Large-eddy Simulation of Turbulent Flow Across a Forest Edge. Part I: Flow Statistics

The statistics of turbulent flow across a forest edge have been examined using large-eddy simulation, and results compared with field and wind-tunnel observations. The moorland-to-forest transition is characterized by flow deceleration in the streamwise direction, upward distortion of the mean flow, formation of a high pressure zone immediately in front of the edge, suppression of the standard deviations and covariance of velocity components, and enhancement of velocity skewnesses. For the selected forest density, it is observed that the maximum distortion angle is about 8 degrees from the horizontal. Instead of approaching a downwind equilibrium state in a monotonic manner, turbulence (standard deviations and covariances of velocity components) and mean streamwise velocity undershoot in the transition zone behind the edge. Evolution of flow statistics clearly reveals the growth of an internal boundary layer, and the establishment of an equilibrium layer downwind of the edge. It is evident that lower-order moments generally adjust more quickly over the new rough surface than do higher-order moments. We also show that the streamwise velocity standard deviation at canopy height starts its recovery over the rough surface sooner than does the vertical velocity standard deviation, but completes full adjustment later than the latter. Despite the limited domain size upstream of the edge, large-eddy simulation has successfully reproduced turbulent statistics in good agreement with field and wind-tunnel measurements.     

The Evolution Of Turbulence Across A Forest Edge

An experiment was set-up to investigate the adjustment of turbulence over a roughness transition (moorland to forest). Results from this experiment support the development of an internal boundary layer (IBL) at the transition, which propagates upwards by turbulent diffusion as a function of distance downwind from the transition. Spectra and length-scale results uphold the hypothesis that, over a transition to a rough surface, the variance distribution shifts towards smaller wavelengths/length scales. However, results suggest that the adjustment of streamwise velocity variance may be faster than the adjustment of the vertical velocity variance. The concept of an equilibrium layer developing above the new surface is supported. Fetch requirements for equilibrium are, however, found to differ between first order and second order (flux) statistics, with second order statistics requiring a longer fetch. Results indicate that fetch should exceed 25 times the height of the measurement above the zero plane, which is a 2° (±0.5) growth angle, for flux equilibrium.     

Mechanisms Controlling Turbulence Development Across A Forest Edge

In this paper we discuss the development of turbulence back from the transition fromopen moorland to a forest. Data from a field study and a wind-tunnel experiment arepresented. These show that the variance in the streamwise velocity begins to adjust tothe new surface between 2 to 4 tree heights downwind of the transition. This is soonerthan either the vertical velocity variance or the shear stress, both of which begin to adjust in a zone 3 to 5 tree heights downwind of the edge. Key terms in the prognostic equations for streamwise and vertical velocity variance are evaluated in order to explain these differences. The flow distortion caused by the forest edge, which extends to 4 tree heights downwind of the forest edge, is shown to be crucial in the delayed turbulence development. Initially the shear production term, which is the dominant source for the streamwise velocity variance, is counteracted by a sink in the vertical advection term. After the flow levels out the pressure redistribution (return-to-isotropy) term becomes the main sink of streamwisevelocity variance and feeds energy into the vertical velocity component. Therefore, thedevelopment of the vertical velocity variance and shear stress cannot begin until afterdevelopment of an increase in the streamwise velocity variance. Results are comparedwith other experiments, including the flow across shelterbelts, and large-eddy simulations of forest flow.     

An Analytical Footprint Model For Non-Neutral Stratification

We propose an analytical model for the so-called footprint of scalar fluxes in the atmospheric boundary layer. It is the generalization of formulations already given in the literature, which allows to account for thermal stability. Our model is only marginally more complicated than these, and it is therefore simple enough to be applicable for a routine footprint analysis within long-term measurements. The mathematical framework of our model is a stationary gradient diffusion formulation with height-independent crosswind dispersion. It uses the solution of the resulting two-dimensional advection – diffusion equation for power law profiles of the mean wind velocity and the eddy diffusivity. To find the adjoint Monin–Obukhov similarity profile, we propose two different approaches, a purely analytical one and a simplenumerical error minimalization.     

纳木错(湖)地区湍流数据质量控制和湍流通量变化特征

利用中国科学院纳木错多圈层综合观测研究站2009年全年的大气湍流观测资料,应用Foot-print模型分析了青藏高原非均匀下垫面湍流观测数据的数据质量、质量评价及不同下垫面对湍流通量的贡献。结果表明:纳木错(湖)地区因不同土地利用类型的差别,导致地表通量分布不均匀,草地对地表通量的贡献最大;对不同大气层结状态,观测站周围200m范围内的地表通量贡献各不相同,上风向通量贡献源区较大,湍流发展较充分。在不稳定状态和中性状态下,纳木错地区地表通量数据质量较高,即白天观测的通量数据质量较高;在稳定状态下数据质量较低,即夜间的通量数据质量较差;纳木错地区的湍流通量受湖陆风和大气稳定性影响较大。     

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.     

