Velocity and Surface Shear Stress Distributions Behind a Rough-to-Smooth Surface Transition: A Simple New Model

A simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The wind velocity is estimated as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary-layer height, corresponds to the upwind velocity profile; the second log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z ₀₁)/ln(δ _i /z ₀₁), where z, δ _i and z ₀₁ are the elevation of the prediction location, the internal boundary-layer height at that downwind distance, and the upwind surface roughness, respectively. Unlike other simple analytical models, the new model does not rely on the assumption of a constant or linear distribution for the turbulent shear stress within the internal boundary layer. The performance of the new model is tested with wind-tunnel measurements and also with the field data of Bradley. Compared with other existing analytical models, the proposed model shows improved predictions of both surface shear stress and velocity distributions at different positions downwind of the transition.     

Numerical analysis of flux footprints for different landscapes

Summary A model for the canopy – planetary boundary layer flow and scalar transport based on E- closure was applied to estimate footprint for CO₂ fluxes over different inhomogeneous landscapes. Hypothetical heterogeneous vegetation patterns – forest with clear-cuts as well as hypothetical heterogeneous relief – a bell-shaped valley and a ridge covered by forest were considered. The distortions of airflow caused by these heterogeneities are shown – the upwind deceleration of the flow at the ridge foot and above valley, acceleration at the crest and the flow separation with the reversed flow pattern at lee slopes of ridge and valley. The disturbances induce changes in scalar flux fields within the atmospheric surface layer comparing to fluxes for homogeneous conditions: at a fixed height the fluxes vary as a function of distance to disturbance. Correspondingly, the flux footprint estimated from model data depends on the location of the point of interest (flux measurement point) and may significantly deviate from that for a flat terrain. It is shown that proposed method could be used for the choice of optimal sensor position for flux measurements over complex terrain as well as for the interpretation of data for existing measurement sites. To illustrate the latter the method was applied for experimental site in Solling, Germany, taking into account the complex topography and vegetation heterogeneities. Results show that in certain situations (summer, neutral stratification, south or north wind) and for a certain sensor location the assumptions of idealized air flow structure could be used for measurement interpretation at this site, though in general, extreme caution should be applied when analytical footprint models are used in the interpretation of flux measurements over complex sites.     

Flux Footprint Simulation Downwind of a Forest Edge

Surface fluxes, originating from forest patches, are commonly calculated from atmospheric flux measurements at some height above that patch using a correction for flux arising from upwind surfaces. Footprint models have been developed to calculate such a correction. These models commonly assume homogeneous turbulence, resulting in a simulated atmospheric flux equal to the average surface flux in the footprint area. However, atmospheric scalar fluxes downwind of a forest edge have been observed to exceed surface fluxes in the footprint area. Variations in atmospheric turbulence downwind of the forest edge, as simulated with an E – model, can explain enhanced atmospheric scalar fluxes. This E – model is used to calculate the footprint of atmospheric measurements downwind of a forest edge. Atmospheric fluxes appear mainly enhanced as a result of a stronger sensitivity to fluxes from the upwind surface. A sensitivity analysis shows that the fetch over forest, necessary to reach equilibrium between atmospheric fluxes and surface fluxes, tends to be longer for scalar fluxes as compared to momentum fluxes. With increasing forest density, atmospheric fluxes deviate even more strongly from surface fluxes, but over shorter fetches. It is concluded that scalar fluxes over forests are commonly affected by inhomogeneous turbulence over large fetches downwind of an edge. It is recommended to take horizontal variations in turbulence into account when the footprint is calculated for atmospheric flux measurements downwind of a forest edge. The spatially integrated footprint is recommended to describe the ratio between the atmospheric flux and the average surface flux in the footprint.     

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.     

