Novel hybrid machine learning framework with decomposition–transformation and identification of key modes for estimating reference evapotranspiration

The accurate estimation of reference evapotranspiration (ETo) is a fundamental requirement for precision irrigation and regional water resource planning. In this regard, the application of the standard model, FAO-56 Penman–Monteith, is limited because of insufficient meteorological data. This study aims to improve the accuracy of ETo calculations in regions with scarce meteorological data. A hybrid model integrating two data preprocessing methods (variational mode decomposition (VMD) and Box–Cox transformation (BC)) into a support vector machine (SVM) model (VMD–BC–SVM) is proposed. The model estimates the daily ETo based on the meteorological data (1980–2019) of 10 stations in the Wei River Basin of China. The VMD method was employed to extract multiple intrinsic mode functions (IMFs) and eliminate non-stationarity. This is achieved by decomposing meteorological factors, which are further transformed by BC to alleviate skewness characteristics. The least absolute shrinkage and selection operator regression (LASSO) identifies the key driving modes from the transformed IMFs, which are used as the input of the SVM model. The VMD–BC–SVM estimation model framework based on decomposition–transformation–identification–estimation is proposed. The performance of each of the hybrid VMD–BC–SVM models was further compared with those of the standalone extreme learning machine (ELM) model and two empirical models (Hargreaves–Samani and Priestley–Taylor models). The results revealed that the hybrid models outperformed the single models. The VMD–BC–SVM model achieved higher accuracy compared with the other models. Specifically, the coefficient of correlation (R) and Nash–Sutcliffe efficiency coefficient (NSE) were both greater than 0.96. Furthermore, the mean absolute percentage error (MAPE) and root mean square error (RMSE) were less than 8.41% and 0.38 mm/d, respectively. In terms of the amount of information provided, the VMD–BC–SVM model is superior to empirical models in identifying high-dimensional and nonlinear information. Moreover, the estimation performance is more stable, and the level of uncertainty is lower. This study provides a novel approach for predicting ETo in regions with limited meteorological data.