Latent and sensible heat flux predictions from a uniform pine forest using surface renewal and flux variance methods

A surface renewal model that links organized eddy motion to the latent and sensible heat fluxes is tested with eddy correlation measurements carried out in a 13m tall uniform Loblolly pine plantation in Duke Forest, Durham, North Carolina. The surface renewal model is based on the occurance of ramp-like patterns in the scalar concentration measurements. To extract such ramp-like patterns from Eulerian scalar concentration measurements, a newly proposed time-frequency filtering scheme is developed and tested. The time-domain filtering is carried out using compactly-supported orthonormal wavelets in conjunction with the Universal Wavelet Thresholding approach of Donoho and Johnstone, while the frequency filtering is carried out by a band-pass sine filter centered around the ramp-occurrence frequency as proposed by other studies. The method was separately tested for heat and water vapour with good agreement between eddy correlation flux measurements and model predictions. The usefulness of the flux-variance method to predict sensible and latent heat fluxes is also considered. Our measurements suggest that the simple flux-variance method reproduces the measured heat and momentum fluxes despite the fact that the variances were measured within the roughness sublayer and not in the surface layer. Central to the predictions of water vapour fluxes using the flux-variance approach is the similarity between heat and water vapour transport by the turbulent air flow. This assumption is also investigated for this uniform forest terrain.     

Influence of Source/Sink Distributions on Flux–Gradient Relationships in the Roughness Sublayer Over an Open Forest Canopy Under Unstable Conditions

The flux–gradient relationships in the unstable roughness sublayer (RSL) over an open canopy of black spruce forest were examined using long-term observations from an instrumented tower. The observed gradients normalised with the surface fluxes and height above the zero-plane displacement showed differences from a universal function established in the surface layer. The magnitude of differences was not constant throughout the year even at the same observation height. Also the magnitude of the differences was different for each scalar, and scalar similarity in the context of the flux–gradient relationship did not always hold. The variation of the differences was explained by the relative contribution of overstorey vegetation to the total flux from the entire ecosystem. This suggests that a mismatch of the vertical source/sink distributions between scalars leads to a different strength of the near-field dispersion effect for each scalar, and this resulted in inequality of eddy diffusivity among scalars in the RSL. An empirical method that predicts the magnitude of differences is proposed. With this method, it is possible to estimate the eddy diffusivity of scalars provided that the relative contribution of overstorey vegetation to the total flux from the ecosystem is known. Also this method can be used to estimate the eddy diffusivity for scalars whose primary sources are at ground level, such as methane and nitrous oxide.     

基于通量方差法对青藏高原东侧高寒草甸地表通量的估算

利用位于青藏高原东侧理塘大气综合观测站2008年观测资料,分析了高寒草甸下垫面上地表通量的时间变化特征,确定了温度、水汽和CO₂的归一化标准差在不稳定情况下随稳定度变化的通量方差关系,应用通量方差法对感热、潜热和CO₂通量进行了计算,并与涡旋相关系统的观测结果进行了比较。结果表明：地表通量月平均日变化呈较为规则的日循环特征,季节变化特征也很明显,雨季（5-9月）潜热大于感热,干季则以感热为主,CO₂通量以6-9月值最大。在不稳定条件下,温度、水汽和CO₂的归一化标准差随稳定度的变化均满足-1/3规律,其通量方差相似性常数分别为1.2,1.4和0.9。通量方差法估算出的通量值与涡旋相关观测得到的通量值有较好的一致性,但感热通量的效果优于潜热通量和CO₂通量。该方法高估了感热通量尤其是潜热通量,而低估了CO₂通量。采用直接观测的感热通量值计算潜热通量和CO₂通量可改善计算结果。     

The Validity of Similarity Theory in the Roughness Sublayer Above Forests

Flux-gradient relationships based upon similarity theory have been reported to severely underestimate scalar fluxes in the roughness sublayer above forests, as compared to independent flux estimates (for example, eddy covariance or energy balance measurements). This paper presents the results of a unique three-month investigation into the validity of similarity theory in the roughness sublayer above forests. Eddy covariance and flux-gradient measurements of carbon dioxide (CO²) exchange were compared above a mixed deciduous forest at Camp Borden, Ontario, both before and after leaf senescence. The eddy covariance measurements used a Li-Cor infrared gas analyzer, and the flux-gradient (similarity theory) measurements featured a tunable diode laser Trace Gas Analysis System (TGAS). The TGAS resolved the CO² concentration difference to 300 parts per trillion by volume (ppt) based upon a half-hour sampling period. The measured enhancement factor (the ratio of independent flux estimates, in this case eddy covariance, to similarity theory fluxes) was smaller and occurred closer to the canopy than in most previous investigations of similarity theory. Very good agreement between the eddy covariance and similarity theory fluxes was found between 1.9 and 2.2 canopy heights (h^c), and the mean enhancement factors measured before and after leaf senescence were 1.10 plusmn; 0.06 and 1.24 ± 0.07, respectively. Larger discrepancies were measured closer to the canopy (1.2 to 1.4 h^c), and mean enhancement factors of 1.60 ± 0.10 and 1.82 ± 0.11 were measured before and after leaf senescence, respectively. Overall, the Borden results suggest that similarity theory can be used within the roughness sublayer with a greater confidence than previously has been believed.     

