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.     

A verification of an analytical formula for estimating the height of the stable internal boundary layer

A stable thermal internal boundary layer (IBL) develops when warm air is advected from warmer land upstream to a cooler sea downstream. It is shown that the analytical model for estimating the height (h) of this stable IBL as formulated by Garratt (1987) is verified. It is also demonstrated that a simpler equation, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGObGaeyisIS% RaaGymaiaaiAdacaWGybWaaWbaaSqabeaadaWcgaqaaiaaigdaaeaa% caaIYaaaaaaaaaa!390B!\[h \approx 16X^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \] (where h is in meters and X, the fetch downwind, is in kilometers), is useful operationally as a first approximation.     

The influence of anisotropy on stress estimation by the indirect dissipation method

A comparison of observations by different authors reveals that systematic differences exist between momentum fluxes measured directly, and momentum fluxes determined indirectly by the dissipation method. This discrepancy is attributed to systematic errors due to the indirect determination of energy dissipation from the presumed inertial subrange spectrum of the horizontal wind component. The discrepancy increases with increasing degree of anisotropy, indicated by the ratio (vertical wind spectrum): (horizontal wind spectrum) deviating from % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaaiaais% daaeaacaaIZaaaaaaa!33E6!\[\frac{4}{3}\]The results support a value of 0.48 for Kolmogoroff's constant.     

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.     

A simple model for the adjustment of velocity spectra in unstable conditions downstream of an abrupt change in roughness and heat flux

A simple model for the equilibrium spectra of velocity fluctuations in the unstable surface layer is developed. All three component spectra are written as a sum of two spectra For the horizontal spectra, the two parts scale with % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcacaWGUb% GaamOEamaaBaaaleaacaWGPbaabeaakiaac+cacaWG1bGaaiilaiaa% dQhadaWgaaWcbaGaamyAaaqabaGccaGGVaGaamitaiaacMcaaaa!4232!\[(nz_i /u,z_i /L)\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaWG6b% Gaai4laiaadwhaaaa!3B5E!\[nz/u\], respectively; the vertical spectrum can be written entirely as a function of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaad6gacaWG6b% Gaai4laiaadwhaaaa!3B5E!\[nz/u\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQhacaGGVa% Gaamitaaaa!3A42!\[z/L\].The equilibrium spectra are utilized as part of a model describing the development of velocity spectra downwind of a change in surface roughness and heat flux.Results are shown for the streamwise component and compared with hotwire measurements from the RISØ 78 experiment. The model shows excellent agreement with the measurements.on leave of absence from RISØ National Laboratory Roskilde, Denmark.     

The effect of changes in surface resistance on temperature and humidity fields and fluxes of sensible and latent heat

In this paper we consider temperature (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiMdeLbae% baaaa!377B!\[\bar \Theta \]) and specific humidity (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyuayaara% aaaa!36DA!\[\bar Q\]) fields in the lower part of the planetary boundary layer and present a method for calculating the way these variables and their fluxes vary over changes in available surface moisture expressed as a surface resistance. Near the surface, the turbulence is close to equilibrium and an eddy diffusivity model enables the changes in (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiMdeLbae% baaaa!377B!\[\bar \Theta \]), % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyuayaara% aaaa!36DA!\[\bar Q\], sensible heat flux (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaara% WaaSbaaSqaaiaadIeaaeqaaaaa!37C8!\[\bar F_H \]), and latent heat flux (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaara% WaaSbaaSqaaiaadweaaeqaaaaa!37C5!\[\bar F_E \]) to be determined in terms of the assumed mean wind, turbulence profiles and upwind profiles of temperature and humidity. An important advantage of this method is that it is possible to consider arbitrary changes in surface properties.     

