Towards a More Effective Postprocessing of Hydrologic Forecasts by Copula-Embedded Bayesian Model Averaging

Abstract:

Bayesian Model Averaging (BMA) develops the probability density function of the forecast variable given the predictions of different models. It applies a linear weighted average to the posterior distributions of individual models to characterize the uncertainty induced by model structures in hydro-climatologic predictions. In the original form of BMA, the posterior distribution of forecast given each model prediction is assumed to be a particular probability distribution (e.g. normal, gamma, etc.). The weight and variance of each conditional PDF is approximated with an iterative Expectation-Maximization algorithm (EM) over a calibration period. In this presentation, we demonstrate the integration of a group of multivariate functions, the so-called copula functions, to approximate the posterior distribution of forecast given individual model predictions. Here we introduce a copula-embedded BMA (Cop-BMA) method that skips the iterative procedure in the EM algorithm and also relaxes any assumptions about the shape of conditional PDFs. Both BMA and Cop-BMA are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations of ten river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are generally overconfident and have insufficient spread after BMA application. In contrast, the post-processed forecasts by Cop-BMA are more accurate and reliable. In addition, Cop-BMA outperforms BMA in the river basins with poor initial forecasts (e.g., dry regions).