Prediction of Meteorological Drought in Xinjiang at Multiple Temporal Scales Based on GWO-SA-ConvBiLSTM

Prediction of Meteorological Drought in Xinjiang at Multiple Temporal Scales Based on GWO-SA-ConvBiLSTM | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Prediction of Meteorological Drought in Xinjiang at Multiple Temporal Scales Based on GWO-SA-ConvBiLSTM Lei Gu, Wen Yu Ma, MeiShuang Yu, PengYu Chen, Shuo Hou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4115134/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Drought is one of the most serious climatic disasters affecting human society. Effective drought prediction can provide a reliable basis for the formulation of anti-drought measures. According to drought characteristics, we construct a multi-time scale GWO-SA-ConvBiLSTM network. In this model, we combine Bidirectional Long Short-Term Memory (BiLSTM) and Convolutional Neural Networks (CNN), and add the self-attention mechanism (SA). On this basis, the grey Wolf optimizer(GWO) is added to make the model choose the optimal hyperparameter faster. We selected Atel region of Xinjiang as the research object, sorted out the meteorological data of 5 meteorological stations in the study area from 1960 to 2018, and imported their SPEI values of 1, 3, 6, 12 and 24 months into the model for training. Compared with other models, our model has better performance in the scenario of drought prediction. Deep Learning Drought Prediction Grey Wolf Optimization Algorithm Time Series Forecasting Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1.Introduction Drought is one of the most serious climatic disasters affecting human society(Cao et al. 2022 ). Effective drought prediction can provide a reliable basis for the formulation of anti-drought measures(Chatterjee et al. 2022 ). Drought can be divided into four categories: meteorological, agricultural, hydrological and socio-economic(Deng et al. 2021 ;Cao et al 2022 ;Hisdal et al. 2024 ). The four types of drought are closely related; they are mainly caused by precipitation, soil moisture, runoff, and socio-economic water use being below average levels over an extended period. The four types of drought are closely related; they are mainly caused by precipitation, soil moisture, runoff, and socio-economic water use being below average levels over an extended period(Herrera-Estrada et al. 2017 ;Wang et al. 2024 ).Compared to other natural disasters, drought is more complex and occurs more frequently(Haile et al. 2020 ).The Intergovernmental Panel on Climate Change in its sixth report pointed out that the risk of extreme weather events will increase in the future and that more regions worldwide will experience more frequent and severe droughts(Wu et al. 2023 ;Moemken et al. 2022 ). Effective drought prediction can provide a reliable basis for the formulation of anti-drought measures(Ali et al. 2020 ). Over the past few decades, various models have been proposed by researchers to prove effective in drought prediction, with statistical models being the most widely used(Mishra et al.2010;Hao et al. 2018). In the past, drought prediction often uses machine learning methods such as support vector machine or artificial neural network, but there are obvious shortcomings in the evaluation of prediction results(Wood et al. 2015 ;Khan et al. 2020 ;Zhang et al. 2019 ). Deep learning has been introduced into the field, it has more powerful modeling capabilities, particularly when dealing with complex nonlinear relationships and long-term dependencies(Al Mamun et al. 2024 ). LSTM (Long Short-Term Memory) is a type of RNN (Recurrent Neural Network) architecture, specifically designed to address long-term dependencies in time series and sequential data(Jiang et al. 2022;Hochreiter et al. 1997). Its forgetting gate mechanism can alleviate gradient explosion and disappearance(Yu et al.2019). BiLSTM (Bidirectional long Short-Term memory recurrent neural network) has the characteristics of extracting bidirectional temporal features, which can further improve the prediction accuracy of the model(Staudemeyer et al. 2019;Lu et al. 2022 ).Michael et al. proposed a BiLSTM-GRU network and found that BiLSTM performs well in long-time prediction of solar irradiance fluctuations(Michael et al.2024). Hameed built a binary sentiment classification model based on BiLSTM and found that a single-layer BiLSTM architecture is competitive in dealing with long-term dependencies(Hamed et al. 2020). BiLSTM focuses on long-term dependencies in time series, but there is still room for improvement in its ability to extract data on certain key temporal features. CNN is an architecture that consists of modules such as convolutional, pooling, and fully-connected layers, and it has excellent characterization and generalization ability to deal with spatially-structured data(Zarandy et al.2015;Bhatt et al. 2021 ;Alzubaidi et al.2021). We want to build a network combining BiLSTM and CNN for the complex application scenario of weather drought prediction. When working with sequential data, Self-Attention Mechanism(SA) is a technique that enables a model to create dependencies between different locations of its input data(Niu et al.2021;Guo et al. 2022;LIU er al.2021). Huang adds SA to the recurrent neural network, and the comparison reveals that the model with the addition of SA has superior accuracy(Huang et al.2017). Ran introduced SA into LSTM to predict complex spatio-temporal traffic dynamics, and the network incorporating SA was found to have better performance(Ran et al.2019). SA allows the model to process each element of a sequence while considering other elements in the sequence. This makes it possible to capture long-range dependencies, high parallel computing power, and good model interpretability. We want to make BiLSTM-CNN networks have superior performance through the SA mechanism. Hyperparameter selection in deep learning often relies on the experience of the researcher, which makes the process difficult(Yu et al.2020). Hyperparameter Optimization(HPO) algorithms can more quickly obtain the optimal hyperparameter settings, resulting in the best network performance(Lorenzo et al.2017;Xiao et al. 2020 ). Liu used GOA (Ant Colony Algorithm) for hyper-parameter selection for 24-hour wind speed prediction network and found it to have better accuracy(Liu et al.2021). Kilinc used GWO (Grey Wolf Optimizer) for hyperparameter optimization of GRU (Gated Recurrent Unit), and the performance improved by 34%(Kilinc et al.2022). Bouktif combined GA (Genetic Algorithms) with LSTM for the study of electric power load forecasting, and the network exhibited superior performance compared to LSTM alone(Bouktif et al.2018). It is evident that optimization algorithms are helpful for hyperparameter selection and enhancing the performance of networks(Karaboga et al.2009;Wang et al.2020;Fu et al.2015). Therefore, for the specific scenario of meteorological drought prediction, this paper constructs a GWO-SA-ConvBiLSTM time series forecasting network. Specifically, the main contributions of this research are as follows: This paper combines BiLSTM with CNN to form ConvBiLSTM and, on this basis, integrates a self-attention mechanism. This enables the network to better adapt to the complex scenarios of meteorological drought prediction. Ultimately, the Grey Wolf Optimization (GWO) is utilized for selection and optimization of the network hyperparameters. The study predicts the fusion based on multi-temporal scale SPEI data, where short-term SPEI helps in identifying features of seasonal or short-term drastic fluctuations, and long-term SPEI reflects the long-term trends of the climate. The results prove that such approach yields higher accuracy compared to predictions using data from a single temporal scale. The GWO-SA-ConvBiLSTM network is compared with other mainstream networks for performance evaluation. The results reveal that the GWO-SA-ConvBiLSTM network proposed by this paper has greater accuracy and convergence speed. The rest of this paper is organized as follows. Section 2 shows the methodology used in this paper, including SPEI value, BiLSTM network, CNN, and attention mechanism. Section 3 introduces the GWO-SA-BiLSTM network framework. Section 4 shows the results of this research. Section 5 is the main contributions. Section 6 includes the conclusion and an outlook for future research. 2.Methodology This section reviews the methodology involved in the research, including the Standardized Precipitation Evapotranspiration Index (SPEI), the Potential Evapotranspiration (PET) Index, Convolutional Neural Networks (CNN), Bidirectional Long Short-Term Memory networks, the self-attention mechanism, and the Grey Wolf Optimization (GWO) algorithm. By listing the advantages and disadvantages of various networks, the model structure proposed in this study is ultimately determined. 2.1 Standardized Precipitation Evapotranspiration Index (SPEI) The Standardized Precipitation Evapotranspiration Index (SPEI) is an extension of the Standardized Precipitation Index (SPI)(Guttman et al.1999), which consists of standardized precipitation and standardized evapotranspiration (PET), and characterizes drought through the extent to which the climatic water balance deviates from the mean state(Stagge et al. 2015 ). For the calculation of Potential Evapotranspiration (PET), the main methods currently in use are those developed by Thornthwaite and Penman-Monteit(Li et al.2022;Al Moteri et al.2024). Considering that temperature, relative humidity, wind speed, and solar radiation are among various meteorological parameters, the latter offers more accurate estimates of potential evapotranspiration under conditions of richer meteorological data. Therefore, this paper selects the latter as the method for calculating PET. Since this paper needs to build a network with multiple time scales, we calculate SPEI based on the first 1 month, 3 months, 6 months, 12 months, and 24 months, respectively. The potential evapotranspiration (PET) within SPEI is estimated using the Penman-Monteith formula. Potential evapotranspiration (PET) was calculated using the Penman-Monteith formula for precipitation and PET to derive a moisture gain/loss series, which was fitted with a log-logistic probability density to obtain the SPEI index. The formula is as follows: $$\varvec{S}\varvec{P}\varvec{E}\varvec{I} = W-({C}_{0}+{C}_{1}W+{C}_{2}{W}^{2})/$$ $$(1+{d}_{1}W+{d}_{2}{W}^{2}+{d}_{3}{W}^{3}) \left(1\right)$$ $$\varvec{P}=1-F\left(x\right) \left(2\right)$$ \(\varvec{F}\left(\varvec{x}\right)=[1+\alpha /(\beta -\gamma \left)\right]\) −1 (3) In the equation, W represents the probability weighted matrix; F(x) is the cumulative distribution function of the log-logistic probability distribution; P is the standardized distribution function; the constant terms \({\varvec{C}}_{0}\) =2.515517, \({\varvec{C}}_{1}\) =0.802853, \({\varvec{C}}_{2}\) =0.010328, \({\varvec{d}}_{1}\) =1.432788, \({\varvec{d}}_{2}\) =0.189269, \({\varvec{d}}_{3}\) =0.001308; \(\varvec{\alpha }\) is the scale parameter, \(\varvec{\beta }\) is the shape parameter, \(\gamma\) is the location parameter, which can be obtained by fitting using the method of moments. When P ≦0.5, \(\varvec{W}=\sqrt{-2ln\left(P\right)}\) ; when P >0.5, \(\varvec{W}=\sqrt{-2ln(1-P)}\) , the sign of SPEI is reversed. Table 1 below shows a commonly used classification scheme for SPEI [46] , where higher positive values represent a more humid environment, and lower negative values indicate a higher degree of aridity. Table 1 SPEI Classification Scheme. SPEI Value Drought Degree > +2 Enormously Wet + 1.5 to + 2 Very Wet + 0.5 to + 1 Wet -0.5 to + 0.5 Normal -1 to -0.5 Mild Drought -1.5 to -1 Moderate Drought -2 to -1.5 Severe Drought <-2 Dangerous Drought 2.2 Convolutional neural network(CNN) Recently, the field has seen vigorous development in the adaptation of 2D Convolutional Neural Networks (2D-CNNs) into 1D Convolutional Neural Networks (1D-CNNs) designs(Qazi et al. 2022 ).The 1D-CNN is a common deep learning algorithm, typically consisting of a feedforward artificial neural network with convolutional and pooling layers. It enables the network to extract relevant features from 1D data. The