Anomalies in Flux-Gradient Relationships Over Forest

Simultaneous profile and eddy correlation flux data gathered over Thetford Forest, U.K., have been analysed to find values of the vertical turbulent diffusivities K _M, K _H and K _E (for momentum, heat and water vapour transfer, respectively) at a reference height z _R, nine roughness lengths above the zero-plane displacement d. The results show: (i), that values of K _M over the forest are not significantly different from these predicted by semiempirical diabatic influence functions appropriate to much smoother surfaces such as short grass; and (ii), that K _H and K _E exceed their values predicted from the semiempirical functions by an average factor of 2 or more in unstable, near neutral and slightly stable conditions. These conclusions are strongly dependent on the assumed behaviour of d, here taken as 0.76 tree heights, independent of both property and stability. Consideration is given to an alternative analysis procedure, in which values of the zero-plane displacements d _H and d _E for heat and water vapour respectively, are obtained from the data by assuming K _H and K _E to be given by semiempirical diabatic influence functions; this procedure is shown to be unacceptable on both practical and physical grounds. To account for the anomalies in K _H and K _E, a mechanism is proposed in which the horizontally inhomogeneous temperature structure of the canopy causes free convection to be maintained by discrete; localized heat sources and/or sinks, effectively enhancing turbulent transport processes even in near neutral conditions.     

Anomalies in flux-gradient relationships over forest

Simultaneous profile and eddy correlation flux data gathered over Thetford Forest, U.K., have been analysed to find values of the vertical turbulent diffusivitiesK _M,K _H andK _E (for momentum, heat and water vapour transfer, respectively) at a reference heightz _R, nine roughness lengths above the zero-plane displacementd. The results show: (i), that values ofK _M over the forest are not significantly different from these predicted by semiempirical diabatic influence functions appropriate to much smoother surfaces such as short grass; and (ii), thatK _H andK _E exceed their values predicted from the semiempirical functions by an average factor of 2 or more in unstable, near neutral and slightly stable conditions. These conclusions are strongly dependent on the assumed behaviour ofd, here taken as 0.76 tree heights, independent of both property and stability. Consideration is given to an alternative analysis procedure, in which values of the zero-plane displacementsd _H andd _E for heat and water vapour respectively, are obtained from the data by assumingK _H andK _E to be given by semiempirical diabatic influence functions; this procedure is shown to be unacceptable on both practical and physical grounds. To account for the anomalies inK _H andK _E, a mechanism is proposed in which the horizontally inhomogeneous temperature structure of the canopy causes free convection to be maintained by discrete; localized heat sources and/or sinks, effectively enhancing turbulent transport processes even in nearneutral conditions.     

Unsteadiness as a cause of non-equality of eddy diffusivities for heat and vapour at the base of an advective inversion

This paper examines the effect of non-stationarity of the wind on similarity of the eddy diffusivities for heat and vapour within a stable layer at the bottom of an internal boundary layer formed downwind of a dry-to-wet transition. First, we present some experimental data taken above a rice crop downwind of very extensive dry range lands at Warrawidgee, NSW, Australia. These data establish that periods of higher wind speed were associated with periods of higher saturation deficit in the canopy of the rice crop, and lower Bowen ratio. It is shown that Bowen ratios calculated for 30-second sub-intervals varied three-fold within a single 20-minute averaging period. Thus periods of higher wind speed corresponded to periods of higher moisture flux and smaller sensible heat flux.An idealized situation is then analysed theoretically. It is assumed that the time scale of the slow variations of the wind is long compared with the surface-layer time scale and that fetch is sufficient that the air near the ground is in continuous equilibrium with the surface. Using a two-scale Reynolds decomposition of the fluctuating wind and scalar variables into active and inactive components, it is shown that unsteadiness can lead to an eddy diffusivity for saturation deficit, calculated as the ratio of average flux to average gradient, that is larger than that for total energy calculated in a similar way. Using this ratio to calculate the ratio of diffusivities for temperature and humidity, K_T/K_q, it is found that the latter can be much larger than one if the Bowen ratio is small and negative. Despite this, assuming K_T = K_q and using the Bowen ratio method to calculate surface energy fluxes will usually incur only minor errors.     