The turbulent heat flux from arctic leads

The turbulent transfer of heat from Arctic leads in winter is one of the largest terms in the Arctic heat budget. Results from the AIDJEX Lead Experiment (ALEX) suggest that the sensible component of this turbulent heat flux can be predicted from bulk quantities. Both the exponential relation N = 0.14R _x ^0.72 and the linear relation N = 1.6 × 10^–3 R _x+ 1400 fit our data well. In these, N is the Nusselt number formed with the integrated surface heat flux, and R _x is the Reynolds number based on fetch across the lead. Because of the similarity between heat and moisture transfer, these equations also predict the latent heat flux. Over leads in winter, the sensible heat flux is two to four times larger than the latent heat flux.The internal boundary layer (IBL) that develops when cold air encounters the relatively warm lead is most evident in the modified downwind temperature profiles. The height of this boundary layer, , depends on the fetch, x, on the surface roughness of the lead, z ₀ and on both downwind and upwind stability. A tentative, empirical model for boundary layer growth is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaaiabes% 7aKbqaaiaadQhadaWgaaWcbaGaaGimaaqabaaaaOGaeyypa0JaeqOS% di2aaeWaaeaacqGHsisldaWcaaqaaiaadQhadaWgaaWcbaGaaGimaa% qabaaakeaacaWGmbaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGim% aiaac6cacaaI4aaaaOWaaeWaaeaadaWcaaqaaiaadIhaaeaacaWG6b% WaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaamaaCaaaleqa% baGaaGimaiaac6cacaaI0aaaaaaa!472D!\[\frac{\delta }{{z_0 }} = \beta \left( { - \frac{{z_0 }}{L}} \right)^{0.8} \left( {\frac{x}{{z_0 }}} \right)^{0.4} \] where L is the Obukhov length based on the values of the momentum and sensible heat fluxes at the surface of the lead, and is a constant reflecting upwind stability.Velocity profiles over leads are also affected by the surface nonhomogeneity. Besides being warmer than the upwind ice, the surface of the lead is usually somewhat rougher. The velocity profiles therefore tend to decelerate near the surface, accelerate in the mid-region of the IBL because of the intense mixing driven by the upward heat flux, and rejoin the upwind profiles above the boundary layer. The profiles thus have distinctly different shapes for stable and unstable upwind conditions.     

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.     

An analytic similarity theory for the planetary boundary layer stabilized by surface buoyancy