Large-eddy Simulation of Turbulent Flow across a Forest Edge. Part II: Momentum and Turbulent Kinetic Energy Budgets

Momentum and turbulent kinetic energy (TKE) budgets across a forest edge have been investigated using large-eddy simulation (LES). Edge effects are observed in the rapid variation of a number of budget terms across this vegetation transition. The enhanced drag force at the forest edge is largely balanced by the pressure gradient force and by streamwise advection of upstream momentum, while vertical turbulent diffusion is relatively insignificant. For variance and TKE budgets, the most important processes at the forest edge are production due to the convergence (or divergence) of the mean flow, streamwise advection, pressure diffusion and enhanced dissipation by canopy drag. Turbulent diffusion, pressure redistribution and vertical shear production, which are characteristic processes in homogeneous canopy flow, are less important at the forest transition. We demonstrate that, in the equilibrated canopy flow, a substantial amount of TKE produced in the streamwise direction by the vertical shear of the mean flow is redistributed in the vertical direction by pressure fluctuations. This redistribution process occurs in the upper canopy layers. Part of the TKE in the vertical velocity component is transferred by turbulent and pressure diffusion to the lower canopy levels, where pressure redistribution takes place again and feeds TKE back to the streamwise direction. In this TKE cycle, the primary source terms are vertical shear production for streamwise velocity variance and pressure redistribution for vertical velocity variance. The evolution of these primary source terms downwind of the forest edge largely controls the adjustment rates of velocity variances.     

Heat Flux Apportionment to Heterogeneous Surfaces Using Flux Footprint Analysis

Heat flux data collected from the Baiyangdian Heterogeneous Field Experiment were analyzed using the footprint method. High resolution (25 m) Landsat-5 satellite imaging was used to determine the land cover as one of four surface types: farmland, lake, wetland, or village. Data from two observation sites in September 2005 were used. One site (Wangjiazhai) was characterized by highly heterogeneous surfaces in the central area of the Baiyangdian: lake/wetland. The other site (Xiongxian) was on land with more uniform surface cover. An improved Eulerian analytical flux footprint model was used to determine "source areas" of the heat fluxes measured at towers located at each site from surrounding landscapes of mixed surface types.In relative terms results show that wetland and lake areas generally contributed most to the observed heat flux at Wangjiazhai, while farmland contributed most at Xiongxian. Given the areal distribution of surface type contributions, calculations were made to obtain the magnitudes of the heat flux from lake, wetland and farmland to the total observed flux and apportioned contributions of each surface type to the sensible and latent heat fluxes. Results show that on average the sensible heat flux from wetland and farmland were comparable over the diurnal cycle, while the latent heat flux from farmland was somewhat larger by about 30-50 W m-2 during daytime. The latent and sensible fluxes from the lake source in daytime were about 50 W m-2 and 100 W m-2 less, respectively, than from wetland and farmland. The results are judged reasonable and serve to demonstrate the potential for flux apportionment over heterogeneous surfaces.     

Canopy Architecture and Turbulence Structure in a Coniferous Forest

Synchronous sonic anemometric measurements at five heightswithin a mixed coniferous forest were used to test two different parameterisations ofcanopy architecture in the application of a second-order turbulence closure model. Inthe computation of the leaf drag area, the aerodynamic sheltering was replaced with anarchitectural sheltering, assumed to be analogous to the clumping index defined in radiativetransfer theory. Consequently, the ratio of leaf area density and sheltering factor was approximatedby the effective leaf area or the mean contact number, both obtained from the inversion of non-destructive optical measurements. The first parameter represents the equivalentrandomly dispersed leaf area in terms of shading, the second is the average number of leavesthat a straight line intercepts penetrating the canopy with a certain zenith angle. Theselection of this direction was determined by the analysis of the mean angle of the wind vectorduring sweep events. The drag coefficient values obtained from the inversion of themomentum flux equation, using the two proposed parameterisations, are in good agreement withvalues found in the literature. The predicted profiles of turbulence statistics reasonablymatch actual measurements, especially in the case of the mean contact numberparameterisation. The vertical profile of leaf drag area, obtained by forcing the turbulence modelto match the observed standard deviation of vertical velocity (_w), is intermediatebetween the two empirical ones. Finally, the proposed canopy parameterisations were appliedto a Lagrangian transport model to predict vertical profiles of air temperature, H₂O andCO₂ concentration.     

