High-Order Statistics of Temperature Fluctuations in an Unstable Atmospheric Surface Layer over Grassland

Skewness(S) and kurtosis(K) of temperature in the surface layer over a grassland are investigated under unstable thermal stratifications. We find that both skewness and kurtosis generally obey Monin–Obukhov similarity theory and tend to be constant values(1.5 and 5.3, respectively) when the stability parameter z/L -2. Quantitative formulas of the similarity functions are proposed. The temperature probability density function(PDF) is close to Gaussian in near neutral stratification and non-Gaussian in unstable stratification. The influence of coherent motions on the PDF behavior is analyzed using the quadrant analysis technique. It shows that PDF behaviors are controlled by ejections and sweeps. The results also indicate that the PDF type of the ejections always follows a Gaussian distribution, while the PDF of the sweeps changes with stability.     

边界层局地相似理论在草原下垫面的适用性检验

利用锡林浩特草原平坦下垫面塔层湍流资料,对常值通量层的高度进行了估计,检验了局地相似理论在均匀草原下垫面的适用性,对Monin-Obukhov相似理论和局地相似理论在常值通量层以上的大气边界层的适用性进行了比较。结果表明:(1)对于锡林浩特草原来说,常值通量层厚度在50m左右;(2)通过分析无量纲风速和温度梯度、无量纲风速方差、无量纲标量(温度T、水汽q、CO2浓度C)方差与稳定度z/L之间的关系,验证了局地相似理论在均匀草原下垫面70m以下大气边界层的适用性;(3)感热通量尺度与浮力长度尺度之间存在线性关系;(4)从经典Monin-Obukhov长度、局地Monin-Obukhov尺度和浮力长度尺度的对比分析来看,局地尺度更适用于50m以上的大气边界层,而浮力长度尺度不适用于50m以上的大气边界层。     

A Scheme for Scalar Exchange in the Urban Boundary Layer

We present a scheme for parameterising scalar transfer in the urban boundary layer, which is divided into an inertial layer and a roughness layer. The latter is further divided into a shear layer and a canyon layer. In the inertial layer, scalar transfer is determined by turbulence related to canyon macroscopic features, while in the roughness layer, it is determined by shear-generated turbulence, canyon vortex and vortex-generated turbulence. We first describe a conceptual model for the canyon flow and the aerodynamic resistance network, and then estimate the resistances from the point of view of drag partition and vortex advection. The results are compared with the measurements from wind-tunnel experiments. It is found that for small canyon aspect ratio, σ_c, the transfer velocity increases with σ_c, reaching a maximum at around σ_c=0.5 and then decreases with σ_c. We also show that the scheme is not sensitive to adjustable parameters     

Scalar Concentration Profiles in the Canopy and Roughness Sublayer

The mean flow and scalar concentration profiles within and above a tall canopy are well known to violate the standard boundary-layer flux-gradient relationships. We present a theory for the scalar concentration profile that is comprised of a canopy exchange model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing-layer analogy for the flow at canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the profiles depend and a set of criteria that allows a reduction in the empiricism associated with earlier forms in the literature. Predictions of the mean scalar concentration profiles are shown to match observations over a wide range of diabatic stabilities for both potential temperature and water vapour.     

A Note on the Flux-Variance Similarity Relationships for Heat and Water Vapour in the Unstable Atmospheric Surface Layer

Atmospheric surface layer (ASL) experiments over the past 10 years demonstrate that the flux-variance similarity functions for water vapour are consistently larger in magnitude than their temperature counterpart. In addition, latent heat flux calculations using the flux-variance method do not compare as favorably to eddy- correlation measurements when compared to their sensible heat counterpart. These two findings, in concert with measured heat to water vapour transport efficiencies in excess of unity, are commonly used as evidence of dissimilarity between heat and water vapour transport in the unstable atmospheric surface layer. In this note, it is demonstrated that even if near equality in flux-profile similarity functions for heat and water vapour is satisfied, the flux-variance similarity functions for water vapour are larger in magnitude than temperature for a planar, homogeneous, unstably-stratified turbulent boundary-layer flow.     

