Characteristics of turbulent fluxes of sensible heat and momentum in the surface boundary layer during the Indian summer monsoon

Turbulent fluctuations of wind and temperature were measured using a three-component sonic anemometer at 8 m on a 30 m micro-meteorological tower erected at the Indian Institute of Technology (IIT) Kharagpur (22.3° N, 87.2° E), India, as part of the Monsoon Trough Boundary Layer Experiment (MONTBLEX). Diurnal and nocturnal variations of fluxes of sensible heat and momentum were estimated by the eddy correlation technique from 42 observations, each of 10 min duration during 6–8 July in the monsoon season of 1989. The estimated heat flux shows a diurnal trend while the momentum flux shows variability but no particular trend. The nocturnal heat flux changes sign intermittently.Fluctuations of vertical wind velocity _wand temperature when normalised with the respective scaling parameters u _*and _* are found to scale with Z/L in accordance with the Monin-Obukhov similarity hypothesis: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaadEhaaeqaaOGaamiEaiaacIcacaWGAbGaai4laiaadYea% caGGPaWaaWbaaSqabeaacaaIXaGaai4laiaaiodaaaaaaa!3FE8!\[\phi _w x(Z/L)^{1/3} \], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabeI7aXbqabaGccaWG4bGaaiikaiaadQfacaGGVaGaamit% aiaacMcadaahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa!40A2!\[\phi _\theta x(Z/L)^{1/3} \] during unstable conditions and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaadEhaaeqaaOGaamiEaiaacIcacaWGAbGaai4laiaadYea% caGGPaaaaa!3D90!\[\phi _w x(Z/L)\], % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabeI7aXbqabaGccaWG4bGaaiikaiaadQfacaGGVaGaamit% aiaacMcadaahaaWcbeqaaiabgkHiTiaaigdaaaaaaa!401F!\[\phi _\theta x(Z/L)^{ - 1} \] during stable conditions. Correlation coefficients for heat and momentum flux % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] and _uwshow stability dependence. For unstable conditions, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] increases with increasing ¦Z/L¦ whereas _uwdecreases. During stable conditions, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS% baaSqaaiaadEhacqaH4oqCaeqaaaaa!3A71!\[\gamma _{w\theta } \] decreases with increasing Z/L while _uwdecreases very slowly from a value -0.36 to -0.37.     

Kolmogoroff constants at the 1976 ITCE

The high-frequency data from 12 sensors at the ITCE 1976^* are analysed to determine the Kolmogoroff constants for velocity, temperature and humidity fluctuation, _u , _T , and _q . The occurrence of aliasing in the spectral analysis in some cases together with the limited response of some sensors at the higher frequencies introduces some uncertainties into the analysis. The Soviet sonic anemometer, fine-wire thermometer and infrared hygrometer and the Australian infrared hygrometer provide the best information, namely that% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda% WgaaWcbaGaamyDaaqabaGccqGH9aqpcaaIWaGaaiOlaiaaiwdacaaI% 5aGaeyySaeRaaGimaiaac6cacaaIWaGaaGymaiaacYcacaqGGaGaae% iiaiaabccacaqGGaGaeqySde2aaSbaaSqaaiaadsfaaeqaaOGaeyyp% a0JaaGimaiaac6cacaaI2aGaaGioaiabgglaXkaaicdacaGGUaGaaG% imaiaaikdacaGGSaGaaeiiaiaabccacaqGGaGaaeiiaiabeg7aHnaa% BaaaleaacaWGXbaabeaakiabg2da9iaaicdacaGGUaGaaG4naiaaiA% dacqGHXcqScaaIWaGaaiOlaiaaicdacaaIZaaaaa!6248!\[\alpha _u = 0.59 \pm 0.01,{\text{ }}\alpha _T = 0.68 \pm 0.02,{\text{ }}\alpha _q = 0.76 \pm 0.03\]where the errors quoted refer solely to statistical errors. The other instruments provide general support to these values.The technique of using spectral density measurements to determine eddy fluxes is illustrated.International Turbulence Comparison Experiment.     

Estimation of the Monin-Obukhov similarity functions from a spectral model

From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function _m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - _m nondimensional mean shear - _H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - _D nondimensional divergence of vertical transports of turbulent linetic energy     

Review of some basic characteristics of the atmospheric surface layer

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, _m and _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 _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 _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, _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!\[\alpha _{uA} \approx 0.60\].Based on an invited paper presented at the EGS Workshop Instrumental and Methodical Problems of Land Surface Flux Measurements, Grenoble 22–26 April, 1994.     

