Hybrid machine learning and deep learning models for multi-step-ahead daily reference evapotranspiration forecasting in different climate regions across the contiguous United States

The daily reference evapotranspiration (ETo) must be accurately forecasted to improve real-time irrigation scheduling and decision-making for water resources allocation. In this study, multi-step (i.e., 1, 3, 7, and 10)-ahead daily ETo at 30 sites is forecasted using three hybrid machine learning approaches: wavelet long short-term memory (WLSTM), wavelet group method of data handling (WGMDH), and wavelet genetic algorithm-adaptive neuro-fuzzy inference system (WGA-ANFIS). The 30 sites are chosen to sample nine climate regions across the contiguous United States. Three input scenarios are considered. This study emphasizes on forecasting ETo using limited meteorological variables. In the first scenario, we consider only solar radiation (Rs) as the input variable owing to the largest correlation coefficient (R) between ETo and Rs compared with the other meteorological variables in most of the study sites. In the second scenario, in addition to Rs, the daily maximum (Tx), minimum (Tn), and mean (Tm) air temperatures are used. The input variables for the third scenario are Rs, Tx, Tn, Tm, and the relative humidity (RH). Data pertaining to 2005–2014 and 2015–2019 are used for the training and forecasting phases, respectively. The model forecasts are compared against ETo estimates from the Penman–Monteith (PM) equation. The third input scenario yields the most accurate results based on the average over all the study sites. In this input scenario, the WLSTM outperforms the other models for 1-day-ahead ETo forecasting in terms of the 30-site average root mean square error (RMSE) = 0.541 mm/d, Nash–Sutcliffe coefficient (NS) = 0.946, and R = 0.973. In contrast, WGMDH outperforms WLSTM and WGAANFIS for 3-, 7-, and 10-day-ahead ETo forecasting with RMSEs of 0.636, 0.649, and 0.651 mm/d; NS of 0.925,0.922, and 0.921; and R of 0.962, 0.961, and 0961, respectively. The highest performances of all models are observed in the Northwest and West climate regions, which exhibit the strongest correlation between Rs and ETo. The accuracy decreases in the South climate region with the weakest correlation between Rs and ETo. The lowest values of Rs, Tn, Tx, and Tm and highest RH are observed in winter. Consequently, among the seasons, the minimum RMSE (highest NS and R) is observed in winter. The worst performance of the models is observed in summer, which involves the highest values of Rs, Tx, Tn, and Tm. The deteriorated performance of the models in warm months is attributable to the high ETo values, as the models cannot accurately capture the peaks of ETo. Deep learning models (i.e., WLSTM and WGMDH) yield more accurate ETo forecasts and can thus facilitate agricultural water management and irrigation scheduling.