The Effect of Chessboard Variability of the Surface Fluxes on the Aggregated Turbulence Fields in a Convective Atmospheric Surface Layer

To what degree the variability of surface features can be identified in the turbulent signals observed in the atmospheric boundary layer is still an unresolved problem. This was investigated by conducting an analytical experiment for a one-dimensional 'chessboard'-type surface-flux distribution on the basis of local free convection scaling. The results showed that, due to their nonlinear dependency on the surface fluxes, the dimensionless gradients of the mean quantities and the dimensionless standard deviations are altered by the surface-flux variability. Furthermore, passive scalars, such as humidity, are considerably more sensitive to surface variability than the main active scalar, temperature. However, the response of the gradients of the mean quantities is fairly negligible in the range of variability studied herein as compared to that of the standard deviations, which were found to be more sensitive to the surface-flux variability. In addition, the phase difference between the active and the passive scalar flux distribution strongly affects the passive scalar turbulence. This dissimilarity between passive and active scalars, or between passive scalars when their source distributions are different, brings into question the use of variance methods for the measurement of a scalar flux, such as evaporation, over variable surfaces. The classical Bowen ratio method, which depends on the validity of the Reynolds analogy for the vertical gradients of the mean quantities, was shown to be relatively more robust. However, under conditions of strong surface variability, it can also be expected to fail.     

An Investigation on Temperature Variance Scaling in the Atmospheric Surface Layer

We present surface-layer measurements of temperature fluctuation variance from a site characterized by small-scale inhomogeneities. Periods of marked radiative forcing are selected. The data characterized by diabatic conditions and vertical heat flux larger than some threshold (here, chosen to be 0.01 K ms⁻¹) agree quite well with the convective scaling in unstable cases, and with the z-less parameterisation (with a large scatter) in stable cases. For near-neutral cases, the similarity function diverges because of the loss of significance of the temperature scale. Departures from similarity are highlighted in cases with smaller thermal fluxes, because horizontal heterogeneity and unsteadiness become important as production terms.     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

Dissimilarity of Scalar Transport in the Convective Boundary Layer in Inhomogeneous Landscapes

A land-surface model (LSM) is coupled with a large-eddy simulation (LES) model to investigate the vegetation-atmosphere exchange of heat, water vapour, and carbon dioxide (CO₂) in heterogeneous landscapes. The dissimilarity of scalar transport in the lower convective boundary layer is quantified in several ways: eddy diffusivity, spatial structure of the scalar fields, and spatial and temporal variations in the surface fluxes of these scalars. The results show that eddy diffusivities differ among the three scalars, by up to 10–12%, in the surface layer; the difference is partly attributed to the influence of top-down diffusion. The turbulence-organized structures of CO₂ bear more resemblance to those of water vapour than those of the potential temperature. The surface fluxes when coupled with the flow aloft show large spatial variations even with perfectly homogeneous surface conditions and constant solar radiation forcing across the horizontal simulation domain. In general, the surface sensible heat flux shows the greatest spatial and temporal variations, and the CO₂ flux the least. Furthermore, our results show that the one-dimensional land-surface model scheme underestimates the surface heat flux by 3–8% and overestimates the water vapour and CO₂ fluxes by 2–8% and 1–9%, respectively, as compared to the flux simulated with the coupled LES-LSM.     

On the Kinetic Energy Budget of the Unstable Atmospheric Surface Layer

We present a new account of the kinetic energy budget within an unstable atmospheric surface layer (ASL) beneath a convective outer layer. It is based on the structural model of turbulence introduced by McNaughton (Boundary-Layer Meteorology, 112: 199–221, 2004). In this model the turbulence is described as a self-organizing system with a highly organized structure that resists change by instability. This system is driven from above, with both the mean motion and the large-scale convective motions of the outer layer creating shear across the surface layer. The outer convective motions thus modulate the turbulence processes in the surface layer, causing variable downwards fluxes of momentum and kinetic energy. The variable components of the momentum flux sum to zero, but the associated energy divergence is cumulative, increasing both the average kinetic energy of the turbulence in the surface layer and the rate at which that energy is dissipated. The tendency of buoyancy to preferentially enhance the vertical motions is opposed by pressure reaction forces, so pressure production, which is the work done against these reaction forces, exactly equals buoyant production of kinetic energy. The pressure potential energy that is produced is then redistributed throughout the layer through many conversions, back and forth, between pressure potential and kinetic energy with zero sums. These exchanges generally increase the kinetic energy of the turbulence, the rate at which turbulence transfers momentum and the rate at which it dissipates energy, but does not alter its overall structure. In this model the velocity scale for turbulent transport processes in the surface layer is (kzɛ)^1/3 rather than the friction velocity, u_*. Here k is the von Kármán constant, z is observation height, ɛ is the dissipation rate. The model agrees very well with published experimental results, and provides the foundation for the new similarity model of the unstable ASL, replacing the older Monin–Obukhov similarity theory, whose assumptions are no longer tenable.     