On the enhanced smoothing over topography in some mesometeorological models

An equation is derived for the components of the horizontal (turbulent) frictional force in the -coordinate system with special attention to mesometeorological flow models. The starting point is the horizontal equation of motion in its flux-form in the -system in which we replace (following Reynolds' procedure) the velocity components u,v and % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbai % aaaaa!37B8! \[ \dot \sigma \] aswell as other relevant quantities by terms of the form u = + u,..., = ± + % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbai % Gbauaaaaa!37C3! \[ \dot \sigma ' \] , etc. ( = time average of u; u = fluctuating part of u.) Next, the equation is averaged with respect to time and terms which we believe are small in mesometeorological flows, are neglected. On expressing by an appropriate expression that involves w, the result shows the appearance of two new terms which, have not been considered previously in the published literature. While the expression earlier used in the literature involved the -derivative of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaaceWG3bGbauaaaaaaaa!380B!\[\overline {u'w'} \] alone, the new terms add the -derivatives of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37EC!\[\overline {u'^2 } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaaceWG2bGbauaaaaaaaa!380A!\[\overline {u'v'} \] for the x-component of the force, and the -derivatives of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG2bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37ED!\[\overline {v'^2 } \]} and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG1bGbauaaceWG2bGbauaaaaaaaa!380A!\[\overline {u'v'} \] for the y-component, where and are the slopes of the -surfaces in the x- and y-directions, respectively. Further, a few numerical simulations of the sea-breeze over topography are carried out with and without the correction terms. It is shown that when corrections terms are not included the effective smoothing is stronger above the sloping regions and may amount to as high as 50 percent of the convergence with slopes of ~.04. The ìnclusìon of the new terms does not lead to any special computational difficulties and for that reason there is no compelling reason to neglect them, all the more so because, as is shown, the addition of the new terms results in a consistent apportioning of the degree of horizontal diffusion.On leave from CIMMS, Norman, OK.Now visiting Dept. of Met., Helsinki, Finland.     

An observational study of the structure of the nocturnal urban boundary layer

The formation mechanism of the nocturnal urban boundary layer (UBL), especially in the winter nighttime, was investigated based on the extensive field observations conducted during November 1984 in Sapporo, Japan. A strong, elevated inversion formed over the Sapporo urban area and the inversion base height was approximately twice the average building height. Velocity fluctuations _u, _w and Reynolds stress % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaam4DamaaCaaa% leqabaGaaGymaaaaaaaaaa!3A9C!\[\overline {u^1 w^1 } \] had nearly uniform profiles within the nocturnal UBL and decreased with height above the UBL. On the other hand, temperature fluctuations _t , and heat fluxes % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaeqiUde3aaWba% aSqabeaacaaIXaaaaaaaaaa!3B56!\[\overline {u^1 \theta ^1 } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG3bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaeqiUde3aaWba% aSqabeaacaaIXaaaaaaaaaa!3B58!\[\overline {w^1 \theta ^1 } \] had peaks at the inversion base and small values within the nocturnal UBL. The turbulent kinetic energy budget showed that the turbulent transport term and shear generation from urban canopy elements are important in the nocturnal UBL development; the role of the buoyancy term is small. The turbulence data analysis and application of a simple advective model showed that the mechanism of UBL formation may be controlled by the downward transport of sensible heat from the elevated inversion caused by mechanically-generated turbulence.Nomenclature g accelaration due to gravity, m s^-2 - k turbulent kinetic energy, m² s^-1 - K _m eddy viscosity, m² s^-1 - L Monin-Obukhov lenght, m - p pressure, Kg m^-2 - U, V, W mean wind speed in the downwind, crosswind, and vertical directions, respectively, m s^-1 - u ¹, w ¹ wind speed fluctuation in the downwind and vertical direction, respectively, m s^-1 - u ₁ friction velocity, m s^-1 - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaam4DamaaCaaa% leqabaGaaGymaaaaaaaaaa!3A9C!\[\overline {u^1 w^1 } \] momentum flux, m²s^-2 - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaam4DamaaCaaa% leqabaGaaGymaaaaaaaaaa!3A9C!\[\overline {u^1 \theta^1 } \] sensible heat flux, m²s^-1°C - WD wind direction, deg - WS wind speed, m s^-1 - z altitude, m - Z _h inversion base height, m - Z _j wind maximum height, m - Z _t inversion top height, m - T _u-r heat island intensity, °C - temperature lapse rate at rural site, °C m^-1 - energy dissipation rate, m²s^-3 - ¹ Potential temperature fluctuation, °C - _* scaling temperature, (=-% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WG1bWaaWbaaSqabeaacaaIXaaaaGGaaOGae8hiaaIaeqiUde3aaWba% aSqabeaacaaIXaaaaaaaaaa!3B56!\[\overline {u^1 \theta ^1 } \]/u_*) °C - mean potential temperature fluctuation, K - density of air, Kgm^-3 - K von Kármán constant (=0.4) - _u, _v, _w standard deviation of wind speed in the downwind, crosswind, and vertical directions, respectively, m s^-1 - standard diviation of temperature, °C     

