A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.     

Flow Over Partially Forested Ridges

Numerical simulations of flow over hills that are partially covered with a forest canopy are performed. This represents a much more realistic situation than previous studies that have generally concentrated on hills that are fully-forested. The results show that the flow over the hill is sensitive to where on the hill the forest is positioned. In particular, for low slopes flow separation is predominantly located within the forest on the lee slope. This has implications for the transport of scalars in the forest canopy. For large hills the results show more variability in scalar concentrations within the canopy compared to either a fully-forested hill or a patch of forest over flat terrain. These results are likely to have implications for a range of applications including the siting and interpretation of flux measurements over forests in complex terrain, predicting wind damage to trees and wind-farm developments. Calculation of the hill-induced pressure drag and canopy-plus-surface stress shows a strong sensitivity to the position of the forest relative to the hill. Depending on the position of the forest the individual drag terms may be strongly enhanced or reduced and may even change sign. The net impact is generally to reduce the total drag compared to an equivalent fully-forested hill, but the amount of the reduction depends strongly on the position of the forest canopy on the hill. In many cases with large, wide hills there is a clear separation of scales between the adjustment of the canopy to a forest edge (of order 6 ? 8L _c, where L _c is the canopy adjustment length scale) and the width of the hill. This separation means that the hill-induced pressure and flow fields and the forest-edge induced pressure and flow fields can in some sense be considered as acting separately. This provides a means of explaining the combined effects of partial forestation and terrain. It also offers a simple method for modelling the changes in drag over a hill due to partial forest cover by considering the impact of the hill and the partial canopy separately. Scaling arguments based on this idea successfully collapse the modelled drag over a range of different hill widths and heights and for different canopy parameters. This offers scope for a relatively simple parametrization of the effects of partial forest cover on the drag over a hill.     

Turbulent Form Drag On Anisotropic Three-Dimensional Orography

Results are presented from a large number of numerical simulations performed to investigate the dependence of the turbulentform drag on three-dimensional ellipsoidal hills upon aspect ratio and wind direction. For isolatedisotropic hills the results are, as expected, found to beindependent of wind direction. However directionaldependence rapidly becomes important as the ridges are elongated,and the results quickly converge onto those obtained in the limitingcase of two-dimensional ridges. Based on the numerical results,a simple parametrization of the drag is proposed.     

Estimation of the Exchange Coefficient of Heat During Low Wind Convective Conditions

For the first time, the exchange coefficient of heat C_H has been estimated from eddy correlation of velocity and virtual temperature fluctuations using sonic anemometer measurements made at low wind speeds over the monsoon land atJodhpur (26°18' N, 73°04' E), a semi arid station. It shows strong dependence on wind speed, increasing rapidly with decreasing wind speed, and scales according to a power law C_H = 0.025U₁₀ ^-0.7 (where U₁₀ is the mean wind speed at 10-m height). A similar but more rapid increase in the drag coefficient C_Dhas already been reported in an earlier study. Low winds (<4 m s^-1) are associated with both near neutral and strong unstable situations. It is noted that C_H increases with increasing instability. The present observations best describe a low wind convective regime as revealed in the scaling behaviour of drag, sensible heat flux and the non-dimensional temperature gradient. Neutral drag and heat cofficients,corrected using Monin–Obukhov (M–O) theory, show a more uniform behaviour at low wind speeds in convective conditions, when compared with the observed coefficients discussed in a coming paper.At low wind convective conditions, M-O theory is unable to capture the observed linear dependence of drag on wind speed, unlike during forced convections. The non-dimensional shear inferred from the present data shows noticeable deviations from Businger's formulation, a forced convection similarity. Heat flux is insensitive to drag associated with weak winds superposed on true free convection. With heat flux as the primary variable, definition of new velocity scales leads to a new drag parameterization scheme at low wind speeds during convective conditionsdiscussed in a coming paper.     

Neutral Flow Over A Series Of Rough Hills: A Laboratory Experiment

This paper presents laboratory experiments of aerodynamically fully rough, neutral flow over a series of sinusoidal hills. Two sets of hills, with maximum gradients (slopes) of 0.2 (10°) and 0.4 (20°), were considered.The flow remained attached in the former case while separation occurredin the latter. Characteristics of the mean flow and turbulence statistics are discussed and compared with profiles over a flat surface covered with the same roughness as the hills. Comparisons are made with linear theory predictions for the flow in the inner region and aloft. Accurate measurements of the surface pressure were also made, enabling the comparison between the measured pressure drag and predictions from theoretical and computational work with different turbulent closure schemes. Organised secondary flow in the spanwise direction, observed previously in both experimental and computational studies, was also observed here over the small hills.     

