tuned with jellyfish search optimizer (JFO) to model groundwater level fluctuations. Ikram et al. (2023) used convolutional neural networks (CNNs) and LSTM deep learning methods calibrated with reptile search algorithm (RSA) and vector weighted average optimization (INFO) to predict water temperatures for Bailong River. Adnan et al. (2023b) evaluated the performance of relevance vector machine tuned (RVM) with gray wolf optimizer (GWO), whale optimization algorithm (WOA), manta ray foraging optimization (MRFO), and improved manta ray foraging optimization (IMRFO) methods to predict monthly pan evaporation values using monthly minimum, maximum temperature, T_a, and periodicity component values for Jingzhou station in Hubei province and Yueyang station in Hunan province between 1962 and 2000 in China. They stated that the RVM-IMRFO method has higher prediction accuracy. Mostafa et al. (2023) proposed the RVM model with quantum-based avian navigation (QANA) optimization to predict PET values for Faisalabad and Peshawar stations with two semi-arid climatic conditions in Pakistan.

Wavelet transform (WT), one of the data decomposition techniques, is used to ensure that ML models provide more sensitive and reliable results in the prediction of hydrological variables that have unstable and non-linear relationships (Yaseen et al. 2020; Baker et al. 2022). It is a method that allows the data to be divided into different frequency bands and their frequency content analyzed (Nooruldeen et al. 2022). In the first known study on water resources, precipitation analysis was performed with W used by Kumar & Foufoula-Georgiou (1993). Lafreniere & Sharp (2003) used W in the analysis of river flows to Bowl Lake in Alberta. For drought prediction, Belayneh & Adamowski (2013) used ANN and support vector regression (SVR) models together with W. It has been stated that W-ANN models used in 3-month and 6-month SPI predictions are more successful. Achite et al. (2023) modeled meteorological, agricultural, and hydrological droughts for the Wadi Ouahrane Basin in Algeria using various ML models and W at different time scales and stated that WT hybrid models were successful in drought prediction.

ML techniques are combined with data processing techniques such as random oversampling (ROS) to address the imbalanced distribution in datasets, often supporting diversity during the learning phase (Snieder et al. 2021). Hybrid modeling studies that use ROS together with ML techniques are limited in the literature (Galar et al. 2013).

According to the literature research mentioned above, the use of ML algorithms in predicting hydrological drought from meteorological drought is quite limited. Thus, an attempt was made to study. In this context, meteorological drought values occurring in Uşak were used to predict the hydrological drought in the Gediz Basin of Turkey. The Gediz Basin is one of the biggest basins in Turkey, discharging its waters into the Aegean Sea and covering a vast area with varying climatic conditions. This geographical diversity allows for a comprehensive analysis of drought patterns and their impacts across different regions within the basin. While the study is focused on the Gediz Basin, the methodologies and findings can be adapted to other similar regions, making the results more widely applicable. In order to decide which stream gauging station should be selected in the basin, correlation analysis was created using each streamflow gauging station and Uşak precipitation (P) and air temperature data (T_a). SRI values are calculated for 3-, 6-, 9-, and 12-month periods using the flow data of the streamflow gauging station selected to define hydrological drought. SPEI values of Uşak meteorology station are also calculated for 3-, 6-, 9-, and 12-month periods. Later, correlation matrices were created between meteorological drought inputs from SPEI(t) to SPEI(t − 12) and SRI(t) for use in hydrological drought models for 3-, 6-, 9-, and 12-month periods. ML models were developed for SRI predictions. Then, discrete wavelet transform (DWT) was applied to increase the performance of the models. It was observed that the W-ML models developed with the obtained subseries and applied hyperparameter analysis have higher performance. By applying ROS to the most successful W-ML models, the predictive power was further improved. With this study, W-ML-ROS was used for the first time in hydrological studies to determine hydrological drought from meteorological drought for long-term effective water resources planning in the region.

Data decomposition by DWT has been used in many studies to increase accuracy in modeling studies in hydrology and other fields. However, the effect of the DWT method on the performance of different ML algorithms has not been compared in studies. At the same time, improving the performance in drought studies by eliminating irregularities in the input datasets with ROS is another innovation offered by the study. The main aim of this study is to develop a completely new hybrid model processed with ROS by determining the right combination of ML models and DWT, thus predicting hydrological drought from meteorological drought. W-ML-ROS estimates were evaluated using different statistical measures and Taylor plots. The results obtained from the study are directly relevant to stakeholders and decision makers involved in combating drought. By using DWT and ROS together, the study provides information that can be used by stakeholders through current models in real hydrological applications. The study is also pioneering in its capacity to influence future research studies. The study has the potential to combine theoretical innovations with practical applications with its comprehensive methodology. In brief, the study's novelty lies in its integration of advanced data decomposition, ML, and data balancing techniques to develop highly accurate and robust models for predicting hydrological drought from meteorological data. The application of these models to the Gediz Basin and the comprehensive methodological approach further enhance the study's originality and impact.