An analytical-empirical method for determining the roughness length and zero-plane displacement

A method based on the principle of the Method of Weighted Residuals for evaluating the roughness-length (z ₀) and zero-plane displacement (d) is presented. This method not only can minimize errors involved during the calculation process but can also smooth and re-distribute the already minimized error in a most favourable manner via using appropriate weighting functions. With the inclusion of d in addition to z ₀, formulae for wind and temperature profiles in the surface layer are presented by:% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGvbGaeyypa0% ZaaSaaaeaacaWG1bWaaSbaaSqaaiaacQcaaeqaaaGcbaGaam4Aaaaa% daWadaqaaiGacYgacaGGUbWaaeWaaeaadaWcaaqaaiaadQhacqGHsi% slcaWGKbaabaGaamOEamaaBaaaleaacaaIWaaabeaaaaaakiaawIca% caGLPaaacqGHRaWkcqaHipqEaiaawUfacaGLDbaaaaa!43FC!\[U = \frac{{u_* }}{k}\left[ {\ln \left( {\frac{{z - d}}{{z_0 }}} \right) + \psi } \right]\]and% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH4oqCcqGHsi% slcqaH4oqCdaWgaaWcbaGaaGimaaqabaGccqGH9aqpcqaH4oqCdaWa% daqaaiGacYgacaGGUbWaaeWaaeaadaWcaaqaaiaadQhacqGHsislca% WGKbaabaGaamOEamaaBaaaleaacaaIWaaabeaaaaaakiaawIcacaGL% PaaacqGHRaWkcqaHipqEdaWgaaWcbaacbmGaa8hvaaqabaaakiaawU% facaGLDbaaaaa!485A!\[\theta - \theta _0 = \theta \left[ {\ln \left( {\frac{{z - d}}{{z_0 }}} \right) + \psi _T } \right]\]where and _T are the integrated diabetic influence functions' for velocity and temperature profiles respectively.Analytical expressions for both and _T as functions of wind shear or, implicitly in terms of the Richardson number have been derived.Presented at the 10th Annual Congress of the Canadian Meteorological Society, Quebec City, Canada, May 26–28, 1976.     

Inertial subrange correlation between temperature and humidity fluctuations in the unstable surface layer above vegetated terrains

Observations of the temperature-humidity cospectrum and correlation spectrum were made with a cold platinum wire and a Ly- hygrometer at 3.7 and 10 m above vegetated surfaces during unstable atmospheric conditions. It was found theoretically that a separation between the temperature and humidity sensors causes a drop-off of the correlation spectrum at wavenumbers > 0.3 ^–1. The observed drop-off follows the theoretical one reasonably well. Measurements made with the temperature sensor placed in the center of the Ly- gap reveal a % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaccaGae8NKby% kaaa!37B5!\[f\]^–5/3 dependence of the temperature-humidity cospectrum in the inertial subrange up to frequencies of 20 Hz. The drop-off at higher frequenties is thought to be caused by limitations inherent to the Ly- humidiometer.     

