Footprints and Fetches for Fluxes over Forest Canopies with Varying Structure and Density

A stochastic trajectory model was used to estimate scalar fluxfootprints in neutral stabilityfor canopies of varying leaf area distributions andleaf area indices. An analytical second-order closure model wasused to predict mean wind speed, second moments and the dissipationrate of turbulent kinetic energy within a forest canopy.The influence of source vertical profile on the flux footprint wasexamined. The fetch is longer for surface sourcesthan for sources at higher levels in the canopy. In order tomeasure all the flux components, and thus the total flux, with adesired accuracy, sources were located at the forest floor in thefootprint function estimation. The footprint functions werecalculated for five observation levels above the canopy top. Itwas found that at low observation heights both canopy density andcanopy structure affect the fetch. The higher abovethe canopy top the flux is measured, the more pronounced is the effectof the canopy structure. The forest fetch for flux measurements isstrongly dependent on the required accuracy: The 90% flux fetchis greater by a factor of two or more compared to the 75% fetch. Theupwind distance contributing 75% of flux is as large as 45 timesthe difference between canopy height and the observation heightabove the canopy top, being even larger for low observationlevels.     

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.     

A Note On The Contribution Of Dispersive Fluxes To Momentum Transfer Within Canopies

Dispersive flux terms are formed when the time-averaged meanmomentum equation is spatially averaged within the canopy volume.These fluxes represent a contribution to momentum transfer arisingfrom spatial correlations of the time-averaged velocity componentswithin a horizontal plane embedded in the canopy sublayer (CSL).Their relative importance to CSL momentum transfer is commonlyneglected in model calculations and in nearly all fieldmeasurement interpretations. Recent wind-tunnel studies suggestthat these fluxes may be important in the lower layers of thecanopy; however, no one study considered their importance acrossall regions of the canopy and for a wide range of canopy roughnessdensities. Using detailed laser Doppler anemometry measurementsconducted in a model canopy composed of cylinders within a largeflume, we demonstrate that the dispersive fluxes are onlysignificant (i.e., >10%) for sparse canopies. These fluxes arein the same direction as the turbulent flux in the lower layers ofthe canopy but in the opposite direction near the canopy top. Fordense canopies, we show that the dispersive fluxes are <5% atall heights. These results appear to be insensitive to theReynolds number (at high Reynolds numbers).     

A Lagrangian Solution To The Relationship Between A Distributed Source And Concentration Profile

A new solution is presented to the problem ofrelating source strength and concentration profiles within a plant canopy. The solution is based on the Lagrangian dispersion theory developed by G. I. Taylor in 1921. A dispersion matrix is derived that relates the source and concentration profiles based on profiles of the turbulent length and velocity scales. The matrix translates the effects of persistence (a temporal effect) into spatialcoordinates and represents the change from near-field to far-field in acontinuous fashion, successfully accounting for both regimes. A test ofthe new model using wind-tunnel data showed excellent quantitative agreement between model and measurements. A comparison was also made withM. R. Raupach's localized near-field theory, which underestimated the near-field effect in the wind-tunnel data and relative to the new model.     

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.     

Turbulence Statistics Above And Within Two Amazon Rain Forest Canopies

The turbulence structure in two Amazon rain forestswas characterised for a range of above-canopystability conditions, and the results compared withprevious studies in other forest canopies and recenttheory for the generation of turbulent eddies justabove forest canopies. Three-dimensional wind speedand temperature fluctuation data were collectedsimultaneously at up to five levels inside and abovetwo canopies of 30–40 m tall forests, during threeseparate periods. We analysed hourly statistics, jointprobability distributions, length scales, spatialcorrelations and coherence, as well as power spectraof vertical and horizontal wind speed.The daytime results show a sharp attenuation ofturbulence in the top third of the canopies, resultingin very little movement, and almost Gaussianprobability distributions of wind speeds, in the lowercanopy. This contrasts with strongly skewed andkurtotic distributions in the upper canopy. At night,attenuation was even stronger and skewness vanishedeven in the upper canopy. Power spectral peaks in thelower canopy are shifted to lower frequencies relativeto the upper canopy, and spatial correlations andcoherences were low throughout the canopy. Integrallength scales of vertical wind speed at the top of thecanopy were small, about 0.15 h compared to avalue of 0.28 h expected from the shear lengthscale at the canopy top, based on the hypothesis that theupper canopy air behaves as a plane mixing layer. Allthis suggests that, although exchange is not totallyinhibited, tropical rain forest canopies differ from other forests in that rapid, coherentdownward sweeps do not penetrate into the lowercanopy, and that length scales are suppressed. This isassociated with a persistent inversion of stability inthat region compared to above-canopy conditions. Theinversion is likely to be maintained by strong heatabsorption in the leaves concentrated near thecanopy top, with the generally weak turbulence beingunable to destroy the temperature gradients over thelarge canopy depth.     

