A non-parametric data-based approach for probabilistic flood forecasting in support of uncertainty communication

Abstract

In addition to structural measures, governmental authorities have set up flood forecasting systems to be used as early warning systems, to minimize the damage of future floods. These flood forecasting systems make use of hydrological and hydrodynamic models and input time series (measured and predicted rainfall, evapotranspiration, water levels and discharges). The uncertainty of these models and time series, certainly the predicted rainfall, is high and not always known. Consequently the prediction power of the flood forecasting systems is often unclear. To calculate the predictive uncertainty in the forecasts, a method has been set up, which involves computation of the exceedance probability of alert and alarm levels. The uncertainty results allow far more complete information to be provided to decision makers (in comparison with deterministic model-based forecasts).

The uncertainty estimation is based on the statistical analysis of historical flood forecasting results. The forecast residuals (differences between predictions and measurements at river gauging stations) have been analysed using a non parametric technique. Because the residuals are correlated with the value of the simulated water level and time horizon, the residuals are split up into discrete classes of simulated water levels and time horizons. For each class, percentile values of the residuals are calculated and stored in a so called ‘three dimensional error matrix’. Based on 3D interpolation in the error matrix, confidence intervals on forecasted water levels are calculated and visualised. The method is implemented in software for post processing of the forecast results, and is connected to the database of a river flood forecasting system in Belgium. Hereby it is possible to update the error matrix in real time, based on new simulations.

Introduction

At Flanders Hydraulics Research, a division of the Flemish governmental authorities in Belgium, hydrodynamic models are used to forecast discharges and water levels at a number of locations along the navigable rivers in the Flanders region of Belgium. The forecasts are issued several times a day and the system produces water level forecasts up to 48 hours in the future. The obtained forecasts are subject to uncertainties originating from the lack of accuracy in the input data (e.g. rainfall forecasts), the quality of the hydrological and hydrodynamic sub-model structures, the accuracy of parameter calibrations, etc. The models provide deterministic results of forecasted water levels and discharges, but perform less well than hoped during the majority of extreme flood events. Similar observations have been made in other countries (Spencer et al., 2006). The disappointing level of performance is not surprising, considering that each large flood event has unique characteristics and that it is very difficult to calibrate a model for these rare events. Inevitably, any model attempting to forecast complex hydrologic and/or hydraulic processes will do so with some (often significant) degree of error (Leedal et al., 2010, Pappenberger et al., 2005). Fig. 1 shows an example of observed versus forecasted water levels along the river Demer at the gauging station of Zichem. Differences between the observation and the forecast up to 1.5 m can be noticed. Given that the bottom level of the river Demer at Zichem is at 14.5 mTAW, this gives a relative error up to 60%, whereas maximum relative errors of 10% are typically considered as acceptable by the responsible authority (Van Looveren et al., 2000).

It consequently can be advised to provide to end users of the forecasts, the water and flood crisis managers and other decision makers, probabilistic information based on estimation of the forecast uncertainty. Such information should take indeed a central role in the presentation of model output to water managers and decision makers. The need for a range of forecast stages with associated probabilities was already addressed by Ingram (1997).

Leedal et al. (2010) state two main obstacles in achieving the goal of estimation and presentation of uncertainty in real-time flood predictions: (1) because calculation time and stability are essential requirements for real time flood forecasting applications, mathematically complex and time consuming methods for uncertainty estimation may not be appropriate, and (2) probabilistic information on model output has to be presented in a useful form, avoiding confusion or misinterpretation. This paper addresses these two obstacles and presents a simple, but robust approach for estimating the uncertainty of real-time flood forecasts.

A review of the existing approaches is given in Section 2 followed by Section 3 which discusses aspects of communication of uncertainty. The methodology selected in this study for uncertainty estimation on river flood forecasting results is explained in Section 4. In that section also the considered flood forecasting models and study cases are presented. In Section 5 results on the applied approach are shown and discussion on the use of these results in communication of the uncertainty to water managers and the larger public. Section 6 summarizes the different conclusions.