1. Introduction

Drought is defined as a reduction in precipitation compared to the annual average and is caused by prolonged periods of below-normal rainfall. It can affect various aspects of the water cycle and as a consequence, one type of drought can become another over time, being a phenomenon that operates at different scales and is influenced by the speed with which a specific area responds to changes. Therefore, the time scale plays a critical role in determining the specific type of drought that is occurring. The different time scales help classify droughts into meteorological (1 month), agricultural (3-6 months), and hydrological (12-24 months) categories. Specifically, hydrological drought occurs when the levels of surface reservoirs such as rivers and lakes gradually decrease, sometimes even depleting completely (^{Esparza, 2014}). Classifying droughts based on these time scales is essential to accurately assess the severity and type of drought in a given region. Drought is also a phenomenon that occurs in cycles in all climates worldwide, although with varying intensity and frequency. In Mexico, droughts occur on average once every 20 years, leading to a hydrological imbalance in the water cycle due to insufficient resource availability.

The lack of rainfall in different regions of the state of Chihuahua has resulted in drought occurring in 64 out of the 67 municipalities of the territory, as described by the Drought Monitor in Mexico in its report published on July 4, 2022. The report details that the state is experiencing all five classifications of drought. The three watersheds that supply water to the municipalities in the region were affected by severe, extreme, or exceptional drought conditions, with the city of Chihuahua experiencing extreme drought (^{SMN, 2022}).

One of the most alarming consequences of drought is the damage to agriculture in recent years. The direct impact of these losses is reflected in the rising prices of basic commodities. Crop loss, in turn, increases the risk of widespread famine due to the inability to ensure a stable food supply. Furthermore, the situation has generated tensions and conflicts at various levels and locations.

The Standardized Precipitation Evapotranspiration Index (SPEI) aims to measure the level of drought at a specific location. It is based on precipitation and temperature data and combines multiscale character with the ability to incorporate temperature variability. Machine learning efficiently captures knowledge within the data to make decisions based on it.

In the work of ^{Belayneh and Adamowski (2013)}, machine learning techniques for Artificial Neural Networks (ANN), Support Vector Regression (SVR), and Wavelet Analysis (WA) were investigated in the Awash River basin in Ethiopia using the Standardized Precipitation Index (SPI). The results show that the WA-ANN is the most accurate model for predicting the values of SPI-3 and SPI-6, with coefficient of determination (R²) values greater than 0.96 and root mean squared error (RMSE) less than 0.025. The study of ^{Zhang et al. (2019)} took place in Shaanxi, China. The Distributed Lag Non-Linear Models (DLNM), ANN model, and Extreme Gradient Boosting (XGBoost) model were constructed, and their validations were compared to predict SPEI one to six months in advance. As a result, the XGBoost model was superior, with R² values between 0.68-0.82, 0.72-0.89, 0.81-0.92, and 0.84-0.95 in three, six, nine, and 12 months, respectively. The study of ^{Mokhtar et al. (2021)} took place on the Tibetan Plateau, China considering SPEI-3 and SPEI-6 to develop the random forest (RF) algorithm, XGBoost, convolutional neural networks (CNN), and Long-Short Term Memory (LSTM) models.

Seven scenarios of various combinations of climate variables were adopted as input to build the models. The best model was the SPEI-3 XGBoost, which obtained an MBE of 0.04 and a Nash-Sutcliffe efficiency (NSE) of 0.70. The study of ^{Dikshit et al. (2021)} uses LSTM networks to predict SPEI-1 and SPEI-3. The model was compared to the RF algorithm and applied in Australia’s New South Wales region. The model achieved an R² value of more than 0.99 for the SPEI-1 and SPEI-3. In the work of ^{Hernández (2021)}, ANNs were evaluated in the Sonora River basin, Mexico, using SPI and SPEI at time scales of three, six, 12, and 24 months. The results showed an average R² of 0.76, and it was observed that the performance of SPEI was better than that of SPI and increased with increasing time scale.

The existing works on machine learning algorithms to predict drought are not exactly focused on hydrological drought, meaning they do not focus on obtaining the best results on the 12- and 24-month time scales. As the SPEI is the improved version of the SPI, this work specializes in the SPEI to obtain more precise and updated information, unlike other studies. The few works in which SPEI and machine learning algorithms work together train only one type of algorithm. Therefore, the results have limitations. Given this, the study’s objective is to anticipate extreme situations by analyzing drought cycles within the city of Chihuahua using a database of the monthly SPEI 12 and SPEI 24 indices from 1901 to 2020. This analysis employs the machine learning methods of SVR, ANN, and LSTM to predict droughts, mitigate their impact, and visualize future trends.

2. Materials and method

2.2 Machine learning algorithms

In the second half of the 20th century, machine learning evolved as a subfield of artificial intelligence, offering a more efficient alternative for capturing knowledge from data. Instead of relying on humans to manually derive rules and construct models through the analysis of vast datasets, machine learning identifies patterns of statistical repetitions to gradually improve the performance of predictive models and make data-driven decisions.

2.2.1 Artificial Neural Networks (ANN)

It is well known that learning takes place within the brain. To understand this process, it is necessary to comprehend the basic element, the neuron. Neurons perform chemical transmissions within the brain, carrying information that can either increase or decrease the neuron’s electrical potential. If this membrane potential reaches a certain threshold, the neuron fires a pulse of specific strength and duration sent down the axon. The axon, in turn, branches out into various connections to other neurons, linking to each of them through synapses.