A Simple Parameterisation for Flux Footprint Predictions

Flux footprint functions estimate the location and relative importance of passive scalar sources influencing flux measurements at a given receptor height. These footprint estimates strongly vary in size, depending on receptor height, atmospheric stability, and surface roughness. Reliable footprint calculations from, e.g., Lagrangian stochastic models or large-eddy simulations are computationally expensive and cannot readily be computed for long-term observational programs. To facilitate more accessible footprint estimates, a scaling procedure is introduced for flux footprint functions over a range of stratifications from convective to stable, and receptor heights ranging from near the surface to the middle of the boundary layer. It is shown that, when applying this scaling procedure, footprint estimates collapse to an ensemble of similar curves. A simple parameterisation for the scaled footprint estimates is presented. This parameterisation accounts for the influence of the roughness length on the footprint and allows for a quick but precise algebraic footprint estimation.     

Turbulence Statistics Inside and Over Forest: Influence on Footprint Prediction

Observations of wind statistics within and above a Scots pine forest are comparedwith those predicted from an analytical second-order closure model. The roughnesssublayer (RSL) effects, and the influence of stability on similarity functions, arestudied using observations. The commonly accepted forms of similarity functionsdescribe the influence of diabatic effects above the RSL well. According to earlierstudies they are expected also to apply within the RSL. As an exception, the averagewind speed normalised with friction velocity was found to be invariant with stabilityclose to the canopy top under unstable conditions. Lagrangian stochastic trajectorysimulations were used to evaluate the influence of canopy turbulence profiles onfootprint prediction. The main uncertainty was found to arise from parameterisationof the random forcing term in the Lagrangian velocity equation. The influence ofdiabatic conditions was studied, and it was found that thermal stability affectssignificantly the footprint function above the forest canopy, but significantuncertainty exists because of uncertainties in the formulation of stability functions.     

An Analytical one-Dimensional Second-Order Closure Model of Turbulence Statistics and the Lagrangian Time Scale Within and Above Plant Canopies of Arbitrary Structure

An analytical one-dimensional second-order closure model is developed to describe the within canopy velocity variances, turbulent intensities, dissipation rates, Lagrangian time scale and Lagrangian far field diffusivities for vegetation canopies of arbitrary structure and density. The model incorporates and extends the model of momentum transfer developed by Massman (1997) and the model of within canopy velocity variances developed by Weil (unpublished) from the second-order closure model of Wilson and Shaw (1977). Model predictions of within and above canopy velocity variances, turbulent intensities, dissipation rates and the Lagrangian time scale are in reasonable agreement with previously measured or estimated values for these parameters. The present model suggests that the Lagrangian time scale and the far field diffusivity could be strongly dependent upon foliage structure and density through the foliage effects on the velocity variances. A simple formulation for the Lagrangian time scale at canopy height is derived from model results. Taken as a whole, the present model may provide a relatively simple way to incorporate turbulence parameters into models of soil/canopy/atmosphere mass transfer.     

Using a One-and-a-Half Order Closure Model of the Atmospheric Boundary Layer for Surface Flux Footprint Estimation

A knowledge of the distribution of the contribution of upwind sources to measurements of vertical scalar flux densities is important for the correct interpretation of eddy covariance data. Several approaches have been developed to estimate this so-called footprint function. Here a new approach based on the ensemble-averaged Navier—Stokes equations is presented. Comparisons of numerical results using this approach with results from other studies under a range of environmental conditions show that the model predictions are robust. Moreover, the approach outlined here has the advantage of a potential wide applicability, due to an ability to take into account the heterogeneous nature of underlying surfaces. For example, the model showed that any variations in surface drag, such as must occur in real life heterogeneous canopies, can exert a marked influence of the shape and extent of flux footprints. Indeed, it seems likely that under such circumstances, estimates of surface fluxes will be weighted towards areas of highest foliage density (and therefore quite likely higher photosynthetic rates) close to the measurement sensor. Three-dimensional footprints during the day and night were also determined for a mixed coniferous forest in european Russia. A marked asymmetry of the footprint in the crosswind direction was observed, this being especially pronounced for non-uniform plant distributions involving vegetation types with different morphological and physiological properties. The model also found that, other things being equal, the footprint peak for forest soil respiration is typically over twice the distance from the above canopy measurement sensor compared to that for canopy photosynthesis. This result has important consequences for the interpretation of annual ecosystem carbon balances by the eddy covariance method.     