The source area influencing a measurement in the Planetary Boundary Layer: The “footprint” and the “distribution of contact distance”

This paper considers the ground area which affects the properties of fluid parcels observed at a given spot in the Planetary Boundary Layer (PBL). We examine two source-area functions; the footprint, giving the source area for a measurement of vertical flux: and the distribution of contact distance, the distance since a particle observed aloft last made contact with the surface. We explain why the distribution of contact distance extends vastly farther upwind than the footprint, and suggest for the extent of the footprint the inequalities: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOabaeqabaGaamyvam% aalaaabaGaamiAaaqaaiabeo8aZnaaBaaaleaacaWGxbaabeaakiaa% cIcacaWGObGaaiykaaaacqGH8aapcaWG4bGaeyipaWJaamyvaKazaa% iadaGabaqaamaaDaaajqwaacqaaiaadIgacaGGVaGabmOEayaacaGa% aiilaiaabccacaGGVbGaaiiDaiaacIgacaGGLbGaaiOCaiaacEhaca% GGPbGaai4CaiaacwgaaeaacaWGubWaaSbaaKazcaiabaGaamitaaqa% baqcKfaGaiaacIcacaWGObGaaiykaiaabYcacaqGGaGaaeiAaiaabc% cacaGGHbGaaiOyaiaac+gacaGG2bGaaiyzaiaabccacaGGZbGaaiyD% aiaackhacaGGMbGaaiyyaiaacogacaGGLbGaeyOeI0IaaiiBaiaacg% gacaGG5bGaaiyzaiaackhaaaaajqgaacGaay5EaaaakeaaaeaacaGG% 8bGaamyEaiaacYhacqGH8aapcqaHdpWCdaWgaaWcbaGaamODaaqaba% GccaGGOaGaamiAaiaacMcadaWcaaqaaiaadIhaaeaacaWGvbaaaaaa% aa!7877!\[\begin{array}{l} U\frac{h}{{\sigma _W (h)}} < x < U\left\{ {_{h/\dot z,{\rm{ }}otherwise}^{T_L (h){\rm{, h }}above{\rm{ }}surface - layer} } \right. \\ \\ |y| < \sigma _v (h)\frac{x}{U} \\ \end{array}\] where U is the mean streamwise (x) velocity, h is the observation height, _L is the Lagrangian timescale, _v and _w are the standard deviations of the cross-stream horizontal (y) and vertical (z) velocity fluctuations, and is the Lagrangian Similarity prediction for the rate of rise of the centre of gravity of a puff released at ground.Simple analytical solutions for the contact-time and the footprint are derived, by treating the PBL as consisting of two sub-layers. The contact-time solutions agree very well with the predictions of a Lagrangian stochastic model, which we adopt in the absence of measurements as our best estimate of reality, but the footprint solution offers no improvement over the above inequality.     

Etude experimentale d'une relation entre le coefficient de frottement et le facteur de rafales en regime de vent faible et au-dessus d'une surface d'eau