Eddy-covariance CO2 flux measurements using open- and closed-path CO2 analysers: Corrections for analyser water vapour sensitivity and damping of fluctuations in air sampling tubes

Methods of calibrating infrared CO₂ analysers for sensitivity to CO₂ and water vapour are described. Equations to correct eddy covariance CO₂ flux measurements are presented for: (i) analyser cross-sensitivity to water vapour and the effects of density fluctuations arising from atmospheric fluxes of water vapour and sensible heat, (ii) flux losses caused by signal processing and limited instrument frequency response for open- and closed-path CO₂ analysers, and (iii) flux losses resulting from damping of concentration fluctuations in a tube used to sample air for closed-path CO₂ analysers. Examples of flux corrections required for typical instruments are presented.     

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.     

Effects of optimized root water uptake parameterization schemes on water and heat flux simulation in a maize agroecosystem

As root water uptake (RWU) is an important link in the water and heat exchange between plants and ambient air, improving its parameterization is key to enhancing the performance of land surface model simulations. Although different types of RWU functions have been adopted in land surface models, there is no evidence as to which scheme most applicable to maize farmland ecosystems. Based on the 2007–09 data collected at the farmland ecosystem field station in Jinzhou, the RWU function in the Common Land Model (CoLM) was optimized with scheme options in light of factors determining whether roots absorb water from a certain soil layer (W_x) and whether the baseline cumulative root efficiency required for maximum plant transpiration (W_c) is reached. The sensibility of the parameters of the optimization scheme was investigated, and then the effects of the optimized RWU function on water and heat flux simulation were evaluated. The results indicate that the model simulation was not sensitive to W_x but was significantly impacted by W_c. With the original model, soil humidity was somewhat underestimated for precipitation-free days; soil temperature was simulated with obvious interannual and seasonal differences and remarkable underestimations for the maize late-growth stage; and sensible and latent heat fluxes were overestimated and underestimated, respectively, for years with relatively less precipitation, and both were simulated with high accuracy for years with relatively more precipitation. The optimized RWU process resulted in a significant improvement of CoLM’s performance in simulating soil humidity, temperature, sensible heat, and latent heat, for dry years. In conclusion, the optimized RWU scheme available for the CoLM model is applicable to the simulation of water and heat flux for maize farmland ecosystems in arid areas.     

The Turbulent Lagrangian Time Scale in Forest Canopies Constrained by Fluxes,Concentrations and Source Distributions

One-dimensional Lagrangian dispersion models, frequently used to relate in-canopy source/sink distributions of energy, water and trace gases to vertical concentration profiles, require estimates of the standard deviation of the vertical wind speed, which can be measured, and the Lagrangian time scale, T _L , which cannot. In this work we use non-linear parameter estimation to determine the vertical profile of the Lagrangian time scale that simultaneously optimises agreement between modelled and measured vertical profiles of temperature, water vapour and carbon dioxide concentrations within a 40-m tall temperate Eucalyptus forest in south-eastern Australia. Modelled temperature and concentration profiles are generated using Lagrangian dispersion theory combined with source/sink distributions of sensible heat, water vapour and CO₂. These distributions are derived from a multilayer Soil-Vegetation-Atmospheric-Transfer model subject to multiple constraints: (1) daytime eddy flux measurements of sensible heat, latent heat, and CO₂ above the canopy, (2) in-canopy lidar measurements of leaf area density distribution, and (3) chamber measurements of CO₂ ground fluxes. The resulting estimate of Lagrangian time scale within the canopy under near-neutral conditions is about 1.7 times higher than previous estimates and decreases towards zero at the ground. It represents an advance over previous estimates of T _L , which are largely unconstrained by measurements.     

