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Review of some basic characteristics of the atmospheric surface layer

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Abstract

Some of the fundamental issues of surface layer meteorology are critically reviewed. For the von Karman constant (k), values covering the range from 0.32 to 0.65 have been reported. Most of the data are, however, found in a rather narrow range between 0.39 and 0.41. Plotting all available atmospheric data against the so-called roughness Reynolds number, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabw% gadaWgaaWcbaGaaeimaaqabaGccqGH9aqpcaWG1bWaaSbaaSqaaiaa% cQcaaeqaaOGaamOEamaaBaaaleaacaaIWaaabeaakiaac+cacqaH9o% GBaaa!3FD0!\[{\rm{Re}}_{\rm{0}} = u_* z_0 /\nu \] or against the surface Rossby number, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaab+% gadaWgaaWcbaGaaeimaaqabaGccqGH9aqpcaWGhbGaai4laiaadAga% caWG6bWaaSbaaSqaaiaaicdaaeqaaaaa!3DF1!\[{\rm{Ro}}_{\rm{0}} = G/fz_0 \] gives no clear indication of systematic trend. It is concluded that k is indeed constant in atmospheric surface-layer flow and that its value is the same as that found for laboratory flows, i.e. about 0.40.

Various published formulae for non-dimensional wind and temperature profiles, Φ m and Φ h respectively, are compared after adjusting the fluxes so as to give % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaiabg2% da9iaaicdacaGGUaGaaGinaiaaicdaaaa!3AC6!\[k = 0.40\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWabeaaii% GacqWFgpGzdaWgaaWcbaGaamiAaaqabaGccaGGVaGae8NXdy2aaSba% aSqaaiaad2gaaeqaaaGccaGLOaGaayzkaaWaaSbaaSqaaiaadQhaca% GGVaGaamitaiabg2da9iaaicdaaeqaaOGaeyypa0JaaGimaiaac6ca% caaI5aGaaGynaaaa!4655!\[\left( {\phi _h /\phi _m } \right)_{z/L = 0} = 0.95\]. It is found that for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWabeaaca% WG6bGaai4laiaadYeaaiaawEa7caGLiWoacqGHKjYOcaaIWaGaaiOl% aiaaiwdaaaa!3F72!\[\left| {z/L} \right| \le 0.5\] the various formulae agree to within 10–20%. For unstable stratification the various formulations for Φ h continue to agree within this degree of accuracy up to at least % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiaac+% cacaWGmbGaeyisISRaeyOeI0IaaGOmaaaa!3BC9!\[z/L \approx - 2\]. For Φ m in very unstable conditions results are still conflicting. Several recent data sets agree that for unstable stratification % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabM% gacqGHijYUcaaIXaGaaiOlaiaaiwdacaWG6bGaai4laiaadYeaaaa!3E0D!\[{\rm{Ri}} \approx 1.5z/L\] up to at least % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaam% OEaiaac+cacaWGmbGaeyypa0JaaGimaiaac6cacaaI1aaaaa!3C8D!\[ - z/L = 0.5\] and possibly well beyond.

For the Kolmogorov streamwise inertial subrange constant, α u , it is concluded from an extensive data set that % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS% baaSqaaiaadwhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI1aGaaGOm% aiabgglaXkaaicdacaGGUaGaaGimaiaaikdaaaa!4178!\[\alpha _u = 0.52 \pm 0.02\]. The corresponding constant for temperature is much more uncertain, its most probable value being, however, about 0.80, which is also the most likely value for the corresponding constant for humidity.

The turbulence kinetic energy budget is reviewed. It is concluded that different data sets give conflicting results in important respects, particularly so in neutral conditions.

It is demonstrated that the inertial-subrange method can give quite accurate estimates of the fluxes of momentum, sensible heat and water vapour from high frequency measurements of wind, temperature and specific humidity alone, provided ‘apparent’ values of the corresponding Kolmogorov constants are used. For temperature and humidity, the corresponding values turn out to be equal to the ‘true’ constants, so % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOSdi2aaS% baaSqaaiaadgeaaeqaaOGaeyisISRaeqOSdiMaeyisISRaaGimaiaa% c6cacaaI4aGaaGimaaaa!4074!\[\beta _A \approx \beta \approx 0.80\]. For momentum, however, the apparent constant % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS% baaSqaaiaadwhacaWGbbaabeaakiabgIKi7kaaicdacaGGUaGaaGOn% aiaaicdaaaa!3E18!\[\alpha _{uA} \approx 0.60\].

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  1. Department of Meteorology, Uppsala University, Uppsala, Sweden

    Ulf Högström

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Högström, U. Review of some basic characteristics of the atmospheric surface layer. Boundary-Layer Meteorol 78, 215–246 (1996). https://doi.org/10.1007/BF00120937

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