Aerodynamic drag coefficient and roughness length for three seasons over a tropical western Indian station

Land Surface Processes Experiment (LASPEX) was conducted over semi-arid region of western India in 1997. As a part of this program, wind and temperature observations were taken using slow as well as fast response sensors over a semi-arid station Anand (22°35′N, 72°55′E) situated in Gujarat state of India. Turbulent parameters such as drag coefficient and sensible heat flux were estimated using eddy correlation method and aerodynamic roughness length was estimated using wind profiles. The analysis has been carried out for the data representing summer, monsoon and winter seasons. It was found that the wind speed does not exceed 5 ms^− 1 during the observational period considered in this study. Relationship of aerodynamic drag coefficient and roughness length with wind speed and stability has been investigated. Aerodynamic roughness length was greater in the stable conditions when the wind speed was low and it reduced drastically during convective conditions. The resulting values of aerodynamic roughness length and drag coefficient for the monsoon period agree well with values reported in literature over Indian subcontinent for homogeneous grass covered surfaces.     

The Impact Of Air-Flow Separation On The Drag Of The Sea Surface

An approach that allows assessment ofthe impact of air-flow separation (AFS) fromwave breaking fronts on the sea-surface drag is presented. Wave breaking fronts are modelled by the discontinuities of the sea-surface slope. It is assumedthat the dynamics of the AFS from wave breaking crests is similar to thatfrom the backward facing step. The form drag supported by an individualbreaker is described by the action of the pressure drop distributed alongthe forward face of the breaking front. The total stress due to the AFS isobtained as a sum of contributions from breaking fronts of different scales.Outside the breaking fronts the drag of the sea surface is supported by theviscous surface stress and the wave-induced stress. To calculate the stressdue to the AFS and the wave-induced stress a physical model of the wind-wavespectrum is used. Together with the model of the air flow described in termsof surface stresses it forms a self-consistent dynamical system for the seasurface-atmosphere where the air flow and wind waves are strongly coupled.Model calculations of the drag coefficient agree with measurements. It is shownthat the dimensionless Charnock parameter (roughness length normalized onthe square of the friction velocity and the acceleration of gravity)increases with the increase of the wind speed in agreement with fieldmeasurements. The stress due to the AFS normalized on the square of thefriction velocity is proportional to the cube of wind speed. At low windsthe viscous surface stress dominates the drag. The role of the form drag,which is the sum of the stress due to the AFS and the wave-induced stress, isnegligible. At moderate and high winds the form drag dominates. At windspeeds higher than 10 m s^-1 the stress supported by the AFS becomescomparable to the wave-induced stress and supports up to 50% of the totalstress.     

Fetch Limited Drag Coefficients

Measurements made at a tower located 2 km off the coast of Denmark inshallow water during the Risø Air Sea Experiment (RASEX) are analyzedto investigate the behaviour of the drag coefficient in the coastal zone.For a given wind speed, the drag coefficient is larger during conditions ofshort fetch (2-5 km) off-shore flow with younger growing waves than it isfor longer fetch (15-25 km) on-shore flow. For the strongest on-shorewinds, wave breaking enhances the drag coefficient. Variation of the neutral drag coefficient in RASEX is dominated byvariation of wave age, frequency bandwidth of the wave spectra and windspeed. The frequency bandwidth is proportional to the broadness of the waveheight spectra and is largest during conditions of light wind speeds. Usingthe RASEX data, simple models of the drag coefficient and roughness length are developed in terms of wind speed, wave age and bandwidth. An off-shoreflow model of the drag coefficient in terms of nondimensional fetch isdeveloped for situations when the wave state is not known.     

Determination Of The Surface Drag Coefficient

This study examines the dependence of the surface drag coefficienton stability, wind speed, mesoscale modulation of the turbulent flux and method of calculation of the drag coefficient. Data sets over grassland, sparse grass, heather and two forest sites are analyzed. For significantly unstable conditions, the drag coefficient does not depend systematically on z/L but decreases with wind speed for fixed intervals of z/L, where L is the Obukhov length. Even though the drag coefficient for weak wind conditions is sensitive to the exact method of calculation and choice of averaging time, the decrease of the drag coefficient with wind speed occurs for all of the calculation methods. A classification of flux calculation methods is constructed, which unifies the most common previous approaches.The roughness length corresponding to the usual Monin–Obukhovstability functions decreases with increasing wind speed. This dependence on wind speed cannot be eliminated by adjusting the stability functions. If physical, the decrease of the roughness length with increasing wind speed might be due to the decreasing role of viscous effectsand streamlining of the vegetation, although these effects cannot be isolated from existing atmospheric data.For weak winds, both the mean flow and the stress vector often meander significantly in response to mesoscale motions. The relationship between meandering of the stress and wind vectors is examined. For weak winds, the drag coefficient can be sensitive to the method of calculation, partly due to meandering of the stress vector.     