Turbulent carbon exchange in very stable conditions

Turbulent fluxes obtained using the conventional eddy covariance approach result in erratic results with large time fluctuations in extremely stable conditions. This can limit efforts to estimate components of the nocturnal energy budget and respiratory CO₂ fluxes. Well-organized fluxes that show a clear dependence on turbulent intensity were obtained when multiresolution decomposition was used to estimate turbulent exchanges. CO₂, heat and water vapour fluxes were observed at a site in the eastern Amazon basin that had been cleared for agricultural purposes. Temporal scales of the carbon transfer were determined and shown to be similar to those of latent heat, but as much as three times larger than those of sensible heat. CO₂ eddy diffusivities at the temporal scales on which most of the vertical CO₂ exchange occurs are shown to be 50 times larger than the eddy diffusivity for heat. A process associated with the vertical scale of the scalar accumulation layer is suggested to explain these different scales and turbulent diffusivities of carbon and sensible heat transfer. For an appreciable range of turbulence intensities, the observed vertical turbulent carbon exchange is insufficient to account for the locally respired CO₂ estimated independently. Evidence that shallow drainage currents may account for this is given.     

Atmospheric turbulent fluxes over snow

On March 26, 1971, eddy fluxes of momentum, sensible heat and water vapour were measured over Lake Mendota, Wisconsin, U.S.A., which was covered by an extensive snowfall. An evaporation rate of about 0.7mm day^–1 (2.2 mW cm^–2) was detected. Wind speeds were light and the atmosphere near the surface was highly stable. In these conditions, the average sensible heat transfer and Reynolds stress were -0.9 mW cm^–2 and 0.10 dyn cm^–2, respectively. Comparison with measured gradients of wind speed, temperature and humidity yield a drag coefficient of about 0.54 × 10^–3, and bulk transfer coefficients for sensible and latent heat of 0.41 × 10^–3 and 0.78 × 10^–3, respectively, applied to 10-m data. When corrected for the effect of atmospheric stability, these three coefficients become (in the same order) 1.2 × 10^–3, 0.9 × 10^–3 and 2.5 × 10^–3. The errors in these estimates are such that the drag coefficient is not significantly different from that corresponding to an aerodynamically smooth surface, while the heat coefficients are similar to those normally applied over liquid water surfaces.     

Spectral Characteristics and Correction of Long-Term Eddy-Covariance Measurements Over Two Mixed Hardwood Forests in Non-Flat Terrain

We present turbulence spectra and cospectra derived from long-term eddy-covariancemeasurements (nearly 40,000 hourly data over three to four years) and the transferfunctions of closed-path infrared gas analyzers over two mixed hardwood forests inthe mid-western U.S.A. The measurement heights ranged from 1.3 to 2.1 times themean tree height, and peak vegetation area index (VAI) was 3.5 to 4.7; the topographyat both sites deviates from ideal flat terrain. The analysis follows the approach ofKaimal et al. (Quart. J. Roy. Meteorol. Soc. 98, 563–589, 1972) whose results were based upon 15 hours of measurements atthree heights in the Kansas experiment over flatter and smoother terrain. Both thespectral and cospectral constants and stability functions for normalizing and collapsingspectra and cospectra in the inertial subrange were found to be different from those ofKaimal et al. In unstable conditions, we found that an appropriate stabilityfunction for the non-dimensional dissipation of turbulent kinetic energy is of the form ₍₎ = (1 - b^-)^-1/4 - c^-, where representsthe non-dimensional stability parameter. In stable conditions, a non-linear functionG_xy() = 1 + b_xy^c _xy (c_xy < 1) was found to benecessary to collapse cospectra in the inertial subrange. The empirical cospectralmodels of Kaimal et al. were modified to fit the somewhat more (neutraland unstable) or less (stable) sharply peaked scalar cospectra observed over forestsusing the appropriate cospectral constants and non-linear stability functions. Theempirical coefficients in the stability functions and in the cospectral models varywith measurement height and seasonal changes in VAI. The seasonal differencesare generally larger at the Morgan Monroe State Forest site (greater peak VAI) andcloser to the canopy.The characteristics of transfer functions of the closed-path infrared gas analysersthrough long-tubes for CO₂ and water vapour fluxes were studied empirically. This was done by fitting the ratio between normalized cospectra of CO₂ or watervapour fluxes and those of sensible heat to the transfer function of a first-order sensor.The characteristic time constant for CO₂ is much smaller than that for water vapour. The time constant for water vapour increases greatly with aging tubes. Three methods were used to estimate the flux attenuations and corrections; from June through August, the attenuations of CO₂ fluxes are about 3–4% during the daytime and 6–10% at night on average. For the daytime latent heat flux (Q_E), the attenuations are foundto vary from less than 10% for newer tubes to over 20% for aged tubes. Correctionsto Q_E led to increases in the ratio (Q_H + Q_E)/(Q^* - Q_G) by about 0.05 to0.19 (Q_H is sensible heat flux, Q^* is net radiation and Q_G is soil heat flux),and thus are expected to have an important impact on the assessment of energy balanceclosure.     

