Dry deposition to a uniform canopy: Evaluation of a first-order-closure mathematical model

Abstract

A mathematical model is developed for the transport of momentum and matter within a canopy consisting of identical elements protruding vertically from a smooth substrate. Turbulent flux is modelled using a mixing-length approach. The loss of momentum (or matter) to individual elements is related to the mean wind speed, and the element-element interaction via the turbulent wind field is represented by a sheltering factor. Careful consideration is given to the formulation of lower boundary conditions. The model assumptions are compared with those of other models. The model predictions are compared with measurements on a vertically- and horizontally-uniform artificial canopy in a wind-tunnel. The model reproduces well the observed relationship between the parameters of the logarithmic wind speed profile above the canopy and the observed deposition velocities of thorium-B (ThB) atoms and particles in the diameter range 0.08–32 μm, using a sheltering factor which is little dependent on wind speed and has the same magnitude for momentum, gas and particles. The predicted dependences of deposition velocity on friction velocity and, for particles, on diameter shed light on the performance of semi-empirical correlations proposed in the literature. For ThB atoms, the calculated deposition velocities are compared with those of other mathematical canopy models: a comparable degree of agreement is obtained here with fewer free parameters. The fraction of deposit on the substrate is underpredicted by an order of magnitude in some cases, pointing to the limitations of the modelling of conditions near the substrate in terms of quasi-shear flow.