core part of a CNN is the convolutional layer, whose main function is to perform convolutional operations on the data by means of a convolutional kernel and output the result to the next layer of the network. The moving step of the receptive field of a single convolutional kernel is set to traverse the entire input set. The convolutional process is as follows: $${ \varvec{h}}_{\varvec{i}}^{\varvec{l}}=f\times ({w}_{i}^{l}*{X}^{l-1}+{B}_{i}^{l}) \left(4\right)$$ In the formula(4),, \({ \varvec{h}}_{\varvec{i}}^{\varvec{l}}\) is the i th feature of the l th , fis the activation function, \({\varvec{w}}_{\varvec{i}}^{\varvec{l}}\) is the weight matrix of the i th convolution kernel of the l th ,the operator * represents the convolution operation, \({\varvec{X}}^{\varvec{l}-1}\) is the output of the layer (l-1), \({\varvec{B}}_{\varvec{i}}^{\varvec{l}}\) is the bias term. Following the convolution operation, an activation function is typically applied to capture the non-linear features of the output data. Common activation functions include Sigmoid and tanh. Unlike saturating non-linear functions, non-saturating non-linear functions can address the issue of gradient explosion and vanishing gradients, thus accelerating convergence. The Rectified Linear Unit (ReLU) is a type of non-linear, non-saturating activation function. It is known for its rapid convergence properties, hence this paper selects ReLU as the activation function of choice. The ReLU activation function is as follows: $${\varvec{f}}_{\varvec{c}\varvec{o}\varvec{v}}\left({\varvec{h}}_{\varvec{i}}^{\varvec{l}}\right)=max(0,{h}_{i}^{l}) \left(5\right)$$ The introduction of pooling layers can reduce the number of parameters in the model and avoid the risk of overfitting. We construct the network using max pooling layers. The specifics are as follows: $${ \varvec{y}}_{\varvec{i}}^{\varvec{l}+1}=\underset{k\in {D}_{j}}{{max}}\left\{{x}_{i}^{l}\right(k\left)\right\} \left(6\right)$$ \({y}_{i}^{l+1}\) is the element of the i-th feature in the (l + 1)-th layer after max pooling, \({\varvec{x}}_{\varvec{i}}^{\varvec{l}}\left(\varvec{k}\right)\) is the element of the i-th feature in the pooling kernel of the l-th layer, and \({\varvec{D}}_{\varvec{j}}\) is the element of the j-th pooling region. The fully connected layer in this paper selects the softmax function for the final feature classification, which is as follows: $$\varvec{p}\left({\varvec{y}}_{\varvec{j}}\right)=\frac{exp\left({y}_{j}\right)}{{\sum }_{k=1}^{m}exp\left({y}_{k}\right)} \left(7\right)$$ In the formula mentioned above, \({\varvec{y}}_{\varvec{j}}\) represents the output of the j-th neuron in the output layer, m represents the number of categories of turbine fault levels, and \(\varvec{p}\left({\varvec{y}}_{\varvec{j}}\right)\) is the probability output of the neuron after passing through the Softmax function. 2.3 Bidirectional Long Short-Term Memory(BiLSTM) Drought forecasting is a complex, long-term nonlinear process. LSTM can only access previous information in sequence data but is incapable of capturing information from subsequent context. BiLSTM, by combining forward and backward LSTM, allows the integration of contextual information, enhances feature extraction from the original sequence, and improves the accuracy of the model's output, especially for sequence-based tasks. CNN consists of multiple layers including input layer, convolutional layers, activation function layers, pooling layers, and fully connected layers, and its typical architecture is depicted in Fig. 2 . In BiLSTM, the forward layer performs forward computation and stores the output of each forward hidden layer step. Subsequently, computations are performed in the backward layer, where the output of each backward hidden layer step is saved. Finally, the outputs of the forward and backward layers are merged to produce the final output. Equation 8 describes the architecture of BiLSTM: $$\left\{\begin{array}{c}{\overrightarrow{\varvec{h}}}_{\varvec{t}}=f({w}_{1}{x}_{t}+{w}_{2}{\overrightarrow{h}}_{t-1}),\\ \\ {\overleftarrow{\varvec{h}}}_{\varvec{t}}=f({w}_{3}{x}_{t}+{w}_{4}{\overleftarrow{h}}_{t+1}),\\ \\ {\varvec{y}}_{\varvec{t}}=g({w}_{5}{\overrightarrow{h}}_{t}+{w}_{6}{\overleftarrow{h}}_{t}+{b}_{y})\end{array}\right.$$ 8 In the formula, \({\overrightarrow{\varvec{h}}}_{\varvec{t}}\) and \({\overleftarrow{\varvec{h}}}_{\varvec{t}}\) are the outputs of the forward LSTM and the backward LSTM respectively; \({\varvec{y}}_{\varvec{t}}\) is the final output of the hidden layer; \(\varvec{f}(·)\) and \(\varvec{g}(·)\) are their corresponding activation functions; \({\varvec{b}}_{\varvec{y}}\) represents the bias term. 2.4 Self-attention mechanism (SA) The attention mechanism, proposed by Bahdanau and colleagues, performs well in machine learning and in solving long-range dependency problems. The primary function of the attention mechanism is to compute the correlation between the source and target sequences by calculating the similarity between elements of the source and target, and assigning corresponding weights based on this calculation to capture key information. When the target is set to the source sequence itself, it is possible to further explore the interconnections between elements within the source sequence, giving rise to the self-attention mechanism (SA) [48] .The characteristic of the SA mechanism is the calculation of the similarity between each element in the source and all elements in the target, as shown in the formula (9): $$\varvec{s}\varvec{i}\varvec{m}(\varvec{q},\varvec{k})=\frac{{q}^{T}.k}{\parallel q\parallel *\parallel k\parallel } \left(9\right)$$ In formula (9), q represents the source element and k represents the target element. Cosine similarity is measured by calculating the cosine of the angle between two vectors, with the value ranging between − 1 and 1, where a value closer to 0 indicates greater similarity. However, cosine similarity only considers the direction of vectors and not their magnitude, which may not accurately measure similarity. Therefore, in our experiments, we explore the optimal method for measuring similarity through the use of Pearson and Spearman correlation coefficients. The input data has three dimensions: height, width, and channels ( H, W, C ). An attention map is obtained by calculating the similarity of the inner product of the feature vectors over a specific time span ( W : the matrix product between key and query). The focused features are the product of the attention map ( W ) and the value ( V ). The attention map represents the similarity between features at different time points and serves as weights when computing the weighted average of the input values, thus obtaining the output vector of the attention module. 2.5 Adam optimizer The Adam (Adaptive Moment Estimation) optimizer was first proposed by Kingma et al(Kingma. 2014). It combines the momentum method with adaptive learning rates. During the training process, it adjusts the learning rate continuously based on estimates of each parameter's gradients and squared gradients. This allows for larger learning rates to be used early in training to accelerate convergence, while adaptively reducing the learning rate later on for more fine-tuning of the parameters. Its main advantages are efficiency and low memory requirements, and it is suitable for sparse gradients and non-stationary objectives. The update rules for the Adam optimizer are as follows: $${ \varvec{m}}_{\varvec{t}}={\beta }_{1}{m}_{t-1}+(1-{\beta }_{1}){g}_{t } \left(10\right)$$ $${ \varvec{v}}_{\varvec{t}}={\beta }_{2}{\upsilon }_{t-1}+(1-{\beta }_{2}){g}_{t}^{2} \left(11\right)$$ $${\varvec{M}}_{\varvec{t}}=\frac{{\upsilon }_{t}}{1-{\beta }_{1}^{t} } \left(12\right)$$ $${\varvec{V}}_{\varvec{t}}=\frac{{\upsilon }_{t}}{1-{\beta }_{2}^{t}} \left(13\right)$$ $${\varvec{\theta }}_{\varvec{t}+1}={\theta }_{t}-\frac{\eta }{\sqrt{{V}_{t}}+ϵ}{M}_{t} \left(14\right)$$ In which, \({\varvec{g}}_{\varvec{t}}\) represents the gradient of the parameters, \({\varvec{\beta }}_{1}\) and \({\varvec{\beta }}_{2}\) are the decay factors for the two exponentially weighted averages, \({\varvec{M}}_{\varvec{t}}\) and \({\varvec{V}}_{\varvec{t}}\) are the bias-corrected moving averages of the gradients, \({\varvec{\theta }}_{\varvec{t}+1}\) is the updated parameter, \(\varvec{\eta }\) is the learning rate, and \(\varvec{ϵ}\) is a very small number used to prevent division by zero. 3. GWO-SA-ConvBiLSTM multiscale network. 3.1 Data acquisition The research is focused around the Ili River Basin in Altay Prefecture, Xinjiang Uigur Autonomous Region of China. Climate data from January 1, 1960 to December 31, 2018 was collected (source from National Meteorological Science Data Center ( https://data.cma.cn/ )), and a total of 5 related monitoring station data were selected. The geographical coordinates of the monitoring stations are shown in Table 2 . Figure 3 is the relevant map with the blue range representing Xinjiang, and the blue pointer's location representing the location of the meteorological monitoring station. The Altay Region is a border area in the northern part of the Xinjiang Uigur Autonomous Region of China, located at the southern foot of the Altay Mountains, north of the Junggar Basin, and bordering Russia, Mongolia, and Kazakhstan. The Altay region is located in the hinterland of the Eurasian continent, with an area of 118,000 square kilometers. It has distinct climatic characteristics, with dry, hot summers, harsh winters, little rainfall, and intense evaporation. The day-night temperature difference is significant here, and monsoons are frequent. The annual average temperature ranges from 0.7 to 4.9 degrees, with possible extreme lows reaching − 51.5 degrees and highs up to 42.2 degrees. Annual average precipitation in the plains ranges from 131 to 223 mm, while evaporation is between 1367 and 2066 mm. The frost-free period in this area is typically 123 to 152 days, and the annual sunshine duration is approximately 2829 to 3045 hours(Fu et al. 2015 ). Table 2 Basic information of meteorological station data Meteorological station name ID Longitude Latitude Data start time Data end time Habahe 51053 86.18 47.87 1960.01.01 2018.12.31 Budongjin 51060 86.83 47.68 1960.01.01 2018.12.31 Hebukesaidong 51156 85.7 46.77 1960.01.01 2018.12.31 Fuhai 51068 87.48 47.1 1960.01.01 2018.12.31 Aletai 51076 88.07 47.72 1960.01.01 2018.12.31 3.2 Data Preprocessing In order to make better drought predictions, we need to preprocess the data. First, we made an organization of data from 1960 to 2018 for six weather stations, and stations with serious missing data were not included in the study; The five available weather station data remaining after data organization and screening are shown in Fig. 3 . At the same time, we need to ensure that the time and spatial scope of the data correspond to each other, confirming that they have consistent data standards and units. We need to align them in terms of time scale and spatial scale, and the alignment of the time scale needs to ensure that the network maintains the same time granularity when training the data, which are one month, three months, six months, twelve months, and twenty-four months. Then, normalize the data to ensure that features are evaluated based on the same standards. 3.3 GWO-SA-ConvBiLSTM Architecture In this chapter, the GWO-SA-ConvBiLSTM model is built. We add a CNN module to the BiLSTM to form the ConvBiLSTM network, add the SA module to help capture key information, and finally, use GWO to update the hyperparameters of the SA-ConvBiLSTM. 