Weakening sensible heat source over the Tibetan Plateau revisited: effects of the land�Catmosphere thermal coupling

The bulk heat transfer coefficient (C _H ) indicates the land?Catmosphere thermal coupling strength. We seek to detect its variability and changes on the Tibetan Plateau (TP) during 1981?C2006, particularly concerned with its effects on the sensible heat source. C _H is parameterized by Monin?CObukhov similarity theory combining routine meteorological measurements. The South Asian monsoon period is characterized by weak sensible heat flux (H), but strong thermal coupling (C _H ). Winter sees the greatest diurnal C _H range, roughly 0.001?C0.008. On average, C _H exhibits a notable nighttime increase (10% decade^?1) and a weak daytime decrease (?5% decade^?1). The strengthening thermal coupling at selected sites alleviates the weakening of H, because it enhances nighttime H increase and reduces daytime H decrease. Moreover, we confirm the finding in earlier studies that sensible heating is weakening on the TP, but find its trend less notable than empirically estimated using C _H ?=?0.004.     

Buoyancy and The Sensible Heat Flux Budget Within Dense Canopies

In contrast to atmospheric surface-layer (ASL) turbulence, a linear relationship between turbulent heat fluxes (F_T) and vertical gradients of mean air temperature within canopies is frustrated by numerous factors, including local variation in heat sources and sinks and large-scale eddy motion whose signature is often linked with the ejection-sweep cycle. Furthermore, how atmospheric stability modifies such a relationship remains poorly understood, especially in stable canopy flows. To date, no explicit model exists for relating F_T to the mean air temperature gradient, buoyancy, and the statistical properties of the ejection-sweep cycle within the canopy volume. Using third-order cumulant expansion methods (CEM) and the heat flux budget equation, a “diagnostic” analytical relationship that links ejections and sweeps and the sensible heat flux for a wide range of atmospheric stability classes is derived. Closure model assumptions that relate scalar dissipation rates with sensible heat flux, and the validity of CEM in linking ejections and sweeps with the triple scalar-velocity correlations, were tested for a mixed hardwood forest in Lavarone, Italy. We showed that when the heat sources (S_T) and F_T have the same sign (i.e. the canopy is heating and sensible heat flux is positive), sweeps dominate the sensible heat flux. Conversely, if S_T and F_T are opposite in sign, standard gradient-diffusion closure model predict that ejections must dominate the sensible heat flux.     

