Stochastic Parameter Perturbation in Grell-Freitas Convective Parameterization

Most global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. With growing evidence that initial-condition uncertainties are not sufficient to entirely explain forecast uncertainty, the role of model uncertainty is receiving increasing attention. In the last decade, a number of different strategies have been proposed to represent uncertainty arising from model error. These approaches include use of multi-dynamic core, multi-physics and combination of both. While multi-physics approach yields desirable results and good performance it has practical and theoretical deficiencies. Maintenance and development of variety of physics is cost intensive. More importantly, this type of ensemble does not form a consistent distribution. Also, each member has its own climatology and error, which makes post-processing for these systems very challenging.

Performance of stochastic parameterization schemes, such as Stochastic Perturbation of Physics Tendencies (SPPT) and Stochastic Kinetic Backscatter Energy (SKEB) has been documented as very good. The fact is that these schemes are added a posteriori to NWP models that have been independently developed and tuned. Ideally, stochastic perturbations should represent model uncertainty where it occurs and should be developed alongside physical parameterizations.

Stochastic Parameter Perturbation (SPP), addresses parameterization uncertainty at its source by perturbing selected parameters within the physics parameterizations. There are two variants: the parameter can be fixed throughout the integration or can vary randomly in time and space. When used for ensembles application, the latter has the advantage that for sufficiently fast variations and/or sufficiently long integration, all ensemble members have the same climatology.

With the aim of representing uncertainty at its source, this study employs the SPP approach within the Grell-Freitas (GF) convective scheme. The purpose is to evaluate the impact of SPP on the scheme performance for both deterministic and ensemble applications. In the present study the focus was on perturbations of closures (there are four different closures in the GF scheme), the PDF’s of the normalized vertical mass flux, and the parameterization of the momentum transport. The experiments were performed using Rapid Refresh (RAP) modeling system with 13-km horizontal grid spacing.