3.3.1 Performance Evaluation In order to test the performance of the model, this paper uses a variety of measurement indicators for evaluation, using root mean square error (RMSE) and mean absolute error (MAE) to measure the average prediction error level, the coefficient of determination (R²) evaluates the linear relationship between the predicted value and the actual value. \(\varvec{R}\varvec{M}\varvec{S}\varvec{E}=\sqrt{\frac{1}{n}\underset{i=1}{\sum ^{n}}({y}_{i}-{\widehat{y}}_{i})}\) 2 (15) $$\varvec{M}\varvec{A}\varvec{E}=\frac{1}{n}\underset{i=1}{\sum ^{n}}\left|{y}_{i}-{\widehat{y}}_{i}\right| \left(16\right)$$ $${ \varvec{R}}^{2}=1-\frac{\underset{i=1 }{\stackrel{n }{\sum {({y}_{i}-{\widehat{y}}_{i})}^{2}}}}{{\underset{i=1}{\sum ^{n}}({y}_{i}-\stackrel{-}{y})}^{2}} \left(17\right)$$ In Formulas (15) and (16), \(\varvec{n}\) is the number of samples, \({\varvec{y}}_{\varvec{i}}\) is the actual value of the I th sample, and \({\varvec{y}}_{\varvec{i}}\) is the corresponding predicted value. In Formula 17, \({\widehat{\varvec{y}}}_{\varvec{i}}\) is the average value of the actual samples. It mainly measures the level of the model's fit to the data. When its value is equal to 1 , it means that the model fits the data perfectly; when its value is equals to 0 , it indicates a random relationship with no explanatory power. If it is less than 0 , the model performs worse than just based on mean predictions. 3.3.2 SA-ConvBiLSTM This part is mainly composed of five sections: the input layer, CNN module, BiLSTM module, Self-Attention module, and output layer. The input layer is where the multi-site, multi-timescale SPEI data are imported into the model and normalized. The CNN module mainly consists of convolutional layers and pooling layers, with the pooling layers processing the spatial features extracted by the convolutional layers to reduce the computational load of the model. The BiLSTM module includes forward and backward information transmission, with units comprising forget gates, input gates, cell states, and output gates. The model was also endowed with a self-attention module to capture the inherent correlations in the data, thereby enhancing the model's predictive precision. The output layer produces the forecast results. Compared to traditional BiLSTM and ConvLSTM models, the SA-ConvBiLSTM network possesses superior spatial feature representation, computational speed, and model accuracy. Table 3 The Range of Hyperparameters Optimized by GWO Optimized Component Hyperparameters Range BiLSTM Time_step 1,3,6,12,24 Hidden_size 32,64,128,256,512 Layers 1,2,3,4,5,6,7,8 Batch_size 16,32,64,128 Convolutional Layers Filter size 1,3,5,7,9 Configuration Dropout Rate 0-0.7 Attention Module Attention_heads 1,2,4,8 Adam Learning_rate 0.0001,0.001,0.01,0.1 3.4 Grey Wolf Optimizer (GWO) The Grey Wolf Optimizer (GWO) is a swarm intelligence-based optimization algorithm proposed by Mirjalili(Mirjalili et al. 2014). In GWO, the search space of the problem represents the territory of a pack of grey wolves, and each solution is abstracted as a wolf. The three best solutions are regarded as the alpha, beta, and delta wolves, which are the leaders. Each wolf updates its position continuously based on the position of the leading wolves and its own current position information, gradually approaching the optimal solution. Throughout the process, grey wolves follow three basic behavioral rules: encircling prey, tracking prey, and besieging prey. This achieves a global search for and a local refinement of the objective function. 4 Experimental Results This section will evaluate the performance of GWO-SA-ConvBiLSTM by comparing it with other models using three different metrics: RMSE, MAE, and R². The models in comparison are GWO-SA-ConvBiLSTM, SA-ConvBiLSTM, ConvBiLSTM, and BiLSTM. The specific experimental environment is shown in Table 4 . Table 4 Experimental Environment Device Parameters CPU Intel(R)Core(TM)i5-9400F [email protected] GPU NVIDIA GeForce RTX 2060 SUPER * 1 RAM 16G CUDA NVIDIA CUDA 12.3.99 driver Programming language Python Operating system Windows 10 Deep learning framework Pytorch 2.0.1 Formulas (15)-(17) are the metrics we use to evaluate the performance of different models. Based on Table 5 , a comparison of the RMSE results of different models reveals that GWO-SA-ConvBiLSTM has lower RMSE and MAE values, indicating that GWO enhances the performance of SA-ConvBiLSTM to a certain extent. The improved model also exhibits superior R² values, proving that the GWO-optimized SA-ConvBiLSTM possesses higher robustness, accuracy, and convergence speed. Table 5 Comparison of Different Models' Performance Through RMSE, MAE, and R² Error Value ID GWO-SA-ConvBiLSTM SA-ConvBiLSTM ConvBiLSTM BiLSTM RMSE 51053 0.0384 0.0412 0.0588 0.0641 51060 0.0417 0.0421 0.0477 0.0491 51156 0.0311 0.0347 0.0384 0.0389 51068 0.0447 0.0476 0.0487 0.0451 51076 0.0298 0.0311 0.0334 0.0393 MAE 51053 0.0132 0.0144 0.0163 0.0179 51060 0.0174 0.0199 0.0211 0.0216 51156 0.0144 0.0152 0.0166 0.0178 51068 0.0136 0.0148 0.0155 0.0163 51076 0.0119 0.0124 0.0136 0.0155 R² 51053 0.9841 0.9811 0.9712 0.9688 51060 0.9815 0.9825 0.9745 0.9611 51156 0.9863 0.9793 0.9801 0.9645 51068 0.9855 0.9817 0.9731 0.9703 51076 0.9832 0.9803 0.9782 0.9691 Figure 6 displays the prediction results of the integrated multi-scale SPEI values for datasets from five meteorological stations, while Fig. 5 presents the performance of the datasets at different models in terms of RMSE and MAE. Lower RMSE and MAE values indicate superior performance, with higher numerical values representing better performance. After averaging the results, we obtained Fig. 5 , where the average RMSE of GWO-SA-ConvBiLSTM decreased by 5.6% compared to SA-ConvBiLSTM, the MAE decreased by 8.1%, and the R²increased by 0.31%. Based on this, it can be demonstrated that GWO-SA-ConvBiLSTM possesses more outstanding model performance, and has a superior ability to extract spatial features from diverse datasets. Figure 7 is a comparison graph of the LOSS values for GWO-SA-ConvBiLSTM and SA-ConvBiLSTM. Observing the trend of values, it can be seen that the model optimized with GWO has a faster convergence rate, higher stability, and lower LOSS values. The model without GWO is less stable, has a slower convergence rate, and has experienced gradient exploding, which may be due to the imprecise manual setting of the model's learning rate. BiLSTM, ConvBiLSTM, SA-ConvBiLSTM, and GWO-SA-ConvBiLSTM each demonstrate distinct model characteristics and performance. BiLSTM shows markedly lower evaluation metrics compared to other models in complex time series prediction tasks involving multiple objectives and scales. The ConvBiLSTM model with CNN improves the stability and accuracy of the model, and is more suitable for the multi-time scale time series prediction in this paper. The introduction of the self-attention mechanism enables the model to capture long-term dependencies more effectively. Based on this, it can be demonstrated that GWO-SA-ConvBiLSTM possesses faster convergence speed, higher accuracy, and more stable model performance. 5. Main Contributions Drought prediction holds significant application value for agricultural management and disaster prevention, and the GWO-SA-ConvBiLSTM demonstrates outstanding model performance and accuracy in the prediction of integrated SPEI values across multiple temporal scales. The main contributions of this paper are as follows: The study on drought prediction is conducted from a multi-temporal scale perspective; data from six meteorological stations in the Altay region of the Xinjiang Uygur Autonomous Region is categorized and organized, and their SPEI values are calculated. Data processing is performed on SPEI values for time scales of 1, 3, 6, 12, and 24 months, with data normalization and forecasting conducted on a weekly basis. This paper combines SA with ConvBiLSTM and finds that its performance exceeds that of ConvBiLSTM alone. The GWO is introduced into the SA-ConvBiLSTM model to select the optimal hyperparameters. Ablation experiments were conducted for various models in the same experimental environment and dataset, revealing that GWO-SA-ConvBiLSTM possesses superior performance in complex time series prediction tasks, with the advantages of fast convergence rate, high accuracy, and model stability. 6. Conclusion Prospect In this paper, the GWO-SA-ConvBiLSTM model is constructed for the complex time series prediction scenario across multiple temporal scales. The model's accuracy, convergence speed, and computational parameters have been verified to have excellent performance. However, there are still some shortcomings. For example, the study is limited by the data range; the results verified by the data from the Altay region of the Xinjiang Uygur Autonomous Region may not be applicable to all areas. Considering the various deficiencies that may exist in this paper, future research directions could include: improvement of hyperparameter optimization algorithms, more diversified cross-regional model adaptability tests, and others.In summary, this study demonstrates the effectiveness of the GWO-SA-ConvBiLSTM model in the prediction of SPEI on multiple temporal scales in the Xinjiang region. However, as there are still shortcomings, future researchers may consider continuing to delve into this direction to achieve more accurate and universally applicable drought prediction models. Declarations Author Contribution L. Mainly completed the manuscript of the paper, the construction of the model and the experiment.W. completed the data acquisition and collation.M. completed the analysis of the data.P. carried out the verification of the experimental results.H. carried out the supervision work.All authors conducted multiple rounds of review to confirm this version of the article. References Alzubaidi, Laith, et al. "Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions." Journal of big Data 8 (2021): 1-74. Ali, Zulfiqar, et al. "Bayesian network based procedure for regional drought monitoring: the seasonally combinative regional drought indicator." Journal of Environmental Management 276 (2020): 111296. Al Mamun, Md Abdullah, et al. 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"Soil moisture as an essential component for delineating and forecasting agricultural rather than meteorological drought." Remote Sensing of Environment 269 (2022): 112833. Cao, Shengpeng, et al. "Effects and contributions of meteorological drought on agricultural drought under different climatic zones and vegetation types in Northwest China." Science of the Total Environment 821 (2022): 153270. Deng, Ying, et al. "Responses of vegetation greenness and carbon cycle to extreme droughts in China." Agricultural and Forest Meteorology 298 (2021): 108307. Fu, Qi, et al. "Ecosystem services evaluation and its spatial characteristics in Central Asia’s arid regions: A case study in Altay Prefecture, China." Sustainability 7.7 (2015): 8335-8353. Guo, Meng-Hao, et al. "Attention mechanisms in computer vision: A survey." Computational visual media 8.3 (2022): 331-368. Guttman, Nathaniel B. "Accepting the standardized precipitation index: a calculation algorithm 1." 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"Short-term streamflow forecasting using hybrid deep learning model based on grey wolf algorithm for hydrological time series." Sustainability 14.6 (2022): 3352. Khan, Najeebullah, et al. "Prediction of droughts over Pakistan using machine learning algorithms." Advances in Water Resources 139 (2020): 103562. LIU et al. "Research progress in attention mechanism in deep learning." Chinese Journal of Engineering 43.11 (2021): 1499-1511. Li, Yang, Yaochen Qin, and Peijun Rong. "Evolution of potential evapotranspiration and its sensitivity to climate change based on the Thornthwaite, Hargreaves, and Penman–Monteith equation in environmental sensitive areas of China." Atmospheric Research 273 (2022): 106178. Lorenzo, Pablo Ribalta, et al. "Particle swarm optimization for hyper-parameter selection in deep neural networks." Proceedings of the genetic and evolutionary computation conference. 2017. Liu, Zhuoyi, Ryoichi Hara, and Hiroyuki Kita. "24 h-ahead wind speed forecasting using CEEMD-PE and ACO-GA-based deep learning neural network." Journal of Renewable and Sustainable Energy 13.4 (2021). Lu, Chuiji, et al. "Short-Term Load Forecasting Model Based on BiLSTM and Attention Mechanism." Annual Conference on Power System and Automation in Chinese Universities. Singapore: Springer Nature Singapore, 2022. Qazi, Emad Ul Haq, Abdulrazaq Almorjan, and Tanveer Zia. "A one-dimensional convolutional neural network (1d-cnn) based deep learning system for network intrusion detection." Applied Sciences 12.16 (2022): 7986. Shaw, Peter, Jakob Uszkoreit, and Ashish Vaswani. "Self-attention with relative position representations." arXiv preprint arXiv:1803.02155 (2018). Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis. "Grey wolf optimizer." Advances in engineering software 69 (2014): 46-61. Michael, Neethu Elizabeth, et al. "A cohesive structure of Bi-directional long-short-term memory (BiLSTM)-GRU for predicting hourly solar radiation." Renewable Energy (2024): 119943. Moemken, Julia, and Joaquim G. Pinto. "Recurrence of drought events over Iberia. part i: methodology and application for present climate conditions." Tellus 74.1 (2022): 222. Mishra, Ashok K., and Vijay P. Singh. "A review of drought concepts." Journal of hydrology 391.1-2 (2010): 202-216. Niu, Zhaoyang, Guoqiang Zhong, and Hui Yu. "A review on the attention mechanism of deep learning." Neurocomputing 452 (2021): 48-62. Wang, Zhenwei, et al. "Temporal and spatial propagation characteristics of meteorological drought to hydrological drought and influencing factors." Atmospheric Research (2024): 107212. Ran, xiangdong, et al. "An LSTM-based method with attention mechanism for travel time prediction." Sensors 19.4 (2019): 861. Stagge, James H., et al. "Candidate distributions for climatological drought indices (SPI and SPEI)." International Journal of Climatology 35.13 (2015): 4027-4040. Staudemeyer, Ralf C., and Eric Rothstein Morris. "Understanding LSTM--a tutorial into long short-term memory recurrent neural networks." arXiv preprint arXiv:1909.09586 (2019). Wu, Haijiang, et al. "Bayesian vine copulas improve agricultural drought prediction for long lead times." Agricultural and Forest Meteorology 331 (2023): 109326. Wood, Eric F., et al. "Prospects for advancing drought understanding, monitoring, and prediction." Journal of Hydrometeorology 16.4 (2015): 1636-1657. Wang, ZhenZhou, and Adam Sobey. "A comparative review between Genetic Algorithm use in composite optimisation and the state-of-the-art in evolutionary computation." Composite Structures 233 (2020): 111739. Xiao, Xueli, et al. "Efficient hyperparameter optimization in deep learning using a variable length genetic algorithm." arXiv preprint arXiv:2006.12703 (2020). Yu, Tong, and Hong Zhu. "Hyper-parameter optimization: A review of algorithms and applications." arXiv preprint arXiv:2003.05689 (2020). Yu, Yong, et al. "A review of recurrent neural networks: LSTM cells and network architectures." Neural computation 31.7 (2019): 1235-1270. Zarándy, Ákos, et al. "Overview of CNN research: 25 years history and the current trends." 2015 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2015. Zhang, Rong, et al. "Meteorological drought forecasting based on a statistical model with machine learning techniques in Shaanxi province, China." Science of the Total Environment 665 (2019): 338-346. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4115134","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":281858776,"identity":"0368d3e6-c427-418b-b15e-2542d84263dd","order_by":0,"name":"Lei Gu","email":"","orcid":"","institution":"Shenyang University of Technology Liaoyang","correspondingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"Gu","suffix":""},{"id":281858777,"identity":"88dc4529-cfdc-4e12-8756-7ad6301ffd6a","order_by":1,"name":"Wen Yu Ma","email":"","orcid":"","institution":"Shenyang University of Technology Liaoyang","correspondingAuthor":false,"prefix":"","firstName":"Wen","middleName":"Yu","lastName":"Ma","suffix":""},{"id":281858778,"identity":"d2d2cde8-6b25-4b9a-95a0-67307098126c","order_by":2,"name":"MeiShuang Yu","email":"","orcid":"","institution":"Shenyang University of Technology Liaoyang","correspondingAuthor":false,"prefix":"","firstName":"MeiShuang","middleName":"","lastName":"Yu","suffix":""},{"id":281858779,"identity":"60d5eddd-5d25-4904-9bc9-f3448388c8d0","order_by":3,"name":"PengYu Chen","email":"","orcid":"","institution":"Shenyang University of Technology Liaoyang","correspondingAuthor":false,"prefix":"","firstName":"PengYu","middleName":"","lastName":"Chen","suffix":""},{"id":281858782,"identity":"7994d6a4-f0e5-45f0-b1d6-ea78b1d25c73","order_by":4,"name":"Shuo Hou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIie3OMQuCQBjG8ZMDXS5blYP6CheCEfhh3gicHGppNRCcjFaFPkQQNBeBLleza7Q2BLc0dtEWcenWcH944Dj4wYuQTveHMTksF6dWsn9/7RsSY0VKQAjakCKPWDMytDJPzNIAM86F6DxQz67BEFMFGWXcp0Uamqxa7igB5Lk1YJqrDqsjH3fSI2H8tMOSjDc1mJioiSckceTjKiSJmxBGJWFuHqHXYcB+El7OKTmH0CWl765DZ1DwS0KVpEq2gswDMK3ker8FQd+uJgehIp85csaiBdDpdDrdt56v4krwjie2EAAAAABJRU5ErkJggg==","orcid":"","institution":"Shenyang University of Technology Liaoyang","correspondingAuthor":true,"prefix":"","firstName":"Shuo","middleName":"","lastName":"Hou","suffix":""}],"badges":[],"createdAt":"2024-03-17 02:29:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4115134/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4115134/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53245442,"identity":"1959ca29-2353-468d-a7ae-e71a23b0a98b","added_by":"auto","created_at":"2024-03-22 11:07:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":95161,"visible":true,"origin":"","legend":"\u003cp\u003eStructure Diagram of CNN\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/18738f370a98deaa0f52f75c.png"},{"id":53245443,"identity":"f663f48b-91cc-4c85-809b-63885c7967b2","added_by":"auto","created_at":"2024-03-22 11:07:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":77818,"visible":true,"origin":"","legend":"\u003cp\u003eDiagram of LSTM and BiLSTM Network Architecture\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/9127f3f282f0c6c98c502f9d.png"},{"id":53245441,"identity":"df98cc06-c412-448d-b3a3-2988bc3813cb","added_by":"auto","created_at":"2024-03-22 11:07:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":84126,"visible":true,"origin":"","legend":"\u003cp\u003eArchitecture diagram of the self-attention module.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/6c0d8d7cabcba3f0b608993d.png"},{"id":53245444,"identity":"1650cc70-6e57-4dd1-95bc-06ca7c4cf644","added_by":"auto","created_at":"2024-03-22 11:07:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1138799,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 3\u003c/strong\u003e. Location map of meteorological monitoring stations in Altay region\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/1db75d2fb0517d1e89b0658a.png"},{"id":53245440,"identity":"db697de4-8d3e-425f-bb0c-a88370ec816a","added_by":"auto","created_at":"2024-03-22 11:07:35","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":112145,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 4\u003c/strong\u003e. The Process of Optimizing SA-ConvBiLSTM using GWO\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/fe7515a5a76f690d775ea948.png"},{"id":53245445,"identity":"d4cc1186-4b72-4eb7-b738-a36455405c15","added_by":"auto","created_at":"2024-03-22 11:07:36","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":23978,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 5\u003c/strong\u003e. Performance Comparison of Different Models\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/acd23b599c6d757401e86575.png"},{"id":53245446,"identity":"98d85757-4c26-4682-9f4f-40ec08e528a5","added_by":"auto","created_at":"2024-03-22 11:07:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":462513,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 6\u003c/strong\u003e. Using GWO-SA-ConvBiLSTM for SPEI Value Prediction at Different Sites\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/8c5e79fc36e5c3c48cf83c1f.png"},{"id":53245447,"identity":"37c4270d-2683-46f6-bbec-cb4fe764608b","added_by":"auto","created_at":"2024-03-22 11:07:36","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":95851,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 7\u003c/strong\u003e. Comparison of LOSS Values Between Two Models\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/3f3f8d92f00c698d6b34af9c.png"},{"id":55868885,"identity":"531877e9-37c5-4ec7-af4f-a733b8c33af4","added_by":"auto","created_at":"2024-05-05 10:27:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2680708,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4115134/v1/0c2def7e-fa37-4e44-86e2-d801d0c781c6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Prediction of Meteorological Drought in Xinjiang at Multiple Temporal Scales Based on GWO-SA-ConvBiLSTM","fulltext":[{"header":"1.Introduction","content":"\u003cp\u003eDrought is one of the most serious climatic disasters affecting human society(Cao et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Effective drought prediction can provide a reliable basis for the formulation of anti-drought measures(Chatterjee et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Drought can be divided into four categories: meteorological, agricultural, hydrological and socio-economic(Deng et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2021\u003c/span\u003e;Cao et al \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e;Hisdal et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The four types of drought are closely related; they are mainly caused by precipitation, soil moisture, runoff, and socio-economic water use being below average levels over an extended period. The four types of drought are closely related; they are mainly caused by precipitation, soil moisture, runoff, and socio-economic water use being below average levels over an extended period(Herrera-Estrada et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2017\u003c/span\u003e;Wang et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).Compared to other natural disasters, drought is more complex and occurs more frequently(Haile et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).The Intergovernmental Panel on Climate Change in its sixth report pointed out that the risk of extreme weather events will increase in the future and that more regions worldwide will experience more frequent and severe droughts(Wu et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2023\u003c/span\u003e;Moemken et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Effective drought prediction can provide a reliable basis for the formulation of anti-drought measures(Ali et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOver the past few decades, various models have been proposed by researchers to prove effective in drought prediction, with statistical models being the most widely used(Mishra et al.2010;Hao et al. 2018). In the past, drought prediction often uses machine learning methods such as support vector machine or artificial neural network, but there are obvious shortcomings in the evaluation of prediction results(Wood et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2015\u003c/span\u003e;Khan et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2020\u003c/span\u003e;Zhang et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Deep learning has been introduced into the field, it has more powerful modeling capabilities, particularly when dealing with complex nonlinear relationships and long-term dependencies(Al Mamun et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). LSTM (Long Short-Term Memory) is a type of RNN (Recurrent Neural Network) architecture, specifically designed to address long-term dependencies in time series and sequential data(Jiang et al. 2022;Hochreiter et al. 1997). Its forgetting gate mechanism can alleviate gradient explosion and disappearance(Yu et al.2019). BiLSTM (Bidirectional long Short-Term memory recurrent neural network) has the characteristics of extracting bidirectional temporal features, which can further improve the prediction accuracy of the model(Staudemeyer et al. 2019;Lu et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).Michael et al. proposed a BiLSTM-GRU network and found that BiLSTM performs well in long-time prediction of solar irradiance fluctuations(Michael et al.2024). Hameed built a binary sentiment classification model based on BiLSTM and found that a single-layer BiLSTM architecture is competitive in dealing with long-term dependencies(Hamed et al. 2020). BiLSTM focuses on long-term dependencies in time series, but there is still room for improvement in its ability to extract data on certain key temporal features. CNN is an architecture that consists of modules such as convolutional, pooling, and fully-connected layers, and it has excellent characterization and generalization ability to deal with spatially-structured data(Zarandy et al.2015;Bhatt et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021\u003c/span\u003e;Alzubaidi et al.2021). We want to build a network combining BiLSTM and CNN for the complex application scenario of weather drought prediction.