A model to estimate the source area contributing to turbulent exchange in the surface layer over patchy terrain

Abstract

The characteristics of turbulence in the surface layer are well understood over spatially homogeneous and smooth surfaces. Current theoretical knowledge is based on measurements over such ‘ideal’, flat and homogeneous surfaces. Over heterogeneous surfaces of a patchy nature (e.g. urban areas, mixed agricultural crops, forest etc.) turbulence is subject to considerable spatial variability over a wide range of scales. A ‘source area’ is defined as the portion of the upstream surface containing the effective sources and sinks contributing to the turbulent exchange processes at a given point in the surface layer. It is noted that the term ‘source area’ refers to sources and sinks on the surface only and does not consider production or dissipation within the atmosphere. the contributions of surface elements are treated as ‘plumes’ of heat or vapour or momentum‐deficiency. A small‐perturbation approach to diffusion theory and a plume‐diffusion model are used in a numerical source‐area model (SAM) to estimate this region, depending on meteorological scaling parameters and the reference location. This model identifies a ‘maximum effect source location’ and the upwind, downwind and lateral dimensions of regions containing various levels of the total contributing effect. It accounts for the different source weight of each point on the surface, depending on its position relative to the reference location. Although the source area is not directly measurable, the results of SAM compare favourably with observed effects of changing source areas. A sensitivity test of SAM results and non‐linear regression leads to a set of simple equations (mini‐SAM) approximating SAM. This short‐cut model provides easily obtainable estimates of the source‐area dimensions and the relative importance of surface elements for a given measurement of turbulent exchange.