Ensemble prediction and parameter estimation system: the method

Abstract In the companion paper (Järvinen et al. , 2011. Q. J. R. Meteorol. Soc. DOI: 10.1002/qj.923) we suggested a concept to estimate numerical weather prediction model closure parameters on‐line, coupled with an operational ensemble prediction system. In this paper, such a method is developed and demonstrated in low‐order numerical tests. The method utilizes the massive amount of operational model predictions to make statistical inference about the underlying probability distributions of the closure parameters. This is achieved with practically no additional computations. The only required change to the ensemble prediction system is to allow perturbation of the model closure parameters for different ensemble members. Otherwise, the method is straightforward. The parametric uncertainty is presented using a hierarchical statistical model. Proposed parameter values are resampled based on their respective likelihood function values, as evaluated against verifying observations. Update formulas are used to feed back the parametric information to the evolving proposal distribution. The method for ensemble prediction and parameter estimation system (EPPES) is demonstrated using a stochastic version of the Lorenz‐95 model. The numerical tests show that the EPPES method is capable of detecting unknown and wrongly specified parameter values, and lead to optimal forecast skill in an independent test run. Potential show‐stoppers are discussed. Our current research is directed towards a realistic ensemble prediction system. Copyright © 2011 Royal Meteorological Society