Multiscale error analysis, correction, and predictive uncertainty estimation in a flood forecasting system

Abstract

[1] River discharge predictions often show errors that degrade the quality of forecasts. Three different methods of error correction are compared, namely, an autoregressive model with and without exogenous input (ARX and AR, respectively), and a method based on wavelet transforms. For the wavelet method, a Vector-Autoregressive model with exogenous input (VARX) is simultaneously fitted for the different levels of wavelet decomposition; after predicting the next time steps for each scale, a reconstruction formula is applied to transform the predictions in the wavelet domain back to the original time domain. The error correction methods are combined with the Hydrological Uncertainty Processor (HUP) in order to estimate the predictive conditional distribution. For three stations along the Danube catchment, and using output from the European Flood Alert System (EFAS), we demonstrate that the method based on wavelets outperforms simpler methods and uncorrected predictions with respect to mean absolute error, Nash-Sutcliffe efficiency coefficient (and its decomposed performance criteria), informativeness score, and in particular forecast reliability. The wavelet approach efficiently accounts for forecast errors with scale properties of unknown source and statistical structure.

Technical Note: The normal quantile transformation and its application in a flood forecasting system

“…In Montanari and Brath (2004) and Montanari and Grossi (2008) some problems of the NQT are discussed regarding its limited possibility of making the probability distribution of bivariate random variables multivariate Gaussian. However, Bogner and Pappenberger (2011) demonstrated that the application of error correction methods could minimize these problems in the case of flood forecasting purposes significantly.…”

“…The problem of a sufficient amount of data is naturally very common for example in flood frequency estimation (Laio et al, 2009), downscaling of climate change scenarios for hydrological applications (Bo et al, 2007;Naveau, 2007, 2008), and hydrology in general (Zhu, 1987;Engeland et al, 2004). This paper will specifically concentrate on the impact of small sample sizes in real-time flood forecasting using ensemble driven systems in combination with the HUP.…”

“…This most convenient property has been incorporated into the HUP (Krzysztofowicz and Kelly, 2000;Krzysztofowicz and Herr, 2001;Krzysztofowicz and Maranzano, 2004), which is now part of several operational forecasting systems (e.g. Reggiani et al, 2009;Bogner and Pappenberger, 2011) in order to estimate the predictive uncertainty of the hydrological forecasts. In Montanari and Brath (2004) and Montanari and Grossi (2008) some problems of the NQT are discussed regarding its limited possibility of making the probability distribution of bivariate random variables multivariate Gaussian.…”

“…However only a very limited number of flood events have been observed during the operational run of the postprocessor and therefore the evaluation of the forecast quality is rather subjective and has to be analysed in more detail. For example the predictive QQ plot (Laio and Tamea, 2007;Thyer et al, 2009;Bogner and Pappenberger, 2011) could be used to assess whether the time-varying predictive distribution of stream-flow is consistent with the observations or similar quantile assessment methods described in Coccia and Todini (2011) could be applied once more forecast data are available.…”

Do probabilistic forecasts lead to better decisions?

“…Krzysztofowicz, 2001;Pappenberger et al, 2005;Bogner and Pappenberger, 2011;Addor et al, 2011). To make the best possible decisions, forecasts with uncertainty estimates are essential.…”