The precipitation (P) and air temperature (T_a) data for the Uşak meteorological observation station located east of the basin were obtained from the Turkish State Meteorological Service. The data for the selected streamflow gauging stations in the study were obtained from the General Directorate of State Hydraulic Works. Streamflow gauging stations (E05A014 (Dereköy), E05A022 (Borlu), and E05A024 (Sazköy)) and Uşak meteorological observation station are located close to each other in the basin and have streamflow, P and T_a data in the same time period (1985–2015). Table 1 provides descriptive statistics of streamflow, P and T_a parameters used in this study.

Values collected at different time scales are transformed into standard deviations based on averages (Vicente-Serrano et al. 2017). SPEI values can be obtained from the empirical Hargreaves equation suggested by Hargreaves & Samani (1985), using precipitation and PET data. In this study, PET values were calculated using the monthly mean air temperature data with the equation suggested by Thornthwaite (1948).

The obtained SRI values, similar to those provided by SPI, are categorized into drought classifications given in Table 2. The index assumes that the values are negative during drought periods and remain less than or equal to −1.0 for at least 1 month. Drought ends when the index value rises above 0.

MLP, a class of artificial neural networks, consists of input, hidden, and output layers. Between consecutive layers, neurons are connected to each other by weighted connections. Minimizing the error between the known output and the output in the training set is essential until the optimal weight values are obtained. Another goal is to get the optimum number of neurons in the hidden layer (Haykin & Network 2004).

Linear regression (LR) is a statistical method used to reveal the cause-and-effect relationship between a dependent variable and one or more independent variables. LR relates the dependent variable to the independent variable or variables with the help of a function. When multiple independent variables are used in the LR method, it is called multiple linear regression (MLR) (Luu et al. 2021).

AdaBoost, one of the ensemble algorithms, is obtained by combining weak learning algorithms such as decision trees (DTs), to create a stronger learning algorithm. While training the model, the algorithm assigns a weight to each example, and this weight is recalculated with iterations. At each iteration, AdaBoost changes the weight to arrive at training samples with higher error in the prediction value so that each subsequent regression tree has a reweighted training dataset (Drucker 1997). To represent n-number of samples, AdaBoost initially assigns equal weights of (1/n) to all samples and AdaBoost includes a learning_rate hyperparameter defined as ‘learning_rate floating point, default = 1’. Thus, a higher learning rate increases the contribution of each classifier. There is a trade-off between the learning_rate and n_estimators parameters.

RF regression is a tree-based technique that involves segmenting the predictor space into a series of simple regions (Wu et al. 2017). In simpler terms, it is a non-parametric ensemble learning method that aggregates results from numerous individual DTs. Each tree is grown using a bootstrap sample to prevent overfitting, and variable subsets are randomly selected at each split. Observations not included in a tree's sample due to the bootstrapping process are referred to as out-of-bag samples, comprising approximately 36% on average. These samples serve as the test set for the tree, aiding in measuring prediction error. The importance of a particular predictor is assessed through permutation, wherein the values of the predictor are randomly shuffled in the out-of-bag samples. The final prediction error is then compared with the error obtained before the shuffle. This permutation-based importance estimate, known as the variable importance measure (VIMP), considers the effects of all interactions by eliminating the predictor's effect on the choice of other variables deeper in the tree (Van der Meer et al. 2017).

In regression analysis, multi-linear connections between independent variables indicate a strong relationship between variables. In this case, although estimates made by the method of least squares are generally accurate, significant variances can be obtained. That is, the predicted values tend to deviate significantly from the actual values. The ridge regression method proposed by Hoerl & Kennard (1970) is used to obtain more stable estimates, especially when multicollinearity problems are encountered. This method focuses on reducing uncertainty between highly correlated independent variables, providing more reliable results in regression analysis.

