Aerodynamic Variables in the Bulk Formulation of Turbulent Fluxes

Aerodynamic variables are required to apply Monin–Obukhov similarity theory in the bulk formulation of surface fluxes. In the literature, these aerodynamic variables are commonly misinterpreted. In this paper, we review the concept of the aerodynamic variable, its connection to surface-layer similarity theory and how and why the aerodynamic variable is replaced with other variables.Observed mean variables below the surface layer, such as the surface radiation temperature, or the air temperature at canopy height, are often used in place of the extrapolated aerodynamic variables in the bulk formula, requiring empirical relationships between aerodynamic and observed variables, or requiring empirical adjustments of bulk resistances. The present study examines the validity of these relationshi Experiment (CODE). The results indicate that using a measured substitute for an aerodynamic variable can lead to significant errors in estimates of turbulent surface fluxes.     

Heat Flux in the Coastal Zone

Various difficulties with application of Monin–Obukhov similarity theory are surveyed including the influence of growing waves, advection and internal boundary-layer development. These complications are normally important with offshore flow. The transfer coefficient for heat is computed from eddy correlation data taken at a mast two kilometres off the Danish coast in RASEX. For these coastal zone data, the thermal roughness length shows no well-defined relation to the momentum roughness length or roughness Reynolds number, in contrast to previous theories. The variation of the momentum roughness length is dominated by wave state. In contrast, the thermal roughness length shows significant dependence on wave state only for small values of wave age where the mixing is apparently enhanced by wave breaking. The development of thin internal boundary layers with offshore flow substantially reduces the heat transfer and thermal roughness length but has no obvious influence on momentum roughness length. A new formulation of the thermal roughness length based on the internal boundary-layer depth is calibrated to the RASEX data. For the very stable case, the turbulence is mainly detached from the surface and existing formulations do not apply.As an alternative to adjusting the thermal roughness length, the transfer coefficient is related directly to the stability and the internal boundary-layer depth. This avoids specification of roughness lengths resulting from the usual integration of the non-dimensional temperature function. The resulting stability function is simpler than previous ones and satisfies free convection similarity theory without introduction of the gustiness factor. The internal boundary layer also influences the moisture transfer coefficient.     

Diurnal Variations of Thermal Roughness Height over a Grassland

The thermal roughness height associated with the surface radiation temperature has been previously found to vary between different surface types. This study finds that the thermal roughness height varies diurnally even over a homogeneous senescent grassland. The corresponding roughness length for momentum is relatively constant.Both the aerodynamic temperature and the surface radiation temperature are found to be closely related to the air temperature in the middle of the grass canopy. However, the aerodynamic temperature is strongly influenced by the horizontally integrated heat transfer, while the surface radiation temperature represents the integrated thermal emission through the grass depth within the field of view of the radiometer. The aerodynamic temperature is less sensitive to variations and measurement errors in sensible heat flux, wind speed, and air temperature than the thermal roughness height. We find that formulating the aerodynamic temperature in terms of the surface radiation temperature is better posed for use in the bulk formula than using the surface radiation temperature directly and adjusting the thermal roughness length.     

Measuring Sensible Heat Flux Density over Pasture Using the ct2-Profile Method

Two large-aperture infrared scintillometers were positioned at heights (z) of 10 and 1.5 m with beams propagated horizontally over pasture for distances of 3.1 km and 141 m, respectively. From each scintillometer a half-hourly average value of the path-averaged, temperature-structure parameter (CT2) was obtained in unstable atmospheric conditions. The result suggested CT2 to scale with height as z-2/3. Using the CT2-profile method a path-averaged measure of the Obukhov length (L0) was calculated for each half-hour period, whence L0 was used to determine the friction velocity, u* and the surface-layer temperature scaling parameter, T*. The scintillometer-based sensible heat flux density Hsc was then calculated from Hsc = Cpu*T*. A time series of half-hourly averaged Hsc compared to Hec obtained by the eddy covariance method agreed to within 10%, with R2 = 0.67, for a range of unstable conditions (- 0.2 z/L0 - 0.01).     

