| An algorithm is developed that generates an ensemble forecast of a discrete-time, continuous-state, non-stationary stochastic process by employing components of the Bayesian forecasting system (BFS). Though the system is derived in the setting of forecasting river stages, it is readily adaptable to forecasting other variates. Most existing ensemble forecasting systems in hydrology generate one member per hydrologic model run and yield fewer than a hundred members; any more, and the system would execute too slowly to be useful in operational forecasting. As is shown, such a small ensemble size results in a forecast that suffers from sizeable sampling error, which could lead to erroneous decisions in critical situations, such as flooding. The proposed system, the ensemble Bayesian forecasting system with randomization (EBFSR), is unique in that one hydrologic model run can yield many ensemble members, thus reducing the sampling error without increasing the number of hydrologic model runs. The system takes in realizations of future precipitation, executes the hydrologic model for those realizations to acquire output time series, and then samples from a posterior distribution provided by the BFS many times per each output time series in order to generate the ensemble members. The EBFSR can also take as input an ensemble precipitation forecast output by a suitable processor of a numerical weather prediction. A byproduct of this research is an algorithm that estimates a predictive one-step transition distribution from an ensemble forecast and an experiment examining its properties; an analysis of the ensemble size required to reasonably estimate three types of forecasts; and an analysis of the sensitivity of the ensemble forecast to the spatiotemporal disaggregation of precipitation input to the EBFSR. |
