A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) this model predictions are more realistic because the surface drag can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing-length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing-length assumption leads to a non-constant mixing-length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (Cd) on wind velocity can be predicted, while both a(z) and Cd must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height-independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing-length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.
Wang, Weiguo and Chuixiang Yi. "A New Nonlinear Analytical Model for Canopy Flow over a Forested Hill." Theoretical and Applied Climatology, vol. 109, no. 3-4, 2012, pp. 549-569, doi: 10.1007/s00704-012-0599-9 . Reprinted in CUNY Academic Works.