\u003c/p\u003e \u003cp\u003eWhen working with sequential data, Self-Attention Mechanism(SA) is a technique that enables a model to create dependencies between different locations of its input data(Niu et al.2021;Guo et al. 2022;LIU er al.2021). Huang adds SA to the recurrent neural network, and the comparison reveals that the model with the addition of SA has superior accuracy(Huang et al.2017). Ran introduced SA into LSTM to predict complex spatio-temporal traffic dynamics, and the network incorporating SA was found to have better performance(Ran et al.2019). SA allows the model to process each element of a sequence while considering other elements in the sequence. This makes it possible to capture long-range dependencies, high parallel computing power, and good model interpretability. We want to make BiLSTM-CNN networks have superior performance through the SA mechanism.\u003c/p\u003e \u003cp\u003eHyperparameter selection in deep learning often relies on the experience of the researcher, which makes the process difficult(Yu et al.2020). Hyperparameter Optimization(HPO) algorithms can more quickly obtain the optimal hyperparameter settings, resulting in the best network performance(Lorenzo et al.2017;Xiao et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Liu used GOA (Ant Colony Algorithm) for hyper-parameter selection for 24-hour wind speed prediction network and found it to have better accuracy(Liu et al.2021). Kilinc used GWO (Grey Wolf Optimizer) for hyperparameter optimization of GRU (Gated Recurrent Unit), and the performance improved by 34%(Kilinc et al.2022). Bouktif combined GA (Genetic Algorithms) with LSTM for the study of electric power load forecasting, and the network exhibited superior performance compared to LSTM alone(Bouktif et al.2018). It is evident that optimization algorithms are helpful for hyperparameter selection and enhancing the performance of networks(Karaboga et al.2009;Wang et al.2020;Fu et al.2015).\u003c/p\u003e \u003cp\u003eTherefore, for the specific scenario of meteorological drought prediction, this paper constructs a GWO-SA-ConvBiLSTM time series forecasting network. Specifically, the main contributions of this research are as follows:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThis paper combines BiLSTM with CNN to form ConvBiLSTM and, on this basis, integrates a self-attention mechanism. This enables the network to better adapt to the complex scenarios of meteorological drought prediction. Ultimately, the Grey Wolf Optimization (GWO) is utilized for selection and optimization of the network hyperparameters.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe study predicts the fusion based on multi-temporal scale SPEI data, where short-term SPEI helps in identifying features of seasonal or short-term drastic fluctuations, and long-term SPEI reflects the long-term trends of the climate. The results prove that such approach yields higher accuracy compared to predictions using data from a single temporal scale.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe GWO-SA-ConvBiLSTM network is compared with other mainstream networks for performance evaluation. The results reveal that the GWO-SA-ConvBiLSTM network proposed by this paper has greater accuracy and convergence speed.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe rest of this paper is organized as follows. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the methodology used in this paper, including SPEI value, BiLSTM network, CNN, and attention mechanism. Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e3\u003c/span\u003e introduces the GWO-SA-BiLSTM network framework. Section \u003cspan refid=\"Sec15\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the results of this research. Section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e5\u003c/span\u003e is the main contributions. Section \u003cspan refid=\"Sec17\" class=\"InternalRef\"\u003e6\u003c/span\u003e includes the conclusion and an outlook for future research.\u003c/p\u003e"},{"header":"2.Methodology","content":"\u003cp\u003eThis section reviews the methodology involved in the research, including the Standardized Precipitation Evapotranspiration Index (SPEI), the Potential Evapotranspiration (PET) Index, Convolutional Neural Networks (CNN), Bidirectional Long Short-Term Memory networks, the self-attention mechanism, and the Grey Wolf Optimization (GWO) algorithm. By listing the advantages and disadvantages of various networks, the model structure proposed in this study is ultimately determined.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Standardized Precipitation Evapotranspiration Index (SPEI)\u003c/h2\u003e \u003cp\u003eThe Standardized Precipitation Evapotranspiration Index (SPEI) is an extension of the Standardized Precipitation Index (SPI)(Guttman et al.1999), which consists of standardized precipitation and standardized evapotranspiration (PET), and characterizes drought through the extent to which the climatic water balance deviates from the mean state(Stagge et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). For the calculation of Potential Evapotranspiration (PET), the main methods currently in use are those developed by Thornthwaite and Penman-Monteit(Li et al.2022;Al Moteri et al.2024). Considering that temperature, relative humidity, wind speed, and solar radiation are among various meteorological parameters, the latter offers more accurate estimates of potential evapotranspiration under conditions of richer meteorological data. Therefore, this paper selects the latter as the method for calculating PET.\u003c/p\u003e \u003cp\u003eSince this paper needs to build a network with multiple time scales, we calculate SPEI based on the first 1 month, 3 months, 6 months, 12 months, and 24 months, respectively. The potential evapotranspiration (PET) within SPEI is estimated using the Penman-Monteith formula. Potential evapotranspiration (PET) was calculated using the Penman-Monteith formula for precipitation and PET to derive a moisture gain/loss series, which was fitted with a log-logistic probability density to obtain the SPEI index.\u003c/p\u003e \u003cp\u003eThe formula is as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\varvec{S}\\varvec{P}\\varvec{E}\\varvec{I} = W-({C}_{0}+{C}_{1}W+{C}_{2}{W}^{2})/$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$(1+{d}_{1}W+{d}_{2}{W}^{2}+{d}_{3}{W}^{3}) \\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\varvec{P}=1-F\\left(x\\right) \\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\varvec{F}\\left(\\varvec{x}\\right)=[1+\\alpha /(\\beta -\\gamma \\left)\\right]\\)\u003c/span\u003e \u003c/span\u003e \u003csup\u003e\u0026minus;1\u003c/sup\u003e (3)\u003c/p\u003e \u003cp\u003eIn the equation, \u003cb\u003eW\u003c/b\u003e represents the probability weighted matrix; \u003cb\u003eF(x)\u003c/b\u003e is the cumulative distribution function of the log-logistic probability distribution; \u003cb\u003eP\u003c/b\u003e is the standardized distribution function; the constant terms \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{C}}_{0}\\)\u003c/span\u003e\u003c/span\u003e=2.515517, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{C}}_{1}\\)\u003c/span\u003e\u003c/span\u003e=0.802853, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{C}}_{2}\\)\u003c/span\u003e\u003c/span\u003e=0.010328, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{d}}_{1}\\)\u003c/span\u003e\u003c/span\u003e=1.432788, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{d}}_{2}\\)\u003c/span\u003e\u003c/span\u003e=0.189269, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{d}}_{3}\\)\u003c/span\u003e\u003c/span\u003e=0.001308; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\alpha }\\)\u003c/span\u003e\u003c/span\u003e is the scale parameter, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\beta }\\)\u003c/span\u003e\u003c/span\u003e is the shape parameter, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\gamma\\)\u003c/span\u003e\u003c/span\u003e is the location parameter, which can be obtained by fitting using the method of moments. When \u003cb\u003eP\u003c/b\u003e≦0.5, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{W}=\\sqrt{-2ln\\left(P\\right)}\\)\u003c/span\u003e\u003c/span\u003e; when \u003cb\u003eP\u003c/b\u003e\u0026gt;0.5, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{W}=\\sqrt{-2ln(1-P)}\\)\u003c/span\u003e\u003c/span\u003e, the sign of \u003cb\u003eSPEI\u003c/b\u003e is reversed.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e below shows a commonly used classification scheme for SPEI\u003csup\u003e[46]\u003c/sup\u003e, where higher positive values represent a more humid environment, and lower negative values indicate a higher degree of aridity.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSPEI Classification Scheme.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSPEI Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDrought Degree\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026gt; +2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEnormously Wet\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e+\u0026thinsp;1.5 to +\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVery Wet\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e+\u0026thinsp;0.5 to +\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWet\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-0.5 to +\u0026thinsp;0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNormal\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-1 to -0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMild Drought\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-1.5 to -1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModerate Drought\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-2 to -1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSevere Drought\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026lt;-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDangerous Drought\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Convolutional neural network(CNN)\u003c/h2\u003e \u003cp\u003eRecently, the field has seen vigorous development in the adaptation of 2D Convolutional Neural Networks (2D-CNNs) into 1D Convolutional Neural Networks (1D-CNNs) designs(Qazi et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).The 1D-CNN is a common deep learning algorithm, typically consisting of a feedforward artificial neural network with convolutional and pooling layers. It enables the network to extract relevant features from 1D data. The core part of a CNN is the convolutional layer, whose main function is to perform convolutional operations on the data by means of a convolutional kernel and output the result to the next layer of the network. The moving step of the receptive field of a single convolutional kernel is set to traverse the entire input set. The convolutional process is as follows:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$${ \\varvec{h}}_{\\varvec{i}}^{\\varvec{l}}=f\\times ({w}_{i}^{l}*{X}^{l-1}+{B}_{i}^{l}) \\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the formula(4),, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ \\varvec{h}}_{\\varvec{i}}^{\\varvec{l}}\\)\u003c/span\u003e\u003c/span\u003eis the i \u003csup\u003eth\u003c/sup\u003e feature of the l \u003csup\u003eth\u003c/sup\u003e, fis the activation function,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{w}}_{\\varvec{i}}^{\\varvec{l}}\\)\u003c/span\u003e\u003c/span\u003e is the weight matrix of the i \u003csup\u003eth\u003c/sup\u003e convolution kernel of the l \u003csup\u003eth\u003c/sup\u003e,the operator * represents the convolution operation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{X}}^{\\varvec{l}-1}\\)\u003c/span\u003e\u003c/span\u003eis the output of the layer (l-1),\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{i}}^{\\varvec{l}}\\)\u003c/span\u003e\u003c/span\u003e is the bias term.