The Footprint for Estimation of Atmosphere-Surface Exchange Fluxes by Profile Techniques

The flux footprint, that is the contribution per unit emission from each element of the upwind surface area to measurement of the vertical flux of a passive scalar, is calculated for fluxes estimated by micrometeorological profile techniques. It is found that the upwind extent of the footprint for concentration-profile flux estimates is similar to that of the footprint for eddy-covariance flux measurements, when the eddy-covariance measurement is made at a height equal to the arithmetic mean of the highest and lowest profile measurement heights for stable stratification or the geometric mean for unstable stratification. The concentration-profile flux footprint depends on the ratio of the highest to the lowest measurement height, but is insensitive to the number of measurement levels. The concentration-profile flux footprint extends closer to the measurement location than does the 'equivalent eddy-covariance flux footprint, and the difference becomes more pronounced as the ratio of the profile measurement heights increases. The flux footprint for the Bowen-ratio technique is identical to that for a two-level profile measurement only for very limited circumstances. In the more general case, a flux footprint cannot be defined for the Bowen-ratio technique and the uniform upwind fetch required for representative flux measurements depends on the specific spatial distribution of surface fluxes.     

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.     

Update of a Footprint-Based Approach for the Characterisation of Complex Measurement Sites

Horizontal heterogeneity can significantly affect the flux data quality at monitoring sites in complex terrain. In heterogeneous conditions, the adoption of the eddy-covariance technique is contraindicated by the lack of horizontal homogeneity and presence of advective conditions. In addition, uncertainty concerning the sources or sinks influencing a measurement compromises the data interpretation. The consideration of the spatial context of a measurement, defined by a footprint analysis, can therefore provide an important tool for data quality assessment. This study presents an update of an existing footprint-based quality evaluation concept for flux measurement sites in complex terrain. The most significant modifications in the present version are the use of a forward Lagrangian stochastic trajectory model for the determination of the spatial context of the measurements, and the determination of effective roughness lengths with a flux aggregation model in a pre-processing step. Detailed terrain data gathered by remote sensing methods are included. This approach determines spatial structures in the quality of flux data for varying meteorological conditions. The results help to identify terrain influences affecting the quality of flux data, such as dominating obstacles upwind of the site, or slopes biasing the wind field, so that the most suitable footprint regions for the collection of high-quality datasets can be identified. Additionally, the approach can be used to evaluate the performance of a coordinate rotation procedure, and to check to what extent the measured fluxes are representative for a target land-use type.     

A Model for the Transport of Sea-Spray Aerosols in the Coastal Zone

We study the dynamics of sea-spray particles in the coastal region of La Reunion Island on the basis of numerical simulations using the transport aerosol model MACMod (Marine Aerosol Concentration Model) and a survey of the aerosol size distributions measured at four locations at two different heights in the north-west part of the island. This allows evaluation of the performance of our model in case of pure marine air masses with implementation of accurate boundary conditions. First of all, an estimate of the aerosol concentration at 10-m height at the upwind boundary of the calculation domain is obtained using a revisited version of the MEDEX (Mediterranean Extinction) model. Estimates of the vertical profile of aerosol concentrations are then provided using aerosol data obtained at two different heights at the upwind boundary of the calculation domain. A parametrization of the vertical profiles of aerosol concentrations for maritime environment is proposed. The results are then compared to the vertical profiles of 0.532 \(\upmu \)m aerosol particle extinction coefficient obtained from lidar data provided by the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) and also to the data provided by the Aerosol Robotic Network (AERONET). This allows validation of the complete vertical profiles in the mixed layer and shows the validity of satellite data for determination of the vertical profiles. Two kinds of simulation were made: one without a particle advection flux at the upwind boundary of the numerical domain, whereas the second simulation was made with a particle advection flux. In the first case, the influence of the distance to the shoreline on the local sea-spray dynamics is investigated. In the second set of simulation, the particles issued from the local production in the surf zone near the shoreline are mixed with aerosols advected from the remote ocean. A good agreement between the model calculations using our boundary conditions and the data was found. The present results then attest the ability of this kind of model, as a first approach to predicting the local transport of sea-spray particles in a pure marine environment.     