A Simple Method of Estimating Scalar Fluxes Over Forests

A simple aerodynamic-variance method is proposed to fill gaps in continuous CO₂ flux measurements in rainy conditions, when open-path analysers do not function. The method requires turbulent conditions (friction velocity greater than 0.1 ms^–1), and uses measurements of mean wind speed, and standard deviations of temperature and CO₂ concentration fluctuations to complement, and at times replace, eddy-covariance measurements of friction velocity, sensible heat flux and CO₂ flux. Friction velocity is estimated from the mean wind speed with a flux-gradient relationship modified for the roughness sublayer. Since normalised standard deviations do not follow Monin-Obukhov similarity theory in the roughness sublayer, a simple classification scheme according to the scalar turbulence scale was used. This scheme is shown to produce sensible heat and CO₂ flux estimates that are well correlated with the measured values.     

Large Wind Farms and the Scalar Flux over an Heterogeneously Rough Land Surface

The influence of surface heterogeneities extends vertically within the atmospheric surface layer to the so-called blending height, causing changes in the fluxes of momentum and scalars. Inside this region the turbulence structure cannot be treated as horizontally homogeneous; it is highly dependent on the local surface roughness, the buoyancy and the horizontal scale of heterogeneity. The present study analyzes the change in scalar flux induced by the presence of a large wind farm installed across a heterogeneously rough surface. The change in the internal atmospheric boundary-layer structure due to the large wind farm is decomposed and the change in the overall surface scalar flux is assessed. The equilibrium length scale characteristic of surface roughness transitions is found to be determined by the relative position of the smooth-to-rough transition and the wind turbines. It is shown that the change induced by large wind farms on the scalar flux is of the same order of magnitude as the adjustment they naturally undergo due to surface patchiness.     

Estimation of Turbulent Fluxes Using the Flux-Variance Method over an Alpine Meadow Surface in the Eastern Tibetan Plateau

The flux-variance similarity relation and the vertical transfer of scalars exhibit dissimilarity over different types of surfaces,resulting in different parameterization approaches of relative transport efficiency among scalars to estimate turbulent fluxes using the flux-variance method.We investigated these issues using eddycovariance measurements over an open,homogeneous and flat grassland in the eastern Tibetan Plateau in summer under intermediate hydrological conditions during rainy season.In unstable conditions,the temperature,water vapor,and CO2 followed the flux-variance similarity relation,but did not show in precisely the same way due to different roles(active or passive) of these scalars.Similarity constants of temperature,water vapor and CO2 were found to be 1.12,1.19 and 1.17,respectively.Heat transportation was more efficient than water vapor and CO2.Based on the estimated sensible heat flux,five parameterization methods of relative transport efficiency of heat to water vapor and CO2 were examined to estimate latent heat and CO2 fluxes.The strategy of local determination of flux-variance similarity relation is recommended for the estimation of latent heat and CO2 fluxes.This approach is better for representing the averaged relative transport efficiency,and technically easier to apply,compared to other more complex ones.     

Observed Wind Profiles and Turbulence Fluxes over an ice Surface with Changing Surface Roughness

Wind profile and eddy-correlation data obtained at two sites on a melting glacier surface in Iceland during the summer of 1996 are presented. Throughout the experiment the surface roughness increased rapidly from smooth to very rough, with the largest roughness element height obtained being about 1.7 m. In a layer close to the rough surface we find that the wind speed profiles were disturbed showing horizontal inhomogeneities as in a roughness sublayer. Its height was approximately two times the height of the main roughness elements (h) at both sites throughout the experiment. From the wind profiles and eddy-correlation data we calculated corrections for the displaced zero plane as a function of time and compared these with results obtained from a drag partitioning model. In general, the agreement was reasonable considering the ranges of uncertainty but the results indicate that the increasing horizontal anisotropy of the surface probably limits the use of the model. The values obtained for the roughness lengths are in good agreement with those calculated from a simple linear model, i.e., z₀/h = 0.5 with the frontal area index. Above the roughness sublayer the wind profiles, normalised standard deviations of wind speed, and the balance of the turbulence kinetic energy budget behaved as over an ideal homogeneous surface thereby confirming similarity of the flow.     