\u003c/p\u003e \u003cp\u003eFollowing the convolution operation, an activation function is typically applied to capture the non-linear features of the output data. Common activation functions include Sigmoid and tanh. Unlike saturating non-linear functions, non-saturating non-linear functions can address the issue of gradient explosion and vanishing gradients, thus accelerating convergence. The Rectified Linear Unit (ReLU) is a type of non-linear, non-saturating activation function. It is known for its rapid convergence properties, hence this paper selects ReLU as the activation function of choice. The ReLU activation function is as follows:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$${\\varvec{f}}_{\\varvec{c}\\varvec{o}\\varvec{v}}\\left({\\varvec{h}}_{\\varvec{i}}^{\\varvec{l}}\\right)=max(0,{h}_{i}^{l}) \\left(5\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe introduction of pooling layers can reduce the number of parameters in the model and avoid the risk of overfitting. We construct the network using max pooling layers. The specifics are as follows:\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$${ \\varvec{y}}_{\\varvec{i}}^{\\varvec{l}+1}=\\underset{k\\in {D}_{j}}{{max}}\\left\\{{x}_{i}^{l}\\right(k\\left)\\right\\} \\left(6\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({y}_{i}^{l+1}\\)\u003c/span\u003e \u003c/span\u003e is the element of the i-th feature in the (l\u0026thinsp;+\u0026thinsp;1)-th layer after max pooling, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{x}}_{\\varvec{i}}^{\\varvec{l}}\\left(\\varvec{k}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the element of the i-th feature in the pooling kernel of the l-th layer, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{D}}_{\\varvec{j}}\\)\u003c/span\u003e\u003c/span\u003e is the element of the j-th pooling region.\u003c/p\u003e \u003cp\u003eThe fully connected layer in this paper selects the softmax function for the final feature classification, which is as follows:\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\varvec{p}\\left({\\varvec{y}}_{\\varvec{j}}\\right)=\\frac{exp\\left({y}_{j}\\right)}{{\\sum }_{k=1}^{m}exp\\left({y}_{k}\\right)} \\left(7\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the formula mentioned above, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{y}}_{\\varvec{j}}\\)\u003c/span\u003e\u003c/span\u003e represents the output of the j-th neuron in the output layer, \u003cb\u003em\u003c/b\u003e represents the number of categories of turbine fault levels, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{p}\\left({\\varvec{y}}_{\\varvec{j}}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the probability output of the neuron after passing through the \u003cb\u003eSoftmax\u003c/b\u003e function.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Bidirectional Long Short-Term Memory(BiLSTM)\u003c/h2\u003e \u003cp\u003eDrought forecasting is a complex, long-term nonlinear process. LSTM can only access previous information in sequence data but is incapable of capturing information from subsequent context. BiLSTM, by combining forward and backward LSTM, allows the integration of contextual information, enhances feature extraction from the original sequence, and improves the accuracy of the model's output, especially for sequence-based tasks. CNN consists of multiple layers including input layer, convolutional layers, activation function layers, pooling layers, and fully connected layers, and its typical architecture is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. In BiLSTM, the forward layer performs forward computation and stores the output of each forward hidden layer step. Subsequently, computations are performed in the backward layer, where the output of each backward hidden layer step is saved. Finally, the outputs of the forward and backward layers are merged to produce the final output.\u003c/p\u003e \u003cp\u003eEquation \u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e8\u003c/span\u003e describes the architecture of BiLSTM:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\left\\{\\begin{array}{c}{\\overrightarrow{\\varvec{h}}}_{\\varvec{t}}=f({w}_{1}{x}_{t}+{w}_{2}{\\overrightarrow{h}}_{t-1}),\\\\ \\\\ {\\overleftarrow{\\varvec{h}}}_{\\varvec{t}}=f({w}_{3}{x}_{t}+{w}_{4}{\\overleftarrow{h}}_{t+1}),\\\\ \\\\ {\\varvec{y}}_{\\varvec{t}}=g({w}_{5}{\\overrightarrow{h}}_{t}+{w}_{6}{\\overleftarrow{h}}_{t}+{b}_{y})\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the formula, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\overrightarrow{\\varvec{h}}}_{\\varvec{t}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\overleftarrow{\\varvec{h}}}_{\\varvec{t}}\\)\u003c/span\u003e\u003c/span\u003e are the outputs of the forward LSTM and the backward LSTM respectively; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{y}}_{\\varvec{t}}\\)\u003c/span\u003e\u003c/span\u003e is the final output of the hidden layer; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{f}(\u0026middot;)\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{g}(\u0026middot;)\\)\u003c/span\u003e\u003c/span\u003e are their corresponding activation functions; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{b}}_{\\varvec{y}}\\)\u003c/span\u003e\u003c/span\u003e represents the bias term.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Self-attention mechanism (SA)\u003c/h2\u003e \u003cp\u003eThe attention mechanism, proposed by Bahdanau and colleagues, performs well in machine learning and in solving long-range dependency problems. The primary function of the attention mechanism is to compute the correlation between the source and target sequences by calculating the similarity between elements of the source and target, and assigning corresponding weights based on this calculation to capture key information. When the target is set to the source sequence itself, it is possible to further explore the interconnections between elements within the source sequence, giving rise to the self-attention mechanism (SA)\u003csup\u003e[48]\u003c/sup\u003e.The characteristic of the SA mechanism is the calculation of the similarity between each element in the source and all elements in the target, as shown in the formula (9):\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$$\\varvec{s}\\varvec{i}\\varvec{m}(\\varvec{q},\\varvec{k})=\\frac{{q}^{T}.k}{\\parallel q\\parallel *\\parallel k\\parallel } \\left(9\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn formula (9), \u003cb\u003eq\u003c/b\u003e represents the source element and \u003cb\u003ek\u003c/b\u003e represents the target element. Cosine similarity is measured by calculating the cosine of the angle between two vectors, with the value ranging between \u0026minus;\u0026thinsp;1 and 1, where a value closer to 0 indicates greater similarity. However, cosine similarity only considers the direction of vectors and not their magnitude, which may not accurately measure similarity. Therefore, in our experiments, we explore the optimal method for measuring similarity through the use of Pearson and Spearman correlation coefficients.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe input data has three dimensions: height, width, and channels (\u003cb\u003eH, W, C\u003c/b\u003e). An attention map is obtained by calculating the similarity of the inner product of the feature vectors over a specific time span (\u003cb\u003eW\u003c/b\u003e: the matrix product between key and query). The focused features are the product of the attention map (\u003cb\u003eW\u003c/b\u003e) and the value (\u003cb\u003eV\u003c/b\u003e). The attention map represents the similarity between features at different time points and serves as weights when computing the weighted average of the input values, thus obtaining the output vector of the attention module.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Adam optimizer\u003c/h2\u003e \u003cp\u003eThe Adam (Adaptive Moment Estimation) optimizer was first proposed by Kingma et al(Kingma. 2014). It combines the momentum method with adaptive learning rates. During the training process, it adjusts the learning rate continuously based on estimates of each parameter's gradients and squared gradients. This allows for larger learning rates to be used early in training to accelerate convergence, while adaptively reducing the learning rate later on for more fine-tuning of the parameters. Its main advantages are efficiency and low memory requirements, and it is suitable for sparse gradients and non-stationary objectives.\u003c/p\u003e \u003cp\u003eThe update rules for the Adam optimizer are as follows:\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$${ \\varvec{m}}_{\\varvec{t}}={\\beta }_{1}{m}_{t-1}+(1-{\\beta }_{1}){g}_{t } \\left(10\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$${ \\varvec{v}}_{\\varvec{t}}={\\beta }_{2}{\\upsilon }_{t-1}+(1-{\\beta }_{2}){g}_{t}^{2} \\left(11\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equk\" name=\"EquationSource\"\u003e\n$${\\varvec{M}}_{\\varvec{t}}=\\frac{{\\upsilon }_{t}}{1-{\\beta }_{1}^{t} } \\left(12\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equl\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equl\" name=\"EquationSource\"\u003e\n$${\\varvec{V}}_{\\varvec{t}}=\\frac{{\\upsilon }_{t}}{1-{\\beta }_{2}^{t}} \\left(13\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equm\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equm\" name=\"EquationSource\"\u003e\n$${\\varvec{\\theta }}_{\\varvec{t}+1}={\\theta }_{t}-\\frac{\\eta }{\\sqrt{{V}_{t}}+ϵ}{M}_{t} \\left(14\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn which, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{g}}_{\\varvec{t}}\\)\u003c/span\u003e\u003c/span\u003e represents the gradient of the parameters, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{\\beta }}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{\\beta }}_{2}\\)\u003c/span\u003e\u003c/span\u003e are the decay factors for the two exponentially weighted averages, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{M}}_{\\varvec{t}}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{V}}_{\\varvec{t}}\\)\u003c/span\u003e\u003c/span\u003e are the bias-corrected moving averages of the gradients, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{\\theta }}_{\\varvec{t}+1}\\)\u003c/span\u003e\u003c/span\u003e is the updated parameter, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\eta }\\)\u003c/span\u003e\u003c/span\u003e is the learning rate, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{ϵ}\\)\u003c/span\u003e\u003c/span\u003e is a very small number used to prevent division by zero.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. GWO-SA-ConvBiLSTM multiscale network.","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Data acquisition\u003c/h2\u003e \u003cp\u003eThe research is focused around the Ili River Basin in Altay Prefecture, Xinjiang Uigur Autonomous Region of China. Climate data from January 1, 1960 to December 31, 2018 was collected (source from National Meteorological Science Data Center (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://data.cma.cn/\u003c/span\u003e\u003cspan address=\"https://data.cma.cn/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e)), and a total of 5 related monitoring station data were selected. The geographical coordinates of the monitoring stations are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e is the relevant map with the blue range representing Xinjiang, and the blue pointer's location representing the location of the meteorological monitoring station. The Altay Region is a border area in the northern part of the Xinjiang Uigur Autonomous Region of China, located at the southern foot of the Altay Mountains, north of the Junggar Basin, and bordering Russia, Mongolia, and Kazakhstan. The Altay region is located in the hinterland of the Eurasian continent, with an area of 118,000 square kilometers. It has distinct climatic characteristics, with dry, hot summers, harsh winters, little rainfall, and intense evaporation. The day-night temperature difference is significant here, and monsoons are frequent. The annual average temperature ranges from 0.7 to 4.9 degrees, with possible extreme lows reaching \u0026minus;\u0026thinsp;51.5 degrees and highs up to 42.2 degrees. Annual average precipitation in the plains ranges from 131 to 223 mm, while evaporation is between 1367 and 2066 mm. The frost-free period in this area is typically 123 to 152 days, and the annual sunshine duration is approximately 2829 to 3045 hours(Fu et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBasic information of meteorological station data\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMeteorological station name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLongitude\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLatitude\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eData start time\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eData end time\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHabahe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e86.