Coupling the maximum overlap discrete wavelet transform and long short-term memory networks for irrigation flow forecasting

Many countries are suffering from water resource constraints due to rising demands from different water-consuming sectors and a changing climate. In some countries, such as Spain, operators of agricultural irrigation are under increasing pressure to improve efficiency. Accordingly, accurate forecasts of water demand are a prerequisite for the successful implementation of water resources planning and management tools in irrigated areas. However, forecasting approaches based on traditional neural networks have challenges to capture temporal dependencies that generally characterize irrigation flow time series. In this study, for the first time, a recurrent long short-term memory network (LSTM) was coupled with the maximum overlap discrete wavelet transformation (MODWT) and bootstrap techniques, for accurate and robust irrigation flow forecasting. For comparative purposes, the study also explored the ability of an Artificial Neural Network (ANN), a Least Squares Support Vector Regression (LSSVR), an Extreme Learning Machine (ELM) and a Multi Linear Regression (MLR), to forecast irrigation flow in Palos de la Frontera, an irrigation district located in Huelva (southern Spain), for a one-day lead time. The autocorrelation function and partial autocorrelation function determined the most significant lagged time series of irrigation flow to be used as model inputs. The wavelet-LSTM (W-ISTM) and waveletbootstrap-ANN models (WB-ANN) had the most accurate forecasts, as measured by statistical metrics including the root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (r(2)), mean relative error (MRE), mean absolute relative error (MARE), Willmott's index, and Nash-Sutcliffe efficiency index (NASH). In this study, the capabilities of LSTMs, along with the MODWT transform analysis and bootstrap techniques, were benchmarked and could be further explored for forecasting other water resources variables in different climatic regions and for multi-step lead time forecasting.