Gradient boosting (GBoost), developed by Friedman (2001), uses the boosting algorithm by extending it to solve a proposed regression problem. It is an integrated model with higher performance and stability. It solves for the minimum value using negative gradients of the loss function such as least squares and least absolute deviation. GBoost, which has strong prediction ability for non-linear data, handles noisy and dirty data well and supports different loss functions. It stops the growth of the tree as soon as possible to solve the problem of overfitting in the DT learning process (Li et al. 2018).

Category boosting (CatBoost) is a gradient DT algorithm that can better handle categorical features by using the entire dataset for training. It obtains categorical features with minimum information loss by using the entire dataset and can combine all categorical features into a single new feature (Prokhorenkova et al. 2018). In addition, it provides faster results with its sequential strengthening feature and deviations in the solution are eliminated (Huang et al. 2019).

DT is one of the frequently used prediction models in binary classification because it simplifies the classification processes (Anyanwu & Shiva 2009). A DT consists of an input dataset, a few test rules, and root, branches, and leaf nodes. Since a node has only one master node, one-way data flow is ensured and loops are prevented (Friedl & Brodley 1997).

Wavelets (W) are mathematical functions that work on components with a resolution identical to their own scale after separating the data into different frequency components (Terzi & Barak 2015). WT, on the other hand, has a flexible window function and is a revision of the short-time Fourier transform regarding signal compactness and shape (Hernández & Weiss 1996). There are two types of WT: continuous (CWT) and discrete (DWT).

Here, τ indicates the position of the wavelet in the time domain and s indicates its position in the frequency domain. The CWT provides information about time and frequency by mapping the x(t) series to the function τ and s (Aguiar-Conraria & Soares 2014).

A wavelet is not just a function, but a whole family of functions that meet certain requirements. The most popular functions include Daubechies, Coiflet, Symlet, Haar, Morlet, Gaussian, Shannon, Meyer, and Mexican Hat (Oteng Mensah et al. 2024).

ROS can provide high-fit models by generating new examples for classes that are few in a population (Chawla et al. 2004). Chawla et al. (2004) used LR of a minority sample with randomly selected kNN when generating new samples. Most class examples are not taken into account when developing recent examples. Therefore, overlaps between minority and majority class samples are inevitable. However, it is frequently used because it is a simple application (Moreo et al. 2016; Mohammed et al. 2020).

Default hyperparameter values given in ML models do not guarantee the best performance by default (Schratz et al. 2019). Therefore, tuning hyperparameter values can significantly impact the performance of a model. The numerous hyperparameters of models make manual adjustment of these values nearly impossible. Hence, many hyperparameter tuning methods are available and used in the literature. There are different frameworks for hyperparameter optimization, such as manual search, random search, grid search, and Optuna. In this study, due to its scalability, versatile design, and usability in different areas, Optuna is used as a framework suggested by Akiba et al. (2019). Optuna, an open-source hyperparameter tuning optimization, aims to find the best values of parameters used to improve the performance of a ML model (Agrawal 2021). Optuna aims to make this process more efficient and effective by automating it. Optuna offers different options to choose the optimization algorithm that will best solve the problem. It can use multiple processes or processes on different machines to speed up the optimization process. This helps perform optimization faster and more efficiently. It also provides a user-friendly application programming interface (API), making operations such as defining the hyperparameter space, selecting the optimization algorithm, and analyzing the results simple and intuitive (Srinivas & Katarya 2022; Can 2024).

As seen in Figure 4, it has been determined that the streamflow gauging station with the highest correlation to P and T_a meteorological parameters is E05A014 station. In addition to the correlation matrices given in Figure 4, the correlation coefficients between meteorological parameters and streamflow values for each month were calculated and given in Table 3, as done by Adib & Tavancheh (2019). According to Table 3, the relationship between streamflow data of E05A014 station and meteorological parameters is better than other stations. While the relationship between E05A014 station and P was found to be high throughout the year, the relationship with T_a was especially higher in autumn and winter. E05A024 station has the lowest correlation coefficient values in all months. This situation also supports the result obtained from the correlation matrices given in Figure 4.

As seen from the correlation matrices, which visually reveal how the correlation values ​​change over time, there was a positive and decreasing relationship between the SPEI values of months t, t − 1, t − 2,…, t − 12 and the SRI values of month t. Dark colors represent higher correlations and light colors represent lower correlations. This color scale emphasizes that correlations decrease over time, but there is a relationship in every time period. Hence, in this study, SPEI values from (t) month to (t − 12) month were used as input parameters for the prediction of hydrological drought from meteorological drought. There are studies in the literature that use the TOPSIS method during the model selection phase (Farajpanah et al. 2020), but since the input parameters were selected instead of the method in this study, correlation matrices were used instead of the TOPSIS method.

