The Effect of Source Distribution on Bulk Scalar Transfer between a Rough Land Surface and the Atmosphere

We investigate the effect of source distribution on the bulk transfer of passive scalars between rough, vegetated land surfaces and the atmosphere, using data from a wind-tunnel experiment in which passive heat was emitted from both the underlying surface and canopy elements of a three-dimensional regular bluff-body array. The experimental results are compared with a simple one-dimensional, two-source model for scalar transfer. We find that: (1) the observed scalar transfer resistance across the boundary layer at the underlying surface is simply related to flat-plate theory by a constant of 0.62, despite the complexity of the turbulent flow within the wind-tunnel canopy; (2) one-dimensional gradient-transfer theory, even with extensions to account for the non-local nature of turbulent transfer within the canopy, does not describe the observed details of scalar concentration gradients in the highly three-dimensional canopy flow, but does provide a reasonable framework for bulk scalar transfer between the composite ground-canopy surface and the flow above the canopy; (3) the kB ⁻¹ parameter (which accounts for bulk excess resistance to scalar transfer over momentum transfer) is highly sensitive to scalar source partition between ground and canopy.     

On the Temperature and Humidity Dissimilarity in the Marine Surface Layer

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

Scaling Variances of Scalars in a Convective Boundary Layer Under Different Entrainment Regimes

For the presentation and analysis of atmospheric boundary-layer (ABL) data, scales are used to non-dimensionalise the observed quantities and independent variables. Usually, the ABL height, surface sensible heat flux and surface scalar flux are used. This works well, so long as the absolute values of the entrainment ratio for both the scalar and temperature are similar. The entrainment ratio for temperature naturally ranges from −0.4 to −0.1. However, the entrainment ratio for passive scalars can vary widely in magnitude and sign. Then the entrainment flux becomes relevant as well. The only customary scalar scale that takes into account both the surface flux and the entrainment flux is the bulk scalar scale, but this scale is not well-behaved for large negative entrainment ratios and for an entrainment ratio equal to −1. We derive a new scalar scale, using previously published large-eddy simulation results for the convective ABL. The scale is derived under the constraint that scaled scalar variance profiles are similar at those heights where the variance producing mechanisms are identical (i.e., either near the entrainment layer or near the surface). The new scale takes into account that scalar variance in the ABL is not only related to the surface flux of that scalar, but to the scalar entrainment flux as well. Furthermore, it takes into account that the production of variance by the entrainment flux is an order of magnitude larger than the production of variance by the surface flux (per unit flux). Other desirable features of the new scale are that it is always positive (which is relevant when scaling standard deviations) and that the scaled variances are always of order 1–10.     

On Extending The Flux-Profile Similarity Theory To Include Quasi-Homogeneous Conditions In The Marine Atmospheric Surface Layer

In order to apply Monin–Obukhov similarity theory to estimatethe profiles of mean quantities and surface fluxes from bulk meteorological parameters, the assumptions of homogeneityand stationarity must be valid. Unfortunately, in coastal zones as well as many other regions of interest, theseassumptions are often violated. In this paper, an extension to the theory is presented that considers systematically varyingstate variables. Along-wind variations of windspeed, atmospheric stratification, and roughness are examined with respectto their relative importance to momentum flux divergence, and the drag coefficient is shown to be systematicallylower in coastal zones. For profiles of scalars, an analysis of the set of quasi-homogeneous terms is only speculated,and the relative importance for the terms will strongly depend on which scalar is of interest.     

Passive scalar diffusion from surface sources in the convective boundary layer

We examine vertical and horizontal diffusion of a passive scalar puff from a surface point source in a convective boundary layer (CBL). Numerical results are presented from a large-eddy simulation (LES) with embedded subgrid Lagrangian particle simulation (LPS). There is good agreement in most respects with previous laboratory and numerical studies. Analytical approximations for the concentration, horizontal flux and vertical flux are found to work reasonably well; they are based on the assumption that the concentration follows a Gaussian function in the horizontal and vertical, and that the dimensionless width and height scales of the puff follow simple functions of time. Fluxes and concentration gradients are related through a continuity relationship, without the need for an eddy diffusivity assumption. The instantaneous, point-source fields can be integrated for any source geometry. We compare predictions from the LES/LPS model for a sinusoidal surface flux with previous results from an LES with sinusoidal buoyancy flux and confirm that the buoyancy perturbations diffuse like a passive scalar. We also consider a continuous point source and derive footprint functions for vertical flux measurements above the surface layer.     

