Aerodynamic Resistance over Canopies: Linking Eddies and Heterogeneities Using a Structure Function Approach

The aerodynamic resistance for heat transfer at large spatial scales is needed in a plethora of applications that span climate, meteorology, air quality, landscape ecology, and eco-hydrology of dry land systems. Operationally, aerodynamic resistance formulations are based on Monin-Obukhov similarity theory (MOST) that are applicable for planar-homogeneous surfaces. Over large scales, heterogeneity in land cover is ubiquitous and disturbs many of the 'niceties' associated MOST. In those cases, using a homogeneous aerodynamic resistance formulation may only yield a rough estimate for the surface-atmosphere exchange of energy because only the spatial means of the flow variables are considered. However, all relevant scales of heterogeneity can contribute to the surface-atmosphere exchange. To include these residual heterogeneity scale effects, the heterogeneous structure function (in spectral space) is linked to the corresponding homogeneous one, representing the lowest wavelength of heterogeneity. Following this approach, aerodynamic resistance can be determined using spectral budget equations for the co-variances and variances by assuming the spectral shape of the homogeneous structure functions (as may be derived from canonical theories of turbulence) as disturbed by heterogeneity. Upon integrating across all scales contributing to the energy spectrum of the vertical velocity and the co-spectrum of heat, the heterogeneity enters as a height-dependent correction factor to the homogeneous case. Because of its height dependency and sensitivity to the overall heat flux, this factor can be added to the stability correction function emerging from MOST for the corresponding homogeneous cases. The derived parametrization is tested against large eddy simulations for two different scenarios of surface heterogeneities and various averaging regions, representing different cells of a regional scale model. The presented technique is not only applicable to improve aerodynamic resistance formulation for heterogeneous surfaces, but can more generally correct for land surface heterogeneity when using MOST to calculate flow quantities.­