Assessing parametrization uncertainty associated with horizontal resolution in numerical weather prediction models.

The need to represent uncertainty resulting from model error in ensemble weather prediction systems has spawned a variety of ad hoc stochastic algorithms based on plausible assumptions about sub-grid-scale variability. Currently, few studies have been carried out to prove the veracity of such schemes and it seems likely that some implementations of stochastic parametrization are misrepresentations of the true source of model uncertainty. This paper describes an attempt to quantify the uncertainty in physical parametrization tendencies in the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System with respect to horizontal resolution deficiency. High-resolution truth forecasts are compared with matching target forecasts at much lower resolution after coarse-graining to a common spatial and temporal resolution. In this way, model error is defined and its probability distribution function is examined as a function of tendency magnitude. It is found that the temperature tendency error associated with convection parametrization and explicit water phase changes behaves like a Poisson process for which the variance grows in proportion to the mean, which suggests that the assumptions underpinning the Craig and Cohen statistical model of convection might also apply to parametrized convection. By contrast, radiation temperature tendency errors have a very different relationship to their mean value. These findings suggest that the ECMWF stochastic perturbed parametrization tendency scheme could be improved since it assumes that the standard deviation of the tendency error is proportional to the mean. Using our finding that the variance error is proportional to the mean, a prototype stochastic parametrization scheme is devised for convective and large-scale condensation temperature tendencies and tested within the ECMWF Ensemble Prediction System. Significant impact on forecast skill is shown, implying its potential for further development.