An analytic solution for a steady, horizontally homogeneous boundary layer with rotation, % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadAgaaaa!38AA! \[ f \] , and surface friction velocity, û_*, subjected to surface buoyancy characterized by Obukhov length L, is proposed as follows. Nondimensional variables are % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeA7a6jabg2 % da9iaadAgacaWG6bGaai4laiabeE7aOnaaBaaaleaacqGHxiIkaeqa % aOGaamyDamaaBaaaleaacqGHxiIkaeqaaOGaaiilaiqadwhagaqcai % abg2da9iabeE7aOnaaBaaaleaacqGHxiIkaeqaaOGabmyvayaajaGa % ai4laiqadwhagaqcamaaBaaaleaacqGHxiIkaeqaaOGaaiilaiqads % fagaqcaiabg2da9iqbes8a0zaajaGaai4laiaadwhadaWgaaWcbaGa % ey4fIOcabeaakiqadwhagaqcamaaBaaaleaacqGHxiIkcaGGSaaabe % aaaaa!5587! \[ \zeta = fz/\eta _ * u_ * ,\hat u = \eta _ * \hat U/\hat u_ * ,\hat T = \hat \tau /u_ * \hat u_{ * ,} \] , where carets denote complex (vector) quantities; Û is the mean velocity; % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiqbes8a0zaaja% aaaa!3994!\[\hat \tau \]is the kinematic turbulent stress; and % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabeE7aOnaaBa % aaleaacqGHxiIkaeqaaOGaeyypa0JaaiikaiaaigdacqGHRaWkcqaH % +oaEdaWgaaWcbaGaamOtaaqabaGccaWG1bWaaSbaaSqaaiabgEHiQa % qabaGccaGGVaGaamOuamaaBaaaleaacaWGJbaabeaakiaadAgacaWG % mbGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaa % aa!4B1F! \[ \eta _ * = (1 + \xi _N u_ * /R_c fL)^{ - 1/2} \]is a stability parameter. The constant % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabe67a4naaBa % aaleaacaWGobaabeaaaaa!3A81! \[\xi _N \] is the ratio of the maximum mixing length(% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaaBaaaleaaca% WGTbaabeaaaaa!38DD!\[_m \]) to the PBL depth, % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadwhadaWgaa % WcbaGaey4fIOcabeaakiaac+cacaWGMbaaaa!3B7C! \[ u_ * /f \] , for neutrally stable conditions; and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadkfadaWgaa% WcbaGaam4yaaqabaaaaa!39AA!\[R_c\](the critical flux Richardson number) is the ratio % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadYgadaWgaa % WcbaGaamyBaaqabaGccaGGVaGaamitaaaa!3B5C! \[ l_m /L \] under highly stable conditions. Profiles of stress and velocity in the ocean (<0) are given by % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaaxacabaGabm % yDayaajaGaeyypa0ZaaiqaaqaabeqaaiabgkHiTiaadMgacqaH0oaz % caWGLbWaaWbaaSqabeaacqaH0oazcqaH2oGEaaGccaqGGaGaaeiiai % aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa % aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca % qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa % bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae % iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG % GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc % cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii % aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGa % GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca % caqGGaGaaeiiaiaabccacaqGGaGaeqOTdONaeyizImQaeyOeI0Iaeq % OVdG3aaSbaaSqaaiaad6eaaeqaaaGcbaGaeyOeI0IaamyAaiabes7a % KjaadwgadaahaaWcbeqaaiabes7aKjabe67a4naaBaaameaacaWGob % aabeaaaaGccqGHsisldaWcaaqaaiabeE7aOnaaBaaaleaacaGGQaaa % beaaaOqaaiaadUgaaaWaamWaaeaaciGGSbGaaiOBamaalaaabaWaaq % WaaeaacqaH2oGEaiaawEa7caGLiWoaaeaacqaH+oaEdaWgaaWcbaGa % amOtaaqabaaaaOGaey4kaSIaaiikaiabes7aKjabgkHiTiaadggaca % GGPaGaaiikaiabeA7a6jabgUcaRiabe67a4naaBaaaleaacaWGobaa % beaakiaacMcacqGHsisldaWcaaqaaiaadggaaeaacaaIYaaaaiabes % 7aKjaacIcacqaH2oGEdaahaaWcbeqaaiaaikdaaaGccqGHsislcqaH % +oaEdaqhaaWcbaGaamOtaaqaaiaaikdaaaGccaGGPaaacaGLBbGaay % zxaaGaaeiiaiaabccacaqGGaGaaeiiaiabeA7a6naaBaaaleaacaaI % WaaabeaakiabgwMiZkabeA7a6jabg6da+iabgkHiTiabe67a4naaBa % aaleaacaWGobaabeaaaaGccaGL7baaaSqabKazbaiabaGabmivayaa % jaGaeyypa0JaamyzamaaCaaajqMaacqabeaacaWGPbGaeqiTdqMaeq % OTdOhaaaaaaaa!C5AA! \[ \mathop {\hat u = \left\{ \begin{array}{l} - i\delta e^{\delta \zeta } {\rm{ }}\zeta \le - \xi _N \\ - i\delta e^{\delta \xi _N } - \frac{{\eta _* }}{k}\left[ {\ln \frac{{\left| \zeta \right|}}{{\xi _N }} + (\delta - a)(\zeta + \xi _N ) - \frac{a}{2}\delta \end{array} \right.}\limits^{\hat T = e^{i\delta \zeta } } \] where % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l % b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr % 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabes7aKjabg2 % da9maabmaabaGaamyAaiaac+cacaWGRbGaeqOVdG3aaSbaaSqaaiaa % d6eaaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIXaGaai4lai % aaikdaaaGccaGG7aGaamyyaiabg2da9iabeE7aOnaaBaaaleaacqGH % xiIkaeqaaOGaaiikaiaaigdacaGGVaGaeqOVdG3aaSbaaSqaaiaad6 % eaaeqaaOGaey4kaSIaamyDamaaBaaaleaacqGHxiIkaeqaaOGaai4l % aiaadAgacaWGmbGaamOuamaaBaaaleaacaWGJbaabeaakiaacMcaca % GGOaGaaGymaiabgkHiTiabeE7aOnaaBaaaleaacqGHxiIkaeqaaOGa % aiykaiaacUdaaaa!5CB6! \[ \delta = \left( {i/k\xi _N } \right)^{1/2} ;a = \eta _ * (1/\xi _N + u_ * /fLR_c )(1 - \eta _ * ); \] and ₀ is the nondimensional surface roughness. The constants are% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiaadkfadaWgaa% WcbaGaam4yaaqabaaaaa!39AA!\[R_c \]= 0.2 and% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaiabe67a4naaBa% aaleaacaWGobaabeaaaaa!3A81!\[\xi _N \]= 0.052. The solutions for the atmosphere are similar except û is the nondimensional velocity The model produces satisfactory predictions of geostrophic drag and near-surface current (wind) profiles under stable stratification.     

