A Physically Based Stochastic Boundary Layer Perturbation Scheme. Part I: Formulation and Evaluation in a Convection-Permitting Model

We present a simple, physically consistent stochastic boundary layer scheme implemented in the Met Office's Unified Model. It is expressed as temporally correlated multiplicative Poisson noise with a distribution that depends on physical scales. The distribution can be highly skewed at convection-permitting scales (horizontal grid lengths around 1 km) when temporal correlation is far more important than spatial. The scheme is evaluated using small ensemble forecasts of two case studies of severe convective storms over the United Kingdom. Perturbations are temporally correlated over an eddy-turnover time scale, and may be similar in magnitude to or larger than the mean boundary layer forcing. However, their mean is zero and hence they, in practice, they have very little impact on the energetics of the forecast, so overall domain-averaged precipitation, for example, is essentially unchanged. Differences between ensemble members grow; after around 12 h they appear to be roughly saturated; this represents the time scale to achieve a balance between addition of new perturbations, perturbation growth, and dissipation, not just saturation of initial perturbations. The scheme takes into account the area chosen to average over, and results are insensitive to this area at least where this remains within an order of magnitude of the grid scale.