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

Abstract

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 UK. Perturbations are temporally correlated over an eddy-turnover timescale, 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.

A Physically Based Stochastic Boundary Layer Perturbation Scheme. Part II: Perturbation Growth within a Superensemble Framework

“…Forecasting of convective events has had a ''step change'' in ability since the advent of convection-permitting models (e.g., Lean et al 2008;Clark et al 2016). In turn, this has led to improvements in the prediction of floods with a rapid rate of rise, i.e., both surface water and flash flooding (e.g., Roberts et al 2009;Cuo et al 2011).…”

“…In turn, this has led to improvements in the prediction of floods with a rapid rate of rise, i.e., both surface water and flash flooding (e.g., Roberts et al 2009;Cuo et al 2011). However, quantitative forecasting of convective precipitation still remains a key challenge due to uncertainty in spatial structure (e.g., Roberts and Lean 2008;Dey et al 2014Dey et al , 2016aFlack et al 2018), timing (e.g., Lean et al 2008), storm structure (e.g., Stein et al 2015) and intensity (e.g., Mittermaier 2014): these issues are covered in more detail by Clark et al (2016).…”

Process‐oriented stochastic perturbations applied to the parametrization of turbulence and shallow convection for ensemble prediction

“…In our study, we found indeed too large temperature spread in the sub cloud layer in some of our ensembles. Clark et al (2021) suggest that a height-dependent length-scale could be used in the scheme. We did some tests where we replaced the constant eddy length-scale of 1,000 m by the Bougeault-Lacarrère mixing length.…”

“…) 1∕2 , a scaling factor depending on time-and length-scales, and a scaling parameter 𝛼. This formulation has similarities with the stochastic perturbation scheme of Clark et al (2021), where, starting from a simplified boundary-layer model and the assumption that turbulent eddies can be considered as random events following a Poisson distribution, they mathematically derive a perturbation of the temperature tendency representing the fluctuations around the mean due to the random presence of eddies.…”

“…Clark et al . (2021) study the representation of eddies as random events following a Poisson distribution inside a bulk model of the convective boundary layer. For simplicity, these kinds of schemes will be referred to as “process‐oriented” schemes in this article.…”