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.     

Aerodynamic roughness of the sea surface at high winds

The role of the surface roughness in the formation of the aerodynamic friction of the water surface at high wind speeds is investigated. The study is based on a wind-over-waves coupling theory. In this theory waves provide the surface friction velocity through the form drag, while the energy input from the wind to waves depends on the friction velocity and the wind speed. The wind-over-waves coupling model is extended to high wind speeds taking into account the effect of sheltering of the short wind waves by the air-flow separation from breaking crests of longer waves. It is suggested that the momentum and energy flux from the wind to short waves locally vanishes if they are trapped into the separation bubble of breaking longer waves. At short fetches, typical for laboratory conditions, and strong winds the steep dominant wind waves break frequently and provide the major part of the total form drag through the air-flow separation from breaking crests, and the effect of short waves on the sea drag is suppressed. In this case the dependence of the drag coefficient on the wind speed is much weaker than would be expected from the standard parameterization of the roughness parameter through the Charnock relation. At long fetches, typical for the field, waves in the spectral peak break rarely and their contribution to the air-flow separation is weak. In this case the surface form drag is determined predominantly by the air-flow separation from breaking of the equilibrium range waves. As found at high wind speeds up to 60 m s⁻¹ the modelled aerodynamic roughness is consistent with the Charnock relation, i.e. there is no saturation of the sea drag. Unlike the aerodynamic roughness, the geometrical surface roughness (height of short waves) could be saturated or even suppressed when the wind speed exceeds 30 m s⁻¹.     

Air-sea interaction including a shallow and coastal zone

We performed special experimental and theoretical research concerning the energy--mass exchange process in shallow waters, which took into account the influence of the basin depth on the evaporation and sensible heat exchange. Data was obtained from deep water basins, as well as from shallow waters, at an open sea, as well as in its coastal zone. A new parameterization model of evaporation and friction velocity from shallow water surfaces under different wind velocities was investigated. Results of models and measurements of the energy/mass exchange intensity of a small shallow lake (LITFASS-experiments) were compared. The validation of these models with the eddy-covariance measurements of the LITFASS-98 and LITFASS-2003 experiments showed good results for the wind sector, with good fetch conditions. Therefore, the models examined may be used for calculating the evaporation of lakes where a standard data set of wind velocity, air and water temperature, air moisture and the depth of the lake is available. It should be remembered that in a coastal zone the roughness of the water surface is transformed and therefore there are additional calculation difficulties for the intensity of the energy-mass exchange. Based on our experimental data of the basin depth influence on the water-atmosphere exchange, a new model for the calculation of the energy-mass exchange in a coastal zone was developed. Our new model in combination with the empirical dependence for the calculation of the energy-mass exchange in a coastal zone allows calculation of the momentum, heat and humidity fluxes values at different distances from a shore.     

近水面层温、湿、风廓线和湍流交换规律

本文分析了官厅水库近水面层的温、湿、风廓线规律,指出水面的波浪状况对廓线规律有影响。给出了中性层结时水面粗糙度、动力摩擦速度及阻力系数与风速和浪高的关系。得出了适用于水面的层结订正函数。还分析了不稳定层结条件下的温度廓线规律,并对温、湿、风廓线的相似性问题进行了讨论。     

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.     

TESTING DRAG COEFFICIENT APPROACHES BY USING THE BUOY DATA COLLECTED IN MODERATE TO HIGH WIND UNDER FOLLOWING, CROSSING AND OPPOSING SWELL CONDITIONS

Hurricane intensity and track are strongly affected by air-sea interactions. Classified as following swells, crossing swells, and opposing swells, the observed wave height was parameterized by using the 10-m wind speed collected on 5 buoys by the National Buoy Data Center during 13 hurricane events. The path information of these 13 hurricanes was obtained from the National Hurricane Center Best Track (NHC-BT). Results show that the wave height increases exponentially with the 10-m wind speed, and the wave height reaches the maximum value, 11.2 m (8.1 m), when 10-m wind speed is 40 m s-1 under the following and crossing (opposing) swell conditions. We find that the wave steepness (the ratio of wave height to wave length) is proportional to the -2/3 power of the wave age (the ratio of wave phase velocity to 10-m wind speed). The parameterizations of friction velocity and drag coefficient are tested using the buoy data collected in moderate to high wind under following, crossing and opposing swell conditions. A wave age dependent equation for drag coefficient is found more accurate and suggested for future usage in numerical models. Further, these algorithms also suggest that wind-swell orientation needs to be considered to retrieve accurate surface drag under high winds and strong swells.     

