On the Parameterisation of the Effective Roughness Length for Momentum Transfer over Heterogeneous Terrain

We develop a parameterisation for the effective roughness length of terrain that consists of a repeating sequence of patches, in which each patch is composed of strips of two roughness types. A numerical model with second-order closure in the turbulent stress is developed and used to show that: (i) the normalised Reynolds stress develops as a self-similar profile; (ii) the mixing-length parameterisation is a good first-order approximation to the Reynolds stress. These findings are used to characterise the blending layer, where the stress adjusts smoothly from its local surface value to its effective value aloft. Previous studies have assumed that this adjustment occurs abruptly at a single level, often called the blending height. The blending layer is shown to be characterised by height scales that arise naturally in linear models of surface layer flow over roughness changes, and calculations with the numerical model show that these height scales remain appropriate in the nonlinear regime. This concept of the blending layer allows the development of a new parameterisation of the effective roughness length, which gives values for the effective roughness length that are shown to compare well with both atmospheric measurements and values determined from the second-order model.     

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.     

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.     

Optimized Computation of Transfer Coefficients in Surface Layer with Different Momentum and Heat Roughness Lengths

A new method for computing the surface transfer coefficients is proposed, based on state-of-the-art empirical flux-profile relationships. The influence of the roughness length ratio is first demonstrated with the classical iterative calculation method. Then a non-iterative algorithm is developed, taking into account the difference between momentum and heat roughness lengths.The new method is validated by comparison with the reference iterative computation. The large gain-in computer processing time (CPU) time gain for the calculation of surface fluxes in Eulerian grid models is finally assessed.     

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。     

An Approximate Analytical Solution Of Flux-Profile Relationships For The Atmospheric Surface Layer With Different Momentum And Heat Roughness Lengths

An approximate method for calculating the relationship between z/L(z = reference height, L = Obukhov length) and the bulk Richardsonnumber is presented. If this relationship is known, the momentum andheat fluxes can be computed easily without any iteration. The avoidance of iteration can speed up computationsin large-scale models considerably (up to 10 times) and cases which do not converge or converge very slowly cannot occur. The proposed formulae take into account the difference between momentum (z_0M) and heat roughnesslengths (z_0H). Because the roughness lengths are not neglected at any step of the derivation, the resulting analytical formulae can be used not only between the surface and the reference height but also between two finite levels z₁ andz₂ (by replacing z_0M and z_0H by z₁ and z by z₂). Theequations remain correct even in the limit z₁ z₂.The formulae are based upon the (partially modified) Businger–Dyer flux–profile relationships and,consequently, they are restricted to predominantly homogeneous terrain.These new approximations are an improvement over the existing solutions because they are simpler than most of the formulae in the literature and are able to match the numerical exact solution for different parameter sets (Businger, Dyer, Högström) with an maximum error of about 2% for a wide range of z/L, z/z_0M and z_0M/z_0H.Furthermore, in stable conditions, schemes with and without a finitecritical bulk Richardson number can be approximated. The possibleambiguity of the exact solution =f(RI_B) in (moderately) stable conditions is discussed briefly. The performance of the new formulae is compared to the exact numerical solution and to different formulae proposed in the literature.     

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.     

Momentum and Heat Transfer over Urban-like Surfaces

Momentum and heat transfer was examined for the urban-like surfaces used within the Comprehensive Outdoor Scale MOdel (COSMO) experiments. Simultaneous and comparative meteorological measurements were made over a pair of scale models with different block geometries. These data were analyzed to investigate the influence of height variations, obstacle elongation, and packing density, λ _p , of blocks on the aerodynamic properties. In addition, the robustness of theoretical expressions of bulk transfer coefficients for momentum and heat with respect to geometric parameters was examined. Our analyses showed: (1) the theoretical framework for the bulk transfer coefficient for momentum, C _m , and that for heat, C _h , was applicable for homogeneous building arrays, (2) the sensitivity of C _h to the surface geometry was smaller than that of C _m , (3) the transfer coefficients were increased by variations of block heights, but not by elongation of blocks, (4) first-order approximations of C _m and C _h for an array of blocks with two different heights can be made by applying simple theoretical assumptions to include the effects of height variation, and (5) variations of block heights increased the momentum flux significantly, but caused little change in the sensible heat flux. This can be explained by the feedback mechanism of aerodynamic– thermal interaction; aerodynamic mixing decreased both the advective velocity and the vertical temperature gradient.     