An Analytical Model for Mean Wind Profiles in Sparse Canopies

Existing analytical models for mean wind profiles within canopies are applicable only in dense canopy scenarios, where all momentum is absorbed by canopy elements and, hence, the effect of the ground on turbulent mixing is not important. Here, we propose a new analytical model that can simulate mean wind profiles within sparse canopies under neutral conditions. The model adopts a linearized canopy-drag parametrization and a first-order turbulence closure scheme taking into account the effects of both the ground and canopy elements on turbulent mixing. The resulting wind profile within a sparser canopy appears to be more like a logarithmic form, with the no-slip condition at the ground being satisfied. The analytical solution converges exactly to the standard surface-layer logarithmic wind profile in the case of zero canopy density (i.e., no-canopy scenario) and tends to be an exponential wind profile for a dense canopy; this feature is unique compared with existing analytical models for canopy wind profiles. Results from the new model are in good agreement with those from laboratory experiments and numerical simulations.     

Footprint estimation for scalar flux measurements in the atmospheric surface layer

The flux footprint is the contribution, per unit emission, of each element of a surface area source to the vertical scalar flux measured at height z _m ; it is equal to the vertical flux from a unit surface point source. The dependence of the flux footprint on crosswind location is shown to be identical to the crosswind concentration distribution for a unit surface point source; an analytic dispersion model is used to estimate the crosswind-integrated flux footprint. Based on the analytic dispersion model, a normalized crosswind-integrated footprint is proposed that principally depends on the single variable z/z _m , where z is a measure of vertical dispersion from a surface source. The explicit dependence of the crosswind-integrated flux footprint on downwind distance, thermal stability and surface roughness is contained in the dependence of z on these variables. By also calculating the flux footprint with a Lagrangian stochastic dispersion model, it is shown that the normalized flux footprint is insensitive to the analytic model assumption of a self-similar vertical concentration profile.The National Center for Atmospheric Research is funded by the National Science Foundation.     

DERIVATION OF FLUXES FROM PROFILES OVER A MODERATELY HOMOGENEOUS FOREST

Measurements of fluxes and profiles of wind andtemperature are performed in the roughness layer ofa moderately homogeneous forest location. Weinvestigate to what extent vertical scalar fluxescan be derived from profile measurements. Theinfluence of inhomogeneities in the upwind terrainis investigated with footprint analysis and with aninhomogeneous surface-layer model. Four methods toestimate displacement height are suggested, amongthem is a method involving the structure parameterof the vertical wind. All methods give a decrease ofdisplacement height with increasing wind speed,while roughness length is found to increase withincreasing wind speed. For near-neutral conditionsdimensionless temperature gradients are found to besubstantially lower than the surface-layer valuesfound in the literature for homogeneous terrain with lowvegetation. Dimensionless shear however iscomparable with the surface-layer value. The heightof the roughness layer is 20 times the roughnesslength. Two schemes with locally derived surfaceparameters are tested to derive friction velocityand sensible heat flux from the profilemeasurements. These site specific schemes performsatisfactorily. A third scheme based on surface parameters chosen a priorifrom the literatureperforms significantly worse especially for low windspeed and unstable cases.     

Fetch and Footprint of Turbulent Fluxes over Vegetative Stands with Elevated Sources

In this study, Raupach's localized near-field (LNF)theory is combined with appropriate parameterizations ofthe turbulence inside a canopy to investigate how airstability and source configuration influence the fluxfootprint and flux adjustment with fetch in theroughness sublayer. The model equations are solvednumerically. The flux footprint from the LNF predictionis in general more contracted than the prediction basedon the inertial sublayer similarity functions. Invery unstable conditions, the near-field effect causes thefootprint of the elevated canopy source to locatefurther upwind than that of the ground-level source, andthe combined footprint can become negative in situationswhere the two sources are of opposite sign. The fluxfootprint and flux adjustment with fetch in theroughness sublayer are sensitive to source configurationand the parameters specifying wind speed and theLagrangian time scale inside the canopy.     