Turbulence Structure of the Unstable Atmospheric Surface Layer and Transition to the Outer Layer

We present a new model of the structure of turbulence in the unstable atmospheric surface layer, and of the structural transition between this and the outer layer. The archetypal element of wall-bounded shear turbulence is the Theodorsen ejection amplifier (TEA) structure, in which an initial ejection of air from near the ground into an ideal laminar and logarithmic flow induces vortical motion about a hairpin-shaped core, which then creates a second ejection that is similar to, but larger than, the first. A series of TEA structures form a TEA cascade. In real turbulent flows TEA structures occur in distorted forms as TEA-like (TEAL) structures. Distortion terminates many TEAL cascades and only the best-formed TEAL structures initiate new cycles. In an extended log layer the resulting shear turbulence is a complex, self-organizing, dissipative system exhibiting self-similar behaviour under inner scaling. Spectral results show that this structure is insensitive to instability. This is contrary to the fundamental hypothesis of Monin--Obukhov similarity theory. All TEAL cascades terminate at the top of the surface layer where they encounter, and are severely distorted by, powerful eddies of similar size from the outer layer. These eddies are products of the breakdown of the large eddies produced by buoyancy in the outer layer. When the outer layer is much deeper than the surface layer the interacting eddies are from the inertial subrange of the outer Richardson cascade. The scale height of the surface layer, z _s, is then found by matching the powers delivered to the creation of emerging TEAL structures to the power passing down the Richardson cascade in the outer layer. It is z _s = u _* ³ /k_s, where u _* is friction velocity, k is the von Kármán constant and _s is the rate of dissipation of turbulence kinetic energy in the outer layer immediately above the surface layer. This height is comparable to the Obukhov length in the fully convective boundary layer. Aircraft and tower observations confirm a strong qualitative change in the structure of the turbulence at about that height. The tallest eddies within the surface layer have height z _s, so z _s is a new basis parameter for similarity models of the surface layer.     

Quantifying the Influence of Random Errors in Turbulence Measurements on Scalar Similarity in the Atmospheric Surface Layer

The influence of random errors in turbulence measurements on scalar similarity for temperature, water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\) is investigated using two eddy-covariance datasets collected over a lake and a cattle feedlot. Three measures of scalar similarity, namely, the similarity constant in the flux–variance relationship, the correlation coefficient between two scalars and the relative transport efficiency, are examined. The uncertainty in the similarity constant \(C_{s}\) in the flux–variance relationship resulting from random errors in turbulence measurements is quantified based on error propagation analyses and a Monte-Carlo sampling method, which yields a distribution instead of a single value for \(C_{s}\). For different scalars, the distributions of \(C_{s}\) are found to significantly overlap, implying that scalars are transported similarly under strongly unstable conditions. The random errors in the correlation coefficients between scalars and the relative transport efficiencies are also quantified through error propagation analyses, and they increase as the atmosphere departs from neutral conditions. Furthermore, the correlation coefficients between three scalars (water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\)) are statistically different from unity while the relative transport efficiencies are not, which highlights the difference between these two measures of scalar similarity. The results suggest that uncertainties in these measures of scalar similarity need to be quantified when using them to diagnose the existence of dissimilarity among different scalars.     