Study Of `Soft' Night-Time Surface-Layer Decoupling Over Forest Canopies In A Land-Surface Model

The cause of a night-time land-surface model cold bias over forest canopies at threedifferent sites is studied in connection with various formulations of turbulent transferand the phenomenon of decoupling between the surface and the boundary layer. Themodel is the Canadian Land Surface Scheme (CLASS), a leading internationally knownmodel that has been tested over a variety of instrumented sites. The bias was first attributed to a deficient turbulent transfer and a few formulations were compared. One formulation is the classical log-linear profile with a sharp cut-off of the fluxes at a critical Richardsonnumber around 0.2, while in the other ones the flux decreases less rapidly with increasingstatic stability. While the surface-layer formulations have an impact on the modelled canopy temperature, other causes were found for the negative bias. The CLASS model neglected the heat capacity of the air trapped inside the canopy and its inclusion multiplied theeffective heat capacity of the canopy, by a factor ranging from 2.3 to 3.4 for the canopies studied, and reduced the error. A correction was also made to the air specific humidity at canopy level and the topsoil thermal conductivity was changed from that of organic matter to that of mineral soil. With these modifications, and using the incoming longwave radiative flux instead of the net longwave flux, the bias almost completely disappeared. Using ascheme with more heat transfer at large static stability, obtained by assuming that thefluxes decrease in magnitude with height in the surface layer, reduced the original biaswhile using the log-linear formulation amplified the cold bias. The impact of the turbulent transfer formulations is much reduced when they are applied to model runs in which the other above modifications have been made.The phenomenon of decoupling is presented and its understanding is complementedwith the new notions of `hard' versus `soft' decoupling and complete versus incompletedecoupling, depending on the impact decoupling has on the model and on the effectiveness of the model in achieving the decoupling. The geostrophic wind speed is a determiningfactor in separating cases of hard decoupling (rare) from the soft cases (frequent) while the completeness of the decoupling primarily depends on the form of the turbulent transfer curve as a function of static stability.     

Estimation of Scalar Source/Sink Distributions in Plant Canopies Using Lagrangian Dispersion Analysis: Corrections for Atmospheric Stability and Comparison with a Multilayer Canopy Model

Source/sink distributions of heat, water vapour andCO₂ within a rice canopy were inferred using aninverse Lagrangian dispersion analysis and measuredmean profiles of temperature, specific humidity andCO₂ mixing ratio. Monin–Obukhov similarity theorywas used to account for the effects of atmosphericstability on _w(z), the standard deviation ofvertical velocity and _L(z), the Lagrangian timescale of the turbulence. Classical surface layer scaling was applied in the inertial sublayer (z > z_ruf)using the similarity parameter = (z - d)/L, where z is height above ground, d is the zero plane displacementheight for momentum, L is the Obukhov length,and z_ruf 2.3h_c, where h_c iscanopy height. A single length scale h_c, was usedfor the stability parameter 3 = h_c/L in the height range 0.25 < z/h_c < 2.5. This choice is justified by mixing layer theory, which shows that within the roughness sublayer there is one dominant turbulence length scaledetermined by the degree of inflection in the windprofile at the canopy top. In the absence of theoretical or experimental evidence for guidance,standard Monin–Obukhov similarity functions, with = h_c/L, were used to calculate the stabilitydependence of _w(z) and _L(z) in the roughness sublayer. For z/h_c < 0.25 the turbulence length and time scales are influenced by the presence of the lowersurface, and stability effects are minimal. With theseassumptions there was excellent agreement between eddycovariance flux measurements and deductions from theinverse Lagrangian analysis. Stability correctionswere particularly necessary for night time fluxes whenthe atmosphere was stably stratified.The inverse Lagrangian analysis provides a useful toolfor testing and refining multilayer canopy models usedto predict radiation absorption, energy partitioningand CO₂ exchanges within the canopy and at thesoil surface. Comparison of model predictions withsource strengths deduced from the inverse analysisgave good results. Observed discrepancies may be dueto incorrect specification of the turbulent timescales and vertical velocity fluctuations close to theground. Further investigation of turbulencecharacteristics within plant canopies is required toresolve these issues.     