Surface-Layer Fluxes in Stable Conditions

Micrometeorological tower data from the Microfronts experiment are analyzed. Scale-dependencies of the flux and flux sampling error are combined to automatically determine Reynolds turbulence cut-off time scales for computing fluxes from time series. The computed downward heat flux at the 3 m height averaged over nine nights with 7.3 hours each night is 20% greater than the downward heat flux computed at the 10 m height. In contrast, there is only a 1.2% difference between 3 m and 10 m heat fluxes averaged over daytime periods, and there is less than a 2% difference between 3 m and 10 m momentum fluxes whether averaged over nighttime or daytime periods.Stability functions, M(z/L) and H(z/L) are extended to z/L up to 10, where z is the observational height and L is the Obukhov length. For 0.01 < z/L < 1 the estimated functions generally agree with Businger-Dyer formulations, though the H estimates include more scatter compared to the M estimates. For 1 < z/L < 10, the flux intermittency increases, the flux Richardson number exceeds 0.2, and the number of flux samples decreases. Nonetheless the estimates of the stability function M based on 3-m fluxes are closer to the formula proposed by Beljaars and Holtslag in 1991 while the M functions based on 10-m fluxes appears to be closer to the formula proposed by Businger et al. in 1971. The stability function H levels off at z/L = 0.5.     

Structure of the atmospheric surface layer over an industrialized equatorial area

This paper is written to report observations of the structure of the atmospheric surface layer over a coastal industrialized equatorial area. The observations were recorded at Prai Industrial Park, Penang (5° 22′ N, 100° 23′ E) a relatively simple terrain area during the south-west monsoon season in the period of three months using slow response systems. The limitations of the instruments used and its effects on the results are discussed. Wind turbulence and temperature were measured on a 10 m tower and analyzed using eddy correlation method and Monin–Obukhov similarity relations to obtain the normalized standard deviation of longitudinal (σ_u/u), lateral (σ_v/u) and vertical wind velocity fluctuations (σ_w/u) with respect to stability parameter z/L. From the results of the analysis, we found that most of turbulence is generated by shear or mechanical force. It was found that the average neutral value of σ_u/u is 2.35, 1.98 for σ_v/u and 1.47 for σ_w/u with a significantly lower than the proportionality to the power of 1/3 during unstable atmospheric conditions, and thus do not obey Monin–Obukhov similarity theory. It was observed that σ_u/u and σ_v/u values increase linearly in the range of 0 < z/L < 2 and fairly well correlated while σ_w/u does not.     

荒漠戈壁下垫面表面动量和感热湍流通量参数化研究

用合理筛选以后的野外观测资料，研究了荒漠戈壁地表湍流通量参数化的问题。首先，分析了Monin-obukhov相似函数的特征，并拟台出了其经验公式。结果表明，风速和温度相似性函数随稳定度参数的变化曲线与典型经验曲线差异较小，并且在经验曲线分布范围以内，但中性时的值有所不同。同时，还用该资料给出了动量和标量粗糙度(感热粗糙度)长度的平均值及其标量粗糙度随摩擦速度的变化关系。发现标量粗糙度的平均值大约比动量粗糙度的小一个量级，并且随摩擦速度的增大而减小，但明显比其理论预测值要大。     

Determination Of The Surface Drag Coefficient

This study examines the dependence of the surface drag coefficienton stability, wind speed, mesoscale modulation of the turbulent flux and method of calculation of the drag coefficient. Data sets over grassland, sparse grass, heather and two forest sites are analyzed. For significantly unstable conditions, the drag coefficient does not depend systematically on z/L but decreases with wind speed for fixed intervals of z/L, where L is the Obukhov length. Even though the drag coefficient for weak wind conditions is sensitive to the exact method of calculation and choice of averaging time, the decrease of the drag coefficient with wind speed occurs for all of the calculation methods. A classification of flux calculation methods is constructed, which unifies the most common previous approaches.The roughness length corresponding to the usual Monin–Obukhovstability functions decreases with increasing wind speed. This dependence on wind speed cannot be eliminated by adjusting the stability functions. If physical, the decrease of the roughness length with increasing wind speed might be due to the decreasing role of viscous effectsand streamlining of the vegetation, although these effects cannot be isolated from existing atmospheric data.For weak winds, both the mean flow and the stress vector often meander significantly in response to mesoscale motions. The relationship between meandering of the stress and wind vectors is examined. For weak winds, the drag coefficient can be sensitive to the method of calculation, partly due to meandering of the stress vector.     

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.     