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.     

étude expérimentale de la couche limite au-dessus d'un relief modéré proche d'une chaîne de montagne

For the heterogeneous site described in the first part, some aspects of the turbulent structure of the planetary boundary layer are studied. Using mixed-layer scaling, the normalized profiles are compared with those obtained over flat terrain during convective conditions. The measurements were made with the same instrumented aircraft at both sites. The dissipative and spectral length scales are smaller over complex terrain within the whole boundary layer. This is due to the shifting of the wavelength peak toward the high frequencies by dynamic turbulence.This last effect can also explain the increase of the dissipation rate over the heterogeneous site during strong wind conditions. The vertical profiles of sensible heat flux and temperature-water vapor correlation show a lack of entrainment process at the top of the boundary layer. This fact suggests that the investigated boundary layer is advected from the neighbouring plain over the complex site (plateau de Lannemezan).     

Pressure drag and effective roughness length with neutral stratification

A two-dimensional numerical mesoscale model is used to determine the pressure drag of sinoidal mountains and valleys in a neutral atmosphere. In the first part, pressure distributions and flow patterns for isolated obstacles are considered. For large aspect ratios, the pressure drag exerted by valleys becomes small compared to that of mountains. In the second part, interactions between several obstacles are investigated. For mountains, the drag on downstream obstacles is reduced considerably by the first obstacle when the obstacles are close together. For valleys there is a slight increase of the average drag exerted by each obstacle. In the limit for a large number of obstacles, average drag exerted by one mountain is equal to average drag for one valley. For smaller aspect ratios, this average drag can be entered into the resistence law from the Rossby number similarity theory to yield an effective roughness length.     

Surface pressure distribution and pressure drag on mountains

Summary A mesoscale numerical model is used to compute the different components of the pressure drag on mountains, i.e.: form drag, wave drag, hydrostatic drag, and total pressure drag, for stable stratification. The Froude number is chosen so that non-breaking lee-waves evolve.The paper explains how the different parts of the drag are computed from the numerical results and how they form part of the horizontal momentum budget.For a single mountain the drag from the evolving stationary solution is compared to the wave drag from linear inviscid theory. Wave drag turns out to be about one third of the value expected from linear theory, and nonlinear interaction between wave and form drag is found. Wave drag is responsible for about 75% of the total drag if blocking is negligible.For two obstacles with varying distance the wave drag in the stationary solution varies between 5% and 30% of the value from linear theory due to partial cancellation between the lee-waves from the two mountains.Finally in an instationary simulation the passage of a cold air mass over a mountain and the respective drag components have been computed. 1500 m above the crestline of the obstacle wave drag is only 10% to 30% of the total drag.From the present results it seems realistic that wave drag from ALPEX experimental data was only a few percent of the value expected from the surface pressure distribution and from linear theory.With 7 Figures     

2021年夏季长白山麓雨滴谱分布特征

利用2021年6—8月吉林靖宇Parsivel2型雨滴谱观测数据,研究长白山麓夏季不同降水类型和不同降水强度条件下雨滴谱特征,并与国内外研究对比。结果表明:长白山麓夏季降水雨滴直径对降水量贡献呈先增大后减小的趋势,贡献较大的直径区间为0.812~2.375 mm,随着降水强度增大,大雨滴(直径D≥2.75 mm)对降水量贡献也增大;对流降水比层云降水的雨滴谱更宽,雨滴数浓度及平均直径也更大;与国外经典对流降水雨滴谱相比,长白山麓对流降水标准截距参数lgNw及质量等效直径Dm特征更接近海洋型降水,与北京延庆及大兴、安徽滁州、江苏浦口相比,长白山麓夏季降水雨滴具有较小的直径和较大的数浓度;长白山麓夏季对流降水和层云降水反射率因子Z与降水强度R拟合关系分别为Z=290.64R1.27和Z=193.36R1.65,经典Z-R关系对该地区降水估测存在低估;形状参数μ、斜率参数Λ存在较好的二项式拟合关系。     

Flow Over Hills with Variable Roughness

The effect of variable roughness length upon the flow characteristics over hills is investigated. The changes considered herein cover a range of flow configurations such as the change from a forested (rough) valley with a moderately smooth hilltop to a grassy valley (smooth) with a “spiky” (rough) mountain top. The effect of moving the roughness with respect to the hill is also considered. Although many of the flow features change when the position of the roughness change is varied with respect to the hill these changes have very little impact upon the global properties used within orographic drag parametrization schemes.     

