<p>Accurate estimation of the evaporation is of great significance for the management of limited agricultural water resources. However, developing highly accurate and universal data- driven models using time-series analysis methods to achieve precise evaporation estimation remains a challenging. Specifically, integrating meta-heuristic algorithms, ensemble deep learning models, and data preprocessing techniques for evaporation prediction is notably scarce. The aim of this paper was to employ time series analysis methods to develop data-driven model with high accuracy and universality to realize accurate estimation of evaporation. To achieve this purpose, the Convolutional neural network (CNN) was integrated with Bidirectional long short-term memory network (BiLSTM) as main estimating module, and the Sparrow search algorithm (SSA) was employed to search the optimal hyperparameters of CNN-BiLSTM. To overcome the drawback that directly using measured evaporation time series to predict evaporation may lead to large error, the Variational mode decomposition (VMD) was used to extract multiscale traits of evaporation time series, and Whale optimization algorithm (WOA) was adopted to find the optimal parameters of VMD, and a novel hybrid deep learning model WOA-VMD-CNN-SSA-BiLSTM was proposed to estimate the evaporation in the Linze County, China. The estimating performance was evaluated by using the statistical accuracy metrics, including R<sup>2</sup>, the mean squared error (MSE), the mean absolute error (MAE), the root mean squared error (RMSE), and the mean absolute percentage error (MAPE). The results show that the Sample entropy (SEn) remains 0.0832 when the optimal values of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16364_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(K\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16364_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(a\)</EquationSource> </InlineEquation> of VMD are 6 and 0.1773, suggesting that VMD optimized by using WOA effectively overcomes the subjectivity in traditional VMD parameter setting and realizes amplitude-dependent feature extraction of evaporation time series in the study area. In addition, the model performance of CNN-SSA-BiLSTM can be significantly improved by coupling CNN-SSA-BiLSTM with WOA-VMD, and the hybrid model WOA-VMD-SSA-CNN-BiLSTM with MSE = 0.1258, RMSE = 0.3547, MAE = 0.2833, and MAPE = 6.17% in testing stage is superior than other hybrid models and ensemble models, which could be highly recommended for estimating evaporation in study area.</p>

Forecasting the daily evaporation by coupling the ensemble deep learning models with meta-heuristic algorithms and data pre-processing in dryland

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2025年8月20日

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Tonglin Fu,
Dong Wang,
Jing Jin

摘要

Accurate estimation of the evaporation is of great significance for the management of limited agricultural water resources. However, developing highly accurate and universal data- driven models using time-series analysis methods to achieve precise evaporation estimation remains a challenging. Specifically, integrating meta-heuristic algorithms, ensemble deep learning models, and data preprocessing techniques for evaporation prediction is notably scarce. The aim of this paper was to employ time series analysis methods to develop data-driven model with high accuracy and universality to realize accurate estimation of evaporation. To achieve this purpose, the Convolutional neural network (CNN) was integrated with Bidirectional long short-term memory network (BiLSTM) as main estimating module, and the Sparrow search algorithm (SSA) was employed to search the optimal hyperparameters of CNN-BiLSTM. To overcome the drawback that directly using measured evaporation time series to predict evaporation may lead to large error, the Variational mode decomposition (VMD) was used to extract multiscale traits of evaporation time series, and Whale optimization algorithm (WOA) was adopted to find the optimal parameters of VMD, and a novel hybrid deep learning model WOA-VMD-CNN-SSA-BiLSTM was proposed to estimate the evaporation in the Linze County, China. The estimating performance was evaluated by using the statistical accuracy metrics, including R², the mean squared error (MSE), the mean absolute error (MAE), the root mean squared error (RMSE), and the mean absolute percentage error (MAPE). The results show that the Sample entropy (SEn) remains 0.0832 when the optimal values of \(K\) and \(a\) of VMD are 6 and 0.1773, suggesting that VMD optimized by using WOA effectively overcomes the subjectivity in traditional VMD parameter setting and realizes amplitude-dependent feature extraction of evaporation time series in the study area. In addition, the model performance of CNN-SSA-BiLSTM can be significantly improved by coupling CNN-SSA-BiLSTM with WOA-VMD, and the hybrid model WOA-VMD-SSA-CNN-BiLSTM with MSE = 0.1258, RMSE = 0.3547, MAE = 0.2833, and MAPE = 6.17% in testing stage is superior than other hybrid models and ensemble models, which could be highly recommended for estimating evaporation in study area.