Advancements in evaporation prediction: introducing the Gated Recurrent Unit–Multi-Kernel Extreme Learning Machine (MKELM)–Gaussian Process Regression (GPR) model

Predicting evaporation is an essential topic in water resources management. It is critical to plan irrigation schedules, optimize hydropower production, and accurately calculate the overall water balance. Thus, researchers have developed many prediction models for predicting evaporation. Despite the development of these models, there are still unresolved challenges. These challenges include selecting the most important input parameters, handling nonstationary data, extracting critical information from data, and quantifying the uncertainty of predicted values. Thus, the main aim of this study is to address these challenges by developing a new prediction model. The new prediction model, named Gated Recurrent Unit–Multi-Kernel Extreme Learning Machine (MKELM)–Gaussian Process Regression (GPR), was used to predict one-month ahead evaporation in the Kashafrood basin, Iran. This model was executed in multiple stages. First, a feature selection algorithm was used to determine the most critical input parameters. A data processing technique was then employed to decompose nonstationary data into stationary intrinsic mode functions (IMFs). The GRU model then processed these components to extract their essential information. In the following step, the extracted information was inserted into the MKELM model to predict evaporation. Finally, the GPR model quantified the uncertainty of predicted values. Our research also introduces a new optimizer called the Salp Swarm Optimization Algorithm–Sine Cosine Optimization Algorithm. This algorithm was used to tune the model parameters. This algorithm's performance and the prediction models’ accuracy were evaluated using several error indices. According to the study results, the GRU–MKELM–GPR model performed better than other models in predicting monthly evaporation. It improved the training and testing mean absolute error values of the other models by 21%-43% and 8.2–33%, respectively. Moreover, the new model improved the R² (R-squared or coefficient of determination) values of other models by 5–12%. Generally, the main findings of this paper included the superior performance of the new model in predicting evaporation data and the superior performance of a new optimizer in adjusting model parameters. These findings highlighted the effectiveness of the suggested model in addressing the challenges associated with evaporation prediction.