UNC-Chapel Hill GEOG 801 - Vegetation-Atmosphere Interaction and Surface Conductance at Leaf, Canopy and Regional Scales

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AGRICULTURAL AND FOREST METEOROLOGY ELSEVIER Agricultural and Forest Meteorology 73 (1995) 151-179 Vegetation-atmosphere interaction and surface conductance at leaf, canopy and regional scales M.R. Raupach CSIRO Centre for Environmental Mechanics, GPO Box 821, Canberra, A.C.T. 2601, Australia Received 10 October 1993; revision accepted 10 March 1994 Abstract The problem of areally averaging descriptions of land-atmosphere energy and mass exchange is common to both the leaf-canopy and canopy-region scale translations. This paper attempts a unified treatment. The starting point is a review of both the basic and equilibrium-departure forms of the Penman-Monteith or combination equation (CE) for the latent and sensible heat fluxes at an evaporating surface; the equilibrium-departure form expresses the evaporation as a linear combination of two other scalar fluxes, those of available energy and saturation deficit. Next, tools for scale translation are established, including (1) the basic conservation requirement that net scalar fluxes average linearly over the land surface and (2) the matching of model form between scales. These tools are applied to the CE for latent and sensible heat fluxes FE and Ft/, leading to a 'flux matching' averaging scheme based on term-by- term matching of the linearly additive scalar flux terms in the CE for F e. Several variations of this scheme are discussed. For FE, all variations satisfy the scalar conservation requirement that fluxes average linearly, but for Fn, none satisfies this requirement exactly, except when long- wave radiative coupling is ignored. By considering a range of canopy-region scale translations, errors in the averaging of F~ are shown to be small in practice. Finally, three averaging schemes (the flux-matching scheme and two schemes based on parallel sums of elemental aerodynamic and surface conductances, respectively) are compared for leaf-canopy scale translations, by constructing a sequence of analytic model canopies at increasing levels of detail. For every canopy model considered, all three averaging schemes give nearly identical definitions of the bulk canopy conductance for typical dry canopies. However, schemes other than the flux matching scheme can become inconsistent over partially wet surfaces, yielding undefined or negative bulk conductances. 0168-1923/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved SSD1 0168-1923(94)05071-6152 M.R. Raupach / Agricultural and Forest Meteorology 73 (1995) 151-179 List of symbols c radiation extinction coefficient cp isobaric specific heat of air cp~ proportionality coefficientfp/~q for Canopies II1 and IV cll proportionality coefficient gs/gm for Canopy lI C concentration of arbitrary scalar entity D potential saturation deficit: D = Qsat(O) - Q f, F scalar flux at small, large scale FEc, F~e vegetation, soil latent heat flux at canopy scale g, G conductance at small, large scale gax maximum elemental aerodynamic conductance (as A -~ 0) gsx maximum stomatal conductance g~ slope dgs/dfe for Canopy III (allJ~,) and Canopy IV (re ~ 0) t I go slope dg~/dOeq for Canopies III and IV: g® = g~e/ce~ h height of well-mixed slab p ratio g~H/(gdq + gr) = rt14/ra14 Q specific humidity Q~t saturation specific humidity r, R resistance at small, large scale rs~ 1/gsx R region enclosed by surface S S closed bounding surface (SL, part coincident land-atmosphere interface; S~, part in air; S~, area of element i) t time T temperature U wind speed v, V arbitrary dependent variable at small, large scale x, X, y, Y arbitrary independent variables at small, large scale X, Y, Z variables defined and used in the Appendix z height above evaporating surface Greek letters 1 ~ dry adiabatic lapse rate 6eq , Aeq equilibrium saturation deficit at small, large scale dimensionless slope of Qsat( T) : e = ( A / cp )dQsat / d T ( coordinate traversing leaf area index potential temperature: O = T + I'z A latent heat of vaporisation of water A leaf area index p density of air ~- canopy transmission O~q, ~eq equilibrium evaporation rate in energy units at small, large scale ~b~, I, 4 isothermal available energy flux at small, large scale Subscripts denoting transferred entities A available energy (sensible plus latent heat) C arbitrary scalar D saturation deficit E latent heat H sensible heatM.R. Raupach / Agricultural and Forest Meteorology 73 (1995) 151-179 153 L longwave (terrestrial) radiation P photosynthetically active radiation (PAR) S shortwave (solar) radiation Subscripts denoting kinds of conductance and resistance a aerodynamic c canopy (vegetation) part of bulk flux, conductance or resistance d deficit g ground (soil) part of bulk flux, conductance or resistance r radiative s surface (element or leaf scale: gs, stomatal conductance; canopy scale: G~, bulk surface conductance (vegetation and soil)) Other subscripts none (for scalar concentration only): value at reference point in ambient air 0 (for scalar concentration only): value at surface i enumerates element i 1. Introduction Land-atmosphere interactions are strongly heterogeneous processes, at practically every spatial scale from individual stomata to the whole Earth. Therefore, theories or models for energy, mass, and momentum fluxes between land surfaces and the atmosphere always involve some kind of implicit or explicit spatial averaging. These models usually express fluxes in terms of transfer coefficients over various exchange pathways, such as aerodynamic or surface resistances. They are also usually nonlinear in the spatially changing independent variables, a good example being the combination equation for evaporation. Because of the nonlinearities, it is not always easy to relate transfer coefficients defined at different scales; for instance, to use empirical knowledge of conductances at a small scale to infer an averaged conductance for use in a bulk model at a larger scale. The 'scaling problem' in land-atmosphere interaction is essentially the problem of using information about exchange processes at one scale, such as empirical transfer coefficients, to characterise the same processes at a larger (or smaller) scale. Three spatial scales of great practical importance are the single energy-exchanging element, the homogeneous


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UNC-Chapel Hill GEOG 801 - Vegetation-Atmosphere Interaction and Surface Conductance at Leaf, Canopy and Regional Scales

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