Optimization of NWP model closure parameters using total energy norm of forecast error as a target

Abstract. We explore the use of dry total energy norm in improving numerical weather prediction (NWP) model forecast skill. The Ensemble Prediction and Parameter Estimation System (EPPES) is utilized to estimate ECHAM5 atmospheric GCM (global circulation models) closure parameters related to clouds and precipitation. The target criterion in the optimization is the dry total energy norm of 3-day forecast error with respect to the ECMWF (European Centre for Medium-Range Weather Forecasts) operational analyses. The results are summarized as follows: (i) forecast error growth in terms of energy norm is slower in the optimized than in the default model up to day 10 forecasts (and beyond), (ii) headline forecast skill scores are improved in the training sample as well as in independent samples, (iii) the decrease of the forecast error energy norm at day three is mainly because of smaller kinetic energy error in the tropics, and (iv) this impact is spread into midlatitudes at longer ranges and appears as a smaller forecast error of potential energy. The interpretation of these results is that the parameter optimization has reduced the model error so that the forecasts remain longer in the vicinity of the analyzed state.

[1]  E. Lorenz.  Predictability of Weather and Climate: Predictability – a problem partly solved , 2006 .

[2]  Brian F. Farrell,et al.  Optimal Excitation of Neutral Rossby Waves , 1988 .

[3]  Heikki Haario,et al.  NWP model forecast skill optimization via closure parameter variations , 2012 .

[4]  Heikki Haario,et al.  Parameter variations in prediction skill optimization at ECMWF , 2013 .

[5]  Roberto Buizza,et al.  Sensitivity Analysis of Forecast Errors and the Construction of Optimal Perturbations Using Singular Vectors , 1998 .

[6]  Robert Pincus,et al.  Parameter estimation using data assimilation in an atmospheric general circulation model: From a perfect toward the real world , 2013 .

[7]  Roberto Buizza,et al.  Singular vectors and the predictability of weather and climate , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[8]  Heikki Haario,et al.  Ensemble prediction and parameter estimation system: the method , 2012 .

[9]  Leonard A. Smith,et al.  Nonlinear Processes in Geophysics Model Error in Weather Forecasting , 2022 .

[10]  Ronald M. Errico,et al.  Interpretations of the total energy and rotational energy norms applied to determination of singular vectors , 2000 .

[11]  Heikki Haario,et al.  Ensemble prediction and parameter estimation system: the concept , 2012 .

[12]  P. Houtekamer,et al.  Ensemble size, balance, and model-error representation in an ensemble Kalman filter , 2002 .

[13]  Roberto Buizza,et al.  Tropical singular vectors computed with linearized diabatic physics , 2001 .

[14]  Luca Bonaventura,et al.  The atmospheric general circulation model ECHAM 5. PART I: Model description , 2003 .

[15]  Edward N. Lorenz,et al.  Available Potential Energy and the Maintenance of the General Circulation , 1955 .

[16]  D. Wilks.  Effects of stochastic parametrizations in the Lorenz '96 system , 2005 .

[17]  Erkki Oja,et al.  Estimation of ECHAM5 climate model closure parameters with adaptive MCMC , 2010 .

[18]  E. Lorenz.  Energy and Numerical Weather Prediction , 1960 .