Relating the Bulk Richardson Number (RiB) to Monin-Obukhov Stability (z/L)

Parameterization of the atmospheric surface-layer turbulent fluxes in numerical model through flux-profile relationships has been the focus of significant research for the past 60 or more years. Monin-Obukhov similarity theory (MOST 1954) has been the foundation for describing vertical gradients of mean winds and temperature. Vertical profiles of winds and temperature can be described through integration of these flux-profile relationships dependent on turbulent fluxes of momentum (u_*) and heat (H). The turbulent transfer of heat and momentum can be obtained from relationships between the momentum drag coefficient (C_M) and heat transfer coefficient (C_H) where, C_M and C_H can be obtained through formulations relating each coefficient to the MOST stability z/L. Typically, relating u_*, θ_*, and L requires numerical iteration techniques.

To avoid this numerical iteration process solving for u_*, θ_*, and L, schemes have been developed relating the bulk Richardson number (Ri_B) to the MOST stability parameter z/L. One attraction of these schemes is that Ri_B can be easily calculated from routine observations. This study presents an evaluation of the relationship between z/L and Ri_B which incorporates a non-unity value for z₀/z_0h where z₀ is the surface roughness and z_0his the temperature surface roughness length. In particular, the utility of the formulation proposed by Li et al (2010) and implemented in WRF V3.6 is demonstrated. The National Oceanic and Atmospheric Administration's Atmospheric Turbulence and Diffusion Division's (NOAA/ATDD) Summer 2014 Convective Initiation program provided the field measurement framework through which the required observations could be obtained.