The bulk aerodynamic formulation over heterogeneous surfaces

This interpretative literature survey examines problems with application of the bulk aerodynamic method to spatially averaged fluxes over heterogeneous surfaces. This task is approached by tying together concepts from a diverse range of recent studies on subgrid parameterization, the roughness sublayer, the roll of large inactive boundary-layer eddies, internal boundary-layer growth, the equilibrium sublayer, footprint theory and the blending height. Although these concepts are not completely compatible, qualitative scaling arguments based on these concepts lead to a tentative unified picture of the qualitative influence of surface heterogeneity for a wide spectrum of spatial scales.Generalization of the velocity scale is considered to account for nonvanishing heat and moisture fluxes in the limit of vanishing time-averaged wind speed and to account for the influence of subgrid mesoscale motions on the grid-averaged turbulent flux. The bulk aerodynamic relationship for the heat flux usually employs the surface radiation temperature or, equivalently, the temperature from the modelled surface energy budget. The corresponding thermal roughness length is quite variable and its dependence on available parameters is predictable only in special cases.An effective transfer coefficient to relate the spatially averaged surface fluxes to spatially averaged air-ground differences of temperature and other scalars can be most clearly defined when the blending height occurs below the reference level (observational level or first model level). This condition is satisfied only for surface heterogeneity occurring over horizontal scales up to a few times the boundary-layer depth, depending on the stability and height of the reference level. For surface heterogeneity on larger scales (small mesoscale), an effective transfer coefficient for the spatially averaged flow must be defined, for which predictive schemes are unavailable. For surface variations on large mesoscales, homogeneous subareas may be maintained where traditional similarity theory is locally applicable. Surface variations on these scales may generate thermally-driven mesoscale motions.     

An investigation of flux-variance methods and universal functions applied to three land-use types in unstable conditions

Fluxes calculated from three flux-variance methods, which depend upon three different forms of the normalized standard deviation functions (referred to as universal functions) of the surface atmospheric stability have been tested and compared with measurements for temperature and water vapour. The flux measurements were made over a fully leafed deciduous forest, a leafless deciduous forest and over a wetland region during the summer. The first method (referred to as the variance method) allows for certain constants, which are associated with the universal functions, to vary with land-use type and the scalar for which the flux is computed; the second method uses the form of the universal function developed by Tillman, which depends upon two constants; and the third method, known as the Wyngaard method, is the simplest and depends upon one constant only. Flux estimates from the variance method yield the best agreement with observations over the three hand-use types and the Wyngaard method appears to yield estimates that are quite comparable. The measurements for the univeral functions agree better with the Wyngaard function for temperature and better with the Tillman function for water vapour, although both show some scatter. The simplest formula developed by Wyngaard may be considered adequate for computing fluxes of temperature and water vapour from their variances. The main advantage of the formulae is to help define an upper limit for actual fluxes.     

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.     

Simplified expressions for adjusting higher-order turbulent statistics obtained from open path gas analyzers

When density fluctuations of scalars such as CO₂ are measured with open-path gas analyzers, the measured vertical turbulent flux must be adjusted to take into account fluctuations induced by ‘external effects’ such as temperature and water vapour. These adjustments are needed to separate the effects of surface fluxes responsible for ‘natural’ fluctuations in CO₂ concentration from these external effects. Analogous to vertical fluxes, simplified expressions for separating the ‘external effects’ from higher-order scalar density turbulence statistics are derived. The level of complexity in terms of input to these expressions are analogous to that of the Webb–Pearman–Leuning (WPL), and are shown to be consistent with the conservation of dry air. It is demonstrated that both higher-order turbulent moments such as the scalar variances, the mixed velocity-scalar covariances, and the two-scalar covariance require significant adjustments due to ‘external effects’. The impact of these adjustments on the turbulent CO₂ spectra, probability density function, and dimensionless similarity functions derived from flux-variance relationships are also discussed.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy 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 a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

城市表面粗糙度长度的确定

讨论了动量粗糙度长度与热量和水汽等标量粗糙度长度在形式上和物理本质上的不同，以及造成这些不同的原因和条件，分析了决定动量粗糙度的几种因素，并给出了确定动量粗糙度长度的简化关系式，并且根据城市冠层与其上惯性次层能量和动量守衡的原因，建立了热量和水汽粗糙度与动量粗糙度之间的联系，得到了确定热量和水汽粗糙度长度的简化关系式，最后，通过数值试验，表明了动量粗糙度和标量粗糙度变化特征以及对一些主要参数的敏感程度，以及动量粗糙度与标量粗糙度的动态关系。     

