Numerical Modelling of Katabatic Flow Over a Melting Outflow Glacier

A realistic simulation of katabatic flows is not a straightforward task for numerical models. One complicating factor is that katabatic flows develop within a stably stratified boundary layer, which is poorly resolved and described in many numerical models. To capture the jet-shaped shallow flow a model set-up with high vertical resolution is also required. In this study, ‘a state of the art’ mesoscale numerical model is applied in a simulation of katabatic flow over a melting glacier. A basic agreement between observations and model results is found. From scale analysis, it is concluded that the simulated flow can be classified as katabatic. Although the background flow varies in strength and direction, the simulated katabatic flow over Breidamerkurjökull is persistent. Two factors vital for this persistence are identified. First, the melting snow maintains the surface temperature close to 0 °C while the air temperature warms adiabatically as it descends the slope. This provides a ‘self enhanced’ negative buoyancy that drives the flow to a balance with local friction. Second, the jet-like shape of the resulting flow gives rise to a large ‘curvature term’ in the Scorer parameter, which becomes negative in the upper jet. This prevents vertical wave propagation and isolates the katabatic layer of the influence from the free troposphere aloft. Our results suggest that the formation of local microclimates dominated by katabatic flow is a general feature over melting glaciers. The modelled turbulence structure illustrates the importance of non-local processes. Neglecting the vertical transport of turbulence in katabatic flows is not a valid assumption. It is also found that the local friction velocity remains larger than zero through the katabatic jet, due to directional shear where the scalar wind speed approaches its maximum.     

Evaluation of Two Energy Balance Closure Parametrizations

A general lack of energy balance closure indicates that tower-based eddy-covariance (EC) measurements underestimate turbulent heat fluxes, which calls for robust correction schemes. Two parametrization approaches that can be found in the literature were tested using data from the Canadian Twin Otter research aircraft and from tower-based measurements of the German Terrestrial Environmental Observatories (TERENO) programme. Our analysis shows that the approach of Huang et al. (Boundary-Layer Meteorol 127:273–292, 2008), based on large-eddy simulation, is not applicable to typical near-surface flux measurements because it was developed for heights above the surface layer and over homogeneous terrain. The biggest shortcoming of this parametrization is that the grid resolution of the model was too coarse so that the surface layer, where EC measurements are usually made, is not properly resolved. The empirical approach of Panin and Bernhofer (Izvestiya Atmos Oceanic Phys 44:701–716, 2008) considers landscape-level roughness heterogeneities that induce secondary circulations and at least gives a qualitative estimate of the energy balance closure. However, it does not consider any feature of landscape-scale heterogeneity other than surface roughness, such as surface temperature, surface moisture or topography. The failures of both approaches might indicate that the influence of mesoscale structures is not a sufficient explanation for the energy balance closure problem. However, our analysis of different wind-direction sectors shows that the upwind landscape-scale heterogeneity indeed influences the energy balance closure determined from tower flux data. We also analyzed the aircraft measurements with respect to the partitioning of the “missing energy” between sensible and latent heat fluxes and we could confirm the assumption of scalar similarity only for Bowen ratios $\approx $ 1.     

Aerodynamic Roughness Length of Fresh Snow

This study presents the results from a series of wind-tunnel experiments designed to investigate the aerodynamic roughness length z ₀ of fresh snow under no-drift conditions. A two-component hot-film anemometer was employed to obtain vertical profiles of velocity statistics in a zero pressure gradient turbulent boundary layer for flow over naturally deposited snow surfaces. The roughness of these snow surfaces was measured by means of digital photography to capture characteristic length scales that can be related to z ₀. Our results show that, under aerodynamically rough conditions, the mean value of the roughness length for fresh snow is \({\langle{z}_{0}\rangle= 0.24}\) mm with a standard deviation σ(z ₀) = 0.05 mm. In this study, we show that variations in z ₀ are associated with variations in the roughness geometry. The roughness measurements suggest that the estimated values of z ₀ are consistent with the presence of irregular roughness structures that develop during snowfalls that mimic ballistic deposition processes.     

Wind-tunnel Modelling of Dispersion from a Scalar Area Source in Urban-Like Roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ _p = λ _f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w _T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness.     