对流边界层中过山气流的数值模拟

采用ARPS4.0非静力中尺度气象模式模拟了对流边界层中气流过山引起的地形波,讨论了地形及大气条件改变对其的影响.模拟表明,当大气边界层是对流边界层时,气流过山引起的地形强迫,仍能在上部稳定层结中造成足够的垂直扰动,产生向上传播的重力内波,重力内波引起的波动阻力仍不可忽略.     

对流云街激发的重力波和波动阻力

大气边界层中的对流活动,可以在其上部稳定层中激发出重力波,并引起垂直动量输送,影响到对流层和平流层中的动量平衡过程.从二层模式中大气波动方程的线性解出发,得出了对流云街激发的重力波波阻解析表达式,并讨论了大气条件对波阻的影响.这些分析可有助于大气环流模式(GCM)中此类重力波波阻参数化表达式的建立和改进.     

Turbulent Pressure and Velocity Perturbations Induced by Gentle Hills Covered with Sparse and Dense Canopies

How the spatial perturbations of the first and second moments of the velocity and pressure fields differ for flow over a train of gentle hills covered by either sparse or dense vegetation is explored using large-eddy simulation (LES). Two simulations are investigated where the canopy is composed of uniformly arrayed rods each with a height that is comparable to the hill height. In the first simulation, the rod density is chosen so that much of the momentum is absorbed within the canopy volume yet the canopy is not dense enough to induce separation on the lee side of the hill. In the second simulation, the rod density is large enough to induce recirculation inside the canopy on the lee side of the hill. For this separating flow case, zones of intense shear stress originating near the canopy-atmosphere interface persist all the way up to the middle layer, ‘contaminating’ much of the middle and outer layers with shear stress gradients. The implications of these persistent shear-stress gradients on rapid distortion theory and phase relationships between higher order velocity statistics and hill-induced mean velocity perturbations (Δu) are discussed. Within the inner layer, these intense shear zones improve predictions of the spatial perturbation by K-theory, especially for the phase relationships between the shear stress (~ ?Δu/?z) and the velocity variances, where z is the height. For the upper canopy layers, wake production increases with increasing leaf area density resulting in a vertical velocity variance more in phase with Δu than with ?Δu/?z. However, background turbulence and inactive eddies may have dampened this effect for the longitudinal velocity variance. The increase in leaf area density does not significantly affect the phase relationship between mean surface pressure and topography for the two simulations, though the LES results here confirm earlier findings that the minimum mean pressure shifts downstream from the hill crest. The increase in leaf area density and associated flow separation simply stretches this difference further downstream. This shift increases the pressure drag, the dominant term in the overall drag on the hill surface, by some 15%. With regards to the normalized pressure variance, increasing leaf area density increases ${\sigma_p/u_{*}^{2}}$ near the canopy top, where u _* is the longitudinally averaged friction velocity at the canopy top and σ _p is the standard deviation of the pressure fluctuations. This increase is shown to be consistent with a primitive scaling argument on the leading term describing the mean-flow turbulent interaction. This scaling argument also predicts the spatial variations in σ _p above the canopy reasonably well for both simulations, but not inside the canopy.     

地形湍流拖曳力参数化及在GRAPES中的应用

分辨率的限制使得不能被模式识别的地形称为次网格尺度地形,次网格尺度地形在热力和动力方面对实际大气有着不可忽略的作用,其效应只能通过参数化的形式回馈给模式。分辨率的提高使得与较小尺度地形相联系的地形湍流拖曳力凸显其重要性。数值模式中地形湍流拖曳力的参数化对完善模式物理过程和改善模式近地层预报效果具有积极意义,其方法包括有效粗糙度法和直接参数化法,而GRAPES模式中并未以任何方法考虑次网格尺度地形的影响。该文通过单柱模式比较了有效粗糙度法和直接参数化法的优劣, 发现后者在有些方面优于前者。最后,将应用于实际的一个直接参数化方案接入GRAPES中尺度模式中,进行个例模拟,并与NCEP再分析资料进行对比,结果表明:考虑地形湍流拖曳力方案对模式预报具有改进作用,尤其对局地低层风场具有积极影响。     

江淮夏季对流云合并发生的天气学条件

应用NCEP再分析资料,根据2005—2006年江淮地区夏季33个对流云合并的个例发生的条件和环流背景分析研究,得出了对流云合并发生的5种天气系统类型：华北槽前型、华北槽后型、副高内部型、副高外部型和东风系统型;不同的天气系统类型触发对流云合并的热力学和动力学物理条件也不同;山区地形对地面气温和能量的影响与对流云的发生和合并有密切关系。