Heat and Water Vapour Diffusivities Near the Base of a Disturbed Stable Internal Boundary Layer

We present results from an experiment that wasdesigned to investigate turbulent transportrelationships in a nearly homogeneous boundary layerdisturbed by unsteady wind swings, as found at thebase of an advective inversion with a convectiveboundary layer overhead. In such a situation wemeasured vertical gradients and eddy fluxes of temperature andhumidity at two heights. From these, the turbulentdiffusivities of heat and water vapour are obtained,and compared to the predictions of Monin–Obukhovsimilarity theory and those of a numericalsecond-order closure model. It is found that themeasured diffusivities exceed both predictions. Thisis interpreted as a consequence of the unsteadyconditions. It is also found that the diffusivity forheat is roughly 10% larger than that for watervapour. This is in agreement with a theoreticaltreatment of the unsteadiness effects that wedeveloped in an earlier publication. This result isnot reproduced by the numerical model because themodel has no provision for unsteady conditions. Ourresult disagrees with that from an earlier, verysimilar, field experiment, which may be due to asystematic underestimation of sensible heat flux inthe older experiment.     

Estimation of Sensible Heat Flux from Surface Temperature Wave and One-Time-of-Day Air Temperature Observation

By means of the algorithm presented here, the temporal course H(t) and the daily mean H¯ of the sensible heat flux H can be estimated from measurements of the thermodynamic surface temperature (as a function of time) and from a one-time-of-day air temperature observation. In addition to these temperatures, one needs estimates for daily mean wind speed, for the roughness lengths of momentum and heat transfer, and for the displacement height. First, a quite general solution of the equation for heat conductance (equation for the vertical profile of potential temperature (z,t)) in the dynamic sublayer will be presented. The undetermined parameters in this solution will be defined with the aid of the above mentioned measurements. The influence of horizontal advection will be taken into account. After that, the sensible heat flux can be evaluated from the temperature difference between surface and air with the well known resistance formulae. In this paper the algorithm is derived for areas with homogeneous surfaces, i.e., with uniform surface temperatures. Finally, the method will be verified by measurements taken during the field campaigns HIBE 89 (Hildesheimer Börde in Germany) and EFEDA 91 (Spain). The root mean square errors (RMSE) for the comparison between measurement and model with regard to the temperature difference of surface and air amount to one or two degrees Kelvin, and the error of H¯ reaches 10 to 25 per cent. The method can be used to determine the sensible heat flux from measurements of surface temperatures by satellites (e.g., METEOSAT), but can also be applied to ground based measurements. For instance, horizontal temperature advection can be estimated from measurements at a single location, especially if more than one near-surface air temperature is available. The procedure can be generalized for larger areas, which consist of various surface types with different surface temperatures. This generalization of the algorithm is in progress and will be addressed in a subsequent paper. It will allow us to improve the estimates for H(t) by means of temperature measurements from, e.g., NOAA/AVHRR or LANDSAT/TM, taking into account the heterogeneity of the area that is contained in one METEOSAT pixel.     

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.     

The Parameterisation of Scalar Transfer over Rough Ice

We test a surface renewal model that is widely used over snow and ice surfaces to calculate the scalar roughness length (z _s ), one of the key parameters in the bulk aerodynamic method. For the first time, the model is tested against observations that cover a wide range of aerodynamic roughness lengths (z ₀). During the experiments, performed in the ablation areas of the Greenland ice sheet and the Vatnajökull ice cap in Iceland, the surface varied from smooth snow to very rough hummocky ice. Over relatively smooth snow and ice with z ₀ below a threshold value of approximately 10^?3 m, the model performs well and in accord with earlier studies. However, with growing hummock size, z ₀ increases well above the threshold and the bulk aerodynamic flux becomes significantly smaller than the eddy-correlation flux (e.g. for z ₀ = 0.01 m, the bulk aerodynamic flux is about 50% smaller). Apparently, the model severely underpredicts z _s over hummocky ice. We argue that the surface renewal model does not account for the deep inhomogeneous roughness sublayer (RSL) that is generated by the hummocks. As a consequence, the homogeneous substrate ice grain cover becomes more efficiently ‘ventilated’. Calculations with an alternative model that includes the RSL and was adapted for use over hummocky ice, qualitatively confirms our observations. We suggest that, whenever exceedance of the threshold occurs (z ₀  >  10^?3 m, i.e., an ice surface covered with at least 0.3-m high hummocks), the following relation should be used to calculate scalar roughness lengths, ln (z _s /z ₀)  =  1.5  ? 0.2 ln (Re _*)  ? 0.11(ln (Re _*))².     