森林近地层大气湍流特性观测分析

利用长白山森林生态系统定位研究站观测资料,及2003年8月和9月涡旋相关资料,分析和比较了该地区近地层包括风速、风向、大气稳定度在内的平均场特征,以及湍流强度、无量纲化风脉动方差相似性和地表通量变化特征。结果表明:(1)8月和9月稳定度都基本集中在0附近;(2)风速2 m·s-1的环境中,湍流发展最为旺盛,随着风速的增大湍流强度先迅速减小,当风速增大到3 m·s-1后,湍流强度偏离0值变大了一些,再继续增大到一定风速大小以后,湍流强度基本不随风速变化;(3)无量纲化三维风脉动方差符合Monin-Obukhov相似理论的"1/3"定律,其最佳通用相似函数在稳定和不稳定条件下都可以拟合得到;(4)地表通量均表现出明显的日变化特征,8月以潜热为主,感热较小;9月仍以潜热为主,但是相比8月明显偏小,感热变化不大。     

Power Spectra and Cospectra for Wind and Scalars in a Disturbed Surface Layer at the Base of an Advective Inversion

This paper reports power spectra and cospectra of windspeed and several scalars measured at two heights nearthe base of an advective inversion. The inversion hadformed over a paddy field downwind of an extensive dryregion. Winds over the paddy field were variable instrength and direction, as a result of convectivemotions in the atmospheric boundary layer passing overfrom the dry region upwind. Fetch over the rice waslarge enough that advective effects on the transportprocesses were small at the upper level and negligibleat the lower level. Results from the lower level areinterpreted in terms of a horizontally homogeneous,but disturbed, surface layer.Power spectra of longitudinal and lateral velocitywere substantially enhanced at low frequencies. Theresulting vertical motions added only a small amountto the spectrum of vertical velocity but this stronglyaffected scalar power spectra and cospectra. Thesewere all substantially enhanced over a range of lowfrequencies. We also found that differences in lowerboundary conditions cause differences among scalarspectra at low frequencies.Our analysis shows that the spectra and cospectra havethree components, characterized by different scalingregimes. We call these the ILS (inner-layer scaling),OLS (outer-layer scaling) and CS (combined scaling)components. Of these, the CS component had notpreviously been identified. We identify CS componentsof spectra by their independence of height andfrequency. Spectra with these characteristics had beenpredicted by Kader and Yaglom for a layer of theatmosphere where spectral matching between ILS and OLSwas proposed. However, we find that the velocity andscalar scales used by Kader and Yaglom do not fit ourresults and that their concept of a matching layer isincompatible with our application. An alternativebasis for this behaviour and alternative scales areproposed.We compare our decomposition of spectra into ILS, CSand OLS components with an extended form of Townsend'shypothesis, in which wind and scalar fluctuations aredivided into active and inactive components. Wefind the schemes are compatible if we identify all OLSspectral components as inactive, and all CS and ILScomponents as active.By extending the implications of our results toordinary unstable daytime conditions,we predict that classical Monin–Obukhovsimilarity theory should be modified. We find that theheight of the convective boundary layer is animportant parameter when describing transportprocesses near the ground, and that the scalar scalein the ILS part of the spectrum, which includes theinertial subrange, is proportional to observationheight times the local mean scalar gradient, and notthe Monin–Obukhov scalar scale parameter. The formerdepends on two stability parameters: the Monin–Obukhovstability parameter and the ratio of the inner-layerand outer-layer velocity scales. The outer-layer scalecan reflect disturbances by topographically-inducededdying as well as by convective motions.     

Scaling Properties of Biologically Active Scalar Concentration Fluctuations in the Atmospheric Surface Layer over a Managed Peatland

The higher-order scalar concentration fluctuation properties are examined in the context of Monin–Obukhov similarity theory for a variety of greenhouse gases that have distinct and separate source/sink locations along an otherwise ideal micrometeorological field site. Air temperature and concentrations of water vapour, carbon dioxide and methane were measured at high frequency (10 Hz) above a flat and extensive peat-land soil in the San Joaquin–Sacramento Delta (California, USA) area, subjected to year-round grazing by beef cattle. Because of the heterogeneous distribution of the sources and sinks of CO₂ and especially CH₄ emitted by cattle, the scaling behaviour of the higher-order statistical properties diverged from predictions based on a balance between their production and dissipation rate terms, which can obtained for temperature and H₂O during stationary conditions. We identify and label these departures as ‘exogenous’ because they depend on heterogeneities and non-stationarities induced by boundary conditions on the flow. Spectral analysis revealed that the exogenous effects show their signatures in regions with frequencies lower than those associated with scalar vertical transport by turbulence, though the two regions may partially overlap in some cases. Cospectra of vertical fluxes appear less influenced by these exogenous effects because of the modulating role of the vertical velocity at low frequencies. Finally, under certain conditions, the presence of such exogenous factors in higher-order scalar fluctuation statistics may be ‘fingerprinted’ by a large storage term in the mean scalar budget.     