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

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

First-Order Chemistry in the Surface-Flux Layer

We have discussed the behavior of a non-conserved scalar in the stationary, horizontally homogeneous, neutral surface-flux layer and, on the basis of conventional second-order closure, derived analytic expressions for flux and for mean concentration of a gas, subjected to a first-order removal process. The analytic flux solution showed a clear deviation from the constant flux, characterizing a conserved scalar in the surface-flux layer. It decreases with height and is reduced by an order of magnitude of the surface flux at a height equal to about the typical mean distance a molecule can travel before destruction. The predicted mean concentration profile, however, shows only a small deviation from the logarithmic behavior of a conserved scalar. The solution is consistent with assuming a flux-gradient relationship with a turbulent diffusivity corrected by the Damköhler ratio, the ratio of a characteristic turbulent time scale and the scalar mean lifetime. We show that if we use only first-order closure and neglect the effect of the Damköhler ratio on the turbulent diffusivity we obtain another analytic solution for the profiles of the flux and the mean concentration which, from an experimental point of view, is indistinguishable from the first analytic solution. We have discussed two cases where the model should apply, namely NO which, by night, is irreversibly destroyed by interaction with mainly O₃ and the radioactive ²²⁰Rn. Only in the last case was it possible to find data to shed light on the validity of our predictions. The agreement seemed such that a falsification of our model was impossible. It is shown how the model can be used to predict the surface flux of ²²⁰Rn from measured concentration profiles.     

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

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

Surface Flux Parameterization in the Tibetan Plateau

This study investigates some basic aspects related to surface-flux parameterization in the Tibetan Plateau, based on the measurement at three sites. These sites are essentially flat and covered by very sparse and short grasses in the monsoon season. The main contributions include: (1) an optimization technique is proposed to estimate aerodynamic roughness length based on wind and temperature profiles. The approach is not sensitive to random measurement errors if the number of data samples is large enough. The optimized values reasonably vary with surface characteristics. (2) At the three sites, kB^-1 (the logarithm of the ratio of aerodynamic roughness length to thermal roughness length) experiences seasonal and diurnal variations in addition to a dependence on surface types. The mean values for the individual sites vary over a range of 2.7 to 6.4 with large standard deviations. (3) A formula for estimatingthe value of kB^-1 isproposed to account for the effect of seasonal variation of aerodynamic roughness length and diurnal variation of surface temperature. With the formula, the flux parameterization with surface temperature estimates sensible heat flux better than profile parameterization for all the sites.     

An Evaluation Of Local Similarity At The Top Of The Mixed Layer Based On Large-Eddy Simulations

Local similarity, referred to as type II similarity,in the interfacial, stably-stratified layer at thetop of the atmospheric (or oceanic) mixed layer isdiscussed. Type II scales for scalars are based onthe local values of scalar gradients. Similaritypredictions are derived from the second-orderclosure model of Yamada and Mellor, and also fromsimilarity arguments. The obtainedformulation is verified for active and passive scalarsbased on the large-eddy simulation model.     

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

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

Source areas for scalars and scalar fluxes

The spatial resolution of meteorological observations of scalars (such as concentrations or temperature) and scalar fluxes (e.g., water-vapour flux, sensible heat flux) above inhomogeneous surfaces is in general not known. It is determined by the surface area of influence orsource area of the sensor, which for sensors of quantities that are subject to turbulent diffusion, depends on the flow and turbulence conditions.Functions describing the relationship between the spatial distribution of surface sources (or sinks) and a measured signal at height in the surface layer have been termed thefootprint function or thesource weight function. In this paper, the source area of levelP is defined as the integral of the source weight function over the smallest possible domain comprising the fractionP of the total surface influence reflected in the measured signal. Source area models for scalar concentration and for passive scalar fluxes are presented. The results of the models are presented as characteristic dimensions of theP=50% source areas (i.e., the area responsible for 50% of the surface influence): the maximum source location (i.e., the upwind distance of the surface element with the maximum-weight influence), the near and the far end of the source area, and its maximal lateral extension. These numerical model results are related directly to non-dimensional surface-layer scaling variables by a non-linear least squares method in a parameterized model which provides a user-friendly estimate of the surface area responsible for measured concentrations or fluxes. The source area models presented here allow conclusions to be made about the spatial representativeness and the localness (these terms are defined in the text) of flux and concentration measurements.     

