Large-Eddy Simulation of Stably-Stratified Flow Over a Steep Hill

Large-eddy simulation (LES) is used to simulate stably-stratified turbulent boundary-layer flow over a steep two-dimensional hill. To parametrise the subgrid-scale (SGS) fluxes of heat and momentum, three different types of SGS models are tested: (a) the Smagorinsky model, (b) the Lagrangian dynamic model, and (c) the scale-dependent Lagrangian dynamic model (Stoll and Porté-Agel, Water Resour Res 2006, doi:). Simulation results obtained with the different models are compared with data from wind-tunnel experiments conducted at the Environmental Flow Research Laboratory (EnFlo), University of Surrey, U.K. (Ross et al., Boundary-Layer Meteorol 113:427–459, 2004). It is found that, in this stably-stratified boundary-layer flow simulation, the scale-dependent Lagrangian dynamic model is able to account for the scale dependence of the eddy-viscosity and eddy-diffusivity model coefficients associated with flow anisotropy in flow regions with large mean shear and/or strong flow stratification. As a result, simulations using this tuning-free model lead to turbulence statistics that are more realistic than those obtained with the other two models.     

A Large-Eddy Simulation Study of Turbulent Flow Over Multiscale Topography

Most natural landscapes are characterized by multiscale (often multifractal) topography with well-known scale-invariance properties. For example, the spectral density of landscape elevation fields is often found to have a power-law scaling behaviour (with a −2 slope on a log–log scale) over a wide span of spatial scales, typically ranging from tens of kilometres down to a few metres. Even though the effect of topography on the atmospheric boundary layer (ABL) has been the subject of numerous studies, few have focussed on multiscale topography. In this study, large-eddy simulation (LES) is used to investigate boundary-layer flow over multiscale topography, and guide the development of parametrizations needed to represent the effects of subgrid-scale (SGS) topography in numerical models of ABL flow. Particular emphasis is placed on the formulation of an effective roughness used to account for the increased aerodynamic roughness associated with SGS topography. The LES code uses the scale-dependent Lagrangian dynamic SGS model for the turbulent stresses and a terrain-following coordinate transformation to explicitly resolve the effects of the topography at scales larger than the LES resolution. The terrain used in the simulations is generated using a restricted solid-on-solid landscape evolution model, and it is characterized by a −2 slope of the elevation power spectrum. Results from simulations performed using elevation fields band-pass filtered at different spatial resolutions indicate a clear linear relation between the square of the effective roughness and the variance of elevation.     

Large-Eddy Simulation of Wind-Turbine Wakes: Evaluation of Turbine Parametrisations

Large-eddy simulation (LES), coupled with a wind-turbine model, is used to investigate the characteristics of a wind-turbine wake in a neutral turbulent boundary-layer flow. The tuning-free Lagrangian scale-dependent dynamic subgrid-scale (SGS) model is used for the parametrisation of the SGS stresses. The turbine-induced forces (e.g., thrust, lift and drag) are parametrised using two models: (a) the ‘standard’ actuator-disk model (ADM-NR), which calculates only the thrust force and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses the blade-element theory to calculate the lift and drag forces (that produce both thrust and rotation), and distribute them over the rotor disk based on the local blade and flow characteristics. Simulation results are compared to high-resolution measurements collected with hot-wire anemometry in the wake of a miniature wind turbine at the St. Anthony Falls Laboratory atmospheric boundary-layer wind tunnel. In general, the characteristics of the wakes simulated with the proposed LES framework are in good agreement with the measurements in the far-wake region. The ADM-R yields improved predictions compared with the ADM-NR in the near-wake region, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces appear to be important. Our results also show that the Lagrangian scale-dependent dynamic SGS model is able to account, without any tuning, for the effects of local shear and flow anisotropy on the distribution of the SGS model coefficient.     

Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

Scalar Transport over Forested Hills

Numerical simulations of scalar transport in neutral flow over forested ridges are performed using both a 1.5-order mixing-length closure scheme and a large-eddy simulation. Such scalar transport (particularly of CO₂) has been a significant motivation for dynamical studies of forest canopy–atmosphere interactions. Results from the 1.5-order mixing-length simulations show that hills for which there is significant mean flow into and out of the canopy are more efficient at transporting scalars from the canopy to the boundary layer above. For the case with a source in the canopy this leads to lower mean concentrations of tracer within the canopy, although they can be very large horizontal variations over the hill. These variations are closed linked to flow separation and recirculation in the canopy and can lead to maximum concentrations near the separation point that exceed those over flat ground. Simple scaling arguments building on the analytical model of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) successfully predict the variations in scalar concentration near the canopy top over a range of hills. Interestingly this analysis suggests that variations in the components of the turbulent transport term, rather than advection, give rise to the leading order variations in scalar concentration. The scaling arguments provide a quantitative measure of the role of advection, and suggest that for smaller/steeper hills and deeper/sparser canopies advection will be more important. This agrees well with results from the numerical simulations. A large-eddy simulation is used to support the results from the mixing-length closure model and to allow more detailed investigation of the turbulent transport of scalars within and above the canopy. Scalar concentration profiles are very similar in both models, despite the fact that there are significant differences in the turbulent transport, highlighted by the strong variations in the turbulent Schmidt number both in the vertical and across the hill in the large-eddy simulation that are not represented in the mixing-length model.     

Large-eddy Simulation of the Dispersion of Solid Particles in a Turbulent Boundary Layer

A large-eddy simulation (LES) with the dynamic Smagorinsky-Germano subgrid-scale (SGS) model is used to study the dispersion of solid particles in a turbulent boundary layer. Solid particles are tracked in a Lagrangian way. The instantaneous velocity of the surrounding fluid is considered to have a large-scale part (directly computed by the LES) and a small-scale part. The SGS velocity of the surrounding fluid is given by a three-dimensional Langevin model written in terms of SGS statistics at a mesh level. An appropriate Lagrangian correlation time scale is considered in order to include the influences of gravity and inertia of the solid particle. Inter-particle collisions and the influence of particles on the mean flow are also taken into account. The results of the LES are compared with the wind-tunnel experiments of Nalpanis et al. (1993 J Fluid Mech 251: 661–685) and of Tanière et al. (1997 Exp in Fluids 23:463–471) on sand particles in saltation and in modified saltation, respectively.     

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.     

The Effects of Canopy Leaf Area Index on Airflow Across Forest Edges: Large-eddy Simulation and Analytical Results

The structure of turbulent flows along a transition between tall-forested canopies and forest clearings continues to be an active research topic in canopy turbulence. The difficulties in describing the turbulent flow along these transitions stem from the fact that the vertical structure of the canopy and its leaf area distribution cannot be ignored or represented by an effective roughness length. Large-eddy simulation (LES) runs were performed to explore the effect of a homogeneous variation in the forest leaf area index (LAI) on the turbulent flow across forest edges. A nested grid numerical method was used to ensure the development of a deep boundary layer above the forest while maintaining a sufficiently high resolution in the region close to the ground. It was demonstrated that the LES here predicted first-order and second-order mean velocity statistics within the canopy that agree with reported Reynolds-Averaged Navier–Stokes (RANS) model results, field and laboratory experiments. In the simulations reported here, the LAI was varied between 2 and 8 spanning a broad range of observed LAI in terrestrial ecosystems. By increasing the forest LAI, the mean flow properties both within the forest and in the clearing near the forest edge were altered in two fundamental ways: near the forest edge and into the clearing, the flow statistical properties resembled the so-called back-facing step (BFS) flow with a mean recirculation zone near the edge. Another recirculation zone sets up downstream of the clearing as the flow enters the tall forest canopy. The genesis of this within-forest recirculation zone can be primarily described using the interplay between the mean pressure gradients (forcing the flow) and the drag force (opposing the flow). Using the LES results, a simplified analytical model was also proposed to explain the location of the recirculation zone inside the canopy and its dependence on the forest LAI. Furthermore, a simplified scaling argument that decomposes the mean velocity at the outflow edge into a superposition of ‘exit flow’ and BFS-like flow with their relative importance determined by LAI was explored.     

