Forecasting Daily Reference Evapotranspiration under Different Hydrological Conditions using a Hybrid Wavelet–Bayesian Optimization–Gaussian Process Regression Model

• W-BO-GPR outperformed the GPR, BO-GPR, and W-GPR models. • Using daily solar radiation, mean air temperature, and relative humidity in addition to reference evapotranspiration ( ET o ) yielded more accurate results. • The best performance of the models was achieved at the Lancang and Nanmulin sites, located in humid and sub-humid climates with the lowest range of ET o variation. • The poorest results of the models were reported for the Hailisu site, which is in an arid area with the highest variations of daily ET o . • The forecast results during the winter were more accurate than those of the summer. This study aimed to forecast daily reference evapotranspiration ( ET o ) for different horizons (1-, 3-, 5-, and 7-d-ahead) at six sites in China using Gaussian process regression (GPR), wavelet transform (WT) with GPR (W-GPR), Bayesian optimization (BO) with GPR (BO-GPR), and W-BO-GPR approaches. These sites were selected to sample various climatic and vegetative conditions. All approaches were subjected to two input configurations: the first consisted of the daily ET o , and the second included the daily mean air temperature, relative humidity, solar radiation, and ET o . Meteorological data from 2010 to 2016 and 2017 to 2019 at each station were used to train and test the models, respectively. The results show that preprocessing the input data with the WT improves the performance of GPR and BO-GPR. For the first (second) input configuration, the six-site average root mean square errors (RMSEs) of ET o forecasts from W-GPR for 1-, 3-, 5-, and 7-d-ahead were 75.6%, 54.2%, 41.6%, and 32.9% (73.6%, 51.6%, 38.2%, and 28.2%) less than those of GPR, respectively. A similar reduction was observed in the RMSEs when BO-GPR was hybridized with the WT approach. The BO can successfully tune the hyperparameters of the GPR. For the first input configuration, the six-site average mean absolute errors (MAEs) of ET o forecasts from BO-GPR for the 1-, 3-, 5-, and 7-d horizons were 0.568, 0.709, 0.741, and 0.765 mm/d, respectively, which were 8.4%, 8.3%, 8.2%, and 7.4% smaller than the GPR MAEs (0.620, 0.773, 0.807, and 0.826 mm/d, respectively). Similarly, for the second input combination, BO-GPR outperformed GPR. Finally, the developed models were evaluated against two benchmark models: random forest (RF) and long short-term memory (LSTM). The proposed W-BO-GPR model demonstrated superior performance compared to the other models.