Intra-field variability of scalar flux densities across a transition between a desert and an irrigated potato field

This paper reports on measurements of sensible and latent heat and CO₂ fluxes made over an irrigated potato field, growing next to a patch of desert. The study was conducted using two eddy correlation systems. One measurement system was located within the equilibrium boundary layer 800 m downwind from the edge of the potato field. The other measurement system was mobile and was placed at various downwind positions to probe the horizontal transition of vertical scalar fluxes. Latent (LE) and sensible (H) heat fluxes, measured at 4 m above the surface, exhibited marked variations with downwind distance over the field. Only after the fetch to height ratio exceeded 75 to 1 didLE andH become invariant with downwind distance. When latent and sensible heat fluxes were measured upwind of this threshold, significant advection of humidity-deficit occurred, causing a vertical flux divergence ofH andLE.The measured fluxes of momentum, heat, and moisture were compared with predictions from a second-order closure two-dimensional atmospheric boundary layer model. There is good agreement between measurements and model predictions. A soil-plant-atmosphere model was used to examine nonlinear feedbacks between humidity-deficits, stomatal conductance and evaporation. Data interpretation with this model revealed that the advection of hot dry air did not enhance surface evaporation rates near the upwind edge of the potato field, because of negative feedbacks among stomatal conductance, humidity-deficits, andLE. This finding is consistent with results from several recent studies.     

盛夏我国东部地区热量平衡的个例计算

本文选取1959年7月23—26日4天正当高空副热带高压控制我国大陆时,对我国东部地区计算了能量方程中各项数值,以及各边界上的能量输送。计算表明,这个地区为能源区城,向外输送热量和水汽。至于在东、西、南、北四个边界上输送的情况有很大的差异,南界以输入为主;东界低层为输出,高层为输入。这种输送是由这个地区低空为大陆热低压,高空为副热带高压的环流特点所决定的。在热量输送中,扰动输送比平均输送为重要。在能量平衡中,支出项主要为平流输送和辐射冷却,而收入项主要是由下垫面向上输送感热和水汽潜热,大气本身的热量和水汽含量的变化在能量平衡中作用较小。湍流感热输送约为蒸发潜热输送的1.84倍。     

Measurements Of Turbulence Transfer In The Near-Surface Layer Over The Southeastern Tibetan Plateau

Turbulent flux measurements at Qamdo site over the Tibetan Plateau during TIPEX from May 18 to June 30, 1998 are presented. Sensible heat dominated,accounting for about 66% of the available energy (the sum of net radiation and soil heat flux) prior to the monsoon(dry period), reducing to about 31%, with latent heat increased to about 56% of available energy,in the monsoon season (wet period). Surface energy budget closure on average was about 0.80 (0.85)prior to the monsoon and 0.89 (0.76) during the monsoon using eddy correlation (profile) methods. The sum of latent and sensible heat fluxes calculated from the flux-profilemethod was smaller by about 15% than that from eddy correlation. Martano's method is used toestimate the surface aerodynamic roughness length z₀ and zero plane displacement d from singlelevel sonic anemometer data, giving d = 0.12 m and z₀ = 0.08 m. The overall neutral dragcoefficient (C_DN) and scalar coefficient (C_HN) were found to be C_DN = 0.0055and C_HN = 0.0059 in the southeastern area of Tibet. Their variations with the mean wind speed at 10 m are discussed.     

Intra-City Variation in Urban Morphology and Turbulence Structure in Helsinki, Finland

Most atmospheric boundary-layer theories are developed over vegetative surfaces and their applicability at urban sites is questionable. Here, we study the intra-city variation of turbulence characteristics and the applicability of boundary-layer theory using building-morphology data across Helsinki, and eddy-covariance data from three sites: two in central Helsinki (400 m apart) and one 4 km away from the city centre. The multi-site measurements enable the analysis of the horizontal scales at which quantities that characterize turbulent transport vary: (i) Roughness characteristics vary at a 10-m scale, and morphometric estimation of surface-roughness characteristics is shown to perform better than the often used rule-of-thumb estimates (average departures from the logarithmic wind profile are 14 and 44 %, respectively). (ii) The drag coefficient varies at a 100-m scale, and we provide an updated parametrization of the drag coefficient as a function of z/z _H (the ratio of the measurement height to the mean building height). (iii) The transport efficiency of heat, water vapour and CO₂ is shown to be weaker the more heterogeneous the site is, in terms of sources and sinks, and strong scalar dissimilarity is observed at all sites. (iv) Atmospheric stability varies markedly even within 4 km across the city: the median difference in nocturnal sensible heat fluxes between the three sites was over 50W m^?2. Furthermore, (v) normalized power spectra and cospectra do not vary between sites, and they follow roughly the canonical theory as developed over vegetated terrain.     

