On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow

Predictions of the surface drag in turbulent boundary-layer flow over two-dimensional sinusoidal topography from various numerical models are compared. For simple 2D terrain, the model results show that the drag increases associated with topography are essentially proportional to (slope)² up to the steepness at which the flow separates. For the purposes of boundary-layer parameterisation within larger-scale models, we propose a representation of the effects of simple 2D topography via an effective roughness length, z ₀ ^eff. The form of the varation of z ₀ ^eff with terrain slope and topographic wavelength is established for small slopes from the model results and a semi-empirical formula is proposed.     

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.     

Measurements Of Thermal Updraft Intensity Over Complex Terrain Using American White Pelicans And A Simple Boundary-Layer Forecast Model

An examination of boundary-layer meteorological and avian aerodynamic theories suggests that soaring birds can be used to measure the magnitude of vertical air motions within the boundary layer. These theories are applied to obtain mixed-layer normalized thermal updraft intensity over both flat and complex terrain from the climb rates of soaring American white pelicans and from diagnostic boundary-layer model-produced estimates of the boundary-layer depth z_i and the convective velocity scale w_*. Comparison of the flatland data with the profiles of normalized updraft velocity obtained from previous studies reveals that the pelican-derived measurements of thermal updraft intensity are in close agreement with those obtained using traditional research aircraft and large eddy simulation (LES) in the height range of 0.2 to 0.8 z_i. Given the success of this method, the profiles of thermal vertical velocity over the flatland and the nearby mountains are compared. This comparison shows that these profiles are statistically indistinguishable over this height range, indicating that the profile for thermal updraft intensity varies little over this sample of complex terrain. These observations support the findings of a recent LES study that explored the turbulent structure of the boundary layer using a range of terrain specifications. For terrain similar in scale to that encountered in this study, results of the LES suggest that the terrain caused less than an 11% variation in the standard deviation of vertical velocity.     

Temporal and Spatial Variations of the Aerodynamic Roughness Length in the Ablation Zone of the Greenland Ice Sheet

To understand the response of the Greenland ice sheet to climate change the so-called ablation zone is of particular importance, since it accommodates the yearly net surface ice loss. In numerical models and for data analysis, the bulk aerodynamic method is often used to calculate the turbulent surface fluxes, for which the aerodynamic roughness length (z ₀) is a key parameter. We present, for the first time, spatial and temporal variations of z ₀ in the ablation area of the Greenland ice sheet using year-round data from three automatic weather stations and one eddy-correlation mast. The temporal variation of z ₀ is found to be very high in the lower ablation area (factor 500) with, at the end of the summer melt, a maximum in spatial variation for the whole ablation area of a factor 1000. The variation in time matches the onset of the accumulation and ablation season as recovered by sonic height rangers. During winter, snow accumulation and redistribution by snow drift lead to a uniform value of z ₀≈ 10⁻⁴ m throughout the ablation area. At the beginning of summer, snow melt uncovers ice hummocks and z ₀ quickly increases well above 10⁻² m in the lower ablation area. At the end of summer melt, hummocky ice dominates the surface with z ₀ > 5  ×  10⁻³ m up to 60 km from the ice edge. At the same time, the area close to the equilibrium line (about 90 km from the ice edge) remains very smooth with z ₀ = 10⁻⁵ m. At the beginning of winter, we observed that single snow events have the potential to lower z ₀ for a very rough ice surface by a factor of 20 to 50. The total surface drag of the abundant small-scale ice hummocks apparently dominates over the less frequent large domes and deep gullies. The latter results are verified by studying the individual drag contributions of hummocks and domes with a drag partition model.     

Formation of horizontal convective rolls in urban areas

The formation of horizontal convective rolls (HCRs) in urban areas is investigated in this paper using observations and fine-scale numerical simulations. Cloud streets organized parallel to the mean boundary-layer wind (a manifestation of HCRs) are seen in the Fengyun-2C satellite imagery around local noon in Beijing. Observed vertical velocity and horizontal wind fields from an urban wind profiler suggest that the time scale for alternating updraft and downdraft in the boundary layer is about 30 min, and the length of the updraft/downdraft is about 9 km. Numerical simulations show that most HCRs occur in the urban areas with − z_i / L < 25 (z_i: the boundary-layer depth, L: the Monin–Obukhov length). Sensitivity tests reveal that HCRs are common in urban boundary layers, while rural areas are more conducive to forming cellular convection; the aspect ratio of HCRs in urban areas is smaller than the typical value over natural landscapes.     

