Uncertainties in flood forecasting: A Bayesian total error perspective

Abstract

In flood forecasting problems where the streamflow response to rainfall is relatively quick, two steps are typically necessary: i) update the rainfall–runoff model and ideally, the probability models that describe errors; and ii) forecast future streamflow using rainfall forecasts. Step ii is a forward propagation of uncertainty, which is contingent on an adequate rainfall forecasting system. On the other hand, Step i represents an inverse problem posing several well‑known challenges that are difficult to resolve. For example, the errors in rainfall and streamflow observations are complex and are poorly approximated in traditional Kalman filter‑type schemes. This paper focuses on Step i. Starting with a probabilistic description of the uncertainties in model inputs, outputs and structure, a Bayesian total error analysis framework is formulated to improve the reliability and precision of forecasting systems. An important feature of this framework is that it infers the parameters of both the rainfall–runoff model and of the error models describing rainfall, streamflow and model uncertainty. This enables ‘training’ of the error models by the data and can improve the reliability of the predictions. However, independent (prior) information is required to ensure well‑posedness.