Modelling Vegetation-Atmosphere Co2 Exchange By A Coupled Eulerian-Langrangian Approach

A Eulerian-Lagrangian canopy microclimate model wasdeveloped with the aim of discerning physical frombiophysical controls of CO₂ and H₂O fluxes. The model couples radiation attenuation with mass,energy, and momentum exchange at different canopylevels. A unique feature of the model is its abilityto combine higher order Eulerian closure approachesthat compute velocity statistics with Lagrangianscalar dispersion approaches within the canopy volume. Explicit accounting for within-canopy CO₂,H₂O, and heat storage is resolved by consideringnon-steadiness in mean scalar concentration andtemperature. A seven-day experiment was conducted inAugust 1998 to investigate whether the proposedmodel can reproduce temporal evolution of scalar(CO₂, H₂O and heat) fluxes, sources andsinks, and concentration profiles within and above auniform 15-year old pine forest. The modelreproduced well the measured depth-averaged canopy surfacetemperature, CO₂ and H₂O concentrationprofiles within the canopy volume, CO₂ storageflux, net radiation above the canopy, and heat andmass fluxes above the canopy, as well as the velocitystatistics near the canopy-atmosphere interface. Implications for scaling measured leaf-levelbiophysical functions to ecosystem scale are alsodiscussed.     

A Flume Experiment on the Adjustment of the Mean and Turbulent Statistics to a Transition from Short to Tall Sparse Canopies

Water-flume experiments are conducted to study the structure of turbulent flow within and above a sparse model canopy consisting of two rigid canopies of different heights. This difference in height specifies a two-dimensional step change from a rough to a rougher surface, as opposed to a smooth-to-rough transition. Despite the fact that the flow is in transition from a rough to a rougher surface, the thickness of the internal boundary layer scales as x ^4/5, consistent with smooth-to-rough boundary layer adjustment studies, where x is the downstream distance from the step change. However, the analogy with smooth-to-rough transitions no longer holds when the flow inside the canopy and near the canopy top is considered. Results show that the step change in surface roughness significantly increases turbulence intensities and shear stress. In particular, there is an adjustment of the mean horizontal velocity and shear stress as the flow passes over the rougher canopy, so that their vertical profiles adjust to give maximum values at the top of this canopy. We also observe that the magnitude and shape of the inflection in the mean horizontal velocity profile is significantly affected by the transition. The horizontal and vertical turbulence spectra compare well with Kolmogorov’s theory, although a small deviation at high frequencies is observed in the horizontal spectrum within the canopy. Here, for relatively low leaf area index, shear is found to be a more effective mechanism for momentum transfer through the canopy structure than vortex shedding.     

Exploring the Effects of Microscale Structural Heterogeneity of Forest Canopies Using Large-Eddy Simulations

The Regional Atmospheric Modeling System (RAMS)-based Forest Large-Eddy Simulation (RAFLES), developed and evaluated here, is used to explore the effects of three-dimensional canopy heterogeneity, at the individual tree scale, on the statistical properties of turbulence most pertinent to mass and momentum transfer. In RAFLES, the canopy interacts with air by exerting a drag force, by restricting the open volume and apertures available for flow (i.e. finite porosity), and by acting as a heterogeneous source of heat and moisture. The first and second statistical moments of the velocity and flux profiles computed by RAFLES are compared with turbulent velocity and scalar flux measurements collected during spring and winter days. The observations were made at a meteorological tower situated within a southern hardwood canopy at the Duke Forest site, near Durham, North Carolina, U.S.A. Each of the days analyzed is characterized by distinct regimes of atmospheric stability and canopy foliage distribution conditions. RAFLES results agreed with the 30-min averaged flow statistics profiles measured at this single tower. Following this intercomparison, two case studies are numerically considered representing end-members of foliage and midday atmospheric stability conditions: one representing the winter season with strong winds above a sparse canopy and a slightly unstable boundary layer; the other representing the spring season with a dense canopy, calm conditions, and a strongly convective boundary layer. In each case, results from the control canopy, simulating the observed heterogeneous canopy structure at the Duke Forest hardwood stand, are compared with a test case that also includes heterogeneity commensurate in scale to tree-fall gaps. The effects of such tree-scale canopy heterogeneity on the flow are explored at three levels pertinent to biosphere-atmosphere exchange. The first level (zero-dimensional) considers the effects of such heterogeneity on the common representation of the canopy via length scales such as the zero-plane displacement, the aerodynamic roughness length, the surface-layer depth, and the eddy-penetration depth. The second level (one-dimensional) considers the normalized horizontally-averaged profiles of the first and second moments of the flow to assess how tree-scale heterogeneities disturb the entire planar-averaged profiles from their canonical (and well-studied planar-homogeneous) values inside the canopy and in the surface layer. The third level (three-dimensional) considers the effects of such tree-scale heterogeneities on the spatial variability of the ejection-sweep cycle and its propagation to momentum and mass fluxes. From these comparisons, it is shown that such microscale heterogeneity leads to increased spatial correlations between attributes of the ejection-sweep cycle and measures of canopy heterogeneity, resulting in correlated spatial heterogeneity in fluxes. This heterogeneity persisted up to four times the mean height of the canopy (h _c ) for some variables. Interestingly, this estimate is in agreement with the working definition of the thickness of the canopy roughness sublayer (2h _c –5h _c ).     