Large Aperture Scintillometer Used Over A Homogeneous Irrigated Area, Partly Affected By Regional Advection

Scintillometer measurements were collected over an irrigated wheat field ina semi-arid region in northwest Mexico. Conditions were unstable in the morning andstable during the afternoon, while latent heat fluxes remained high throughout the day.Regional advection was observed during near-neutral conditions. Monin–Obukhovsimilarity relationships for the structure parameter of temperature were verified in both unstable and stable conditions, but were violated close to near-neutral conditions. We found that, using additional measurements of radiation, soil heat flux and windspeed, areally averages of both sensible and latent heat fluxes can be reliably predicted by large aperture scintillometer measurements, as long as the net radiation is greater than zero.     

Utility of Radiometric–aerodynamic Temperature Relations for Heat Flux Estimation

In many land-surface models using bulk transfer (one-source) approaches, the application of radiometric surface temperature observations in energy flux computations has given mixed results. This is due in part to the non-unique relationship between the so-called aerodynamic temperature, which relates to the efficiency of heat exchange between the land surface and overlying atmosphere, and a surface temperature measurement from a thermal-infrared radiometer, which largely corresponds to a weighted soil and canopy temperature as a function of radiometer viewing angle. A number of studies over the past several years using multi-source canopy models and/or experimental data have developed simplified methods to accommodate radiometric–aerodynamic temperature differences in one-source approaches. A recent investigation related the variability in the radiometric–aerodynamic relation to solar radiation using experimental data from a variety of landscapes, while another used a multi-source canopy model combined with measurements over a wide range in vegetation density to derive a relationship based on leaf area index. In this study, simulations by a detailed multi-source soil–plant–environment model, Cupid, which considers both radiative and turbulent exchanges across the soil–canopy–air interface, are used to explore the radiometric–aerodynamic temperature relations for a semi-arid shrubland ecosystem under a range of leaf area/canopy cover, soil moisture and meteorological conditions. The simulated radiometric-aerodynamic temperatures indicate that, while solar radiation and leaf area both strongly affect the magnitude of this temperature difference, the relationships are non-unique, having significant variability depending on local conditions. These simulations also show that soil–canopy temperature differences are highly correlated with variations in the radiometric–aerodynamic temperature differences, with the slope being primarily a function of leaf area. This result suggests that two-source schemes with reliable estimates of component soil and canopy temperatures and associated resistances may be better able to accommodate variability in the radiometric–aerodynamic relation for a wider range in vegetated canopy cover conditions than is possible with one-source schemes. However, comparisons of sensible heat flux estimates with Cupid using a simplified two-source model and a one-source model accommodating variability in the radiometric-aerodynamic relation based on vegetation density gave similar scatter. On the other hand, with experimental data from the shrubland site, the two-source model generally outperformed the one-source scheme. Clearly, vegetation density/leaf area has a major effect on the radiometric–aerodynamic temperature relation and must be considered in either one-source or two-source formulations. Hence these adjusted one-source models require similar inputs as in two-source approaches, but provide as output only bulk heat fluxes; this is not as useful for monitoring vegetation conditions.     

Flux-profile Relationships for Wind Speed and Temperature in the Stable Atmospheric Boundary Layer

Wind and temperature profiles in the stable boundary layer were analyzed in the context of MoninObukhov similarity. The measurements were made on a 60-m tower in Kansas during October 1999 (CASES-99). Fluxprofile relationships, obtained from these measurements in their integral forms, were established for wind speed and temperature. Use of the integral forms eliminates the uncertainty and accuracy issues resulting from gradient computations. The corresponding stability functions, which were nearly the same for momentum and virtual sensible heat, were found to exhibit different features under weakly stable conditions compared to those under strongly stable conditions. The gradient stability functions were found to be linear, namely _m = 1+ 5.8 and _h = 1 + 5.4 up to a limit of the MoninObukhov stability parameter = 0.8; this is consistent with earlier findings. However, for stronger stabilities beyond a transition range, both functions were observed gradually to approach a constant, with a value of approximately 7. To link these two distinct regimes, a general but pliable functional form with only two parameters is proposed for the stability functions, covering the entire stability range from neutral to very stable conditions.     