海气界面动量通量算法的改进

COARE（Coupled Ocean-Atmosphere Response Experiment）算法是国际上较先进的计算海气界面通量的算法。最新的COARE 3.0算法包含TY01方案和O02方案两种考虑真实海浪状态的海面空气动力学粗糙度方案;当有效波高和谱峰周期缺省时,利用Taylor01风浪特征量参数化方案可对它们进行参数化。在此基础上引入自主设计的WHP（Wind-wave significant wave Height and dominant wave Period）风浪特征量参数化方案和三种海面空气动力学粗糙度方案,即SCOR方案、GW03方案、PYP07方案以及更简单的Andreas12、Vickers15摩擦速度算法,利用NDBC（National Data Buoy Center）浮标数据、解放军理工大学风浪流水槽实验数据,针对中高风速条件（10 m/s≤U₁₀≤25 m/s）比较上述方案对摩擦速度的预测效果。结果表明:WHP方案在COARE 3.0算法中的应用效果优于Taylor01方案,且新引入的SCOR、GW03、PYP07海面粗糙度方案对风浪特征量的观测误差敏感性更小、稳定度更高;水槽实测数据的对比结果表明,WHP方案结合SCOR海面粗糙度方案计算的摩擦速度与实测值最接近;引入其他三种实测数据的检验结果表明,原始COARE 3.0算法会低估摩擦速度,而WHP方案结合SCOR海面粗糙度方案能更准确地预测摩擦速度随10 m风速的增长趋势。      

Drag coefficient modeling for the near coastal zone

Using the JONSWAP spectrum for describing the surface wave state in the near coastal zone, models for the roughness length and the drag coefficient are used to simulate the dependence of the wind stress on fetch and depth. The results of each model are then compared with a compiled set of past investigations of the neutral drag coefficient over a variety of conditions. It is found that the models of Donelan, Hsu, and Kitaigorodskii correctly predict the trends in the drag coefficient with fetch and depth. Although it did not account for all the observed variations in the neutral drag coefficient. Kitaigorodskii's model, when incorporating the JONSWAP spectrum, more accurately simulated the slopes of the various C_DN regressions against windspeed.     

Near Wall Flow over Urban-like Roughness

In this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s^-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry.The results haveconfirmed the strong three-dimensionalityof the turbulent flow inthe roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can,together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves.The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the `roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates.     

不同下垫面空气动力学参数的研究

文中利用中国科学院沙漠研究所与日本国家农业环境技术研究所合作于1990—1994年在中国内蒙古自治区奈曼市半干旱地区沙丘和植被区下垫面观测的微气象数据,根据Monin-Obukhov相似性理论,计算了重度干扰草原、中度干扰草原、轻度干扰草原、无干扰草原、沙丘、沙丘内地、草地、稻田、小麦田、大豆田和玉米田11种下垫面的空气动力学参数粗糙度长度z0,零平面位移d,摩擦速度u*,并分析了它们与水平风速u和Richardson数的关系,比较了不同人为干扰草原生态系统条件下的空气动力学特征。结果表明:地表生物量和覆盖率随着人为干扰强度的增加而减少。不同人为干扰下垫面的粗糙长度与生物量和植被高度以及地表起伏程度有着密切关系;Richardson数也是其影响因子。风速、粗糙度都与摩擦速度成正相关,但对于不同下垫面有所不同,从中可以看到草地对沙漠化有一定的防治作用。同一种下垫面不同时期的空气动力学参数也存在差异。这些结果对建立陆面过程和区域气候模式具有重要的意义。     

On the impact of thermal stability on some rough flow effects over mobile surfaces

Calculations are made of the effects of thermal stability under a range of conditions, over the sea and land, on the physical factors (including the critical wind speed) affecting dust-storm generation, snow drift, and rough sea conditions. The computational procedure involves the surface friction velocity, u _*, and its relation with the aerodynamic roughness over aerodynamically rough, mobile surfaces. The results indicated that even at relatively high wind speeds, thermal effects under extreme advection situations may be significant, particularly for those properties of the agitated surface dependent on u _* ³ and u _* ⁴.     