Boundary Conditions for Scalar (Co)Variances over Heterogeneous Surfaces

The problem of boundary conditions for the variances and covariances of scalar quantities (e.g., temperature and humidity) at the underlying surface is considered. If the surface is treated as horizontally homogeneous, Monin–Obukhov similarity suggests the Neumann boundary conditions that set the surface fluxes of scalar variances and covariances to zero. Over heterogeneous surfaces, these boundary conditions are not a viable choice since the spatial variability of various surface and soil characteristics, such as the ground fluxes of heat and moisture and the surface radiation balance, is not accounted for. Boundary conditions are developed that are consistent with the tile approach used to compute scalar (and momentum) fluxes over heterogeneous surfaces. To this end, the third-order transport terms (fluxes of variances) are examined analytically using a triple decomposition of fluctuating velocity and scalars into the grid-box mean, the fluctuation of tile-mean quantity about the grid-box mean, and the sub-tile fluctuation. The effect of the proposed boundary conditions on mixing in an archetypical stably-stratified boundary layer is illustrated with a single-column numerical experiment. The proposed boundary conditions should be applied in atmospheric models that utilize turbulence parametrization schemes with transport equations for scalar variances and covariances including the third-order turbulent transport (diffusion) terms.     

Length Scales of Scalar Diffusion in the Convective Boundary Layer: Laboratory Observations

A laboratory study of scalar diffusion in the convective boundary layer has found results that are consistent with a 1999 large-eddy simulation (LES) study by Jonker, Duynkerke and Cuijpers. For bottom-up and top-down scalars (introduced as ‘infinite’ area sources of passive tracer at the surface and inversion, respectively) the dominant length scale was found to be much larger than the length scale for density fluctuations, the latter being equal to the boundary-layer depth h. The variance of the normalized passive scalar grew continuously with time and its magnitude was about 3–5 times larger for the top-down case than for the bottom-up case. The vertical profiles of the normalized passive scalar variance were found to be approximately constant through the convective boundary layer (CBL) with a value of about 3–8c_*² for bottom-up and 10–50c_*² for top-down diffusion. Finally, there was some evidence of a minimum in the variance and dominant length scale for scalar flux ratios (top-down to bottom-up flux) close to −0.5. All these convection tank results confirm the LES results and support the hypothesis that there is a distinct difference in behaviour between the dynamic and passive variables in the CBL.     

Influence of surface heterogeneity on scalar dissimilarity in the roughness sublayer

While it is generally known that surface heterogeneity weakens the application of Monin–Obukhov similarity (MOS), few studies have investigated how seasonal changes in the degree of surface heterogeneity at a particular site may influence the validity of the similarity application. Exploiting seasonal changes in forest function associated with senescence, we conduct a unique evaluation of the effects of surface heterogeneity on the validity of similarity theory at two sites through time. Using high frequency (10 Hz) velocity and scalar time series collected within the roughness sublayer over mixed hardwood deciduous and coniferous forests during both periods of peak leaf area and senescence of deciduous foliage, we examined conformity with proposed universal flux-variance predictions and agreement amongst normalized standard deviations of different scalars (temperature, water vapour and carbon dioxide concentrations). Normalized scalar standard deviations were elevated above MOS flux-variance predictions, with more pronounced deviations observed during and following senescence, particularly in the case of CO₂. Power-law scaling of normalized standard deviations as a function of stability was upheld and robust to seasonal changes in surface heterogeneity. However, dissimilarity of normalized standard deviations for the scalars increased during senescence, as heterogeneity in the source/sink field increased. Scalewise decomposition of scalar time series using wavelet analysis indicated that correlations between scalars were conservative through much of the inertial cascade but decayed for eddies < 10 m. Senescence lowered correlations between scalars over a wide range of eddy sizes. These results demonstrate how seasonal changes in surface physiology can cause a temporal production of heterogeneity in the source/sink field, thus weakening similarity applications in the roughness sublayer.     