The drag coefficient as determined by the dissipation method and its relation to intermittent convection in the surface layer

The influence of intermittent convection on surface-layer stress estimates during the GARP Atlantic Tropical Experiment (GATE) is described. A negative correlation between the drag coefficient (C _D) and the wind speed (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]) is found when short averaging periods are used. Well-defined, discrete events produce this negative correlation, and these events are shown to correspond to the passage of convective plumes. Constraints on averaging times necessary to obtain reasonable stress estimates using the bulk method are discussed.Conditional sampling is used to produce average values of dissipation (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae% baaaa!37AB!\[\bar \varepsilon \]), wind speed (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]), and virtual temperature (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmivayaara% WaaSbaaSqaaiaaiw8aaeqaaaaa!385B!\[\bar T_\upsilon \]) for each high turbulent intensity event, and for the quiescent periods in between. Such statistics indicate that the highly turbulent states coincide with the presence of plumes and account for the negative correlation between C _D and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]. Some of these statistics are also stability dependent.The probability distributions of the dissipation rate are bimodally log-normal which suggests that turbulence generated at two different heights is being sampled. This, along with other results of this paper, support a picture of a boundary layer which is dominated by vertical exchange.Contribution Number 409, Department of Atmospheric Sciences, University of Washington.     

Measurement of the vertical flux of turbulent kinetic energy with a single Doppler radar

The Doppler radar velocity azimuth display (VAD) technique for obtaining first and second moments of radial wind velocities is expanded to third-moment calculations. By scanning at an elevation angle of 50.8°, terms of the third-moment equation can be reduced to yield the vertical flux of turbulent kinetic energy, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaaceWGXbGbauaaaaaaaa!3807!\[\overline {w'q'} \]. The technique has been applied to summertime radar measurements of the convective boundary layer in Illinois. Resulting vertical profiles of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaaceWGXbGbauaaaaaaaa!3807!\[\overline {w'q'} \] follow the expected shape, and the magnitudes compare well with those of aircraft measurements in previous studies.     

An international turbulence comparison experiment (ITCE 1976)

Turbulence data for the International Turbulence Comparison Experiment (ITCE) held at Conargo, N.S.W. (35° 18′ S., 145° 10′ E.) during October, 1976 are analysed. The standard deviation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiqado% hagaqbamaaCaaaleqabaGaaGOmaaaakiaacMcadaahaaWcbeqaaiaa% igdacaGGVaGaaGOmaaaaaaa!3B93!\[(s'^2 )^{1/2} \] and covariance % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaace% WG3bGbauaaceWGZbGbauaaaaaaaa!3809!\[\overline {w's'} \] measured by a number of instruments and instrument arrays have been compared to assess their field performance and calibration accuracy. Satisfactory agreement, i.e. typically 5% for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikamaana% aabaGabm4CayaafaWaaWbaaSqabeaacaaIYaaaaaaakiaacMcadaah% aaWcbeqaaiaaigdacaGGVaGaaGOmaaaaaaa!3BA4!\[(\overline {s'^2 } )^{1/2} \] (except in humidity) and of the order of 20% for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiqado% hagaqbamaaCaaaleqabaGaaGOmaaaakiaacMcadaahaaWcbeqaaiaa% igdacaGGVaGaaGOmaaaaaaa!3B93!\[(s'^2 )^{1/2} \], was achieved, but only after consideration of:

1. Instrumental response at high frequencies.
2. Flow distortion induced by instruments and supporting structures.
3. Spatial separation of instruments used for covariance measurements.
4. Statistical errors associated with single point measurements over a finite averaging time, and with lateral separation of two sensor arrays being compared.

     

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.     

Prediction of the Monin-Obukhov similarity functions from a second-order-closure model