The R² value indicates model's overall explanatory power and accuracy. A higher R² value signifies better model performance. RMSE indicates the magnitude of the model's prediction error and quantifies the dispersion between predicted and real data. A lower RMSE value indicates better model performance. Therefore, it is common to use these two metrics together when evaluating the performance of regression models. When used together, these metrics provide a comprehensive evaluation to understand how well the model is performing and the magnitude of prediction errors (Legates & McCabe 1999; Chai & Draxler 2014).

As seen from Table 4, for the 3-month period, the SVR model generally shows the best performance. With the input set, SPEI(t − 7)₃ to SPEI(t)₃, the SVR model achieved a testing R² value of 0.450 and an RMSE value of 0.705, the best results overall. The LR model was only tested with the input set SPEI(t)₃ and showed the lowest performance with a testing R² value of 0.240 and an RMSE value of 0.827. Based on this information, it seems reasonable to prefer the SVR model. For the 6-month period, the AdaBoost algorithm, using SPEI₃ values up to the (t − 12)th month as inputs, demonstrated the most optimal performance among the constructed SRI₃ prediction models at (t)th month (Table 5).

In Table 6, similar to the 6-month period, for the 9-month period, the LGBM algorithm exhibited successful performance when using an input set composed of SPEI₉ values up to the (t − 12)th month, outperforming other models for prediction of SRI₉ at (t)th month.

For the 12-month period, the kNN model showed the best performance with the input set SPEI(t − 11)₁₂ to SPEI(t)₁₂, achieving a testing R² value of 0.590 and an RMSE value of 0.692. Overall, the kNN model obtained high R² and low RMSE values with different input sets, indicating that the model performed consistently well. The RF model, on the other hand, showed the lowest performance (Table 7).

Moreover, stacking regressor approach has been used for kNN-SVR, kNN-RIDGE, and kNN-RF hybrid ML models, which gave the best results for SRI₁₂ and R² values were obtained as 0.560, 0.560, and 0.540, respectively. Similarly, for SRI₉, R² values of LGBM-ADABOOST, LGBM-RIDGE, and RIDGE-ADABOOST hybrid ML models were obtained as 0.450, 0.470, and 0.480, respectively. For SRI₆, R² values of ADABOOST-kNN and ADABOOST-RF hybrid ML models were 0.480 and 0.540, respectively. For SRI₃, R² values for MLP-kNN, MLP-SVR, and kNN-SVR were found to be 0.390, 0.440, and 0.450, respectively. Since the success rate is higher in ML models developed with DWT, W-ML models were continued in the study.

In this part of the study, W-ML hybrid models were developed. The DWT was applied to 3-, 6-, 9-, and 12-month periods of SPEI values. These SPEI series were decomposed into eight detail components (2-4-8-16-32-64-128-256) (D1, D2, D3, D4, D5, D6, D7, and D8). In this study, the Daubechies wavelet was chosen due to its characteristic orthogonality and compact support, which are considered suitable for hydrometeorological time series in the creation of subseries (Nourani et al. 2018). The correlations between the subseries obtained by DWT and 3-, 6-, 9-, and 12-month periods of SRI series were calculated and given in Table 8.

From Table 8, it can be seen that the highest correlation values for SRI(t)₃ were obtained between the D2,D3 wavelet subseries of the SPEI(t)₃ input variables. Similarly, the highest correlation values were obtained with D4,D5 wavelet subseries of SPEI(t)₆ input variables for SRI(t)₆, D4,D5 wavelet subseries of SPEI(t)₉ input variables for SRI(t)₉, and D4,D5 wavelet subseries of SPEI(t)₁₂ input variables for SRI(t)₁₂. Various combinations of these subseries, individually and by adding them together, have been tried. An increase was observed in the performance of W-ML hybrid models in which subseries were used separately as input parameters for each period. Therefore, the number of inputs in the W-ML hybrid models developed to estimate the SRI(t) value was twice as much as in the ML models. The input sets and R²–RMSE values of the W-ML hybrid models developed to estimate 3-, 6-, 9-, and 12-month SRI(t) values are given in Tables 9–12.