Edge Flow and Canopy Structure: A Large-Eddy Simulation Study

Sharp heterogeneities in forest structure, such as edges, are often responsible for wind damage. In order to better understand the behaviour of turbulent flow through canopy edges, large-eddy simulations (LES) have been performed at very fine scale (2 m) within and above heterogeneous vegetation canopies. A modified version of the Advanced Regional Prediction System (ARPS), previously validated in homogeneous conditions against field and wind-tunnel measurements, has been used for this purpose. Here it is validated in a simple forest-clearing-forest configuration. The model is shown to be able to reproduce accurately the main features observed in turbulent edge flow, especially the “enhanced gust zone” (EGZ) present around the canopy top at a few canopy heights downwind from the edge, and the turbulent region that develops further downstream. The EGZ is characterized by a peak in streamwise velocity skewness, which reflects the presence of intense intermittent wind gusts. A sensitivity study of the edge flow to the forest morphology shows that with increasing canopy density the flow adjusts faster and turbulent features such as the EGZ become more marked. When the canopy is characterized by a sparse trunk space the length of the adjustment region increases significantly due to the formation of a sub-canopy wind jet from the leading edge. It is shown that the position and magnitude of the EGZ are related to the mean upward motion formed around canopy top behind the leading edge, caused by the deceleration in the sub-canopy. Indeed, this mean upward motion advects low turbulence levels from the bottom of the canopy; this emphasises the passage of sudden strong wind gusts from the clearing, thereby increasing the skewness in streamwise velocity as compared with locations further downstream where ambient turbulence is stronger.     

Turbulence Statistics Measurements in a Northern Hardwood Forest

Tower-based turbulence measurements were collected in and over a mixed hardwood forest at the University of Michigan BiologicalStation (UMBS) UMBSflux site in the northern summerof 2000. Velocity and temperature fluctuations were measured at five levels within the canopy (up to the canopy height, H = 21.4 m), using one- and three-dimensional sonic anemometers and fine-wire thermocouples. Six additional thermocouples were distributed over the canopy-layer depth. Three-dimensional velocities and sonic temperatures were also measured above the canopy at 1.6H and at 2.15H on the AmeriFlux tower located at the UMBSflux site. Vertical profiles of buoyancy flux, mean horizontal velocity, Reynolds stress, and standard deviation and skewness of velocity components were calculated. The analysis of these measurements aims at a multi-layer parameterization framework of turbulence statistics forimplementation in Lagrangian stochastic models. Turbulence profiles and power spectra above the canopy were analyzed in the context of Monin-Obukhov similarity theory (MOST) and Kolmogorov theory, as determined by stability at the top level (2.15H), to assess the extent to which surface scaling is valid as the canopy top is approached. Velocity spectra were computed to explore the potential of estimating the viscous dissipation rate, and results show that the high frequency range of the spectra above the canopy exhibits the roll-off predicted by Kolmogorov theory. Similarly, velocity standard deviations above the canopy converge to MOST predicted values toward the top level, and spectral peaks shift with stability, as expected. Within the canopy, both turbulence statistics profiles and spectral distributions follow the general known characteristics inside forests.     

Footprint Analysis: A Closed Analytical Solution Based On Height-Dependent Profiles Of Wind Speed And Eddy Viscosity

Based on the theoretical background of existing models for the crosswind-integrated footprint, a new model is presented, which, in contrast to the existing models, describes the normalized footprint by a closed analytical formula. This was made possible by using well-known power profiles for wind speed and eddy viscosity instead of Monin–Obukhov based profiles at a certain stage of model development. However, the major difference between the new model and the existing models is that the so-called shape parameter of vertical plume dispersion, a function of upwind distance in the existing models, is set constant in the new model in order to circumvent a formal inconsistency found in the derivation of the existing models. Due to this inconsistency, the existing models do not generally satisfy the fundamental condition that the cumulative normalized footprint must approach unity for the upwind distance tending towards infinity.     

非均匀下垫面湍流通量观测的印痕分析

利用2005年在北京昌平区小汤山开展的非均匀下垫面观测实验的观测数据,分别处理了涡旋相关法和大孔径闪烁仪LAS测得的感热通量,并运用印痕模型对数据进行“源区”分析。分析结果表明:在复杂地表上,涡旋相关的测量值由于混杂了其他下垫面的通量信息,不能真实地反映其观测区域的湍流特征,存在着观测误差。而LAS观测出现的低估问题则与掺混高度和“源区”有关。通过用印痕方法进行数据订正后,以上问题均得到很好的改善,订正结果与LAS观测通量的线性关系良好,两者的相关系数达到0.9。实验结果验证了印痕模型在非均匀下垫面的适用性。     