Predicting plume meandering and averaging time effects on mean and fluctuating concentrations in atmospheric dispersion simulated in a water channel

Plume meandering and averaging time effects were measured directly using a high spatial resolution, high frequency, linescan laser-induced fluorescence (LIF) technique for measuring scalar concentrations in a plume dispersing in a water channel. Post-processing of the collected data removed time dependent background dye levels and corrected for attenuation across the laser beam to produce accurate measurements over long sample times in both a rough surface boundary-layer shear flow and shear free grid-generated turbulent flow. The data were used to verify the applicability of a meandering plume model for predicting the properties of mean and fluctuating concentrations. The centroid position of the crosswind concentration profile was found to have a Gaussian probability density function and the instantaneous plume spread about the centroid fluctuated log-normally. A modified travel-time power law model for averaging time adjustment was developed and compared to the widely used, but much less accurate, 0.2 power-law model.     

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.     

Impact of subgrid scale scheme on topography and landuse for better regional scale simulation of meteorological variables over the western Himalayas

An attempt is made to integrate subgrid scale scheme on the work of Dimri and Ganju (Pure Appl Geophys 167:1–24, 2007) to understand the overall nature of surface heterogeneity and landuse variability along with resolvable finescale micro/meso scale circulation over the Himalayan region, which is having different altitudes and orientations causing prevailing weather conditions to be complex. This region receives large amount of precipitation due to eastward moving low-pressure synoptic weather systems, called western disturbances, during winter season (December, January, February—DJF). Surface heterogeneity and landuse variability of the Himalayan region gives rise to numerous micro/meso scale circulation along with prevailing weather. Therefore, in the present work, a mosaic type parameterization of subgrid scale topography and landuse within a framework of a regional climate model (RegCM3) is extended to study interseasonal variability of surface climate during a winter season (October 1999–March 2000) of the work of Dimri and Ganju (Pure Appl Geophys 167:1–24, 2007). In this scheme, meteorological variables are disaggregated from the coarse grid to the fine grid, land surface calculations are then performed separately for each subgrid cell, and surface fluxes are calculated and reaggregated onto the coarse grid cell for input to the atmospheric model. By doing so, resolvable finescale structures due to surface heterogeneity and landuse variability at coarse grid are subjected to parameterize at regular finescale surface subgrid. Model simulations show that implementation of subgrid scheme presents more realistic simulation of precipitation and surface air temperature. Influence of topographic elevation and valleys is better represented in the scheme. Overall, RegCM3 with subgrid scheme provides more accurate representation of resolvable finescale atmospheric/surface circulations that results in explaining mean variability in a better way.     

Differences and sensitivities in potential hydrologic impact of climate change to regional-scale Athabasca and Fraser River basins of the leeward and windward sides of the Canadian Rocky Mountains respectively

Sensitivities to the potential impact of Climate Change on the water resources of the Athabasca River Basin (ARB) and Fraser River Basin (FRB) were investigated. The Special Report on Emissions Scenarios (SRES) of IPCC projected by seven general circulation models (GCM), namely, Japan’s CCSRNIES, Canada’s CGCM2, Australia’s CSIROMk2b, Germany’s ECHAM4, the USA’s GFDLR30, the UK’s HadCM3, and the USA’s NCARPCM, driven under four SRES climate scenarios (A1FI, A2, B1, and B2) over three 30-year time periods (2010–2039, 2040–2069, 2070–2100) were used in these studies. The change fields over these three 30-year time periods are assessed with respect to the 1961–1990, 30-year climate normal and based on the 1961–1990 European Community Mid-Weather Forecast (ECMWF) re-analysis data (ERA-40), which were adjusted with respect to the higher resolution GEM forecast archive of Environment Canada, and used to drive the Modified ISBA (MISBA) of Kerkhoven and Gan (Adv Water Resour 29(6):808–826, 2006). In the ARB, the shortened snowfall season and increased sublimation together lead to a decline in the spring snowpack, and mean annual flows are expected to decline with the runoff coefficient dropping by about 8% per °C rise in temperature. Although the wettest scenarios predict mild increases in annual runoff in the first half of the century, all GCM and emission combinations predict large declines by the end of the twenty-first century with an average change in the annual runoff, mean maximum annual flow and mean minimum annual flow of −21%, −4.4%, and −41%, respectively. The climate scenarios in the FRB present a less clear picture of streamflows in the twenty-first century. All 18 GCM projections suggest mean annual flows in the FRB should change by ±10% with eight projections suggesting increases and 10 projecting decreases in the mean annual flow. This stark contrast with the ARB results is due to the FRB’s much milder climate. Therefore under SRES scenarios, much of the FRB is projected to become warmer than 0°C for most of the calendar year, resulting in a decline in FRB’s characteristic snow fed annual hydrograph response, which also results in a large decline in the average maximum flow rate. Generalized equations relating mean annual runoff, mean annual minimum flows, and mean annual maximum flows to changes in rainfall, snowfall, winter temperature, and summer temperature show that flow rates in both basins are more sensitive to changes in winter than summer temperature.     