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.     

Sensible Heat Flux-Radiometric Surface Temperature Relationship Over Sparse Vegetation: Parameterizing B-1

In the bulk formulation of vegetation-atmosphere transfer, theparameter B^-1 is needed for evaluating the sensible heatflux from radiometric surface temperature. An excess resistance,expressed as a function of B^-1 (r_rB^-1/u_*, whereu_* is the friction velocity), shouldbe added to the aerodynamic resistance calculated between thelevel of apparent sink of momentum and the reference height.Over sparse vegetation, B^-1 (and consequently the excessresistance) can be very large and variable. A one-dimensionaltwo-layer model of the canopy-atmosphere interaction is used toinvestigate the behaviour of this fitting parameter and to derive anoperational parameterization in terms of structural and viewingcharacteristics. Besides canopy structural characteristics andradiometer viewing angle, input variables include weather data,stomatal and substrate resistances. B^-1 varies with almostall the input variables; however, the leaf area index (LAI) andthe view angle of the radiometer appear as the most significantfactors of variation. Using a set of weather data and componentresistances randomly generated between fixed limits, `average'curves representing B^-1 as a function of LAI for differentview angles are inferred from the model and polynomial expressionsare fitted to the simulated curves. This set of parameterizations isobtained from ranges of input data wide enough to be representativeof a large variety of experimental conditions. It is successfully testedagainst other parameterizations, using both simulated data andmeasurements made over contrasted surfaces in Niger, France andCalifornia. As the formulations proposed depend on the range ofvalues prescribed in the simulation process for each input data, theyare modifiable and adjustable to any experimental conditions.     

Estimation of the Exchange Coefficient of Heat During Low Wind Convective Conditions

For the first time, the exchange coefficient of heat C_H has been estimated from eddy correlation of velocity and virtual temperature fluctuations using sonic anemometer measurements made at low wind speeds over the monsoon land atJodhpur (26°18' N, 73°04' E), a semi arid station. It shows strong dependence on wind speed, increasing rapidly with decreasing wind speed, and scales according to a power law C_H = 0.025U₁₀ ^-0.7 (where U₁₀ is the mean wind speed at 10-m height). A similar but more rapid increase in the drag coefficient C_Dhas already been reported in an earlier study. Low winds (<4 m s^-1) are associated with both near neutral and strong unstable situations. It is noted that C_H increases with increasing instability. The present observations best describe a low wind convective regime as revealed in the scaling behaviour of drag, sensible heat flux and the non-dimensional temperature gradient. Neutral drag and heat cofficients,corrected using Monin–Obukhov (M–O) theory, show a more uniform behaviour at low wind speeds in convective conditions, when compared with the observed coefficients discussed in a coming paper.At low wind convective conditions, M-O theory is unable to capture the observed linear dependence of drag on wind speed, unlike during forced convections. The non-dimensional shear inferred from the present data shows noticeable deviations from Businger's formulation, a forced convection similarity. Heat flux is insensitive to drag associated with weak winds superposed on true free convection. With heat flux as the primary variable, definition of new velocity scales leads to a new drag parameterization scheme at low wind speeds during convective conditionsdiscussed in a coming paper.     

Flux-Variance Method for Latent Heat and Carbon Dioxide Fluxes in Unstable Conditions

Applied previously to momentum and heat fluxes, the present study extends the flux-variance method to latent heat and CO₂ fluxes in unstable conditions. Scalar similarity is also examined among temperature (θ), water vapour (q), and CO₂ (c). Temperature is adopted as the reference scalar, leading to two feasible strategies to estimate latent heat and CO₂ fluxes: the first one relies on flux-variance similarity relations for scalars, while the second is based on the parameterization of relative transport efficiency in terms of scalar correlation coefficient and a non-dimensional quantity. The relationship between the θ-to-q transport efficiency (λ _{θ q} ) and θ-q correlation coefficient (R _{θ q} ) is used to describe the intermediate hydrological conditions. We also parameterize the θ-to-c transport efficiency (λ _{θ c} ) as a function of the θ-c correlation coefficient (R _{θ c} ) by introducing a new non-dimensional ratio (α). The flux-variance method is a viable technique for flux gap-filling, when turbulence measurements of wind velocity are not available. It is worth noting that the extended method is not exempt from a correction for density effects when used for estimating water or carbon exchange.