4.5 A STOCHASTIC PARAMETERIZATION SCHEME WITHIN NCEP GLOBAL ENSEMBLE FORECAST SYSTEM Dingchen Hou, Zoltan Toth and Yuejian Zhu Environmental Modeling Center/NCEP/NOAA, Camp Springs, Maryland 1. INTRODUCTION Current operational ensemble forecast systems have a common shortcoming: the ensemble spread is significantly less than root mean square error of the ensemble mean forecast (Buizza et al, 2004). For the NCEP Global Ensemble Forecast System (GEFS), there is also significant bias in the mean forecast. Specifically, the mean error averaged over the northern or southern hemispheric extratropics for the 500hPa height and 850hPa temperature can be over 10m and C ° 1 , respectively, in medium range forecasts. These deficits are mainly due to the inadequate representation of model uncertainty. In the operational GEFS system, model related uncertainties are neglected. Effort has been made to represent model uncertainties since 1990s. Toth and Kalnay (1995) deliberately inflate the ensemble perturbations during the integration to increase the ensemble spread. Multi-model and multi-model version approaches are employed in both operational systems (e.g. Houtekamer et al., 1996) and experimental tests (e.g. Stensrud et al. 2000 and Hou et al. 2001). However, the attempt to include model uncertainty in GEFS, represented by the two available cumulus parameterization schemes lead to insignificant improvement in the forecasts of the atmospheric circulation variables (Hou et al. 2004). On the other hand, the use of stochastic noise to represent unpredictable small-scale variability, in the form of stochastic physics with the ECMWF ensemble forecast system (Buizza, et al, 1999) and the stochastic backscatter applied to the UK Met Office model (Frederiksen and Davies 1997), appear to have beneficial effect on forecast skills and synoptic variability. Based on these considerations, research is being conducted at EMC/NCEP to develop a practical and effective stochastic parameterization scheme within GEFS. The results from some experiments with the scheme are reported in this paper. * Corresponding author address: Dingchen Hou, Environmental Modeling Center/NCEP/NOAA,W/NP2 NOAA WWB #207, 5200 Auth Road, Camp Springs MD 20746; email: dingchen.hou@noaa.gov. 2. FORMULATION AND CHARACTERISTICS The stochastic formulation of the ECMWF ensemble system (Buizza et al. 1999) links stochastic forcing to regions in the atmosphere where conventional subgrid parameterization is active (Palmer, 2001). A different approach, similar to the “stochastic backscatter”, is adopted in the current scheme. With this approach, the stochastic forcing is linked to the total conventional forcing (including the grid scale and subgrid scale parameterizations). In addition, the stochastic forcing is sampled from the differences in the conventional tendency between the ensemble members and the control forecast and the scheme is applied every 6 hours. With subscripts i and j representing one of the N ensemble members, i=1,2,…,N, 0 the control forecast and t the time after the initialization of the integration, the conventional model equation i i T X = & is replaced by ( ) ( ) [ ] ( ) ( ) [ ] ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − − − + = − − hr X X X X T X h t t h t j t j i i i 6 6 0 0 6 α & for t=k x 6hr, k=1,2,3,….., where the coefficients α’s represent rescaling of the stochastic forcing perturbations to a representative size in each of the 3 domains of northern hemisphere extratropics (NH), southern hemisphere extratropics (SH) and the tropics (TR), using 500hPa kinetic energy as the norm. Note that α’s can be positive, negative or 0, and they sum to unity: 0 = ∑ i i α . Fig.1 An example of stochastic forcing terms for vorticity near 500hPa, valid at t=18h in the forecast initialized at 00Z, Sep. 25, 2004.