On the Temperature and Humidity Dissimilarity in the Marine Surface Layer

The dissimilarity of temperature and humidity transfer in the marine surface layer (MSL) is investigated through the relative transport efficiency and correlation coefficient of these two scalars. We examine their variability and relationship with mean values, as well as spectral characteristics. It is shown that the dissimilarity between these two scalars in the MSL is a function of stability, the boundary-layer depth, and flow steadiness. In general the temperature and humidity are less correlated in shallow marine boundary layers compared to deep marine boundary layers, due to the stronger impact of the boundary-layer scale in breaking the “same source, same sink” assumption for scalar similarity. This is supported by the combination of our spectral analysis of scalar fluxes and corresponding measured and modelled boundary-layer depth. This assumption is also broken in near-neutral conditions, when there is an efficient latent heat transfer but negligible sensible heat transfer. Our data suggest that parametrization of humidity fluxes via similarity theory could still be reliable when the correlation coefficient $>$ 0.5, and in near-neutral conditions the humidity flux can be estimated without use of the sensible heat flux.     

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

Although the bulk aerodynamic transfer coefficients for sensible (C _H ) and latent (C _E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C _H and C _E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C _E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s^–1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10^–3 and 1.5 × 10^–3.     

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.     

A Study of Correlations of Scalar Quantities in the Atmospheric Surface Layer

Standard deviations for vertical velocity and scalar quantities, such as temperature, T, and specific humidity, q, were analyzed on the basis of Monin-Obukhov (M-O) similarity theory in the atmospheric surface layer. The correlation coefficient between scalar quantities T and q, R_Tq, was derived from the similarity functions and can be expressed as the ratio of B_T/B_q (B_T≤ B_q), where parameter B is the value of the normalized standard deviation of any scalar quantity at neutral conditions.     

HUBEX试验区近地面层的湍流输送

1998年淮河流域能量和水循环试验(HUBEX)期间曾进行了1个月的近地面层湍流观测.分析不稳定条件下湍流的统计特性和谱特征,并与Monin-Obukhov相似理论进行了比较.结果表明,不稳定的时候各湍流量的统计特征与相似理论的预期相符.虽然不稳定条件下温度和湿度涨落的相关系数很高,谱的式样也相近,但湿度谱的峰值频率高于温度谱.协谱曲线的形状显示感热通量的谱峰较宽,表现出w和T在较宽范围的强相关性,而水汽通量谱在高频段下降很快,说明水汽的输送更多地出现在低频部分.从谱相关系数可见,在近中性的时候,各尺度湍流涡的热量输送效率普遍较低,随着不稳定性增强而显著提高.分析还发现,不论不稳定性的程度如何,小尺度湍流的水汽输送效率都较低.水汽通量谱的相关系数随稳定度的变化不如热通量的谱相关系数大,表明近中性时除小尺度湍流外其他湍流涡的水汽输送效率高于热量输送.     

Turbulent Transport of Momentum and Scalars Above an Urban Canopy

Turbulent transport of momentum and scalars over an urban canopy is investigated using the quadrant analysis technique. High-frequency measurements are available at three levels above the urban canopy (47, 140 and 280 m). The characteristics of coherent ejection–sweep motions (flux contributions and time fractions) at the three levels are analyzed, particularly focusing on the difference between ejections and sweeps, the dissimilarity between momentum and scalars, and the dissimilarity between the different scalars (i.e., temperature, water vapour and $\hbox {CO}_{2})$ . It is found that ejections dominate momentum and scalar transfer at all three levels under unstable conditions, while sweeps are the dominant eddy motions for transporting momentum and scalars in the urban roughness sublayer under neutral and stable conditions. The flux contributions and time fractions of ejections and sweeps can be adequately captured by assuming a Gaussian joint probability density function for flow variables. However, the inequality of flux contributions from ejections and sweeps is more accurately reproduced by the third-order cumulant expansion method (CEM). The incomplete cumulant expansion method (ICEM) also works well except for $\hbox {CO}_{2}$ at 47 m where the skewness of $\hbox {CO}_{2}$ fluctuations is significantly larger than that for vertical velocity. The dissimilarity between momentum and scalar transfers is linked to the dissimilarity in the characteristics of ejection–sweep motions and is further quantified by measures of transport efficiencies. Atmospheric stability is the controlling factor for the transport efficiencies of momentum and heat, and fitted functions from the literature describe their behaviour fairly accurately. However, transport efficiencies of water vapour and $\hbox {CO}_{2}$ are less affected by the atmospheric stability. The dissimilarity among the three scalars examined in this study is linked to the active role of temperature and to the surface heterogeneity effect.