A Review of the Various Treatments of the Surface Momentum Flux in Severe Storms Simulations: Assumptions, Deficiencies, and Alternatives

I will review the various ways that the shear stress at the lower boundary (i.e., the surface momentum flux) has been parameterized in convective storm simulations. These include setting the shear stress to zero at the lower boundary (what might be referred to as a "traditional" free-slip lower boundary condition), setting it to match the shear stress at the first grid point above the surface (this also has been referred to as a free-slip condition), and a parameterization of the shear stress that assumes a rough surface and an overlying surface-layer vertical wind profile that obeys a log law [i.e., assuming that Monin-Obukhov (M-O) similarity theory holds]. All of the boundary conditions are problematic, unfortunately.

Although it is tempting to surmise that a boundary condition that includes the effects of surface drag would be the most realistic (the third one listed above), the assumption of a logarithmic surface-layer wind profile is unjustified within and near convective storms. M-O similarity theory requires horizontal homogeneity and stationarity, neither of which are satisfied within the outflow of a convective storm. These conditions may not even be met within the near-storm environment, especially in baroclinic boundary layers (i.e., boundary layers with a large variation of the geostrophic wind with height), within boundary layers in which winds are rapidly accelerating toward a storm updraft, or in boundary layers within complex terrain. Moreover, the M-O predictions of near-surface vertical shear, upon which drag boundary conditions are based, apply to mean quantities, not the vertical profiles at every instant at every grid point, which is most often how the boundary conditions are specified in convective storm simulations.

The presentation also will discuss which aspects of storm simulations are likely to be most influenced by the choice of lower boundary condition, as well as some techniques that can be adopted from the engineering community to improve the handling of near-surface turbulence in convective storm simulations.