A model study of kB(H)-1 for vegetated surfaces using 'localized near-field' Lagrangian theory

Models of energy and mass exchange between vegetation canopies and the atmosphere usually include some formulation of the bulk boundary layer resistance (Rb or the related parameter kB-1) to describe the effects of molecular diffusion occurring near the leaf and soil surfaces. Present formulations of kB-1 are either empirical expressions or are physically based models derived from a K-theory approach. However, K-theory does not describe the observed counter gradient flow within canopies and the empirical expressions usually lump both canopy and soil effects into a single surface resistance (single source approach). For areas of partial canopy cover, single source formulations have been difficult to formulate with any certainty and often do not agree with observations. This study uses 'localized near-field' (LNF) Lagrangian theory to develop a model of kB-1 (for heat transfer) for the vegetation component of a dual source model and for the combined effects of canopy and soil in a single source approach. The present model also uses a physically based, one-dimensional, analytical model to describe the influence of canopy structure and density upon the within-canopy far field diffusivity and Lagrangian time scale which are central to the LNF Lagrangian theory. The canopy turbulence model is designed for arbitrary foliage structure and density and kB-1 is defined in terms of heat and momentum fluxes rather than the more conventional logarithm of the ratio of the momentum and thermal roughness lengths. The resulting kB-1 model is used for sensitivity studies of kB-1 for canopies only (i.e. no soil contribution) and for the coupled canopy-soil system (i.e. a single source model). Results indicate that foliage density (Drag Area Index or Leaf Area Index), wind speed, leaf size, possible sheltering effects, and, to a lesser extent, the vertical foliage distribution and the vertical variation of the temperature difference between the foliage and the near-leaf air space can influence kB-1. For the single source model the soil boundary layer resistance was found to be significant for areas of partial canopy cover. In spite of the relative complexity of the full LNF model of kB-1, a simple expression that varies smoothly between bare soil and full canopy cover is developed that captures much of the modeled and observed variation in kB-1 for the single source approach.