Effective stomatal and boundary-layer resistances of heterogeneous surfaces

In nature surfaces are rarely uniform, so terms such as ‘surface’, ‘stomatal’ or ‘canopy’ resistance usually indicate some kind of average over a population of sub-areas, each with its own separate resistance. Questions then arise as to how gross measurements of these resistances should be interpreted in terms of the components, or how components should be aggregated into representative single values. Aggregation schemes have been published by Raupach (1991, Vegetatio 91, 105–120) and Lhomme (1992, Agriculture and Forest Meteorology 61, 11–21), but these are different for reasons that were not explained. This paper develops the idea that averaging schemes should be designed to serve particular purposes, and that they can be varied to suit these purposes. It is shown that the ‘effective’ resistances defined by Raupach and Lhomme preserve different quantities. A further averaging scheme is developed which preserves both correct transpiration rate and CO₂ flux when used in the Penman-Monteith equation and an equation describing assimilation. All of these schemes are fairly complex, so the work provides a warning against naive use of effective variables.