A modified parameterization of flux-profile relationships in the surface layer using different roughness length values for heat and momentum

The surface-layer flux-profile formulae of Louis (1979), used in many atmospheric models, are modified in a simple way to allow for different values of the roughness lengths for heat and momentum. The modified set of formulae simplifies the calculation of surface-layer fluxes over most natural land surfaces, where the roughness length for momentum can be almost an order of magnitude greater than that for heat.     

Pressure drag and effective roughness length with neutral stratification

A two-dimensional numerical mesoscale model is used to determine the pressure drag of sinoidal mountains and valleys in a neutral atmosphere. In the first part, pressure distributions and flow patterns for isolated obstacles are considered. For large aspect ratios, the pressure drag exerted by valleys becomes small compared to that of mountains. In the second part, interactions between several obstacles are investigated. For mountains, the drag on downstream obstacles is reduced considerably by the first obstacle when the obstacles are close together. For valleys there is a slight increase of the average drag exerted by each obstacle. In the limit for a large number of obstacles, average drag exerted by one mountain is equal to average drag for one valley. For smaller aspect ratios, this average drag can be entered into the resistence law from the Rossby number similarity theory to yield an effective roughness length.     

On the effective roughness length for use in numerical three-dimensional models

We present analytical and numerical calculations of the effective roughness length (ERL) over a flat surface with varying roughness elements, for use in large-scale models. It is shown that ERL is mostly determined by the roughest elements present inside the averaging domain and that, more surprisingly, the ERL increases as the first level of the numerical model gets closer to the surface and its altitude approaches the value of the largest local roughness length. This effect further increases the drag coefficient, in addition to the well-known increase due to the lowering of the first model level.     

Estimation of momentum and heat fluxes in the constant flux layer from temperature measurements

Global estimates of momentum and heat fluxes are required for the application of any general atmospheric and oceanic circulation model. A new technique for the estimation of these fluxes in a constant flux boundary layer is developed. The new approach is a modification of the dissipation technique but the only required measurements are the mean and fluctuating temperatures at two levels within the constant flux layer. All other flux estimation techniques require measurement of both temperature and velocity. Data are presented to compare flux estimation results with the conventional eddy-correlation technique. Also discussed are the limitations of the procedure and restrictions on its applicability.     

干旱区热力学粗糙度特征及对感热通量估算的影响

利用ＨＥＩＦＥ的实测资料估算了黑河实验区几个沙漠戈壁表面上的热力学粗糙度（以附加阻尼ｋＢ＾－１的形式）,发现在任一测站ｋＢ＾－１值的变化范围较大,同时分析了附加阻尼项在估算感热通量时的作用,而忽略该附加阻尼将会导致对感热通量的明显高估,提出在利用阻尼型公式计算感热通量时,不能采用简单的ｚ０ｍ＝ｚ０ｈ的假设,否则会带来较大误差。     

Resistance law,effective roughness length,and deviation angle over hilly terrain

In this note, we derive from the resistance law of Rossby number similarity theory the expressions for the drag coefficient and the deviation angle for strongly unstable and strongly stable stratifications. The extension of the applicability of the resistance laws to inhomogeneous terrain is discussed. A determination of the deviation angle over inhomogeneous terrain from a numerical experiment is presented.On leave from: Institute of Limnology, Academy of Sciences of the USSR, 196199 Leningrad.     

基于MODIS资料的中国东部时间序列空气动力学粗糙度和零平面位移高度估算

空气动力学粗糙度和零平面位移高度是很多气候模型和陆面模式中的重要参数,采用气象学方法推导这两个参数对于大范围长时间序列的计算需要大量长期的野外观测,而遥感方法可以快速经济的提供大范围数据,在本研究中采用形态学模型,以MOD IS产品数据作为数据源,计算植被冠层面积指数,估算了中国东部2001—2003年归一化到植被高度的1 km空间分辨率时间序列空气动力学粗糙度和零平面位移高度,结果表明空气动力学粗糙度和零平面位移高度均存在季节变化特征,并对所采用的模型和参数估算的结果进行了讨论。     

