Inverting Surface Observations to Find Boundary Layer Depth

Atmospheric Boundary layer depth is a critical input for a number of meteorological problems including that of modeling the transport and dispersion of an airborne contaminant. Traditionally this value is found directly, though either in situ or remote sensing measurements of some boundary layer property such as temperature or aerosol content. Both approaches are expensive. Here we propose a relatively simple and inexpensive method to obtain this variable and other important variables in the convective boundary layer. For this method, two issues must be overcome to ascertain the convective boundary layer depth. First, one must find a set of similarity formulae that contain only the unknowns, such as the boundary layer depth and the buoyancy flux, and cheaply measured turbulence statistics. Second, one must devise a nonlinear optimization technique capable of robustly inverting these equations for the two unknowns in the face of the observational noise. We develop a method of estimating both boundary layer depth and the buoyancy flux from just the surface layer profiles of the first two moments of wind speed, U, and the longitudinal turbulence component, or the first moment of temperature and the second moment of wind speed. The wind speed (temperature) profile is used in the Monin-Obukhov similarity theory to determine the friction velocity (Temperature Scale), u*(T*), and the Obukhov length, L. These quantities are used to calculate the buoyancy flux directly via the definition of L, and boundary layer depth by inverting the similarity theory for the longitudinal turbulence component. The former inversion requires a sophisticated nonlinear optimization technique. We apply a hybrid Genetic Algorithm / Nelder-Mead Downhill-Simplex method. The method is tested on data from several sources.