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1960.01.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2018.12.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBudongjin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e86.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1960.01.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2018.12.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHebukesaidong\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e85.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1960.01.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2018.12.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFuhai\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e87.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1960.01.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2018.12.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAletai\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e88.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1960.01.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2018.12.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Data Preprocessing\u003c/h2\u003e \u003cp\u003eIn order to make better drought predictions, we need to preprocess the data. First, we made an organization of data from 1960 to 2018 for six weather stations, and stations with serious missing data were not included in the study; The five available weather station data remaining after data organization and screening are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e. At the same time, we need to ensure that the time and spatial scope of the data correspond to each other, confirming that they have consistent data standards and units. We need to align them in terms of time scale and spatial scale, and the alignment of the time scale needs to ensure that the network maintains the same time granularity when training the data, which are one month, three months, six months, twelve months, and twenty-four months. Then, normalize the data to ensure that features are evaluated based on the same standards.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 GWO-SA-ConvBiLSTM Architecture\u003c/h2\u003e \u003cp\u003eIn this chapter, the GWO-SA-ConvBiLSTM model is built. We add a CNN module to the BiLSTM to form the ConvBiLSTM network, add the SA module to help capture key information, and finally, use GWO to update the hyperparameters of the SA-ConvBiLSTM.\u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Performance Evaluation\u003c/h2\u003e \u003cp\u003eIn order to test the performance of the model, this paper uses a variety of measurement indicators for evaluation, using root mean square error (RMSE) and mean absolute error (MAE) to measure the average prediction error level, the coefficient of determination (R\u0026sup2;) evaluates the linear relationship between the predicted value and the actual value.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\varvec{R}\\varvec{M}\\varvec{S}\\varvec{E}=\\sqrt{\\frac{1}{n}\\underset{i=1}{\\sum ^{n}}({y}_{i}-{\\widehat{y}}_{i})}\\)\u003c/span\u003e \u003c/span\u003e \u003csup\u003e2\u003c/sup\u003e (15)\u003cdiv id=\"Equn\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equn\" name=\"EquationSource\"\u003e\n$$\\varvec{M}\\varvec{A}\\varvec{E}=\\frac{1}{n}\\underset{i=1}{\\sum ^{n}}\\left|{y}_{i}-{\\widehat{y}}_{i}\\right| \\left(16\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equo\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equo\" name=\"EquationSource\"\u003e\n$${ \\varvec{R}}^{2}=1-\\frac{\\underset{i=1 }{\\stackrel{n }{\\sum {({y}_{i}-{\\widehat{y}}_{i})}^{2}}}}{{\\underset{i=1}{\\sum ^{n}}({y}_{i}-\\stackrel{-}{y})}^{2}} \\left(17\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn Formulas (15) and (16), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\\)\u003c/span\u003e\u003c/span\u003e is the number of samples, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{y}}_{\\varvec{i}}\\)\u003c/span\u003e\u003c/span\u003e is the actual value of the I \u003csup\u003eth\u003c/sup\u003e sample, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{y}}_{\\varvec{i}}\\)\u003c/span\u003e\u003c/span\u003e is the corresponding predicted value. In Formula 17, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{\\varvec{y}}}_{\\varvec{i}}\\)\u003c/span\u003e\u003c/span\u003e is the average value of the actual samples. It mainly measures the level of the model's fit to the data. When its value is equal to \u003cb\u003e1\u003c/b\u003e, it means that the model fits the data perfectly; when its value is equals to \u003cb\u003e0\u003c/b\u003e, it indicates a random relationship with no explanatory power. If it is less than \u003cb\u003e0\u003c/b\u003e, the model performs worse than just based on mean predictions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 SA-ConvBiLSTM\u003c/h2\u003e \u003cp\u003eThis part is mainly composed of five sections: the input layer, CNN module, BiLSTM module, Self-Attention module, and output layer. The input layer is where the multi-site, multi-timescale SPEI data are imported into the model and normalized. The CNN module mainly consists of convolutional layers and pooling layers, with the pooling layers processing the spatial features extracted by the convolutional layers to reduce the computational load of the model. The BiLSTM module includes forward and backward information transmission, with units comprising forget gates, input gates, cell states, and output gates. The model was also endowed with a self-attention module to capture the inherent correlations in the data, thereby enhancing the model's predictive precision. The output layer produces the forecast results. Compared to traditional BiLSTM and ConvLSTM models, the SA-ConvBiLSTM network possesses superior spatial feature representation, computational speed, and model accuracy.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe Range of Hyperparameters Optimized by GWO\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOptimized Component\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHyperparameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRange\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBiLSTM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTime_step\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1,3,6,12,24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHidden_size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e32,64,128,256,512\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLayers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1,2,3,4,5,6,7,8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBatch_size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16,32,64,128\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConvolutional Layers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFilter size\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1,3,5,7,9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfiguration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDropout Rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0-0.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAttention Module\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAttention_heads\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1,2,4,8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdam\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLearning_rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0001,0.001,0.01,0.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Grey Wolf Optimizer (GWO)\u003c/h2\u003e \u003cp\u003eThe Grey Wolf Optimizer (GWO) is a swarm intelligence-based optimization algorithm proposed by Mirjalili(Mirjalili et al. 2014). In GWO, the search space of the problem represents the territory of a pack of grey wolves, and each solution is abstracted as a wolf. The three best solutions are regarded as the alpha, beta, and delta wolves, which are the leaders. Each wolf updates its position continuously based on the position of the leading wolves and its own current position information, gradually approaching the optimal solution. Throughout the process, grey wolves follow three basic behavioral rules: encircling prey, tracking prey, and besieging prey. This achieves a global search for and a local refinement of the objective function.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Experimental Results","content":"\u003cp\u003eThis section will evaluate the performance of GWO-SA-ConvBiLSTM by comparing it with other models using three different metrics: RMSE, MAE, and R\u0026sup2;. The models in comparison are GWO-SA-ConvBiLSTM, SA-ConvBiLSTM, ConvBiLSTM, and BiLSTM. The specific experimental environment is shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental Environment\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDevice\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCPU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntel(R)Core(TM)i5-9400F [email protected]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNVIDIA GeForce RTX 2060 SUPER * 1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRAM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16G\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCUDA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNVIDIA CUDA 12.3.99 driver\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProgramming language\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePython\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOperating system\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWindows 10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDeep learning framework\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePytorch 2.0.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFormulas (15)-(17) are the metrics we use to evaluate the performance of different models. Based on Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, a comparison of the RMSE results of different models reveals that GWO-SA-ConvBiLSTM has lower RMSE and MAE values, indicating that GWO enhances the performance of SA-ConvBiLSTM to a certain extent. The improved model also exhibits superior \u003cb\u003eR\u0026sup2;\u003c/b\u003e values, proving that the GWO-optimized SA-ConvBiLSTM possesses higher robustness, accuracy, and convergence speed.