Tracking down the origin of NWP model uncertainty : coarse-graining studies

Abstract

Current implementations of the perturbed parametrization tendency method for representing uncertainty rely on ad hoc assumptions about its magnitude and its spatial and temporal correlation scales. Ideally one would use observational data to ascertain the statistical character of parametrization tendency errors and use the resulting probability distribution functions to devise and calibrate the perturbed tendency approach. The reality is that observations rarely have the coverage, representativity and accuracy to form a useful comparison with model data. A less satisfactory alternative is to use high resolution modelling to provide a ‘truth’ simulation and then compare this with an equivalent but lower resolution simulation. Tendency fields from both simulations are coarse-grained to a resolution compatible with the assumed horizontal correlation scale in the perturbed tendency method and the bias-corrected differences between them are used to quantify statistical uncertainty. Early results using the ECMWF IFS forecasts appear to show that the variance of the coarse-grained tendency differences is proportional to the tendency in the lower-resolution forecast. However the current perturbed parametrization tendency scheme at ECMWF assumes that the standard deviation of the perturbations is proportional to the tendency itself. Probability distribution functions of the high-resolution model tendency, sub-sampled by narrow ranges of the low-resolution model tendency, seem to be consistent with an underlying Poisson process.