标量粗糙度对地气交换的影响

为提高地-气间感热和潜热通量的精度,利用Garratt的公式将标量粗糙度Z0T和Z0q引入BATS,对六种不同的植被作对比试验。结果表明:标量粗糙度Z0T和Z0q均远远小于动量粗糙度Z0,约相差3～10个数量级不等。晴天状况下,农作物区Z0/Z0T最小,约103,阔叶林最大,达1010;雨天状况下,各种植被间标量粗糙度的差异减小了。计算的地表温度、感热通量、潜热通量较原BATS的更为合理。     

Numerical Studies with a Regional Atmospheric Climate Model Based on Changes in the Roughness Length for Momentum and Heat Over Antarctica

A regional atmospheric climate model is used toexamine the effect of changes in the roughnesslengths of momentum (_z0m) and heat (_z0h)on the structure of the lower atmosphere and on thesurface energy fluxes over Antarctica. Fourexperiments were carried out in which _z0mand/or _z0h were altered with respect to acontrol experiment. The changes consisted of (1) alowering of _z0m from a field aggregated froma vegetation map with an orographic correction basedon the European Centre for Medium-Range WeatherForecasts _z0m field, to a constant value of10^-3 m; and (2) a lowering of _z0h from a valueequal to _z0m to a constant value of 10^-3 mor a value dependent on the wind speed via a surfacerenewal model. A reduction of _z0m results in theexpected increase in near-surface wind speed. It alsoresults in an increase in the depth of the layer in whichsouth-easterly near-surface winds prevail, and in adecrease in the strength of the large-scale flow overthe continent, in particular in summer. In theescarpment region a decrease of _z0m is foundto result in too high wind speeds. Surface temperatureson average decrease while atmospheric temperaturesincrease, resulting in an increase of near-surfacestatic stability. Changes in roughness lengths donot significantly change the temperature profiles.The surface fluxes, on average found reduced, aremodelled best by using the _z0h based on thesurface renewal method.     

城市表面粗糙度长度的确定

讨论了动量粗糙度长度与热量和水汽等标量粗糙度长度在形式上和物理本质上的不同，以及造成这些不同的原因和条件，分析了决定动量粗糙度的几种因素，并给出了确定动量粗糙度长度的简化关系式，并且根据城市冠层与其上惯性次层能量和动量守衡的原因，建立了热量和水汽粗糙度与动量粗糙度之间的联系，得到了确定热量和水汽粗糙度长度的简化关系式，最后，通过数值试验，表明了动量粗糙度和标量粗糙度变化特征以及对一些主要参数的敏感程度，以及动量粗糙度与标量粗糙度的动态关系。     

A Simple Method of Estimating Scalar Fluxes Over Forests

A simple aerodynamic-variance method is proposed to fill gaps in continuous CO₂ flux measurements in rainy conditions, when open-path analysers do not function. The method requires turbulent conditions (friction velocity greater than 0.1 ms^–1), and uses measurements of mean wind speed, and standard deviations of temperature and CO₂ concentration fluctuations to complement, and at times replace, eddy-covariance measurements of friction velocity, sensible heat flux and CO₂ flux. Friction velocity is estimated from the mean wind speed with a flux-gradient relationship modified for the roughness sublayer. Since normalised standard deviations do not follow Monin-Obukhov similarity theory in the roughness sublayer, a simple classification scheme according to the scalar turbulence scale was used. This scheme is shown to produce sensible heat and CO₂ flux estimates that are well correlated with the measured values.     

Large-Eddy Simulation of Atmospheric Boundary-Layer Flow Over Fluvial-Like Landscapes Using a Dynamic Roughness Model

A recently developed dynamic surface roughness model (Anderson and Meneveau, J Fluid Mech 679:288–314, 2011) for large-eddy simulation (LES) of atmospheric boundary-layer flow over multi-scale topographies is applied to boundary-layer flow over several types of fluvial-like landscapes. The landscapes are generated numerically with simulation of a modified Kardar–Parisi–Zhang equation (Passalacqua et al., Water Resour Res 42:WOD611, 2006). These surfaces possess the fractal-like channel network and anisotropic features often found in real terrains. The dynamic model is shown to lead to accurate flow predictions when the surface-height distributions exhibit power-law scaling (scale invariance) in the prevalent mean flow direction. In those cases, the LES provide accurate predictions (invariant to resolution) of mean velocity profiles. Conversely, some resolution dependence is found for applications in which the landscape’s streamwise spectra do not exhibit pure power-law scaling near wavenumbers corresponding to the LES grid resolution.     