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of Different Models' Performance Through RMSE, MAE, and R\u0026sup2;\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eError Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGWO-SA-ConvBiLSTM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSA-ConvBiLSTM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eConvBiLSTM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBiLSTM\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0588\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0641\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0421\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0477\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0491\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0347\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0389\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0447\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0476\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0487\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0451\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0298\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0334\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0393\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0132\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0179\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0174\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0199\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0211\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0216\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0166\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0178\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0136\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0163\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0119\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0136\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0155\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9841\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9712\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9688\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9815\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9825\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9745\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9611\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9863\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9793\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9801\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9645\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9855\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9817\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9731\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9703\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e51076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9832\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9803\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9782\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9691\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e displays the prediction results of the integrated multi-scale SPEI values for datasets from five meteorological stations, while Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the performance of the datasets at different models in terms of RMSE and MAE. Lower RMSE and MAE values indicate superior performance, with higher numerical values representing better performance. After averaging the results, we obtained Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e, where the average RMSE of GWO-SA-ConvBiLSTM decreased by 5.6% compared to SA-ConvBiLSTM, the MAE decreased by 8.1%, and the R\u0026sup2;increased by 0.31%. Based on this, it can be demonstrated that GWO-SA-ConvBiLSTM possesses more outstanding model performance, and has a superior ability to extract spatial features from diverse datasets.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003e is a comparison graph of the LOSS values for GWO-SA-ConvBiLSTM and SA-ConvBiLSTM. Observing the trend of values, it can be seen that the model optimized with GWO has a faster convergence rate, higher stability, and lower LOSS values. The model without GWO is less stable, has a slower convergence rate, and has experienced gradient exploding, which may be due to the imprecise manual setting of the model's learning rate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBiLSTM, ConvBiLSTM, SA-ConvBiLSTM, and GWO-SA-ConvBiLSTM each demonstrate distinct model characteristics and performance. BiLSTM shows markedly lower evaluation metrics compared to other models in complex time series prediction tasks involving multiple objectives and scales. The ConvBiLSTM model with CNN improves the stability and accuracy of the model, and is more suitable for the multi-time scale time series prediction in this paper. The introduction of the self-attention mechanism enables the model to capture long-term dependencies more effectively. Based on this, it can be demonstrated that GWO-SA-ConvBiLSTM possesses faster convergence speed, higher accuracy, and more stable model performance.\u003c/p\u003e"},{"header":"5. Main Contributions","content":"\u003cp\u003eDrought prediction holds significant application value for agricultural management and disaster prevention, and the GWO-SA-ConvBiLSTM demonstrates outstanding model performance and accuracy in the prediction of integrated SPEI values across multiple temporal scales. The main contributions of this paper are as follows:\u003c/p\u003e \u003cp\u003eThe study on drought prediction is conducted from a multi-temporal scale perspective; data from six meteorological stations in the Altay region of the Xinjiang Uygur Autonomous Region is categorized and organized, and their SPEI values are calculated. Data processing is performed on SPEI values for time scales of 1, 3, 6, 12, and 24 months, with data normalization and forecasting conducted on a weekly basis.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cem\u003eThis paper combines SA with ConvBiLSTM and finds that its performance exceeds that of ConvBiLSTM alone. The GWO is introduced into the SA-ConvBiLSTM model to select the optimal hyperparameters.\u003c/em\u003e \u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAblation experiments were conducted for various models in the same experimental environment and dataset, revealing that GWO-SA-ConvBiLSTM possesses superior performance in complex time series prediction tasks, with the advantages of fast convergence rate, high accuracy, and model stability.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eProspect In this paper, the GWO-SA-ConvBiLSTM model is constructed for the complex time series prediction scenario across multiple temporal scales. The model's accuracy, convergence speed, and computational parameters have been verified to have excellent performance. However, there are still some shortcomings. For example, the study is limited by the data range; the results verified by the data from the Altay region of the Xinjiang Uygur Autonomous Region may not be applicable to all areas.\u003c/p\u003e \u003cp\u003eConsidering the various deficiencies that may exist in this paper, future research directions could include:\u003c/p\u003e \u003cp\u003eimprovement of hyperparameter optimization algorithms, more diversified cross-regional model adaptability tests, and others.In summary, this study demonstrates the effectiveness of the GWO-SA-ConvBiLSTM model in the prediction of SPEI on multiple temporal scales in the Xinjiang region. However, as there are still shortcomings, future researchers may consider continuing to delve into this direction to achieve more accurate and universally applicable drought prediction models.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eL. Mainly completed the manuscript of the paper, the construction of the model and the experiment.W. completed the data acquisition and collation.M. completed the analysis of the data.P. carried out the verification of the experimental results.H. carried out the supervision work.All authors conducted multiple rounds of review to confirm this version of the article.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlzubaidi, Laith, et al. \u0026quot;Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions.\u0026quot; Journal of big Data 8 (2021): 1-74.\u003c/li\u003e\n\u003cli\u003eAli, Zulfiqar, et al. \u0026quot;Bayesian network based procedure for regional drought monitoring: the seasonally combinative regional drought indicator.\u0026quot; Journal of Environmental Management 276 (2020): 111296.\u003c/li\u003e\n\u003cli\u003eAl Mamun, Md Abdullah, et al. \u0026quot;Identification of influential weather parameters and seasonal drought prediction in Bangladesh using machine learning algorithm.\u0026quot; Scientific Reports 14.1 (2024): 566.\u003c/li\u003e\n\u003cli\u003eAl Moteri, Moteeb, et al. \u0026quot;An enhanced drought forecasting in coastal arid regions using deep learning approach with evaporation index.\u0026quot; Environmental Research (2024): 118171.\u003c/li\u003e\n\u003cli\u003eBhatt, Dulari, et al. \u0026quot;CNN variants for computer vision: History, architecture, application, challenges and future scope.\u0026quot; Electronics 10.20 (2021): 2470.\u003c/li\u003e\n\u003cli\u003eBouktif, Salah, et al. \u0026quot;Optimal deep learning lstm model for electric load forecasting using feature selection and genetic algorithm: Comparison with machine learning approaches.\u0026quot; Energies 11.7 (2018): 1636.\u003c/li\u003e\n\u003cli\u003eCao, Meng, et al. \u0026quot;Assessing the performance of satellite soil moisture on agricultural drought monitoring in the North China Plain.\u0026quot; Agricultural Water Management 263 (2022): 107450.\u003c/li\u003e\n\u003cli\u003eChatterjee, Sumanta, et al. \u0026quot;Soil moisture as an essential component for delineating and forecasting agricultural rather than meteorological drought.\u0026quot; Remote Sensing of Environment 269 (2022): 112833.\u003c/li\u003e\n\u003cli\u003eCao, Shengpeng, et al. \u0026quot;Effects and contributions of meteorological drought on agricultural drought under different climatic zones and vegetation types in Northwest China.\u0026quot; Science of the Total Environment 821 (2022): 153270.\u003c/li\u003e\n\u003cli\u003eDeng, Ying, et al. \u0026quot;Responses of vegetation greenness and carbon cycle to extreme droughts in China.\u0026quot; Agricultural and Forest Meteorology 298 (2021): 108307.\u003c/li\u003e\n\u003cli\u003eFu, Qi, et al. \u0026quot;Ecosystem services evaluation and its spatial characteristics in Central Asia\u0026rsquo;s arid regions: A case study in Altay Prefecture, China.\u0026quot; Sustainability 7.7 (2015): 8335-8353. 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IEEE, 2015.\u003c/li\u003e\n\u003cli\u003eZhang, Rong, et al. \u0026quot;Meteorological drought forecasting based on a statistical model with machine learning techniques in Shaanxi province, China.\u0026quot; Science of the Total Environment 665 (2019): 338-346.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Deep Learning, Drought Prediction, Grey Wolf Optimization Algorithm, Time Series Forecasting","lastPublishedDoi":"10.21203/rs.3.rs-4115134/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4115134/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDrought is one of the most serious climatic disasters affecting human society. Effective drought prediction can provide a reliable basis for the formulation of anti-drought measures. According to drought characteristics, we construct a multi-time scale GWO-SA-ConvBiLSTM network. In this model, we combine Bidirectional Long Short-Term Memory (BiLSTM) and Convolutional Neural Networks (CNN), and add the self-attention mechanism (SA). On this basis, the grey Wolf optimizer(GWO) is added to make the model choose the optimal hyperparameter faster. We selected Atel region of Xinjiang as the research object, sorted out the meteorological data of 5 meteorological stations in the study area from 1960 to 2018, and imported their SPEI values of 1, 3, 6, 12 and 24 months into the model for training. Compared with other models, our model has better performance in the scenario of drought prediction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"Prediction of Meteorological Drought in Xinjiang at Multiple Temporal Scales Based on GWO-SA-ConvBiLSTM","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-22 11:07:30","doi":"10.21203/rs.3.rs-4115134/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"34629be1-bf97-433f-ad06-d8bf0644d2fd","owner":[],"postedDate":"March 22nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-05-05T10:25:52+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-22 11:07:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4115134","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4115134","identity":"rs-4115134","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}