A Stochastic Data-Driven Ensemble Forecasting Framework for Water Resources: A Case Study Using Ensemble Members Derived From a Database of Deterministic Wavelet-Based Models

In water resources applications (e.g., streamflow, rainfall-runoff, urban water demand [UWD], etc.), ensemble member selection and ensemble member weighting are two difficult yet important tasks in the development of ensemble forecasting systems. We propose and test a stochastic data-driven ensemble forecasting framework that uses archived deterministic forecasts as input and results in probabilistic water resources forecasts. In addition to input data and (ensemble) model output uncertainty, the proposed approach integrates both ensemble member selection and weighting uncertainties, using input variable selection and data-driven methods, respectively. Therefore, it does not require one to perform ensemble member selection and weighting separately. We applied the proposed forecasting framework to a previous real-world case study in Montreal, Canada, to forecast daily UWD at multiple lead times. Using wavelet-based forecasts as input data, we develop the Ensemble Wavelet-Stochastic Data-Driven Forecasting Framework, the first multiwavelet ensemble stochastic forecasting framework that produces probabilistic forecasts. For the considered case study, several variants of Ensemble Wavelet-Stochastic Data-Driven Forecasting Framework, produced using different input variable selection methods (partial correlation input selection and Edgeworth Approximations-based conditional mutual information) and data-driven models (multiple linear regression, extreme learning machines, and second-order Volterra series models), are shown to outperform wavelet- and nonwavelet-based benchmarks, especially during a heat wave (first time studied in the UWD forecasting literature).