According to Table 9, for the 3-month period, the W-GBOOST hybrid model, using the SPEI(t − 12 to t)(D2,D3)₃ wavelet subseries as inputs for predicting SRI₃ values in month t, provided the highest R² and the lowest RMSE values. For the 6-month period, the W-SVR hybrid model, using SPEI(t − 7 to t)(D4,D5)₆ wavelet subseries as inputs, demonstrated the best performance among SRI₆ prediction models (Table 10).

In Table 11, for the 9-month period, the W-SVR hybrid model showed the best performance when using set of SPEI(t − 11 to t)(D4,D5)₉ wavelet subseries as input. For the 12-month period, the W-MLP hybrid model gave the best results with an input set consisting of SPEI(t − 10 to t)(D4,D5)₁₂ subseries in Table 12.

Hyperparameter tuning is also performed using the Optuna framework for W-ML hybrid models. The hyperparameters selected for the best models are given in Table 13.

The performance of the 3-, 6-, 9-, and 12-month period W-ML hybrid models is detailed in Figure 10 through Taylor plots. Figure 10(d) and 10(c) shows that the RMSE value for W-MLP and W-SVR models for SRI₁₂ and SRI₉, respectively, is close to 0.300, and the correlation between the predictions and the SRI₁₂ and SRI₉ values is around 0.900. This indicates that the standard deviations of the predictions are close to the actual values. Therefore, it is understood that the W-MLP and W-SVR models for SRI₁₂ and SRI₉ have very good performance, respectively. Similarly, the Taylor plots for SRI₆ show that the W-SVR model also has reasonable performance (Figure 10(b)). However, the W-GBOOST model for SRI₃ (Figure 10(a)) has poor performance compared with 6-, 9-, and 12-month periods.

Then, the improvement stage is performed to enhance the success of the obtained W-ML hybrid models. Thus, the W-ML-ROS hybrid models were developed by resampling with ROS for 3-, 6-, 9-, and 12-month periods. This approach resulted in a more homogeneously distributed dataset. The R² and RMSE values for testing sets obtained W-ML-ROS hybrid models are summarized in Table 14.

Scatter diagrams provide a good visual tool for comparing the performance of models. In general, the concentration of points on or near the 45-degree inclined line indicates that the model is making predictions with high accuracy. It is observed that the model in the 12-month period W-MLP-ROS shows the best performance and the point clustering is the densest. The model in the 9-month period W-SVR-ROS also performs quite well.

When all models were examined, it was seen that the best performance in predicting SRI₃ in the 3-month period was obtained by using the W-GBOOST-ROS model for inputs from SPEI(t)₃ to SPEI(t − 12)₃. Similarly, in the 6- and 9-month periods, with inputs from SPEI(t)₆ to SPEI(t − 7)₆ and SPEI(t)₉ to SPEI(t − 11)₉ good SRI₆ and SRI₉ estimations are provided by W-SVR-ROS, respectively. Moreover, in the 12-month period, the best SRI₁₂ model belongs to the W-MLP-ROS model with inputs from SPEI(t)₁₂ to SPEI(t − 10)₁₂. After observing any meteorological drought level occurring in the region, the value of a possible hydrological drought can be predicted with great accuracy in periods of 3-, 6-, 9-, and 12-months with a delay of approximately 7 − 11 months.

In general, it is observed from the results that both DWT and ROS algorithms significantly improve ML models in the prediction of hydrological drought. The R² values obtained for the test set in the models developed with ML algorithms for 3-, 6-, 9-, and 12-month periods are found as 0.450, 0.570, 0.530, and 0.590, respectively. The R² values for the test set in the W-ML models developed with DWT process are obtained as 0.484, 0.763, 0.889, and 0.935, respectively. With the application of ROS to the W-ML models, the R² values increased to 0.893, 0.851, 0.940, and 0.999, respectively. The W-ML-ROS models provided better efficiency than ML and W-ML models.

From the literature on prediction of hydrological drought from meteorological drought, Achite et al. (2022) developed DT, ANFIS, ANN, and SVM models using SPI values for predicting hydrological drought (SRI) in Wadi Ouahrane Basin in Algeria. They obtained the highest R² value of 0.95 for the SVM model at the 12-month periods and stated that R² values decreased at smaller periods. Hao et al. (2023) preferred LSTM, CNN, and CATBOOST methods while determining agricultural and hydrological droughts from meteorological droughts. Among the developed models, the CNN model obtained the highest accuracy with a Nash–Sutcliffe coefficient of 0.70. They found a delay between meteorological drought and hydrological drought for 8–11 months.

