Pan evaporation estimation by relevance vector machine tuned with new metaheuristic algorithms using limited climatic data

This study investigates the feasibility of a relevance vector machine tuned with improved Manta-Ray foraging optimization (RVM-IMRFO) in predicting monthly pan evaporation using limited climatic input data (e.g. temperature). The accuracy of the RVM-IMRFO was evaluated by comparing it with RVM tuned by gray wolf optimization, RVM tuned with a whale optimization algorithm, and RVM tuned with Manta Ray foraging optimization concerning root mean square errors (RMSE), mean absolute errors (MAE), determination coefficient (R2) and Nash-Sutcliffe Efficiency (NSE) and new graphical inspection methods. The models were assessed using data acquired from two stations in China and data were divided into three equal parts. The models were tested using each data set. The application outcomes revealed that the proposed algorithm considerably improved the accuracy of a single RVM in monthly pan evaporation prediction by an average improvement in RMSE, MAE, R2, and NSE as 27.65%, 27.53%, 8.40% and 8.63%, respectively. It is also found that the proposed algorithm showed significant dominance over others models with respect to improvement in overall mean values of RMSE, MAE, R2, and NSE statistics from 34.7–38.2 to 18.2–19.5, 36.2–36.4 to 19.1–18.5, 12.5–13.8 to 3.6–3.7, and 12.4–14.6 to 3.6–3.9%, for both climatic stations, respectively. Importing extraterrestrial radiation and periodicity component (month number of the data) into the model inputs improved the prediction accuracy of the implemented models. The outcomes revealed that the RVM-IMRFO performed superior to the other methods in predicting monthly pan evaporation using only temperature data which is essential, especially in developing countries where other climatic data are missing or unavailable. The RVM model was also compared with standard multi-layer perceptron neural networks (MLPNN) and found that the first acts better than the latter in monthly pan evaporation prediction.