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.     

The influence of stratification on heat and momentum turbulent transfer in antarctica

Data from the Antarctic winter at Halley Base have been used in order to evaluate qualitatively and quantitatively how the stratification in the low atmosphere (evaluated with the gradient Richardson number, Ri) influences the eddy transfers of heat and momentum. Vertical profiles of wind and temperature up to 32 m, and turbulent fluxes ( , and ) measured from three ultrasonic thermo-anemometers installed at 5, 17 and 32 m are employed to calculate Ri, the friction velocity (u _*) and the eddy diffusivities for heat (K _h ) and momentum (K _m ). The results show a big dependence of stability onK _m ,K _h andu _*, with a sharp decrease of these turbulent parameters with increasing stability. The ratio of eddy diffusivities (K _h /K _m ) is also analyzed and presents a decreasing tendency as Ri increases, reaching values even less than 1, i.e., there were situations where the turbulent transfer of momentum was greater than that of heat. Possible mechanisms of turbulent mixing are discussed.     

Evaluating Source Area Contributions from Aircraft Flux Measurements Over Heterogeneous Land Using Large-Eddy Simulation

The estimation of spatial patterns in surface fluxes from aircraft observations poses several challenges in the presence of heterogeneous land cover. In particular, the effects of turbulence on scalar transport and the different behaviour of passive (e.g. water vapour) versus active (e.g. temperature) scalars may lead to large uncertainties in the source area/flux-footprint estimation for sensible (H) and latent (LE) heat-flux fields. This study uses large-eddy simulation (LES) of the land–atmosphere interactions to investigate the atmospheric boundary-layer (ABL) processes that are likely to create differences in airborne-estimated H and LE footprints. We focus on 32~m altitude aircraft flux observations collected over a study site in central Oklahoma during the Southern Great Plains experiment in 1997 (SGP97). Comparison between the aircraft data and traditional model estimates provide evidence of a difference in source area for turbulent sensible and latent heat fluxes. The LES produces reasonable representations of the observed fluxes, and hence provides credible evidence and explanation of the observed differences in the H and LE footprints. Those differences can be quantified by analyzing the change in the sign of the spatial correlation of the H and LE fields provided by the LES model as a function of height. Dry patterns in relatively moist surroundings are able to generate strong, but localized, sensible heating. However, whereas H at the aircraft altitude is still in phase with the surface, LE presents a more complicated connection to the surface as the dry updrafts force a convergence of the surrounding moist air. Both the observational and LES model evidence support the concept that under strongly advective conditions, H and LE measured at the top of the surface layer (≈50 m) can be associated with very different upwind source areas, effectively contradicting surface-layer self-similarity theory for scalars. The results indicate that, under certain environmental conditions, footprint models will need to predict differing source area/footprint contributions between active (H) and passive (LE) scalar fluxes by considering land-surface heterogeneity and ABL dynamics.     

An alternative analysis of flux-gradient relationships at the 1976 ITCE

An extensive micrometeorological data set from the 1976 International Turbulence Comparison Experiment (ITCE) is analysed to determine flux-gradient relationships in an unstable atmosphere for momentum, sensible heat and water vapour transfers. The data are first analysed for internal consistency, resulting in the rejection of some data. Following a least-square fit to the remaining data in the form /k = (1 – z/L)^-/k, rounded-off values of k, , and are selected for each form of transfer consistent with the statistical accuracy of the measurements. The equations finally adopted are _M = (1 – 28z/L)^-1/4 and _{H, W} = (1 – 14z/L)^-1/2 with k _M = k_H = k_W = 0.40.These expressions fit the averaged observations to within a few per cent in the stability range of the experiment (-4 < z/L < -0.004).