An Intercomparison of Measures of Spatial Inhomogeneity for Surface Fluxes of Passive Scalars

The flux-footprint formalism is used to calculate blending and internal boundary layer heights for scalar fluxes in the atmospheric surface layer. For neutral stratification, the footprint-based predictions of blending and internal boundary layer heights are found to be similar to the results of J.R. Philip (Boundary Layer Meteorology: 1996, 1997). However, these heights are also found to be strong functions of atmospheric stability. The blending height z_bh has a functional dependence on atmospheric stability and on the length scale X of streamwise surface flux variations that is similar to the dependence of <z> on atmospheric stability and streamwise distance. Here <z> is the first moment of the vertical distribution of a scalar downwind of a surface point source and is an essential parameter in our calculation of the flux footprint. The internal boundary layer height z_ibl similarly depends on atmospheric stability and on s, the streamwise distance downwind of a step change in the surface flux. To a fair approximation, z_bh=1.7 <z>(X/z_o, z_o/L) and z_ibl=3.2 <z>(s/z_o, z_o/L), where z_o is the surface roughness length and L is the Monin-Obukohov length scale characterizing thermal stability in the surface flux layer.