^{McCulloch and Pitts (1943)} introduced the first mathematical model of an artificial neuron that could capture the essential elements of how a neuron functions by emulating its operations and determining whether it should fire. Subsequently, Frank ^{Rosenblatt (1958)} invented the first neural network known as the Perceptron, and later, ^{Bernard Widrow and Ted Hoff (1997)} published the adaptive linear neuron algorithm (ADALINE) algorithm, which can be considered an improvement. This algorithm consisted of a collection of McCulloch-Pitt neurons and inputs and weights.

ADALINE is particularly interesting because it illustrates the concept of defining and minimizing cost functions, laying the foundation for understanding more advanced machine learning algorithms for classification and regression models. In addition, backpropagation is the process that seeks the best parameters to reduce the network’s error.

2.2.2 Long Short-Term Memory (LSTM)

^{Juergen Schmidhuber (1997)} introduced the so-called LSTM units, which are managed in memory blocks with self-connections. Their advantage lies in their ability to store the temporal state of the network. LSTM cells have special multiplicative units called gates, which control the data flow. The components of memory blocks include the input gate (it), which controls the flow of input activations into a cell; the output gate (ot), where the flow of output from the cell’s activation is controlled; and the forget gate (ft), where the input information is filtered (xt) and the previous output is filtered (Fig. 1).

Fig. 1 Graphic representation of the structure of a Long-Short Term Memory (LSTM) model where: x _n is the input of the model, h _n is the output, f _t is the forget gate, i _t is the input gate y ĉ _t is the update cell, c _t is the state cell and o _t is the output gate. Obtained from ^{Zhu et al. (2020)}. 

2.2.3 Support Vector Regression (SVR)

SVR uses the perceptron algorithm to minimize classification errors. Its objective is to maximize the distance between the separation hyperplane and the closest training samples to it, referred to as support vectors. In a dataset where it is not possible to separate the samples using a linear hyperplane as a boundary with the assistance of linear models, kernel methods attempt to create nonlinear combinations of features to project them into a higher-dimensional space through mapping, where linear separation becomes feasible (Fig. 2).

Fig. 2 Graphic representation of the support vector machine’s (SVM) work and the intention to maximize the margin. Obtained from ^{Raschka (2015)}. 

3. Results

The best results are presented in Tables VI and VII. Comparison graphs of actual data with predicted values in the validation set and loss graphs for the ANN and LSTM methods are also shown (Figs. 3 and 4).

Fig. 3 Graph of actual SPEI values (black line) and predicted values (red line) from the Support Vector Regression (SVR) model for SPEI 12. Both with scaled gamma, C = 1, Degree = 1, and polynomial kernel. (SPEI: standardized precipitation evapotranspiration index.) 

Fig. 4 Graph of real (black line) and predicted (red line) SPEI values from the LSTM model for SPEI 24 with 32-32-32 neurons. (SPEI: Standardized Precipitation Evapotranspiration Index; LSTM: Long-Short Term Memory). 

The loss graphs for MSE, obtained epoch by epoch during the training of ANN and LSTM, reveal that the training was stable due to the inverse exponential behavior. This also indicates that the algorithm is learning correctly without overfitting.

4. Discussion

In this research, we created predictive models using ANNs, LSTM, and SVR to estimate the temporal scales of SPEI 12 and SPEI 24 from 1901 to 2020 in Chihuahua, Chihuahua, Mexico. A total of 956 experiments were carried out, involving variations in parameters such as the number of neurons, kernel, and polynomial degree, among others. The two best models were chosen for each method, and the outcomes indicated the following performance metrics: MSE = 0.0047, MAE = 0.0517, MBE = 0.0193, R² = 0.8618, Kendall’s coefficient = 0.7620 for SPEI 12, and MSE = 0.0022, MAE = 0.0353, MBE = 0.0135, R² = 0.9293, Kendall’s coefficient = 0.8653 for SPEI 24.

As reported by ^{Hernández (2021)}, it is observed that the precision of the models is better as the time scale increases, probably due to greater short-term variability of the conditions. The improvement in reducing errors from SPEI 12 to SPEI 24 was between 30-50%, and the increase in the other metrics was 7-11%, so the assumption can be complemented. In this study, the performance of the SVR algorithms was very good compared to all the methods used, and as it is unusual to see this technique in other papers, it is interesting to consider that there is an area of opportunity. On the other hand, the XGBoost algorithm has performed outstandingly in several studies and was not tested in this work. Future experiments should consider studying and applying it to improve the accuracy of trained models. Although the purpose of this paper is limited to training machine learning models, the possibility of working on its application opens up.

5. Conclusions

The models developed during the project performed well and were not very different from each other. However, the polynomial SVR achieved greater accuracy in the case of SPEI 12, while LSTM 32-32-32 was slightly better for SPEI 24.

Notably, in all models, there was a challenging peak to adapt to and predict. This value corresponds to the smallest in the database (indicating the highest presence of drought) and is located in January 2011, which was the driest year in recent times in the Mexican territory.

Based on related articles, the project’s results are determined to be at a highly competitive level. The most accurate model fulfills the objective of having the potential to help predict droughts within the city of Chihuahua.

Future projects could focus on conducting more experiments to obtain even more accurate models and developing an executable program with an interface that indicates the region’s current and future drought conditions.