精细的城市边界层模拟中热力粗糙度引入的初步研究

运用南京大学城市尺度边界层模式（UBLM）以100 m水平网格距的精细高分辨率，诊断分析小规模城市（水平范围在一二十公里）的气象环境与边界层结构。就高分辨率精细模拟分析研究了两个问题:（1）在模式中引入热力粗糙度，就引入热力粗糙度前后的模拟结果与实测结果进行对比，结果表明引入后的模拟结果与自动气象站的观测结果吻合较好，能够很好地反映出地面气温的日变化规律。冬季，白天不引入热力粗糙度比引入热力粗糙度会高估小规模城市地区感热通量约60 W/m2，而对乡间农作物地区约10 W/m2。（2）以四种不同水平网格距对同一下垫面及气象条件进行诊断分析，结果表明以100 m网格距精细模拟效果明显优于以较大网格距进行的模拟效果。以这样的精细高分辨率模式所获模拟结果分析了小规模城市的边界层特征，表明:冬季白天和夜间小规模城市与乡村气温差分别为0.8℃和0.6℃；风速明显低于乡村地区；湍能高于乡村地区，白天和夜间湍能一般为乡村的3倍左右；白天混合层发展较乡村迅速，且高度高于乡村地区。这样的特征在当今城市规划布局工作中，为特大型城市的卫星城市的建设规划提供了有益的科学实验依据。模拟效果表明以如此高的水平分辨率实施的模式和模拟是可行和有意义的。     

Stability Dependence of Height Scales and Effective Roughness Lengths of Momentum and Heat Transfer Over Roughness Changes

It is widely accepted that the correct formulation of an effective roughness length, defined as the area average of the roughness length in heterogeneous terrain, relies upon the appropriate de-termination of a height scale. At this height a meteorological quantity is approximately in equilibrium with local surface conditions and independent of horizontal position. This research note determines explicitly the different height scales from the perturbation solutions of flow velocity and temperature, as well as the fluxes of momentum and heat, in a stratified boundary layer. These solutions are derived from the asymptotic approximation theory and shown to capture major characteristics of momentum and heat transfer over heterogeneous terrain with changes of the underlying roughness lengths. The effective roughness lengths can then be computed by use of these height scales. The dependence of height scales and effective roughness lengths upon stratification is also discussed briefly.     

The Characteristics and Parameterization of Aerodynamic Roughness Length over Heterogeneous Surfaces

Aerodynamic roughness length (z0m is a key factor in surface flux estimations with remote sensing algorithms and/or land surface models. This paper calculates z0m over several land surfaces, with 3 years of experimental data from Xiaotangshan. The results show that z0m is direction-dependent, mainly due to the heterogeneity of the size and spatial distribution of the roughness elements inside the source area along different wind directions. Furthermore, a heuristic parameterization of the aerodynamic roughness length for heterogeneous surfaces is proposed. Individual z0m over each surface component (patch) is calculated firstly with the characteristic parameters of the roughness elements (vegetation height, leaf area index, etc.), then z0m over the whole experimental field is aggregated, using the footprint weighting method.     

Determination of Roughness Lengths for Heat and Momentum Over Boreal Forests

The roughness length for momentum (z_0m), zero-plane displacementheight (d), and roughness length for heat (z_0h) are importantparameters used to estimate land-atmosphere energy exchange. Although many different approaches have been developed to parameterizemomentum and heat transfer, existing parameterizations generally utilizehighly simplified representations of vegetation structure. Further, a mismatch exists between the treatments used for momentum and heat exchange and those used for radiative energy exchanges. In this paper, parameterizations are developed to estimate z_0m, d, and z_0h for forested regimes using information related to tree crown density and structure. The parameterizations provide realistic representationfor the vertical distribution of foliage within canopies, and include explicit treatment for the effects of the canopy roughness sublayer and leaf drag on momentum exchange. The proposed parameterizationsare able to realistically account for site-to-site differences in roughness lengths that arise from canopy structural properties.Comparisons between model predictions and field measurements show good agreement, suggesting that the proposed parameterizations capture the most important factors influencing turbulent exchange of momentumand heat over forests.     

Large-Eddy Simulation of Coherent Turbulence Structures Associated with Scalar Ramps Over Plant Canopies

Large-eddy simulations were performed of a neutrally-stratified turbulent flow within and above an ideal, horizontally- and vertically-homogeneous plant canopy. Three simulations were performed for shear-driven flows in small and large computational domains, and a pressure-driven flow in a small domain, to enable the nature of canopy turbulence unaffected by external conditions to be captured. The simulations reproduced quite realistic canopy turbulence characteristics, including typical ramp structures appearing in time traces of the scalar concentration near the canopy top. Then, the spatial structure of the organised turbulence that caused the scalar ramps was examined using conditional sampling of three-dimensional instantaneous fields, triggered by the occurrence of ramp structures. A wavelet transform was used for the detection of ramp structures in the time traces. The ensemble-averaged results illustrate that the scalar ramps are associated with the microfrontal structure in the scalar, the ejection-sweep structure in the streamwise and vertical velocities, a laterally divergent flow just around the ramp-detection point, and a positive, vertically-coherent pressure perturbation. These vertical structures were consistent with previous measurements made in fields or wind tunnels. However, the most striking feature is that the horizontal slice of the same structure revealed a streamwise-elongated region of high-speed streamwise velocity impacting on another elongated region of low-speed velocity. These elongated structures resemble the so-called streak structures that are commonly observed in near-wall shear layers. Since elongated structures of essentially similar spatial scales were observed in all of the runs, these streak structures appear to be inherent in near-canopy turbulence. Presumably, strong wind shear formed just above the canopy is involved in their formation. By synthesis of the ensemble-averaged and instantaneous results, the following processes were inferred for the development of scalar microfronts and their associated flow structures: (1) a distinct scalar microfront develops where a coherent downdraft associated with a high-speed streak penetrates into the region of a low-speed streak; (2) a stagnation in flow between two streaks of different velocities builds up a vertically-coherent high-pressure region there; (3) the pressure gradients around the high-pressure region work to reduce the longitudinal variations in streamwise velocity and to enhance the laterally-divergent flow and lifted updrafts downstream of the microfront; (4) as the coherent mother downdraft impinges on the canopy, canopy-scale eddies are formed near the canopy top in a similar manner as observed in conventional mixing-layer turbulence.     

