Estimation method for \(\hbox {ET}_{0}\) with PSO-LSSVM based on the HHT in cold and arid data-sparse area

A coupled particle swarm optimization (PSO) least squares support vector machine (LSSVM) model based on the Hilbert–Huang transform (HHT) was established to provide accurate estimations of reference crop evapotranspiration \((\hbox {ET}_{0})\) in cold and arid areas that lack the required meteorological data. Daily data (2000–2009) from the Hetian Xinjiang meteorological station (China) were used for training and double-day data used for validation. The accuracy of the method was compared with two machine models, the conventional PSO-LSSVM model and a generalized regression neural network, and three empirical methods, the Hargreaves, FAO-24 Penman, and Priestley–Taylor models. Under the condition of the same parameters of meteorological data, the accuracies of the machine models were found better than the empirical models, and the precision of the PSO-LSSVM coupled algorithm based on the HHT was the highest. The relative importance of the prediction elements was Rs > Tmax > Tmin > RH > Wn. When the deletion combination was Tmax/Tmin/RH/Wn, Tmax/RH/Wn, Tmin/Wn, and Wn, the mean square error was 0.407, 0.185, 0.149, 0.135, respectively, which shows this method is adequate for estimating \(\hbox {ET}_{0}\) in data-sparse areas.