Estimation of surface heat and momentum fluxes using the flux-variance method above uniform and non-uniform terrain

Eddy-correlation measurements above an uneven-aged forest, a uniform-irrigated bare soil field, and within a grass-covered forest clearing were used to investigate the usefulness of the fluxvariance method above uniform and non-uniform terrain. For this purpose, the Monin and Obukhov (1954) variance similarity functions were compared with direct measurements. Such comparisons were in close agreement for momentum and heat but not for water vapor. Deviations between measured and predicted similarity functions for water vapor were attributed to three factors: 1) the active role of temperature in surface-layer turbulence, 2) dissimilarity between sources and sinks of heat and water vapor at the ground surface, and 3) the non-uniformity in water vapor sources and sinks. It was demonstrated that the latter non-uniformity contributed to horizontal gradients that do not scale with the vertical flux. These three factors resulted in a turbulence regime that appeared more efficient in transporting heat than water vapor for the dynamic convective sublayer but not for the dynamic sublayer. The agreement between eddy-correlation measured and flux-variance predicted sensible heat flux was better than that for latent heat flux at all three sites. The flux-variance method systematically overestimated the latent heat flux when compared to eddy-correlation measurements. It was demonstrated that the non-uniformity in water vapor sources reduced the surface flux when compared to an equivalent uniform terrain subjected to identical shear stress, sensible heat flux, and atmospheric water vapor variance. Finally, the correlation between the temperature and water vapor fluctuations was related to the relative efficiency of surface-layer turbulence in removing heat and water vapor. These relations were used to assess critical assumptions in the derivation of the flux-variance formulation.     

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.     

Zero-plane displacement and roughness length for tall vegetation,derived from a simple mass conservation hypothesis

A method for the determination of the zero-plane displacement, d, and roughness length, z ₀, for tall vegetation is described. A new relationship between d and z ₀ is developed by imposing the condition of mass conservation on the logarithmic wind profile. Further, d and z ₀ can be evaluated directly if independent measurements of friction velocity are available in addition to wind profile measurements. The proposed method takes into account the existence of a transition layer immediately above the vegetation where the logarithmic wind profile law is not valid. Only one level of wind speed measurements is necessary within the inertial sub-layer.The method is applied to wind profile and eddy correlation measurements taken in and above an 18.5 m pine forest to yield d = 12.7 m and z ₀ = 1.28 m. The choice of height for the upper level of measurement and problems with measuring canopy flow are discussed.Work carried out while on leave at the Institute of Hydrology.     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Wind profiles,momentum fluxes and roughness lengths at Cabauw revisited

We describe the results of an experiment focusing on wind speed and momentum fluxes in the atmospheric boundary layer up to 200 m. The measurements were conducted in 1996 at the Cabauw site in the Netherlands. Momentum fluxes are measured using the K-Gill Propeller Vane. Estimates of the roughness length are derived using various techniques from the wind speed and flux measurements, and the observed differences are explained by considering the source area of the meteorological parameters. A clear rough-to-smooth transition is found in the wind speed profiles at Cabauw. The internal boundary layer reaches the lowest k-vane (20 m) only in the south-west direction where the obstacle-free fetch is about 2 km. The internal boundary layer is also reflected in the roughness lengths derived from the wind speed profiles. The lower part of the profile (< 40 m) is not in equilibrium and no reliable roughness analysis can be given. The upper part of the profile can be linked to a large-scale roughness length. Roughness lengths derived from the horizontal wind speed variance and gustiness have large footprints and therefore represent a large-scale average roughness. The drag coefficient is more locally determined but still represents a large-scale roughness length when it is measured above the local internal boundary layer. The roughness length at inhomogeneous sites can therefore be determined best from drag coefficient measurements just above the local internal boundary layers directly, or indirectly from horizontal wind speed variance or gustiness. In addition, the momentum and heat fluxes along the tower are analysed and these show significant variation with height related to stability and possibly surface heterogeneity. It appears that the dimensionless wind speed gradients scale well with local fluxes for the variety of conditions considered, including the unstable cases.     

