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We apply a recently developed method, the Ensemble Prediction and Parameter Estimation System (EPPES), to demonstrate how numerical weather prediction (NWP) model closure parameters can be optimized. As proof of concept, we tune the medium-range forecast skill of the ECMWF model HAMburg version (ECHAM5) atmospheric general circulation model using an ensemble prediction system (EPS) emulator. Initial state uncertainty is represented in the EPS emulator by applying the initial state perturbations generated at the European Centre for Medium-range Weather Forecasts (ECMWF). Model uncertainty is represented in the emulator via parameter variations at the initial time. We vary four closure parameters related to parametrizations of subgrid-scale physical processes of clouds and precipitation. With this set-up, we generate ensembles of 10-day global forecasts with the ECHAM5 model at T42L31 resolution twice a day over a period of three months. The cost function in the optimization is formulated in terms of standard forecast skill scores, verified against the ECMWF operational analyses. A summarizing conclusion of the experiments is that the EPPES method is able to find ECHAM5 model closure parameter values that correspond to smaller values of the cost function. The forecast skill score improvements verify positively in dependent and independent samples. The main reason is the reduced temperature bias in the tropical lower troposphere. Moreover, the optimization improved the top-of-atmosphere radiation flux climatology of the ECHAM5 model, as verified against the Clouds and the Earth's Radiant Energy System (CERES) radiation data over a 6-year period, while the simulated tropical cloud cover was reduced, thereby increasing a negative bias as verified against the International Satellite Cloud Climatology Project (ISCCP) data.

In the companion paper (Jarvinen 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

This paper discusses algorithmic estimation of numerical weather prediction (NWP) model closure parameters which appear in physical parametrizations of sub-grid scale processes. Currently, these parameters are specified manually. Our hypothesis is that the NWP model forecast skill is sensitive to the specified parameter values. Therefore some parameter value combinations score better than others, but it is very demanding to manually specify the optimal combination. First, we approximate the number of test forecasts that would be needed to estimate the posterior probability densities of a limited number of closure parameters, in a spirit of the Bayesian parameter estimation approach. Second, we discuss various options to accommodate the related huge computational task; we end up proposing that operational ensemble prediction might be a potential host. Third, we analyse the ensemble prediction system characteristics from the parameter estimation point of view. We rule out various standard parameter estimation methods; instead we suggest an estimation concept that can be on-line coupled with existing ensemble prediction systems to utilize the operational ensemble simulations. Thus practically no additional computations are introduced. Such a method, the ensemble prediction and parameter estimation system (EPPES), is developed here and demonstrated in low-order numerical tests in the companion paper (Laine M, Solonen A, Haario H, Jarvinen H. 2011. Q. J. R. Meteorol. Soc. DOI: 10.1002/qj.922). Copyright © 2011 Royal Meteorological Society