A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO _x –O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO _x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w _* as the velocity unit, and the surface temperature flux divided by w _* as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.     

An Analytical Model for the Two-Scalar Covariance Budget Inside a Uniform Dense Canopy

The two-scalar covariance budget is significant within the canopy sublayer (CSL) given its role in modelling scalar flux budgets using higher-order closure principles and in estimating the segregation ratio for chemically reactive species. Despite its importance, an explicit expression describing how the two-scalar covariance is modified by inhomogeneity in the flow statistics and in the vertical variation in scalar emission or uptake rates within the canopy volume remains elusive even for passive scalars. To progress on a narrower version of this problem, an analytical solution to the two-scalar covariance budget in the CSL is proposed for the most idealized flow conditions: a stationary and planar homogeneous flow inside a uniform and dense canopy with a constant leaf area density distribution. The foliage emission (or uptake) source strengths are assumed to vary exponentially with depth while the forest floor emission is represented as a scalar flux. The analytical solution is a superposition of a homogeneous part that describes how the two-scalar covariance at the canopy top is transported and dissipated within the canopy volume, and an inhomogeneous part governed by local production mechanisms of the two-scalar covariance. The homogeneous part is primarily described by the canopy adjustment length scale, and the attenuation coefficients of the turbulent kinetic energy and the mean velocity. Conditions for which the vertical variation of the two-scalar covariance is controlled by the rapid attenuation in the mean velocity and turbulent kinetic energy profiles, vis-à-vis the vertical variation of the scalar source strength, are explicitly established. This model also demonstrates how dissimilarity in the emissions from the ground, even for the extreme binary case with one scalar turned ‘on’ and the other scalar turned ‘off’, modifies the vertical variation of the two-scalar covariance within the CSL. To assess its applicability to field conditions, the analytical model predictions were compared with observations made at two different forest types—a sparse pine forest at the Hyytiälä SMEAR II-station (in Finland) and a dense alpine hardwood forest at Lavarone (in Italy). While the model assumptions do not represent the precise canopy morphology, attenuation properties of the turbulent kinetic energy and the mean velocity, observed mixing length, and scalar source attenuation properties for these two forest types, good agreement was found between measured and modelled two scalar covariances for multiple scalars and for the triple moments at the Hyytiälä site.     

Coherent Structures and the Dissimilarity of Turbulent Transport of Momentum and Scalars in the Unstable Atmospheric Surface Layer

Atmospheric stability effects on the dissimilarity between the turbulent transport of momentum and scalars (water vapour and temperature) are investigated in the neutral and unstable atmospheric surface layers over a lake and a vineyard. A decorrelation of the momentum and scalar fluxes is observed with increasing instability. Moreover, different measures of transport efficiency (correlation coefficients, efficiencies based on quadrant analysis and bulk transfer coefficients) indicate that, under close to neutral conditions, momentum and scalars are transported similarly whereas, as the instability of the atmosphere increases, scalars are transported increasingly more efficiently than momentum. This dissimilarity between the turbulent transport of momentum and scalars under unstable conditions concurs with, and is likely caused by, a change in the topology of turbulent coherent structures. Previous laboratory and field studies report that under neutral conditions hairpin vortices and hairpin packets are present and dominate the vertical fluxes, while under free-convection conditions thermal plumes are expected. Our results (cross-stream vorticity variation, quadrant analysis and time series analysis) are in very good agreement with this picture and confirm a change in the structure of the coherent turbulent motions under increasing instability, although the exact structure of these motions and how they are modified by stability requires further investigation based on three-dimensional flow data.     

The air density correction to eddy flux measurements

Under the usual assumptions for the atmospheric surface layer, we show that air density fluctuations, particularly those due to temperature fluctuations associated with a heat flux, result in a small mean vertical wind velocity. Because of this, there can be a significant correction to eddy flux measurements of passive scalars, for example CO₂, whose average concentration is very large compared to concentration fluctuations associated with the eddy flux.     

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.