Estimation of turbulent sensible heat and momentum fluxes over a heterogeneous urban area using a large aperture scintillometer

The accurate determination of surface-layer turbulent fluxes over urban areas is critical to understanding urban boundary layer (UBL) evolution. In this study, a remote-sensing technique using a large aperture scintillometer (LAS) was investigated to estimate surface-layer turbulent fluxes over a highly heterogeneous urban area. The LAS system, with an optical path length of 2.1 km, was deployed in an urban area characterized by a complicated land-use mix (residential houses, water body, bare ground, etc.). The turbulent sensible heat (Q H) and momentum fluxes (τ) were estimated from the scintillation measurements obtained from the LAS system during the cold season. Three-dimensional LAS footprint modeling was introduced to identify the source areas ("footprint") of the estimated turbulent fluxes. The analysis results showed that the LAS-derived turbulent fluxes for the highly heterogeneous urban area revealed reasonable temporal variation during daytime on clear days, in comparison to the land-surface process-resolving numerical modeling. A series of sensitivity tests indicated that the overall uncertainty in the LAS-derived daytime Q H was within 20%-30% in terms of the influence of input parameters and the non-dimensional similarity function for the temperature structure function parameter, while the estimation errors in τ were less sensitive to the factors of influence, except aerodynamic roughness length. The 3D LAS footprint modeling characterized the source areas of the LAS-derived turbulent fluxes in the heterogeneous urban area, revealing that the representative spatial scales of the LAS system deployed with the 2.1 km optical path distance ranged from 0.2 to 2 km2 (a "micro-α scale"), depending on local meteorological conditions.     

Estimates of effective surface roughness over complex terrain

Turbulence data collected in an area of three-dimensional complex terrain using instruments atteched to the tether cable of a captive balloon together with radiosonde ascents are presented. In addition, data collected using only radiosonde ascents in an area of two-dimensional complex terrain of large slope are also shown. Eddy correlation measurements of the turbulent momentum flux and wind velocity profiles are used to deduce the magnitude of the effective roughness from the drag coefficient and normalised velocity profiles. A relationship connecting the terrain characteristics and the roughness length is compared with the experimental data for both types of terrain plus previous experimental estimates of the roughness length over complex terrain. The formula taken from previous work by Grant and Mason (1990) is found to agree with the data when representing an area of order 100 km².     

洋面动量、感热和潜热通量计算的研究

整体传输公式是一种常用的计算洋面海气通量的方法。在作气候平均计算时,存在两种平均方法:方法一F_1=AB及方法二F_2=AB。显然,方法一是合理的,而方法二是对方法一的近似。本文利用COADS资料针对不同的平均时间计算分析了方法二对方法一的近似程度,结果表明:利用方法二计算长期气候平均,平滑时间超过5天则对计算结果必须进行订正;对感热和潜热通量,月平均方法二在20％的精度内可代替方法一,而旬平均方法二则可在10％的精度内代替方法一;动量通量月平均和旬平均精度分别为40％和20％。因此方法二在计算月平均动量通量时必须作订正,或直接用方法一进行计算,本文同时计算比较了1972年(E1 Nino年)和1975年(非E1 Nino年)太平洋洋面的各项能量及总能量收支,发现1972年洋面能量收支年变化幅度比1975年小得多,其差别主要决定于感热和潜热的变化。     

On the determination of zero-plane displacement and roughness length for flow over forest canopies

This paper discusses the importance of the aerodynamic characteristics of forest and other similar canopies to modelling of boundary-layer flow and to estimating the diffusivity coefficients of turbulence transfer mechanisms over such canopies.The hypothesis of Marunich (1971) reported by Tajchman (1981) that the zero-plane displacement, d, equals the upward displacement of the flow trajectory, is critically examined. It is concluded that Marunich's hypothesis is conceptually incorrect and that calculations of d based on Marunich's hypothesis are inherently in error.This paper presents a method based on the mass conservation principle and uses wind profiles in and above a forest canopy as the sole input for determining d, z ₀ and u _*.Sensitivities of calculated results to measurements errors of wind profile data are evaluated. It is found that an error of less than 1% in wind in the logarithmic regime above the canopy can introduce up to 100% errors in calculated values of d, z ₀ and u _*. It is also found that the high sensitivity to wind data accuracy, characteristic of the present method, can be used as a guide for the selection of high quality canopy wind data.     

