ORIGINAL PAPER The ensemble particle filter (EnPF) in rainfall-runoff models G. van Delft Æ G. Y. El Serafy Æ A. W. Heemink Published online: 13 January 2009 Ó Springer-Verlag 2008 Abstract Rainfall-runoff models play a very important role in flood forecasting. However, these models contain large uncertainties caused by errors in both the model itself and the input data. Data assimilation techniques are being used to reduce these uncertainties. The ensemble Kalman filter (EnKF) and the particle filter (PF) both have their own strengths. Research was carried out to a possible combi- nation between both types of filters that will lead to a new type of filters that joins the strengths of both. The so called ensemble particle filter (EnPF) new combination is tested on flood forecasting problems in both the hindcast mode as well as the forecast mode. Several proposed combinations showed considerable improvement when a hindcast com- parison on synthetic data was considered. Within the forecast comparison with field data, the suggested EnPF showed remarkable improvements compared to the PF and slight improvements compared to the EnKF. Keywords Rainfall-runoff models  Ensemble Kalman filter  Particle filter  Ensemble particle filter 1 Introduction Rainfall-runoff (RR) models are widely used in flood forecasting. Governments throughout the world are inter- ested in flood forecasts. When accurate forecasts are available one might be able to respond to upcoming high water levels. Governments might issue orders to, tempo- rarily, raise the dikes to prevent a country from flooding or in extreme floods to evacuate. A lot of uncertainties are involved in flood forecasting. First the model used to forecast the flood is never perfect. The model is a simplification of the real world process and thus contains errors. Weather forecasts are needed in order to make any prediction on the flood. For example, if there is no information and/or forecast of the amount of pre- cipitation for the upcoming days, it will be impossible to predict the water level accurately. From time to time measurements of the water level are available. These measurements can be combined with predictions obtained from the model. Through data assimilation the system state (i.e. model variables), and thus the model predictions, can be improved. Various data assimilation methods exist. The Kalman filter probably being the most well known. The original Kalman Filter, as introduced by Kalman (1960), will not be considered here, because of its limitation to linear models. The ensemble Kalman filter (EnKF) and particle filters (PF) are both suitable for non-linear models. The ensemble Kalman filter was introduced by Evensen (1994). The particle filter was introduced by Isard and Blake (1998). The PF can represent any kind of posterior probability density function, where the EnKF will assume all errors to be Gaussian distributed. This is considered as an advantage when working with RR models. One of the disadvantages of the PF would be that during the update step, no real update is being carried out. Resampling can cause filter failure (degeneracy) when the model output and/or state ‘‘domain’’ are far from the measurements domain (ref). The EnKF scheme on other hand will minimize the variance of the ensemble members. And thus all ensemble members will be updated by the EnKF. G. van Delft  A. W. Heemink Delft University of Technology, Delft, The Netherlands G. Y. El Serafy (&) Deltares, Rotterdamseweg 185, 2629 HD Delft, The Netherlands e-mail: ghada.elserafy@deltares.nl 123 Stoch Environ Res Risk Assess (2009) 23:1203–1211 DOI 10.1007/s00477-008-0301-z