The atmospheric surface layer model of Lewellen and Teske (1973) is extended. Obvious discrepancies between model results and empirical data suggest the use of improved closure schemes for the non-diffusive parts of the pressure-velocity correlations in the Reynolds stress equations. Subsequently a time scale for the surface layer, which is based on vertical velocity fluctuations, is tested by means of the extended model. Finally the extended model is optimized by variation of the diffusion parameters, and an additional equation is introduced for the dissipation rate of Reynolds stresses. Investigations show that the normalized mean velocity and temperature gradients are verified by all model versions favorably, whereas the other turbulence variables % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaamaanaaabaGaam% yDaGqaciaa-DcacaWFGaGaamyDaiaa-DcaaaGaaiilaiaabccadaqd% aaqaaiabew8a1jaa-DcacaWFGaGaeqyXduNaa83jaaaacaqGSaGaae% iiamaanaaabaGaae4Daiaa-DcajaaqcaWFGaGccaqG3bGaa83jaaaa% caqGSaGaaeiiamaanaaabaGaamyDaiaa-DcajaaqcaWFGaGccaWFub% Gaa83jaaaaaaa!4DB4!\[\overline {u' u'} ,{\rm{ }}\overline {\upsilon ' \upsilon '} {\rm{, }}\overline {{\rm{w}}' {\rm{w}}'} {\rm{, }}\overline {u' T'} \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-rfaca% WFNaqcaaKaa8hiaOGaa8hvaiaa-Dcaaaa!3BB8!\[T' T'\] cannot be simulated so easily. Complications especially arise in unstable temperature stratification.     

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.     

Testing of a higher-order closure model for modeling airflow within and above plant canopies

A higher-order closure model was developed to simulate airflow within and above vegetative environments. The model consists of equations for the mean wind, turbulent kinetic energy (TKE) components, tangential stress and simplified equations for the third-order transport terms that appear in the second-order equations. The model in general successfully simulated wind speed profiles within and above maize, been, soybeen, wheat, orange and spruce canopies. Profiles 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% WG3bGbauaadaahaaWcbeqaaiaaikdaaaaaaaaa!37EE!\[\overline {w'^2 } \] for the maize canopy were overestimated near the top of the canopy where both shear and wake production of TKE are high. These errors are believed to be caused by incorrect parameterizations for either the dissipation rate of TKE and/or the pressure-velocity correlations in the budget equations for the second moments.     

The turbulent kinetic energy budget in the atmospheric surface layer: A review and an experimental reexamination in the field

The one-dimensional equation for the turbulent kinetic energy budget in steady, horizontally-homogeneous flow near the ground is reviewed, and some of the many experimental evaluations of its stability-dependent terms obtained during the last twenty years are compared. Uncertainties attributable to instrument error and inadequate sites are discussed, and it is demonstrated that improved equipment makes it possible to evaluate contributions to the budget with comparatively simple experiments. A preliminary field study finds a von Karman constant of k=0.387±0.016 and a wind shear function for the unstable surface layer% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiaad2gaaeqaaOGaeyypa0JaaiikaiaaigdacqGHsislcaaI% YaGaaGOmaiaac6cacaaI2aGaamOEaiaac+cacaWGmbGaaiykamaaCa% aaleqabaGaeyOeI0IaaGymaiaac+cacaaI0aaaaaaa!4587!\[\phi _m = (1 - 22.6z/L)^{ - 1/4} \]: the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaaig% dacqGHsislcaaIXaGaaGynaiaac6cacaaIXaGaamOEaiaac+cacaWG% mbGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIZaaaaa% aa!419C!\[(1 - 15.1z/L)^{ - 1/3} \] fits equally well over the limited range of instability observed. Turbulence dissipation is found to be 15 to 20% too small to balance the production of energy by wind shear in the neutral surface layer, and this deficit appears to remain approximately constant relative to the total rate of energy production as instability increases to% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiaac+% cacaWGmbGaeyypa0JaeyOeI0IaaGimaiaac6cacaaIXaGaaGOmaaaa% !3D45!\[z/L = - 0.12\]. Renormalized dissipation rates originally measured by others are shown to exhibit similar behavior beyond this narrow range. Combining these results with those of the present study suggests a dissipation function of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOXdy2aaS% baaSqaaiabew7aLbqabaGccqGH9aqpcqaHgpGzdaWgaaWcbaGaamyB% aaqabaGccqGHsislcaWG6bGaai4laiaadYeacqGHRaWkcaWGJbaaaa!42A3!\[\phi _\varepsilon = \phi _m - z/L + c\] in which c = -0.16 represents a near constant, net negative contribution made by the sum of the divergent transport terms.School of Earth and Atmospheric Sciences, Georgia Institute of Technology.Work sponsored by the National Science Foundation under Grant Nos. ATM-8714025 and ATM-9019682, in part through The University of Chicago.     