According to the literature given above, different ML and deep learning methods have been tried in the prediction of hydrological drought. However, in this study, in addition to these ML algorithms, DWT and ROS were applied, and then hybrid ML models (W-ML-ROS) with higher accuracy were obtained. Also in this and similar studies, high accuracy prediction values were mostly found in models for the 12-month period (Keskin et al. 2009, 2011; El Ibrahimi& Baali 2018; Docheshmeh Gorgij et al. 2022).

In other study conducted in the Gediz Basin, Kumanlioglu (2020) examined the relationship between meteorological (SPEI, SPI) and hydrological droughts (SRI) and stated that a 12-month period can be considered to accurately predict the delay between meteorological and hydrological droughts since the hydrological cycle occurs in a 12-month period. Like the results obtained by Hao et al. (2023), in this study, this delay remained between 7 and 11 months in the 3-, 6-, 9-, and 12-month periods in the prediction of hydrological drought in the region.

In this study, hydrological drought events around the Uşak province in the Gediz Basin of Turkey were predicted by using meteorological data obtained from the Uşak meteorological observation station and streamflow data obtained from various streamflow gauging stations. The analysis revealed that station E05A014 exhibited the highest correlation with P and T_a, making this station the most effective streamflow gauging station for determining hydrological drought. Drought indices, SPEI for meteorological drought and SRI for hydrological drought, were calculated for 3-, 6-, 9-, and 12-month periods. Time series analysis showed a noticeable delay between meteorological and hydrological drought indices over each period. Correlation matrices were created for different time shifts to determine the inputs of ML models depending on this delay, and a decreasing but positive relationship emerged between SPEI values ​​and SRI for each time shift. ML regression models were then used to predict hydrological drought from meteorological drought, taking into account a monthly shift for up to 12 months. Models covering MLP, kNN, SVR, LR, AdaBoost, RF, LGBM, ridge, DT, CatBoost, and GradientBoosting algorithms were evaluated using R² and RMSE. Additionally, hyperparameter tuning using the Optuna framework resulted in improved R² and RMSE values for all models. For each period, certain models demonstrated superior performance. For example, the W-GBOOST model with a 12-month time shift gives the best results in the 3-month period (t − 7). The W-SVR model with inputs up to 6 months demonstrated excellence over a 6-month period. It was also observed for the 9-month period that W-SVR algorithms performed extremely well. The best model with inputs up to (t − 10) months for a 12-month period is provided by W-MLP. To further improve model performance, hybrid models were developed by applying ROS to create a more balanced dataset. This approach resulted in improvements in prediction accuracy, as evidenced by the reduced RMSE values. In hydrological drought prediction models, R² values show very high performance by remaining between 0.851 and 0.999 when tested in 3-, 6-, 9-, and 12-month periods.

In summary, the following results were obtained from this study:

• In this study, it was concluded that by separating the dataset into its subseries using DWT, the prediction performance was higher than the original dataset. Planning sustainable water resources in the region and predicting hydrological drought with high accuracy are an exemplary study in terms of the need to combat drought.

• W-ML-ROS hybrid models were successfully used to predict hydrological drought from meteorological drought for the first time.

• The development of hybrid models and hyperparameter tuning contributed to increased prediction accuracy, emphasizing the effectiveness of these techniques in hydrological drought predicting.

• The use of W-ML-ROS models to monitor drought, which is one of the natural disasters of meteorological origin, and to create emergency precaution plans for hydrological drought that may occur in the region, increases the attractiveness of the study as it provides successful results in a shorter time than other methods.

• It aims to improve the results by testing new W-ML algorithms in the future.

The study is based on datasets from the years 1985–2015. This is one of the limitations in the study. Another limitation is that only data from the Gediz Basin were used. Including a broader dataset and more stations could enhance the generalizability of the results.

For future studies, the suitability of the W-ML-ROS hybrid models proposed in this study for the prediction of hydrological drought for different regions can be investigated, and the model can be updated with additional studies for future drought predictions. It is recommended to try different optimization methods such as fish swarm and artificial bee colonies that can increase the performance of the developed model. Additionally, SHAP (SHapley Additive exPlanations) analysis can be performed to examine the effect of input parameters on outputs to test other value sets in future studies.

E.D.T.: Conceptualization, Methodology, Writing – original draft, Investigation, Software, and Visualization.

The author declares that no funds, grants, or other support were received during the preparation of this manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.