In usual aerodynamic bulk formulas, the drag coefficient C _d has been best estimated in the 5 to 16 m s^–1 range of mean wind velocity; a value of 1.3 × 10^–3 is often considered for operational use. However, in the 0 to 5 m s^–1 range of mean wind velocity, corresponding to meteorological conditions of very light wind, experimental results have not resulted in any convincing agreement between various authors (Hicks et al., 1974; Wu, 1969; Kondo and Fujinawa, 1972; Mitsuta, 1973; Brocks and Krugermeyer, 1970).In the present paper, the drag coefficient is experimentally determined in conditions of very light wind and limited fetch (about 250 m). Due to this limited fetch, we have to be cautious in the extrapolation of our results to other sites. Nevertheless, some of experimental results are worth describing, considering the paucity of data in light wind conditions.Mean value and standard deviation (respectively 1.84 × 10^–3 and 1.24 × 10^–3) are obtained from 70 runs of 10-min duration. Mean wind velocities observed at 2 m above water surface are found to lie between 1.2 and 3.6 m s^–1. Whereas this mean value is in fair agreement with C _{d 10} = 1.3 × 10^–3, usually given for the 5 to 16 m s^–1 range (Kraus, 1972), the above value for the standard deviation seems too large to be left without further analysis.A more exhaustive analysis of the 70 values obtained for C _d shows that it depends on a parameter characteristic of longitudinal fluctuations of the wind velocity. A similar idea was put forward earlier by Kraus (1972). Relations between the drag coefficient and wind fluctuations may be tentatively given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% igdacaGGUaGaaGimaiaaiEdacqGHRaWkcaaIXaGaaGinaiaac6caca% aIZaGaaGinamaalaaabaGaeq4Wdm3aaSbaaSqaaiaadwhacaGGNaaa% beaaaOqaaaaaaiaawIcacaGLPaaaruqqYLwySbacfaGaa8hEaiaa-b% cacaaIXaGaaGimamaaCaaaleqabaGaeyOeI0IaaG4maaaakiaabcca% caqGGaGaaeiiaiaabccacaqGXaGaaeOlaiaabAdacaqGGaGaaeyBai% aabccacaqGZbWaaWbaaSqabeaacaqGTaGaaeymaaaakiabgsMiJkqa% dwhagaqeamaaBaaaleaacaaIYaaabeaakiabgsMiJkaaiodacaGGUa% GaaGOnaiaab2gacaqGGaGaae4CamaaCaaaleqabaGaaeylaiaabgda% aaaaaa!634E!\[C_{d2} = \left( { - 1.07 + 14.34\frac{{\sigma _{u'} }}{{}}} \right)x 10^{ - 3} {\text{ 1}}{\text{.6 m s}}^{{\text{ - 1}}} \leqslant \bar u_2 \leqslant 3.6{\text{m s}}^{{\text{ - 1}}} \] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa% aaleaacaWGKbGaaGOmaaqabaGccqGH9aqpdaqadaqaaiabgkHiTiaa% iodacaGGUaGaaGioaiaaiAdacqGHRaWkcaaIZaGaaiOlaiaaiodaca% aI2aGaam4raaGaayjkaiaawMcaaerbbjxAHXgaiuaacaWF4bGaa8hi% aiaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaIZaaaaOGaaeilaa% aa!4B42!\[C_{d2} = \left( { - 3.86 + 3.36G} \right)x 10^{ - 3} {\text{,}}\] where _u/\-u ₂ and G, respectively, represent the standard deviation of u normalized with \-u ₂ and the longitudinal gust factor quoted in Smith (1974).We have established a relationship between these fluctuation parameters and the stability as given by a bulk layer Richardson number (between 0 and 2 m). These relations are given by: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHdpWCdaWgaaWcbaGaamyDaiaacEcaaeqaaaGcbaGabmyDayaaraWa% aSbaaSqaaiaaikdaaeqaaaaakiabg2da9iaaicdacaGGUaGaaGymai% aaikdacqGHRaWkcaaIZaGaaiOlaiaaiIdacaaI1aGaaeiiaiaabkfa% caqGPbWaaSbaaSqaaiaabcdacaqGTaGaaeOmaaqabaaaaa!4802!\[\frac{{\sigma _{u'} }}{{\bar u_2 }} = 0.12 + 3.85{\text{ Ri}}_{{\text{0 - 2}}} \] and G=1.35+14.56 Ri_0–2. The increase in gustiness with stability is in qualitative agreement with Goptarev (1957)'s experimental results.In spite of the high-level correlation between C _d and _u/\-u ₂(G) on the one hand and between _u/\-u ₂(G) and Ri_0–2on the other hand, we found a poor relationship between C _d and Ri_0–2. It is worth noting too that the trend observed here for C _d to increase with stability is in complete disagreement with the usual theoretical expectation for C _d to decrease with increasing layer stability above water.

---

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E.R.A. du C.N.R.S. n 259.     

Near-field dispersion from instantaneous sources in the surface layer

This paper considers the near-field dispersion of an ensemble of tracer particles released instantaneously from an elevated source into an adiabatic surface layer. By modelling the Lagrangian vertical velocity as a Markov process which obeys the Langevin equation, we show analytically that the mean vertical drift velocity w(t) is w()=bu _*(1–e ^–(1+)), where is time since release (nondimensionalized with the Lagrangian time scale at the source), b Batchelor's constant, and u _*, the friction velocity. Hence, the mean height and mean depth of the ensemble are calculated. Although the derivation is formally valid only when 1, the predictions for w, mean height and mean depth are consistent in the downstream limit ( 1) with surface-layer Lagrangian similarity theory and with the diffusion equation. By comparing the analytical predictions with numerical, randomflight solutions of the Langevin equation, the analytical predictions are shown to be good approximations at all times, both near-field and far-field.     