大气科学论著中"量"的运算和"单位"的变化

针对大气科学论著中“量和单位”复杂、易错的特点，详细分析了一些“量”的物理意义、推导过程和表达形式。并给出相应的单位。认为在大气科学论著中正确使用“量和单位”是非常必要和重要的。     

Fluxes and Gradients in the Convective Surface Layer and the Possible Role of Boundary-Layer Depth and Entrainment Flux

We study the relation between fluxes and gradients in the very unstable surface layer by comparing recent proposals in the literature with the well-known Businger–Dyer functions. The recent proposals include results from large-eddy simulation (LES), which account for entrainment effects and effects of the boundary-layer depth. A comparison of the relationships is made with experimental data. The LES-based gradient functions show the impact of entrainment in the surface layer, but the scatter in the field data is too large to confirm this. Therefore this result is preliminary and future tests against new observations are recommended. It appears that the Businger–Dyer relationship behaves differently to the alternatives, and that it deviates from observations for large stability.     

A Scale-Dependent Dynamic Model for Scalar Transport in Large-Eddy Simulations of the Atmospheric Boundary Layer

An important challenge in large-eddy simulationsof the atmospheric boundarylayer is the specification of the subgrid-scale(SGS) model coefficient(s)and, in particular, how to account for factorssuch as position in the flow,grid/filter scale and atmospheric stability.A dynamic SGS model (thatassumes scale invariance of the coefficients)is implemented in simulationsof a neutral boundary layer with a constantand uniform surface flux of apassive scalar. Results from our simulationsshow evidence that the lumpedcoefficient in the eddy-diffusion modelcomputed with the dynamic proceduredepends on scale. This scale dependence isstronger near the surface, and itis more important for the scalar than for thevelocity field (Smagorinskycoefficient) due to the stronger anisotropicbehaviour of scalars. Based onthese results, a new scale-dependent dynamicmodel is developed for theeddy-diffusion lumped coefficient. The newmodel, which is similar to theone proposed earlierfor the Smagorinsky coefficient,is fully dynamic, thus not requiring anyparameter specification or tuning.Simulations with the scale-dependent dynamicmodel yield the expected trendsof the coefficients as functions of positionand filter/grid scale.Furthermore, in the surface layer the newmodel gives improved predictionsof mean profiles and turbulence spectra ascompared with the traditionalscale-invariant dynamic model.     

Transport of Temperature and Humidity Variance and Covariance in the Marine Surface Layer

In this paper we address the budget of potential temperature T and moisture mixing ratio q variances as well as the q-T covariance budget. We focus on the vertical transport and study the quantities contained in these terms. Estimates of transport terms are rare and to the best of our knowledge they have never been shown together in the literature. For this purpose an extensive set of humidity and temperature turbulence data from two heights in a marine environment has been analysed. We discuss and compare our results with results from earlier studies for a range of stability from near-neutral to unstable. Similarity and differences between T and q behaviour in the surface layer over water are presented.     

Time Scales in the Unstable Atmospheric Surface Layer

Calculation of eddy covariances in the atmospheric surface layer (ASL) requires separating the instantaneous signal into mean and fluctuating components. Since the ASL is not statistically stationary, an inherent ambiguity exists in defining the mean quantities. The present study compares four methods of calculating physically relevant time scales in the unstable ASL that may be used to remove the unsteady mean components of instantaneous time signals, in order to yield local turbulent fluxes that appear to be statistically stationary. The four mean-removal time scales are: (t _c ) based on the location of the maximum in the ogive of the heat flux cospectra, () the location of the zero crossing in the multiresolution decomposition of the heat flux, (t ^*) the ratio of the mixed-layer depth over the convective velocity, and () the convergence time of the vertical velocity and temperature variances. The four time scales are evaluated using high quality, three-dimensional sonic anemometry data acquired at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility located on the salt flats of Utah’s western desert. Results indicate that and , with t _c achieving values about 2–3 times greater than t ^*. The sensitivity of the eddy covariances to the mean-removal time scale (given a fixed 4-h averaging period during midday) is also demonstrated.