Minimum friction velocity and heat transfer in the rough surface layer of a convective boundary layer

A simple model is deduced for the surface layer of a convective boundary layer for zero mean wind velocity over homogeneous rough ground. The model assumes large-scale convective circulation driven by surface heat flux with a flow pattern as it would be obtained by conditional ensemble averages. The surface layer is defined here such that in this layer horizontal motions dominate relative to vertical components. The model is derived from momentum and heat balances for the surface layer together with closures based on the Monin-Obukhov theory. The motion in the surface layer is driven by horizontal gradients of hydrostatic pressure. The balances account for turbulent fluxes at the surface and fluxes by convective motions to the mixed layer. The latter are the dominant ones. The model contains effectively two empirical coefficients which are determined such that the model's predictions agree with previous experimental results for the horizontal turbulent velocity fluctuations and the temperature fluctuations. The model quantitatively predicts the decrease of the minimum friction velocity and the increase of the temperature difference between the mixed layer and the ground with increasing values of the boundary layer/roughness height ratio. The heat transfer relationship can be expressed in terms of the common Nusselt and Rayleigh numbers, Nu and Ra, as Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaGOmaaaaaaa!3779!\[{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\]}. Previous results of the form Nu ~ Ra^{% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaaG4maaaaaaa!377A!\[{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\]} are shown to be restricted to Rayleigh-numbers less than a certain value which depends on the boundary layer/roughness height ratio.     

Large-sample estimates of wind fluctuations over the ocean

The best quality wind data from the Norwegian sector of the North Sea, consisting of 3662 20-min time series measured at the top of the Statfjord A drilling derrick, are analyzed. Identification of Autoregressive wind models with Akaike's AIC and Achwarz's BIC measures appears to give rather arbitrary results. Spectral estimation with FFT- and AIC-identified AR-methods give almost identical results in the mean. At the higher frequencies (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa!36D7!\[f\] > 10^–2 s^–1) the spectrum is estimated to follow the usual inertial subrange law with little variability. The small-scale turbulent intensity is estimated to be very low, even in hurricane conditions. Comparatively, the low-frequency (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa!36D7!\[f\] ~ 10^–3 s^–1) fluctuations are more energetic than expected. None of the chosen low-frequency characteristica appear to be significantly linearly correlated to the available mean weather variables. However, some nonlinear relations appear to exist.     

Impact of density fluctuations on flux measurements of trace gases: Implications for the relaxed eddy accumulation technique

A simple and fast approach to determine when density fluctuations are non-negligible in the calculation of the flux of trace gases (F _c ) is proposed. The correction (F _c – F _c (raw)), when expressed as the percentage of the flux, is dependent on the ratio of background concentration of the trace gas over its flux (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeikaiabeg% 8aYnaaBaaaleaacaWGJbaabeaakiaab+cacaWGgbWaaSbaaSqaaiaa% dogaaeqaaOGaaeykaaaa!3CBC!\[{\rm{(}}\rho _c {\rm{/}}F_c {\rm{)}}\], on the partitioning of available energy between sensible (F _T ) and latent (F _v ) heat fluxes, and on the flux measuring system. An increase from 100 to 200 W m^-2 in available energy and from 0 to 20% in F _T /(F _T + F _v ) led to a threefold reduction in the required value of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaacq% aHbpGCdaWgaaWcbaGaam4yaaqabaaaaOGaai4laiaadAeadaWgaaWc% baGaam4yaaqabaaaaa!3B6D!\[\overline {\rho _c } /F_c \] to have a density correction of 10%. A trace gas with a % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaceaaca% WGgbWaaSbaaSqaaiaadogaaeqaaaGccaGLhWUaayjcSdGaai4lamaa% naaabaGaeqyWdi3aaSbaaSqaaiaadogaaeqaaaaaaaa!3E91!\[\left| {F_c } \right|/\overline {\rho _c } \] value above 0.014 m s^-1 has a density correction on flux of less than 10%, for even the worst case scenario. Values of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa% aaleaacaWGJbaabeaakiaac+cadaqdaaqaaiabeg8aYnaaBaaaleaa% caWGJbaabeaaaaaaaa!3B6D!\[F_c /\overline {\rho _c } \] for several trace gases computed from typical situations show that the fluxes of N₂O, NO, CO₂, CH₄ and O₃ need to be corrected, while those of pesticides and volatile organic compounds, for example, do not. The corrections required with the newly developed relaxed eddy accumulation technique are discussed and equation development is shown for two sampling systems.Land Resource Research Centre Contribution No 91-61.