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。     

Diurnal Variations of Thermal Roughness Height over a Grassland

The thermal roughness height associated with the surface radiation temperature has been previously found to vary between different surface types. This study finds that the thermal roughness height varies diurnally even over a homogeneous senescent grassland. The corresponding roughness length for momentum is relatively constant.Both the aerodynamic temperature and the surface radiation temperature are found to be closely related to the air temperature in the middle of the grass canopy. However, the aerodynamic temperature is strongly influenced by the horizontally integrated heat transfer, while the surface radiation temperature represents the integrated thermal emission through the grass depth within the field of view of the radiometer. The aerodynamic temperature is less sensitive to variations and measurement errors in sensible heat flux, wind speed, and air temperature than the thermal roughness height. We find that formulating the aerodynamic temperature in terms of the surface radiation temperature is better posed for use in the bulk formula than using the surface radiation temperature directly and adjusting the thermal roughness length.     

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.     

Characteristics of Momentum and Heat Transfer over Semiarid Grasslands with Different Grazing Intensities in Inner Mongolia, China

The drag coefficient (C d) and heat transfer coefficient (C h) with the bulk transfer scheme are usually used to calculate the momentum and heat fluxes in meteorological models.The aerodynamic roughness length (z 0m) and thermal roughness length (z 0h) are two crucial parameters for bulk transfer equations.To improve the meteorological models,the seasonal and interannual variations of z 0m,z 0h,coefficient kB 1,C d,and C h were investigated based on eddy covariance data over different grazed semiarid grasslands of Inner Mongolia during the growing seasons (May to September) from 2005 to 2008.For an ungrazed Leymus chinensis grassland (ungrazed since 1979),z 0m and z 0h had significant seasonal and interannual variations.z 0m was affected by the amount and distribution of rainfall.kB 1 exhibited a relatively negative variation compared with z 0h,which indicates that the seasonal variation of z 0h cannot be described by kB 1.To parameterize z 0m and z 0h,the linear regressions between ln(z 0m),ln(z 0h),and the leaf area index (LAI) were performed with R 2 =0.71 and 0.83.The monthly average kB 1 was found to decrease linearly with LAI.The four-year averaged values of C d and C h were 4.5×10 3 and 3.9×10 3,respectively.The monthly average C d only varied by 8% while the variation of C h was 18%,which reflects the different impacts of dead vegetation on momentum and heat transfer at this natural grassland.Moreover,with the removal of vegetation cover,grazing intensities reduced z 0m,z 0h,C d,and C h.     

黑河中上游不同下垫面动量总体输送系数和地表粗糙度对比分析

利用廓线法计算了黑河中上游地区盈科农田站、冰沟稀疏草地站、阿柔牧场站和大冬树山垭口积雪观测站的总体输送系数和地表粗糙度。结果表明,地表粗糙度与植被覆盖度和高度以及下垫面的性质有关,夏季地表粗糙度大小是农田站最大,其次是牧场站和稀疏草地站,高寒草甸站最小。下垫面状况还影响动量总体输送系数对稳定度的依赖程度,地表粗糙度大的地区强于地表粗糙度小的地区。     

荒漠戈壁下垫面表面动量和感热湍流通量参数化研究

用合理筛选以后的野外观测资料，研究了荒漠戈壁地表湍流通量参数化的问题。首先，分析了Monin-obukhov相似函数的特征，并拟台出了其经验公式。结果表明，风速和温度相似性函数随稳定度参数的变化曲线与典型经验曲线差异较小，并且在经验曲线分布范围以内，但中性时的值有所不同。同时，还用该资料给出了动量和标量粗糙度(感热粗糙度)长度的平均值及其标量粗糙度随摩擦速度的变化关系。发现标量粗糙度的平均值大约比动量粗糙度的小一个量级，并且随摩擦速度的增大而减小，但明显比其理论预测值要大。     

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.