Toward Improved Probabilistic Predictions for Flood Forecasts Generated Using Deterministic Models

Uncertainties in flood forecasts are inevitable, and the key issue is to develop probabilistic predictions so that the predictive uncertainty (PU) bounds can be estimated. We develop and test a general method for probabilistic forecasting and PU estimation that is based on a theoretical and practical analysis of the actual nature of the model residuals, which reveals that the residual mean, standard deviation, and distributional form can all vary with time. Our approach is to condition the nature of the residual distribution on the magnitude of the corresponding streamflow value, but other kinds of conditioning are also possible. Using real data, we illustrate seven progressively more realistic sets of assumptions regarding the model residuals, ranging from homogenous Gaussian to fully heterogeneous non-Gaussian. Our results show that the estimated probabilistic predictions become progressively better as the assumptions better conform to the actual properties of the residuals. As benchmarks, we compare against results from the state-of-the-art power transformation approach. Our method is generally applicable to any situation where a deterministic model is used to generate predictions, and where empirical probabilistic predictions are required without developing a stochastic version of that model.