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

Although the bulk aerodynamic transfer coefficients for sensible (C _H ) and latent (C _E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C _H and C _E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C _E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s^–1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10^–3 and 1.5 × 10^–3.     

Using Temperature Fluctuation Measurements to Estimate Meteorological Inputs for Modelling Dispersion During Convective Conditions in Urban Areas

We examine the performance of several methods to estimate meteorological inputs for modelling dispersion in urban areas during convective conditions. Sensible heat flux, surface friction velocity and turbulent velocities are estimated from measurements of mean wind speed and the standard deviation of temperature fluctuations at a single level on a tower at two suburban sites and at one urban site in Riverside, California. These estimates are compared with observations made at these sites during a field study conducted in 2007. The sensible heat flux is overestimated in the urban area, while it is underestimated at a suburban site when temperature fluctuations are used in the free convection formulation to estimate heat flux. The bias in heat flux estimates can be reduced through a correction that depends on stability. It turns out that the bias in heat flux estimates has a minor effect on the prediction of surface friction velocity and turbulent velocities. Estimates of sensible heat flux, surface friction velocity and turbulent velocities are sensitive to estimates of aerodynamic roughness length, and we suggest estimating the aerodynamic roughness length through detailed micrometeorological measurements made during a limited field study. An examination of the impact of the uncertainty in estimating surface micrometeorology on concentrations indicates that, at small distances from a surface release, ground-level concentrations computed using estimates of heat flux and surface friction compare well with the those based on observed values: the bias is small and the 95% confidence interval of the ratio of the two concentrations is 1.7. However, at distances much larger than the Obukhov length, this confidence interval is close to 2.3 because errors in both friction velocity and heat flux affect plume spread. Finally, we show that using measurements of temperature fluctuations in estimating heat flux is an improvement on that based on the surface energy balance, even when net radiation measurements are available.     

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.     

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.     

Wind profiles,momentum fluxes and roughness lengths at Cabauw revisited

We describe the results of an experiment focusing on wind speed and momentum fluxes in the atmospheric boundary layer up to 200 m. The measurements were conducted in 1996 at the Cabauw site in the Netherlands. Momentum fluxes are measured using the K-Gill Propeller Vane. Estimates of the roughness length are derived using various techniques from the wind speed and flux measurements, and the observed differences are explained by considering the source area of the meteorological parameters. A clear rough-to-smooth transition is found in the wind speed profiles at Cabauw. The internal boundary layer reaches the lowest k-vane (20 m) only in the south-west direction where the obstacle-free fetch is about 2 km. The internal boundary layer is also reflected in the roughness lengths derived from the wind speed profiles. The lower part of the profile (< 40 m) is not in equilibrium and no reliable roughness analysis can be given. The upper part of the profile can be linked to a large-scale roughness length. Roughness lengths derived from the horizontal wind speed variance and gustiness have large footprints and therefore represent a large-scale average roughness. The drag coefficient is more locally determined but still represents a large-scale roughness length when it is measured above the local internal boundary layer. The roughness length at inhomogeneous sites can therefore be determined best from drag coefficient measurements just above the local internal boundary layers directly, or indirectly from horizontal wind speed variance or gustiness. In addition, the momentum and heat fluxes along the tower are analysed and these show significant variation with height related to stability and possibly surface heterogeneity. It appears that the dimensionless wind speed gradients scale well with local fluxes for the variety of conditions considered, including the unstable cases.     

Characteristics of the Drag Coefficient in the Roughness Sublayer over a Complex Urban Surface

The statistics of momentum exchange in the urban roughness sublayer are investigated. The analysis focuses on the characteristics of the dimensionless friction velocity, \({u_{*}}/U\) , which is defined as the square root of the drag coefficient. The turbulence observations were made at a height of 47 m above the ground on the 325-m meteorological tower, which is located in a very inhomogeneous urban area in Beijing. Under neutral conditions, the dependence of the drag coefficient on wind speed varies with wind direction. When the airflow is from the area of densely built-up buildings, the drag coefficient does not vary with wind speed, while when the airflow is from the area covered by vegetation, the drag coefficient appears to decrease with increasing wind speed. Also, the drag coefficient does not vary monotonically with the atmospheric stability. Both increasing stability and increasing instability lead to the decrease of the drag coefficient, implying that the roughness length and zero-plane displacement may vary in urban areas.     