An examination of turbulence statistics in the surface boundary layer

Simulated data derived from random numbers are used to show that the process of relating % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7C!\[\sigma _w /u_ * \]and similar properties to the stability parameter % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQhacaGGVa% Gaamitaaaa!3A42!\[z/L\]is highly susceptible to error. An alternative method, making use of Ri as a stability index, is not affected in this way and is used to re-examine the data obtained in the 1968 Kansas micrometeorological experiment. The relationship % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG3baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baGccqWIdjYocaaIXaGaaiOlaiaaikdacaaI1aaaaa!419F!\[\sigma _w /u_ * \simeq 1.25\] % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaabmaabaGaaG% ymaiabgkHiTiaaikdacaWG6bGaai4laiaadYeaaiaawIcacaGLPaaa% daahaaWcbeqaaiaaigdacaGGVaGaaG4maaaaaaa!4087!\[\left( {1 - 2z/L} \right)^{1/3} \]is found to provide a good fit to the unstable data, but it is unclear as to whether a small peak observed in stable conditions is real (perhaps associated with gravity waves) or not (possibly a consequence of measurement errors).The properties % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacaWG1bWaaSbaaSqaaiabgEHiQaqa% baaaaa!3D7A!\[\sigma _u /u_ * \] are found to attain a relatively constant value ( 3) in conditions more unstable than about Ri = -0.4. The shape ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaWG1baabeaakiaac+cacqaHdpWCdaWgaaWcbaGaamODaaqa% baaaaa!3E4F!\[\sigma _u /\sigma _v \] is found to decrease to less than unity in very unstable conditions, possibly as a consequence of some undetected error in measurement of _u . In the case of temperature fluctuations, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacqaHepaDaeqaaOGaai4laiaadsfadaWgaaWcbaGaey4fIOca% beaakiabg2da9iaaicdacaGGUaGaaGyoaiaaiwdacaGGOaGaeyOeI0% IaamOEaiaac+cacaWGmbGaaiykamaaCaaaleqabaGaeyOeI0IaaGym% aiaac+cacaaIZaaaaaaa!4A30!\[\sigma _\tau /T_ * = 0.95( - z/L)^{ - 1/3} \] is found to provide an excellent fit in unstable conditions (Ri < -0.1), even though this form also agrees well with random behavior.Now With: Atmospheric Turbulence and Diffusion Laboratory, NOAA, P. O. Box E, Oak Ridge Tenn., 37830, U.S.A.     

A framework for evaluating air quality models

This paper describes a framework to evaluate air quality model predictions against observations. We propose the following relationship between observations and predictions from an adequate model% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% WaaSbaaSqaaiaaicdaaeqaamXvP5wqonvsaeHbfv3ySLgzaGqbaOGa% e8hkaGIaamiEamaaBaaaleaacaaIXaaabeaakiaacYcacaWG4bWaaS% baaSqaaiaaikdaaeqaaOGae8xkaKIaeyypa0Jabm4qayaajaWaaSba% aSqaaiaadchaaeqaaOGae8hkaGIaamiEamaaBaaaleaacaaIXaaabe% aakiab-LcaPiab-TcaRiabew7aLjab-HcaOiaadIhadaWgaaWcbaGa% aGOmaaqabaGccqWFPaqkaaa!4F93!\[\hat C_0 (x_1 ,x_2 ) = \hat C_p (x_1 ) + \varepsilon (x_2 )\],where x ₁ refers to the inputs used in the model prediction C _p(x ₁), and x ₂denotes unknown variables which affect the observed concentration C ₀. The hats associated with C _pand C ₀denote transformations to convert the residual to a white noise sequence which is normally distributed. In this paper we assume % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% GaeyyyIORaciiBaiaac6gacaWGdbaaaa!3B39!\[\hat C \equiv \ln C\].The standard deviation of determines the expected deviation between model prediction and observation. The purpose of model improvement is to make this deviation as small as possible.The formalism we have proposed is applied to the evaluation of two models developed by this author. We show how careful analysis of residuals can lead to improvements in the model. We have also estimated for each of the models.In the last part of the part of the paper we show how the statistics of can be used to interpret model predictions.     

Measuring C T 2 , C Q 2 , and C TQ in the unstable surface layer,and relations to the vertical fluxes of heat and moisture

The structure parameters of temperature (C _T ² ), humidity (C _Q ² ) and temperature-humidity (C _TQ ) were observed at a height of 4 m in the unstable surface layer using thin platinum wires and two Ly- hygrometers. Two ways of measuring structure parameters were employed: one using spaced sensors, the other using time-delayed observations at one location. It is found that the three structure parameters follow free-convection scaling down to -z/L 0.02. The scaling functions % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₁ (of C _T ² ), % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₂ (of C _TO ) and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₃ (of C _Q ² ) are found to be related through % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₂/% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₁ 0.69 and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₃/% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbaaaa!3346!\[f\]₁ 0.84. The usefulness of the structure parameters for inferring the fluxes of heat and water vapor, as well as the Bowen ratio, is demonstrated. The scatter is about 30% on either side of the mean.This work was done while the author was a visiting scientist at the Wave Propagation Laboratory, NOAA, ERL, Boulder, U.S.A. He received support from the Netherlands Minister for Science Policy and the U.S. Army Research Office.     

