A statistical approach to evaluate theparametrisation of turbulence in convection-permitting models using radar-retrieved eddy dissipation rates

Abstract

The effects of turbulence on the evolution of convective clouds remains uncertain both in observations and in numerical weather prediction (NWP) models. Turbulent processes remain parametrised in convection-permitting models (CPMs), and simulated clouds remain highly sensitive to the configuration of sub-filter turbulence schemes. It remains unclear whether assumptions implicit in these schemes are valid for CPMs, indicating the need for thorough evaluation of their performance using observations; the primary aim of this thesis. Eddy dissipation rates e, are retrieved in radar data by applying a comprehensive method to infer the turbulent component of the Doppler spectrum variance. Hydrometeor fall-speed variances are shown to be negligible when sampling at elevations lower than 11.5°. Shear is calculated directly by applying a linear velocity model to Doppler velocities. New equations are presented to account for variance from azimuthal shear – an unseen dimension in rangeheight scans. Resulting values of e are insensitive to the scale over which shear is calculated. A thorough statistical analysis of e in observed clouds suitable for model evaluation is presented for the first time. Retrievals of e were analysed for two contrasting case studies; shallow “shower” clouds and more vigorous “deep” clouds. Values of e range from 10−3 − 10−1 m2 s −3 in shower clouds and from 10−3 − 1 m2 s −3 in deep clouds. Turbulent intensity increases with height in deep clouds while remaining constant in shower clouds. In both cases, significant positive correlations are demonstrated between e and many cloud characteristics. The strongest correlations are found between the velocity and horizontal shear in updrafts. Coherent features of e are found to have typical spatial scales of 0.5 – 1 km. Results are compared with equivalent statistics derived in 100-m and 55-m grid-length Met Office Unified Model simulations of the observed cases to evaluate the SmagorinskyLilly sub-grid mixing scheme. Simulated turbulence is characterised by small, intense regions of e more strongly co-located with shear around updrafts than observed. The 95th and 99th percentiles of model e are one and two orders of magnitude larger than observations, respectively, with similar median values. Values of e increase consistently with the mixing length and appear insensitive to grid-length suggesting 100-m was sufficient to resolve an inertial sub-range.