An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations

This paper compares a number of one-dimensional closure models for the planetary boundary layer (PBL) that are currently in use in large-scale atmospheric models. Using the results of a large-eddy simulation (LES) model as the standard of comparison, the PBL models are evaluated over a range of stratifications from free convective to neutral and a range of surface shear stresses. Capping inversion strengths for the convective cases range from weakly to strongly capped. Six prototypical PBL models are evaluated in this study, which focuses on the accuracy of the boundary-layer fluxes of momentum, heat, and two passive scalars. One scalar mimics humidity and the other is a top-down scalar entrained into the boundary layer from above. A set of measures based on the layer-averaged differences of these fluxes from the LES solutions is developed. In addition to the methodological framework and suite of LES solutions, the main result of the evaluation is the recognition that all of the examined PBL parameterizations have difficulty reproducing the entrainment at the top of the PBL, as given by the LES, in most parameter regimes. Some of the PBL models are relatively accurate in their entrainment flux in a subset of parameter regimes. The sensitivity of the PBL models to vertical resolution is explored, and substantive differences are observed in the performance of the PBL models, relative to LES, at low resolution typical of large scale atmospheric models.     

Large-Eddy Simulation of Inhomogeneous Canopy Flows Using High Resolution Terrestrial Laser Scanning Data

The effect of sub-tree forest heterogeneity in the flow past a clearing is investigated by means of large-eddy simulation (LES). For this purpose, a detailed representation of the canopy has been acquired by terrestrial laser scanning for a patch of approximately 190 m length in the field site “Tharandter Wald”, near the city of Dresden, Germany. The scanning data are used to produce a high resolution plant area distribution (PAD) that is averaged over approximately one tree height (30 m) along the transverse direction, in order to simplify the LES study. Despite the smoothing involved with this procedure, the resulting two-dimensional PAD maintains a rich vertical and horizontal structure. For the LES study, the PAD is embedded in a larger domain covered with an idealized, horizontally homogeneous canopy. Simulations are performed for neutral conditions and compared to a LES with homogeneous PAD and recent field measurements. The results reveal a considerable influence of small-scale plant distribution on the mean velocity field as well as on turbulence data. Particularly near the edges of the clearing, where canopy structure is highly variable, usage of a realistic PAD appears to be crucial for capturing the local flow structure. Inside the forest, local variations in plant density induce a complex pattern of upward and downward motions, which remain visible in the mean flow and make it difficult to identify the “adjustment zone” behind the windward edge of the clearing.     

New Approaches in Two-equation Turbulence Modelling for Atmospheric Applications

The turbulence closure in atmospheric boundary-layer modelling utilizing Reynolds Averaged Navier–Stokes (RANS) equations at mesoscale as well as at local scale is lacking today a common approach. The standard kɛ model, although it has been successful for local scale problems especially in neutral conditions, is deficient for mesoscale flows without modifications. The k–ɛ model is re-examined and a new general approach in developing two-equation turbulence models is proposed with the aim of improving their reliability and consequently their range of applicability. This exercise has led to the replacement of the ɛ-transport equation by the transport equation for the turbulence inverse length scale (wavenumber). The present version of the model is restricted to neutrally stratified flows but applicable to both local scale and mesoscale flows. The model capabilities are demonstrated by application to a series of one-dimensional planetary boundary-layer problems and a two-dimensional flow over a square obstacle. For those applications, the present model gave considerably better results than the standard k–ɛ model.     