Mesoscale nocturnal jetlike winds within the planetary boundary layer over a flat,open coast

Mesoscale nocturnal jetlike winds have been observed over a flat, open coast. They occur within the planetary boundary layer between 100 and 600 m. At times the wind shear may reach 15 m s^-1 per 100 m. Unlike the common low-level jet that occurs most often at the top of the nocturnal inversion and only with a wind from the southerly quadrant, this second kind of jet exists between nocturnal ground-based inversion layers formed by the cool pool, or mesohigh, and the elevated mesoscale inversion layer over the coast. It occurs mostly when light % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiabgs% MiJkaaiwdacqGHsislcaaI2aGaaeyBaiaabccacaqGZbWaaWbaaSqa% beaacqGHsislcaaIXaaaaOGaaiykaaaa!3FCF!\[( \leqslant 5 - 6{\text{m s}}^{ - 1} )\] geostrophic winds blow from land to sea and when the air temperature over adjacent seas is more than 5 °C warmer than that over the coast. This phenomenon may be explained by combined Venturi and gravity-wind effects existing in a region from just above the area a few kilometres offshore to 100–600 m in height approximately 40–50 km inland because this region is sandwiched between the aforementioned two inversion layers.     

Boundary-layer dynamics of a developing vortex

The dynamics of the boundary layer of a developing vortex is studied. To keep the mathematical treatment simple, axisymmetric vortices in both solid and non-solid rotation are considered. The governing equations are subjected to a similarity transformation and the resulting non-linear parabolic partial differential equations are solved by a Galerkin technique for simplified initial conditions which permit non-zero tangential and vertical velocities at the lower and upper boundaries. The application of a time-dependent Taylor boundary condition at the lower extremity of the vortex causes the fluid to spin-down gradually. By doing so, the no-slip steady-state solutions are progressively approached. On the other hand the employment of the customary Taylor boundary condition made the vortex to spin down rapidly causing a large-amplitude oscillatory vertical velocity.Analyses of the linearized equations and of the numerical solutions of the non-linear problem indicate the presence in the radial and tangential fields of inertial oscillations of frequency % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaKaaaj% aad6gakmaaleaaleaaruqqYLwySbacfaGaa8xmaaqaaiaa-jdaaaac% ciGccqGFPoWvaaa!3D19!\[2n\tfrac{1}{2}\Omega \] (: angular velocity of the flow and n: a parameter such that n=1 signifies solid rotation and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaWefv% 3ySLgznfgDOjdaryqr1ngBPrginfgDObcv39gaiuaacqWFKjcHcaWG% Ubaaaa!461C!\[0 \leqslant n\] <1 non-solid rotation). Thus the frequency of inertial oscillations is reduced for non-rigid rotation.     

Stability functions correct at the free convection limit and consistent for for both the surface and Ekman layers

For the thermal stability function _h used to calculate heat and moisture fluxes in the surface layer, we choose a formulation which has the theoretically correct free convection limit % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabgk% HiTGqaciaa-PhacaqGVaGaamitaiaabMcadaahaaWcbeqaaiabgkHi% TiaaigdacaGGVaGaaG4maaaaaaa!3DFE!\[{\rm{(}} - z{\rm{/}}L{\rm{)}}^{ - 1/3} \]. We then use the experimental result that z/L Ri to deduce a formulation with an exponent -1/6 for the momentum stability function _m. This formulation also resolves the matching problem at the interface between the surface and Ekman layers. The proposed functions are found to remain reasonably close to another formulation that is well supported by observations and has exponents -1/2 for _h and -1/4 for _m. The intent of the proposals is mainly to clarify and simplify the parameterization of the convective boundary layer in present day atmospheric models, without significantly altering the results.     

