Addressing the incorrect usage of wavelet-based hydrological and water resources forecasting models for real-world applications with best practices and a new forecasting framework

摘要

Many recent studies propose wavelet-based hydrological and water resources forecasting models that have been incorrectly developed and that cannot properly be used for real-world forecasting problems. The incorrect development of these wavelet-based forecasting models occurs during wavelet decomposition (the process of extracting high- and low-frequency information into different sub-time series known as wavelet and scaling coefficients, respectively) and as a result introduces error into the forecast model inputs. The source of this error is due to the boundary condition that is associated with wavelet decomposition (and the wavelet and scaling coefficients) and is linked to three main issues: 1) using 'future data' (i.e., data from the future that is not available); 2) inappropriately selecting decomposition levels and wavelet filters; and 3) not carefully partitioning calibration and validation data. By not addressing these boundary conditions during wavelet decomposition, incorrectly developed wavelet-based forecasting models often result in much better performance than what is realistically achievable. We demonstrate that the discrete wavelet transform (DWT) multiresolution analysis (DWT-MRA) and maximal overlap discrete wavelet transform (MODWT) multiresolution analysis (MODWT-MRA), two commonly adopted wavelet decomposition methods used in the development of hydrological and water resources wavelet-based forecasting models, suffer from these boundary conditions and cannot be used properly for real-world forecasting. However, by following a proposed set of best (correct) practices, we show that the MODWT and a trous algorithm (AT) can be used to correctly forecast target (e.g., hydrological and water resources) processes in real-world scenarios. In this vein, we contribute a set of best practices, which focusses on deriving "boundary-corrected" wavelet and scaling coefficients from time series data, overcoming the boundary condition issues and providing hydrol