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Performance assessment of a Bayesian Forecasting System (BFS) for real-time flood forecasting D. Biondi, D.L. De Luca ⇑ Department of Soil Conservation, University of Calabria, Italy a r t i c l e i n f o Article history: Received 16 April 2012 Received in revised form 20 October 2012 Accepted 8 November 2012 Available online 19 November 2012 This manuscript was handled by Andras Bardossy, Editor-in-Chief, with the assistance of Peter F. Rasmussen, Associate Editor Keywords: Flood forecasting Uncertainty estimation Bayesian approach Rainfall–runoff modeling Stochastic rainfall prediction s u m m a r y The paper evaluates, for a number of flood events, the performance of a Bayesian Forecasting System (BFS) , with the aim of evalua ting total uncer taint y in real-time flood foreca sting . The predictiv e uncertainty of future streamflow is estimated through the Bayesian integration of two separate processors. The former evaluates the propagation of input uncertainty on simulated river discharge, the latter com- putes the hydrological uncertainty of actual river discharge associated with all other possible sources of error. A stochastic model and a distributed rainfall–runoff model were assumed, respectively, for rainfall and hydrological response simulations. A case study was carried out for a small basin in the Calabria region (southern Italy). The performance assessment of the BFS was performed with adequate verification tools suited for probabilistic forecasts of continuous variables such as streamflow. Graphical tools and scalar metrics were used to evaluate several attributes of the forecast quality of the entire time-varying predictive dis- tributions: calibration, sharpness, accuracy, and continuous ranked probability score (CRPS). Besides the overall system, which incorporates both sources of uncertainty, other hypotheses resulting from the BFS properties were examined, corresponding to (i) a perfect hydrological model; (ii) a non- informative rainfall forecast for predicting streamflow; and (iii) a perfect input forecast. The results emphasize the importance of using different diagnostic approaches to perform comprehen- sive analyses of predi ctive distrib utions , to arrive at a multif aceted view of the attributes of the prediction. For the case study, the selected criteria revealed the interaction of the different sources of error, in particular the crucial role of the hydrological uncertainty processor when compensating, at the cost of wider forecast intervals, for the unreliable and biased predictive distribution resulting from the Precipi- tation Uncertainty Processor. 2012 Elsevier B.V. All rights reserved. 1. Introduction The use of suitable techniques for evaluating predictive uncertainty is a current issue in hydrological research, especially in view of the increasing interest in probabilistic flood forecasting. Proba- bilistic forecasts, indeed, explicitly and honestly acknowledge the many uncertainties arising from a set of causes, by giving a predictive distribution for the future values of the quantity of interest. In the case of continuous variables such as streamflow, it takes the form of density forecasts or predictive intervals. Methods currently available to the hydrological community for prob abilistic fore casts can be disti ngui shed by the tech niqu es they adopt to evaluate uncertainty (probabilistic structure of the fore cast ing model ; anal ysis of the statist ical propert ies of the forecast error series; simulation and re-sampling techniques) and by the sources of uncertai nty (inputs , model structu re, mode l par ame te rs, initial and bounda ry con dit ions, etc .) ta ken int o account either individually or collectively. Following the success of its appli cation in wea ther forecast ing, ensemble stre amfl ow prediction (ESP) based on numerical weather predictions (NWPs) are widely used ( Cloke and Pappenber ger, 2009). Other approaches use ense mble forecast ing methods base d on data assimila tion (Mor adk ha ni et al. , 2005; Seo et al. , 2009; Vr ugt et al ., 2005 ), multi-modeling platforms (Ajami et al., 2007; Coccia and Todini, 2011; Georgakakos et al., 2004; Todini, 2008 ), probabilistic post- proc essor s of dete rmin istic fore cast s (Krzysztofowicz and Kelly, 2000; Montanari and Brath, 2004; Reggiani and Weerts, 2008; Seo et al., 2006; Weerts et al., 2011 ) and other probabilistic forecastin g systems (Krzysztofowicz, 2002). Neverthe less, to date the issue of critical assessment and valida- tions of predictive uncertai nty associated with hydrological proba- bil istic foreca sti ng (fo r which the standard goo dness-of- fit 0022-1694/$ - see front matter 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2012.11.019 ⇑ Corresponding author. Tel.: +39 0984496593. E-mail addresses: [email protected] (D. Biond i), [email protected] (D.L. De Luca). Journal of Hydrology 479 (2013) 51–63 Contents lists available at SciVerse ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol

baysian analysis

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