The Influence of Local Stability on Heat and Momentum Transfer within Open Canopies

Eddy-covariance data have been analyzed to investigate the influence of local stability on heat transfer within open canopies. The flux–gradient relationship for heat is derived from the temperature variance equation, and the stability dependence of the flux–gradient relationship is examined and discussed. The results indicate that the strong stability dependence of the nondimensional standard deviation of temperature, and the small contributions of turbulent transport to the temperature variance, lead to a strong stability dependence of the nondimensional temperature gradient within open canopies. Quadrant analysis and hole size analysis were performed for momentum and heat fluxes in the subcanopy, and the results indicate that the contribution of each quadrant to the total flux depends on both the local stability and canopy depth. The intermittency of the turbulent flux does not show a clear dependence on local stability. As the contribution of ejections to the heat flux increases, the vertical flux of the temperature variance changes sign from negative to positive, leading to small temperature variance transport in unstable conditions. Multi-resolution analysis indicates that heat and momentum are transported with different dominant time scales in very unstable conditions, suggesting a different role of local buoyancy in heat and momentum transfer.     

Assessing Tower Flux Footprint Climatology and Scaling Between Remotely Sensed and Eddy Covariance Measurements

We describe pragmatic and reliable methods to examine the influence of patch-scale heterogeneities on the uncertainty in long-term eddy-covariance (EC) carbon flux data and to scale between the carbon flux estimates derived from land surface optical remote sensing and directly derived from EC flux measurements on the basis of the assessment of footprint climatology. Three different aged Douglas-fir stands with EC flux towers located on Vancouver Island and part of the Fluxnet Canada Research Network were selected. Monthly, annual and interannual footprint climatologies, unweighted or weighted by carbon fluxes, were produced by a simple model based on an analytical solution of the Eulerian advection-diffusion equation. The dimensions and orientation of the flux footprint depended on the height of the measurement, surface roughness length, wind speed and direction, and atmospheric stability. The weighted footprint climatology varied with the different carbon flux components and was asymmetrically distributed around the tower, and its size and spatial structure significantly varied monthly, seasonally and inter-annually. Gross primary productivity (GPP) maps at 10-m resolution were produced using a tower-mounted multi-angular spectroradiometer, combined with the canopy structural information derived from airborne laser scanning (Lidar) data. The horizontal arrays of footprint climatology were superimposed on the 10-m-resolution GPP maps. Monthly and annual uncertainties in EC flux caused by variations in footprint climatology of the 59-year-old Douglas-fir stand were estimated to be approximately 15–20% based on a comparison of GPP estimates derived from EC and remote sensing measurements, and on sensor location bias analysis. The footprint-variation-induced uncertainty in long-term EC flux measurements was mainly dependent on the site spatial heterogeneity. The bias in carbon flux estimates using spatially-explicit ecological models or tower-based remote sensing at finer scales can be estimated by comparing the footprint-weighted and EC-derived flux estimates. This bias is useful for model parameter optimizing. The optimization of parameters in remote-sensing algorithms or ecosystem models using satellite data will, in turn, increase the accuracy in the upscaled regional carbon flux estimation.     

The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer

Using an incomplete third-order cumulant expansion method (ICEM) and standard second-order closure principles, we show that the imbalance in the stress contribution of sweeps and ejections to momentum transfer (ΔS _o ) can be predicted from measured profiles of the Reynolds stress and the longitudinal velocity standard deviation for different boundary-layer regions. The ICEM approximation is independently verified using flume data, atmospheric surface layer measurements above grass and ice-sheet surfaces, and within the canopy sublayer of maturing Loblolly pine and alpine hardwood forests. The model skill for discriminating whether sweeps or ejections dominate momentum transfer (e.g. the sign of ΔS _o ) agrees well with wind-tunnel measurements in the outer and surface layers, and flume measurements within the canopy sublayer for both sparse and dense vegetation. The broader impact of this work is that the “genesis” of the imbalance in ΔS _o is primarily governed by how boundary conditions impact first and second moments.