A Parameterisation of the Effective Roughness Length over Inhomogeneous, Flat Terrain

A parameterisation ofthe effective roughness length is presented for an arbitrary givenroughness distribution z₀(x,y) over flat terrainat neutral stratification.Beyond pure averaging, it takes into account the spatial structure of the distribution, especially the influence of length scales, and inflow direction.To allow for interactions between different rough areas, Boussinesq-approximated equations with a turbulence closure of first order are considered and solved using perturbation theory.As a result, the logarithm of the effective roughness length isrepresented as a sum over the product of the Fourier transformation of log z₀ and a so-called dynamic function, which describesthe response of the flow field to a single wavelength of z₀.Although the numerical expenditure is larger than for simple averaging formulae,this method could be used by large-scale models to calculateeffective roughness lengths in every close-to-surface grid cell.     

非均匀地表类型有效粗糙度的计算和特征分析

利用湍流通量相等原理和ECMWF的总体湍流输送系数参数化方案,研究了气候数值模式中非均匀地表类型的有效粗糙度计算问题。结果表明,当存在两种地表类型且粗糙变率为2.3时,有效粗糙度比通常采用的对数加权平均值大40％左右,相应的总体湍流输送系数大16％左右,光滑地表类型和粗糙地表类型所占面积百分比分别为60％和40％时,有效粗糙度及相应的总体湍流输送系数和相应的对数加权平均值之差最大,并且有效粗糙度对大气层结不敏感,因而在气候模式中有实用价值。     

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.     

The Influences of Thermodynamic Characteristics on Aerodynamic Roughness Length over Land Surface

It has previously been shown that aerodynamic roughness length changes significantly along with nearsurface atmospheric thermodynamic state; however, at present, this phenomenon remains poorly understood, and very little research concerning this topic has been conducted. In this paper, by using the data of different underlying surfaces provided by the Experimental Co-observation and Integral Research in Semi-arid and Arid Regions over North China, aerodynamic roughness length (z₀) values in stable, neutral, and unstable atmospheric stratifications are compared with one another, and the relationship between z₀ and atmospheric thermodynamic stability (ζ) is analyzed. It is found that z₀ shows great differences among the stable, neutral, and unstable atmospheric thermodynamic states, with the difference in z₀ values between the fully thermodynamic stable condition and the neutral condition reaching 60% of the mean z₀. Furthermore, for the wind speed range in which the wind data are less sensitive to z₀, the surface z₀ changes more significantly with ζ, and is highly correlated with both the Monin-Obukhov stability (ζ₀) and the overall Richardson number (R_ib), with both of their correlation coefficients greater than 0.71 and 0.47 in the stable and unstable atmospheric stratification, respectively. The empirical relation fitted with the experimental observations is quite consistent with the Zilitinkevich theoretical relation in the stable atmosphere, but the two are quite distinct and even show opposite variation tendencies in the unstable atmosphere. In application, however, verification of the empirical fitted relations by using the experimental data finds that the fitted relation is slightly more applicable than the Zilitinkevich theoretical relation in stable atmospheric stratification, but it is much more suitable than the Zilitinkevich relation in unstable atmospheric stratification.     

The Effect of Stratification on the Aerodynamic Roughness Length and Displacement Height

The roughness length, z _0u , and displacement height, d _0u , characterise the resistance exerted by the roughness elements on turbulent flows and provide a conventional boundary condition for a wide range of turbulent-flow problems. Classical laboratory experiments and theories treat z _0u and d _0u as geometric parameters independent of the characteristics of the flow. In this paper, we demonstrate essential stability dependences—stronger for the roughness length (especially in stable stratification) and weaker but still pronounced for the displacement height. We develop a scaling-analysis model for these dependences and verify it against experimental data.