A STOCHASTIC PERTURBATION SCHEME TO REPRESENT MODEL RELATED ERRORS IN NUMERICAL ATMOSPHERIC FORECASTS

D. Hou1,  Z. Toth2
1SAIC at EMC/NCEP/NWS/NOAA, USA; 2Environmental Modeling Center, NCEP/NWS/NOAA, USA
Zoltan.Toth@noaa.gov

     It has been demonstrated that ensemble (Monte Carlo) forecast systems can describe forecast uncertainty associated with errors in the initial conditions of chaotic dynamical systems. The realistic description of model-related forecast errors is a more challenging task. Despite the development and application of various related techniques (see, e.g., Toth and Vannitsem [1]), ensemble forecast systems in general are under-dispersive and cannot properly account for model-related uncertainty.

To represent model-related forecast uncertainty in numerical atmospheric general circulation models, a stochastic perturbation scheme has been developed for and tested with the National Centers for Environmental Prediction (NCEP) Global Ensemble Forecast System (GEFS). The scheme is based on the time evolving perturbations in an ensemble forecast system. The stochastic perturbations are defined based on the total conventional forcing, including the grid scale processes and the sub-grid scale parameterizations. Specifically, the stochastic perturbation (i.e., an extra forcing term) for a particular ensemble member is a weighted combination of the tendencies of the ensemble perturbations, i.e the differences in tendency between the ensemble members and the control forecast. The combination coefficients (see Fig. 1) are generated through a temporally correlated stochastic process using constraints that keep the perturbations quasi-orthogonal. The resulting flow dependent perturbations are applied to all model state variables.

The scheme will be assessed in the context of how well it captures forecast errors that cannot be explained by perturbing the initial state of the system. Initial tests with the stochastic perturbation scheme show a significant reduction in the number of outliers (i.e., cases when the verifying truth lies outside of the ensemble of forecasts), and an increase in the spread of the ensemble, reaching the level of root mean square error of the ensemble mean forecast. Also, a marked decrease in systematic errors is observed, along with an improvement in probabilistic forecast performance. Interestingly, the positive effects of the stochastic perturbation scheme are complementary to the effect of statistical post-processing used for reducing systematic errors. When statistical bias correction is applied on the stochastically perturbed ensemble, the performance significantly surpasses that of an ensemble that is either only statistically bias-corrected or only stochastically perturbed.

References

[1] Toth Z, Vannitsem S: Model errors and ensemble forecasting. Proceedings of the 8th ECMWF Workshop on Meteorological Operational Systems. November 12-16, 2001, Reading, England, 2002, pp. 146-154.

Fig. 1. Linear coefficients used to combine tendency perturbations for stochastic forcing to be applied on a particular ensemble member, based on all members of the ensemble (lines with various colors), as a function of forecast lead time