Radiometrically determined skin temperature and scalar roughness to estimate surface heat flux part II: Performance of parameterized scalar roughness for the determination of sensible heat

Several formulations and proposals to determine the value of the radiometric scalar roughness for sensible heatz _0h,r are tested with respect to their performance in the estimation of the sensible heat flux by means of the profile equations derived from Monin-Obukhov similarity theory. The equations are applied to the data set of spatially averaged surface skin temperature and profiles of wind speed and temperature observed in a pasture field during a growing season. The use of a physical model developed for a dense canopy to estimate scalar roughness for sensible heatz _0h,r produced sensible heat fluxH with a correlation coefficientr=0.884, the ratio of means being H _s /H=1.19 in a comparison with reference values ofH _s . In comparison, a proposal for a fixed value ofz _0h yieldedr=0.887, H _s /H=0.879. In both cases, the validity ofz _0h =z _0h,r was assumed. All expressions derived to estimatez _0h,r from a multiple linear regression with such predictors as leaf area index, solar radiation and the ratio of solar radiation to extraterrestrial radiation, were found to produce a better result, withr better than 0.90 and H _s /H around 1.0. However, when the constantsc andf of a linear regression equationHs=cH+f are used to evaluate the equations, a marked difference in performance of each formulation appeared. In general, equations with smaller numbers of predictors tend to produce a biased result, i.e., an overestimation ofH at largeH _s . These values ofH are used in conjunction with the energy balance equation to derive values of the latent heat fluxLE, which are shown to be in good agreement with the reference valuesLE _s , withr greater than 0.97.     

Surface-layer scintillation measurements of daytime sensible heat and momentum fluxes

Line-averaged measurements of the structure parameter of refractive index (C _n ² ) were made using a semiconductor laser diode scintillometer above two markedly different surfaces during hours of positive net radiation. The underlying vegetation comprised in the first instance a horizontally homogeneous, pasture sward well-supplied with water, and in the second experiment, a sparse thyme canopy in a semi-arid environment. Atmospheric stability ranged between near neutral and strongly unstable (–20). The temperature structure parameterC _T ² computed from the optical measurements over four decades from 0.001 to 2 K² m^–2/3 agreed to within 5% of those determined from temperature spectra in the inertial sub-range of frequencies. Spectra were obtained from a single fine thermocouple sensor positioned near the midway position of the 100m optical path and at the beam propagation height (1.5m).With the inclusion of cup anemometer measurements, rule-of-thumb assumptions about surface roughness, and Monin-Obukhov similarity theory, path-averaged optical scintillations allow calculation of surface fluxes of sensible heat and momentum via a simple iterative procedure. Excellent agreement was obtained between these fluxes and those measured directly by eddy correlation. For sensible heat, agreement was on average close to perfect over a measured range of 0 to 500 W m^–2 with a residual standard deviation of 30 W m^–2. Friction velocities agreed within 2% over the range 0–0.9 m s^–1 (residual standard deviation of 0.06 m s^–1). The results markedly increase the range of validation obtained in previous field experiments. The potential of this scintillation technique and its theoretical foundation are briefly discussed.     

Measuring surface-layer fluxes of heat and momentum using optical scintillation

An experiment is described showing that an optical scintillation instrument gives reliable values of heat and momentum fluxes in the surface layer, subject to the usual restrictions of homogeneity and steady state. This instrument measures the turbulence inner scale and refractive-index structure parameter, which are used to obtain the fluxes from Monin-Obukhov similarity relationships. The instrument gives space-averaged values over a propagation path that can range in length from tens to hundreds of meters. The history of the use of optical propagation to estimate fluxes is reviewed.