Study of Aerodynamic Parameters on Different Underling Surfaces

Aerodynamic parameters including the zero-plane displacement (d), roughness length (20), and friction velocity (u*) on the different underlying surfaces of heavy-grazing site, medium-grazing site, light-grazing site, no-grazing site, dune, inter-dune, grassland, rice paddy site, wheat site, soybean site, and maize site have been computed based on the Monin-Obukhov similarity theory by utilizing the micrometeorologically observed data of dune and vegetation in the semi-arid area at Naiman, Inner Mongolia of China, conducted jointly by the Institute of Desert Research, Chinese Academy of Sciences and the National Institute of Agro-Environmental Sciences of Japan in 1990-1994. And their relationships between wind speed and Richardson number are analyzed. The aerodynamic characteristics of different man-made disturbed grassland ecosystems are also compared. Result shows that the vegetation coverage and the above-ground biomass decrease with the increase in man-made stress of the grassland. The roughness length for different underlying surfaces is closely related to vegetation height, above-ground biomass, and ground surface undulation, and Richardson number Ri is also its influencing factor. The friction velocity varies largely on different underlying surfaces, and it is positively proportional to wind speed and roughness length. The aerodynamic parameters of various times on the same underlying surface are different, too. Above results indicate that grassland and vegetation are of significance in preventing desertification, especially in the arid and semi-arid land ecosystems. And the results of this paper are also important for constructing the land surface physical process as well as regional climate model.     

Improvement and Application of the Similarity Saltation Model: Wind-Tunnel Experimental Investigation and Numerical Simulation of the Vertical Sand Mass Flux Distribution in the Saltation Layer

Based upon comparisons between published experimental data and simulated results on the vertical sand flux distribution in the saltation layer, Shao’s similarity saltation model has been greatly improved by correcting the average vertical particle lift-off velocity and using a more suitable universal roughness length. By the improved model, the vertical sand flux profile over the bare, dry and loose uniform sandy surface, which is quite representative of real desert surfaces, can be reproduced very well. Meanwhile, the surface transport rate and the characteristic and average saltation heights have been simulated and analyzed in detail, disclosing their relationships with friction velocity, particle size and roughness length, and the possible underlying mechanisms. Besides, the average particle lift-off velocity and the average mean vertical aerodynamic action upon the ascending particle, which determine the saltation process, are explicitly expressed by parameters involved in the similarity model, and their relationships with friction velocity, particle size and roughness length are also described concisely. The corrected average particle lift-off velocity makes it possible to investigate the characteristic particle trajectory, whose initial velocity equals the average lift-off velocity, so as to estimate the average particle against surface impacting velocity and the average aerodynamic action upon the saltation process.     

The influence of atmospheric stratification on the growth of water waves

The atmospheric surface layer over sea has a density stratification which varies with moisture content and air/sea temperature difference. This influences the growth of water waves. To study the effect quantitatively, the Reynolds equations are solved numerically. For given wind speed and surface roughness, wave growth is found to be more rapid in unstably stratified conditions than in stable conditions. This is due to an increase in turbulence, primarily caused by an increase of mixing length.Under the assumption of a Charnock relation between surface roughness and friction velocity, it is found that for large inverse wave age (u _*/c>0.07), the effect of stratification on wave growth is weell described by Monin-Obukhov scaling of the friction velocity. For smaller values ofu _*/c, Monin-Obukhov scaling overpredicts.The effect on duration-limited wave growth is studied with the third-generation WAM surface wave model driven by 10 m winds. Effects of stratification on the significant wave height are found to be of the order of 10%. The results are comparable to those of a recent reanalysis of field measurements, although the measured stratification effect is somewhat stronger. Implementation of a stratification-dependent growth in wave models is recommended, as it can lead to small but significant improvements in wave forecasts when accurate air and sea temperatures are available.