An Approximate Analytical Solution Of Flux-Profile Relationships For The Atmospheric Surface Layer With Different Momentum And Heat Roughness Lengths |
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| Authors: | K Blümel |
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| Institution: | (1) Institut für Meteorologie der Freien, Universität Berlin, Carl-Heinrich-Becker-Weg 6-10, 12165 Berlin, Germany |
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| Abstract: | An approximate method for calculating the relationship between z/L(z = reference height, L = Obukhov length) and the bulk Richardsonnumber is presented. If this relationship is known, the momentum andheat fluxes can be computed easily without any iteration. The avoidance of iteration can speed up computationsin large-scale models considerably (up to 10 times) and cases which do not converge or converge very slowly cannot occur. The proposed formulae take into account the difference between momentum (z0M) and heat roughnesslengths (z0H). Because the roughness lengths are not neglected at any step of the derivation, the resulting analytical formulae can be used not only between the surface and the reference height but also between two finite levels z1 andz2 (by replacing z0M and z0H by z1 and z by z2). Theequations remain correct even in the limit z1 z2.The formulae are based upon the (partially modified) Businger–Dyer flux–profile relationships and,consequently, they are restricted to predominantly homogeneous terrain.These new approximations are an improvement over the existing solutions because they are simpler than most of the formulae in the literature and are able to match the numerical exact solution for different parameter sets (Businger, Dyer, Högström) with an maximum error of about 2% for a wide range of z/L, z/z0M and z0M/z0H.Furthermore, in stable conditions, schemes with and without a finitecritical bulk Richardson number can be approximated. The possibleambiguity of the exact solution  =f(RIB) in (moderately) stable conditions is discussed briefly. The performance of the new formulae is compared to the exact numerical solution and to different formulae proposed in the literature. |
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| Keywords: | Analytical solution Bulk Richardson number Non-iterative Obukhov length Roughness length |
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