Combination of ANFIS and MLP with GRU and VMD models for predicting pan evaporation

Predicting pan evaporation is crucial for agriculture and irrigation management. Thus, our study proposes the variational mode decomposition (VMD)- gated recurrent unit (GRU)- adaptive fuzzy neuro systems (ANFIS) and VMD-GRU-multi-layer perceptron (MLP) models to accurately predict pan evaporation in one of the large basins of Iran. The models operate in several steps. First, VMD converts the time series into the intrinsic mode functions (IMFs). IMFs are subseries with more stationary features than the original time series. Then, IMFs are inserted into GRU to capture the data features. Finally, the features are inserted into the ANFIS and MLP models to produce pan evaporation data. Our results showed that the VMD-GRU-ANFIS model enhanced the mean absolute error, Nash–Sutcliffe efficiency (NSE), uncertainty at 95%, and explained variance score values of nine other prediction models by 21%–52%, 1%–16%, 1–82%, and 14%, respectively.