Hybrid extreme learning machine with meta-heuristic algorithms for monthly pan evaporation prediction

Accurate estimation of pan evaporation (Ep) is of great significance to the development of agricultural irrigation systems and agricultural water resources management. The purpose of this study was to explore the applicability of coupling extreme learning machine (ELM) model with two new meta-heuristic algorithms, i.e. whale optimization algorithm (WOA) and flower pollination algorithm (FPA) for monthly Ep prediction. To achieve this goal, two hybrid models of WOAELM and FPAELM were developed for predicting monthly Ep in the Poyang Lake Basin of Southern China as a case study. Their performances were further compared with the differential evolution algorithm-optimized ELM (DEELM), improved M5 model tree (M5P) and artificial neural networks (ANN) models. Monthly climatic parameters, including maximum and minimum temperature (Tmax and Tmin), sunshine duration (n), relative humidity (RH), wind speed (U) and Ep from four weather stations in the basin from 2001 to 2015 were collected, those of which during 2001–2010 were used for model training and those during 2011–2015 for model testing. The obtained results showed that the hybrid FPAELM model exhibited the highest prediction accuracy at all the four stations, followed by the hybrid WOAELM model, both of which were superior to the other traditional models. Heuristic algorithms, especially FPA, are highly recommended for improving performance of standalone machine learning models. Compared with the combination of multi-meteorological elements, the combination of Tmax, Tmin and extraterrestrial solar radiation achieved higher but still satisfactory prediction accuracy, with the absolute error less than 0.1 mm d−1 averaged over the four stations. Tmax, Tmin and extraterrestrial solar radiation were thus suggested to be used for monthly Ep estimation in this area considering the convenience of data acquisition.