Potential impact of climate change on the water availability of South Saskatchewan River Basin

The potential hydrologic impact of climatic change on three sub-basins of the South Saskatchewan River Basin (SSRB) within Alberta, namely, Oldman, Bow and Red Deer River basins was investigated using the Modified Interactions Soil-Biosphere-Atmosphere (MISBA) land surface scheme of Kerkhoven and Gan (Advances in Water Resources 29:808–826 2006). The European Centre for Mid-range Weather Forecasts global re-analysis (ERA-40) climate data, Digital Elevation Model of the National Water Research Institute, land cover data and a priori soil parameters from the Ecoclimap global data set were used to drive MISBA to simulate the runoff of SSRB. Four SRES scenarios (A21, A1FI, B21 and B11) of four General Circulation Models (CCSRNIES, CGCM2, ECHAM4 and HadCM3) of IPCC were used to adjust climate data of the 1961–1990 base period (climate normal) to study the effect of climate change on SSRB over three 30-year time periods (2010–2039, 2040–2069, 2070–2099). The model results of MISBA forced under various climate change projections of the four GCMs with respect to the 1961–1990 normal show that SSRB is expected to experience a decrease in future streamflow and snow water equivalent, and an earlier onset of spring runoff despite of projected increasing trends in precipitation over the 21st century. Apparently the projected increase in evaporation loss due to a warmer climate over the 21st century will offset the projected precipitation increase, leading to an overall decreasing trend in the basin runoff of SSRB. Finally, a Gamma probability distribution function was fitted to the mean annual maximum flow and mean annual mean flow data simulated for the Oldman, Bow and Red Deer River Basins by MISBA to statistically quantify the possible range of uncertainties associated with SRES climate scenarios projected by the four GCMs selected for this study.     

A Lagrangian Model to Predict the Modification of Near-Surface Scalar Mixing Ratios and Air–Water Exchange Fluxes in Offshore Flow

A model was developed to predict the modification with fetch in offshore flow of mixing ratio, air–water exchange flux, and near-surface vertical gradients in mixing ratio of a scalar due to air–water exchange. The model was developed for planning and interpretation of air–water exchange flux measurements in the coastal zone. The Lagrangian model applies a mass balance over the internal boundary layer (IBL) using the integral depth scale approach, previously applied to development of the nocturnal boundary layer overland. Surface fluxes and vertical profiles in the surface layer were calculated using the NOAA COARE bulk algorithm and gas transfer model (e.g., Blomquist et al. 2006, Geophys Res Lett 33:1–4). IBL height was assumed proportional to the square root of fetch, and estimates of the IBL growth rate coefficient, α, were obtained by three methods: (1) calibration of the model to a large dataset of air temperature and humidity modification over Lake Ontario in 1973, (2) atmospheric soundings from the 2004 New England Air Quality Study and (3) solution of a simplified diffusion equation and an estimate of eddy diffusivity from Monin–Obukhov similarity theory (MOST). Reasonable agreement was obtained between the calibrated and MOST values of α for stable, neutral, and unstable conditions, and estimates of α agreed with previously published parametrizations that were valid for the stable IBL only. The parametrization of α provides estimates of IBL height, and the model estimates modification of scalar mixing ratio, fluxes, and near-surface gradients, under conditions of coastal offshore flow (0–50 km) over a wide range in stability.     

A Perspective on Thirty Years of the Webb,Pearman and Leuning Density Corrections

The density correction theory of Webb et al. (1980, Q J Roy Meteorol Soc 106: 85–100, hereafter WPL) is a principle underpinning the experimental investigation of surface fluxes of energy and masses in the atmospheric boundary layer. It has a long-lasting influence in boundary-layer meteorology and micrometeorology, and the year 2010 marks the 30th anniversary of the publication of the WPL theory. We provide here a critique of the theory and review the research it has spurred over the last 30 years. In the authors’ opinion, the assumption of zero air source at the surface is a fundamental novelty that gives the WPL theory its enduring vitality. Considerations of mass conservation show that, in a non-steady state, the WPL mean vertical velocity and the thermal expansion velocity are two distinctly different quantities of the flow. Furthermore, the integrated flux will suffer a systematic bias if the expansion velocity is omitted or if the storage term is computed from time changes in the CO₂ density. A discussion is provided on recent efforts to address several important practical issues omitted by the original theory, including pressure correction, unintentional alternation of the sampled air, and error propagation. These refinement efforts are motivated by the need for an unbiased assessment of the annual carbon budget in terrestrial ecosystems in the global eddy flux network (FluxNet).     

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.