Turbulent Flux Measurements Above and Below the Overstory of a Boreal Aspen Forest

Turbulent flux measurements both above and beneath the canopy of a boreal aspen forest are described. Velocity skewness showed that, beneath the aspen canopy, turbulence was dominated by intermittent, downward penetrating gusts. Eulerian horizontal length scales calculated from integration of the autocorrelation function or spectral peaks were 9.0 and 1.4 times the mean aspen height of 21.5 m respectively. Above-canopy power spectral slopes for all velocity components followed the -2/3 power law, whereas beneath-canopy slopes were closer to -1 and showed a spectral short cut in the horizontal and vertical components. Cospectral patterns were similar both above and beneath the canopy. The Monin–Obukhov similarity function for the vertical wind velocity variance was a well-defined function of atmospheric stability, both above and beneath the canopy. Nocturnal flux underestimation and departures of this similarity function from that expected from Monin–Obukhov theory were a function of friction velocity. Energy balance closure greater than 80% was achieved at friction velocities greater than 0.30 and 0.10 m s-1, above and below the aspen canopy, respectively. Recalculating the latent heat flux using various averaging periods revealed a minimum of 15 min were required to capture 90% of the 30-min flux. Linear detrending reduced the flux at shorter averaging periods compared to block averaging. Lack of energy balance closure and erratic flux behaviour led to the recalculation of the latent and sensible heat fluxes using the ratio of net radiation to the sum of the energy balance terms.     

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.     

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.     

Creating Surface Flux Maps from Airborne Measurements: Application to the Mackenzie Area GEWEX Study MAGS 1999

The objective of this study is to produce two-dimensional maps of the sensible and the latent heat fluxes from airborne measurements, based on the analysis of a flight pattern, called grid flights. A footprint model with along-wind and cross-wind components was used to project the measured fluxes onto the surface map. The method was applied to measurements over Arctic tundra during the Mackenzie Area GEWEX (Global Energy and Water Cycle Experiment) Study (MAGS) 1999. The resulting flux estimates were computed by integration of a wavelet transform, and corrected for long wavelength losses using information from 100 km long regional runs that were conducted close to the grid flights. The random flux error was estimated based on the flight length that is represented in each map element, and a map resolution of 3 × 3 km was chosen in order to keep the average random error of the latent heat flux below 25%. The random error of the sensible heat flux was smaller by a factor of 1.4 on average. An analysis of airborne flux measurements at different altitudes showed no significant increase of flux estimates for measurement heights below 90 m. Thus, the fluxes measured at heights between 48 and 64 m were not corrected for vertical flux divergence. The resulting flux maps provide quantitative two-dimensional estimates of the energy exchange between the surface and the atmosphere during the snow melt period in an Arctic environment, which are well-suited for calibration and validation of numerical models.     

Footprint Analysis For Measurements Over A Heterogeneous Forest

The air flow and vertical distribution of sources/sinks inside aforest canopy have been taken into accountin the analysis of the contribution of sources/sinks to measured fluxes and concentrations above a forest. Thestochastic estimators for concentrations and fluxes are described and their evaluation is performed by simulationof an ensemble of fluid parcel trajectories. The influence of the forest canopy on the footprint is important forobservation levels up to a few times the forest height. The influence of along-wind turbulent diffusion, whichanalytical atmospheric surface layer (ASL) footprint models do not account for, is significant even at higherlevels. The footprint analysis has been performed to deduce the Douglas fir canopy carbon dioxide uptake from eddycovariance flux measurements above a mixed Douglas fir–beech forest during the pre-leaf periods of the beech.The scatter in the results indicates that such an analysis is limited, presumably due to horizontal inhomogenetiesin flow statistics, which were not included in trajectory simulation. The analysis, however, is useful for theestimation of the qualitative effect of the forest canopy on the footprint function.     

CoLM模式在中国温带混交林和亚热带人工针叶林的水热通量模拟性能评估

利用中国陆地生态系统通量观测研究网络(ChinaFLUX)在长白山温带混交林观测站点和千烟洲亚热带人工针叶林观测站点的强化观测资料,考察了一个较为完善的陆面过程模式(Common LandModel,CoLM)在这两种不同植被类型下垫面的模拟性能,特别是其对潜热通量的模拟。模拟结果与强化观测资料的对比表明,CoLM能较好地模拟出实验站点地表能量平衡的基本特征以及潜热通量的日变化和季节变化。其中长白山站和千烟洲站潜热通量日平均的观测值与模拟值的相关系数分别为0.804和0.692,均通过了0.001的显著性水平检验。总体而言,CoLM在长白山站的模拟效果更好一些,模式对不同植被覆盖类型的土壤—植被—大气间水热传输过程的处理可能是造成差别的原因。