Impacts of a Stochastic Subgrid-Scale Mixing Scheme in Deep Convection Simulations for Application to the Convective Gray Zone

The convective “grey” zone (i.e. grid spacings of 1-10 km) continues to gain relevance in the numerical modeling community as global models approach convection-permitting resolution but global large eddy simulation (LES) remains intractable. One well-known problem in the grey zone, specifically models run at 1-3 km horizontal grid spacing, is the inability to resolve the wide range of updraft core sizes that are seen in LES and observations. The coarse effective resolution at these grid spacings results in updrafts that are generally too wide, acting to reduce horizontal gradients of scalars and vertical velocity (and thus deformation) and ultimately resulting in reduced mixing and dilution. A method is presented to address this under-mixing by applying a stochastic multiplicative factor to the horizontal eddy diffusivity coefficient within the Smagorinsky-type turbulence closure, thus allowing for variable and enhanced mixing in time and space. Conceptually, this framework allows some updrafts to mix vigorously with dry, mid-level environmental air while also allowing updrafts at other times and locations to remain relatively undilute.

This study applies the stochastic framework to quasi-idealized ensemble simulations of squall lines using the Weather Research and Forecasting model. Initial thermodynamic conditions are based on soundings from the Midlatitude Continental Convective Clouds Experiment (MC3E). The scale applicability of the stochastic scheme is evaluated by testing horizontal grid spacings of 0.25, 0.5, 1, 2, and 4 km and comparing these ensembles to baseline simulations using the same grid spacings but the standard, non-stochastic Smagorinsky turbulence closure as well as a 125-m grid spacing LES. Finally, to test the robustness of sensitivity to the stochastic mixing, stochastic realizations are compared to a small ensemble with the standard mixing scheme but small-amplitude grid-scale noise added to the potential temperature field. Preliminary results show that the stochastic scheme is able to create spatiotemporal variability of mixing and alters vertical profiles of mass flux and vertical velocities in a manner not capable by simply diagnostically applying a constant multiplicative factor to the diffusion coefficient. The sensitivity of other key squall line features will be explored and expansion of the framework to non-idealized, “real” three-dimensional case studies will be discussed.