A model of turbulence spectra in the atmospheric surface layer

The spectral equations of turbulent kinetic energy and temperature variance have been solved by using Onsager's energy cascade model and by extending Onsager's model to closure of terms that embody the interaction of turbulent and mean flow.The spectral model yields the following results: In a stably stratified shear flow, the peak wave numbers of the spectra of energy and temperature variance shift toward larger wave numbers as stability increases. In an unstably stratified flow, the peak wave numbers of energy spectra move toward smaller wave numbers as instability increases, whereas the opposite trend is observed for the peak wave numbers of temperature variance spectra. Hence, the peak wave numbers of temperature spectra show a discontinuity at the transition from stable to unstable stratification. At near neutral stratification, both spectra reveal a bimodal structure.The universal functions of the Monin-Obukhov similarity theory are predicted to behave as _m ~ _H ~ (- Z/L)^-1/3 in an extremely unstable stratification and as _m ~ _H ~ z/L in an extremely stable stratification. For a stably stratified flow, a constant turbulent Prandtl number is expected.     

Atmospheric effects in the remote sensing of phytoplankton pigments

We investigate the accuracy with which relevant atmospheric parameters must be estimated to derive phytoplankton pigment concentrations (chlorophyll a plus phaeophytin a ) of a given accuracy from measurements of the ocean's apparent spectral radiance at satellite altitudes. The analysis is limited to an instrument having the characteristics of the Coastal Zone Color Scanner scheduled to orbit the Earth on NIMBUS-G. A phytoplankton pigment algorithm is developed which relates the pigment concentration (C) to the three ratios of upwelling radiance just beneath the sea surface which can be formed from the wavelengths () 440, 520 and 550 nm. The pigment algorithm explains from 94 to 98% of the variance in log₁₀ C over three orders of magnitude in pigment concentration. This is combined with solutions to the radiative transfer equation to simulate the ocean's apparent spectral radiance at satellite altitudes as a function of C and the optical properties of the aerosol, the optical depth of which is assumed to be proportioned to ^-n . A specific atmospheric correction algorithm, based on the assumption that the ocean is totally absorbing at 670 nm, is then applied to the simulated spectral radiance, from which the pigment concentration is derived. Comparison between the true and derived values of C show that: (1) n is considerably more important than the actual aerosol optical thickness; (2) for C 0299-1 0.2 g l^-1 acceptable concentrations can be determined as long as n is not overestimated; (3) as C increases, the accuracy with which n must be estimated, for a given relative accuracy in C, also increases; and (4) for C greater than about 0.5 g 1^-1, the radiance at 440 nm becomes essentially useless in determining C. The computations also suggest that if separate pigment algorithms are used for C 1gl^-1 and C 1 gl^-1, accuracies considerably better than ±± in log C can be obtained for C 1 g l^-1 with only a coarse estimate of n, while for C 10 gl^-1, this accuracy can be achieved only with very good estimates of n.Contribution No. 387 from the NOAA/ERL Pacific Environmental Laboratory.On leave from Department of Physics, University of Miami, Coral Gables, Florida.     

On the mean monthly equivalent potential temperature and rainfall in West Africa

Summary Rainfall in West Africa is examined in relation to monthly mean equivalent potential temperature ( _e )at the earth's surface. The study revealed that monthly mean equivalent potential temperature ( _e ) and monthly rainfall (R) generally decreased northwards from the equator.A good relationship existed betweenR and _e in the northern zone of West Africa (i.e., north of 7.5° N). No definite relationship existed in the southern zone. In the northern zone, the departure of _e from its annual mean ( ) first became positive about a month before the onset of the rains. Positive departures from ) generally resulted in more than normal (or average) rainfall in this zone. In general, little or no rainfall occurred in West Africa whenever _e was less than 320 K.

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Zusammenfassung Der Niederschlag (MonatssummeR) in Westafrika wird in Zusammenhang mit der mittleren monatlichen Äquivalent-temperatur ( _e ) an der Erdoberfläche untersucht. Es zeigte sich, daß die Monatswerte beider Elemente im allgemeinen vom Äquator nach Norden abnehmen.ZwischenR und _e ergab sich für das nördliche Westafrika (nördlich von 7.5° N) eine gute, für die südliche Zone jedoch keine beweisbare Übereinstimmung. In der nördlichen Zone übertraf _e das Jahresmittel erstmals etwa einen Monat vor Beginn der Regenzeit. Positive Abweichungen vom mittleren _e hatten immer übernormalen Niederschlag in dieser Zone zur Folge. Dagegen gab es wenig oder keinen Niederschlag in Westafrika, wenn _e unter 320 K lag.

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With 7 Figures