Experimental evaluation of analytical and Lagrangian surface-layer flux footprint models

Three surface-layer flux footprint models have been evaluated with the results of an SF₆ tracer release experiment specifically designed to test such models. They are a Lagrangian stochastic model, an analytical model, and a simplified derivative of the analytical model. Vertical SF₆ fluxes were measured by eddy correlation at four distances downwind of a near-surface crosswind line source in an area of homogeneous sagebrush. The mean fluxes were calculated for 136 half-hour test periods and compared to the fluxes predicted by the footprint models. All three models gave similar predictions and good characterizations of the footprint over the stability range -0.01 < z ₀/L < 0.005. The predictions of the three models were within the limits of the uncertainty of the experimental measurements in all but a few cases within this stability range. All three models are unconditionally recommended for determining the area defined by the footprint over short vegetative canopies in this range. They are also generally appropriate for estimating flux magnitudes within the limits of experimental uncertainties. Most of the mean differences observed between the measured and predicted fluxes at each of the four towers reflect a tendency for the measured fluxes to be greater than those predicted by the three models. Rigorous verification of the models in strongly stable conditions was complicated by the need to obtain very accurate measurements of small fluxes in only marginally stationary conditions. Verification in strongly unstable conditions was hampered by the limited number of appropriate data.     

Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.     

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.     

一个压力坐标下的海洋环流模式

A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-σ coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approxima tions. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations.     

Variation in wind velocity over water

Starting from the equations of motion and continuity, a theoretical model is deduced in this paper for the variation in wind velocity over water caused by abrupt changes in surface roughness and temperature when air flows from land to water, based on the consideration that the turbulent exchange coefficient varies with height and distance from the upwind edge. According to the computation of this model, the variation in wind velocity over water, as the drift of air is from land to water, occurs mainly in the first few kilometers from the upwind edge. The wind velocity over water increases to a maximum when the air over land is stable, it tends to moderate when neutral condition is reached, and least variation is shown in unstable condition. And when the air over land is unstable the wind velocity is less over water than over land in strong winds, but some-what greater in light winds.     

A Three-Dimensional Backward Lagrangian Footprint Model For A Wide Range Of Boundary-Layer Stratifications

We present a three-dimensional Lagrangian footprint model with the ability to predict the area of influence (footprint) of a measurement within a wide range of boundary-layer stratifications and receptor heights. The model approach uses stochastic backward trajectories of particles and satisfies the well-mixed condition in inhomogeneous turbulence for continuous transitions from stable to convective stratification. We introduce a spin-up procedure of the model and a statistical treatment of particle touchdowns which leads to a significant reduction of CPU time compared to conventional footprint modelling approaches. A comparison with other footprint models (of the analytical and Lagrangian type) suggests that the present backward Lagrangian model provides valid footprint predictions under any stratification and, moreover, for applications that reach across different similarity scaling domains (e.g., surface layer to mixed layer, for use in connection with aircraft measurements or with observations on high towers).     

模式降水与温度预报的不一致性特征

为探讨模式产品预报不一致性问题,利用2015年11月—2016年10月业务中常用的GQEC,GQJP及T639模式的12 h降水、2 m温度网格产品,采用跳跃指数定量计算方法,研究了产品在不同区域内跳跃指数变化与预报不一致性问题。结果表明:产品多日平均跳跃指数随预报时效延长而增大;长时效预报比短时效预报跳跃频率大、预报不一致性也大;对比两种要素可知,降水的跳跃指数比温度大,跳跃频率高,预报不一致性大;对比不同模式发现,GQEC不仅跳跃指数值小,且跳跃频率低,预报不一致性小,GQJP虽然跳跃指数值小于T639,但其跳跃频率更高,预报一致性较T639低;产品跳跃频率存在季节差异,夏季降水和温度预报跳跃频率最高而冬季最低,夏季预报不一致性最大。研究还发现:基于跳跃指数的预报不一致性特征与选取的区域大小密切相关,区域越大,跳跃指数和预报不一致性越小;区域内跳跃指数分布特征与地理位置和地形等有关。