Momentum flux of stratospheric gravity waves generated by Typhoon Ewiniar(2006)

The momentum flux of stratospheric gravity waves generated by Typhoon Ewiniar (2006) is examined using a Weather Research and Forecasting (WRF) model. In the stratosphere, zonal momentum flux with a positive sign by eastward-propagating waves is significant during the northward moving of the typhoon, while both zonal and meridional momentum fluxes with positive signs are significant during the typhoon decaying stage in which the typhoon moves northeastward. The magnitude of the momentum flux is greater during the mature stage of the typhoon than the decaying stage, and the phase speeds of the dominant momentum flux are less than 30 m s^?1 with a peak at 10–16 m s^?1. Positive momentum flux decreases with height overall in the stratosphere for both zonal and meridional components. The resultant gravity-wave drag forcing plays a role to decelerate the easterly background wind in the stratosphere. This drag forcing is relatively large above z = 40 km and below z = 20 km, and lower stratospheric wave drag is expected to affect the typhoon dynamics by modifying the background wind shear and inducing the secondary circulation in the troposphere.     

The Parameterisation of Scalar Transfer over Rough Ice

We test a surface renewal model that is widely used over snow and ice surfaces to calculate the scalar roughness length (z _s ), one of the key parameters in the bulk aerodynamic method. For the first time, the model is tested against observations that cover a wide range of aerodynamic roughness lengths (z ₀). During the experiments, performed in the ablation areas of the Greenland ice sheet and the Vatnajökull ice cap in Iceland, the surface varied from smooth snow to very rough hummocky ice. Over relatively smooth snow and ice with z ₀ below a threshold value of approximately 10^?3 m, the model performs well and in accord with earlier studies. However, with growing hummock size, z ₀ increases well above the threshold and the bulk aerodynamic flux becomes significantly smaller than the eddy-correlation flux (e.g. for z ₀ = 0.01 m, the bulk aerodynamic flux is about 50% smaller). Apparently, the model severely underpredicts z _s over hummocky ice. We argue that the surface renewal model does not account for the deep inhomogeneous roughness sublayer (RSL) that is generated by the hummocks. As a consequence, the homogeneous substrate ice grain cover becomes more efficiently ‘ventilated’. Calculations with an alternative model that includes the RSL and was adapted for use over hummocky ice, qualitatively confirms our observations. We suggest that, whenever exceedance of the threshold occurs (z ₀  >  10^?3 m, i.e., an ice surface covered with at least 0.3-m high hummocks), the following relation should be used to calculate scalar roughness lengths, ln (z _s /z ₀)  =  1.5  ? 0.2 ln (Re _*)  ? 0.11(ln (Re _*))².     

Estimation of atmospheric surface layer parameters and numerical simulation using MM5 at Mangalore, West Coast of India

Atmospheric surface layer meteorological observations obtained from 20-m-high meteorological tower at Mangalore, situated along the west coast of India are used to estimate the surface layer scaling parameters of roughness length (z _o) and drag coefficient (C _D), surface layer fluxes of sensible heat and momentum. These parameters are computed using the simple flux–profile relationships under the framework of Monin–Obukhov (M–O) similarity theory. The estimated values of z _o are higher (1.35–1.54 m) than the values reported in the literature (>0.4–0.9 m) probably due to the undulating topography surrounding the location. The magnitude of C _D is high for low wind speed (<1.5 m s^?1) and found to be in the range 0.005–0.03. The variations of sensible heat fluxes (SHF) and momentum fluxes are also discussed. Relatively high fluxes of heat and momentum are observed during typical days on 26–27 February 2004 and 10–11 April 2004 due to the daytime unstable atmospheric conditions. Stable or near neutral conditions prevail after 1700 h IST with negative SHF. A mesoscale model PSU/NCAR MM5 is run using a high-resolution (1 km) grid over the study region to examine the influence of complex topography on the surface layer parameters and the simulated fluxes are compared with estimated values. Spatial variations of the frictional velocity (u _*), C _D, surface fluxes, planetary boundary layer (PBL) height and surface winds are noticed according to the topographic variations in the simulation.     

An interpolation method of randomly distributed atmospheric data in the height-time domain

A numerical method for objective interpolation of boundary-layer data in the height-time domain is presented. The method is based on a diffusive transport hypothesis and allows for the determination of the optimal ratio between the height and time scales to be used for non-dimensionalising the independent variables z and t. This ratio, with dimensions of a velocity, may be related to the vertical transfer properties of the atmosphere. A few cases during springtime with different stability conditions are discussed, showing that this ratio varies by at least one order of magnitude between day and night.     

Aircraft estimates of the geostrophic drag coefficient and the rossby similarity functions A and B over the sea

Estimates of the geostrophic drag coefficient and the Rossby similarity functions, A and B obtained from data collected by an instrumented aircraft over the sea are presented. The average value of the geostrophic drag coefficient is 0.027 and is independent of the geostrophic windspeed. The dependence of the similarity functions A and B on boundary-layer parameters is investigated. The function A is found to depend on baroclinicity parameters, while B depends on the parameter u _*/fh (where u _* is the surface friction velocity, f is the Coriolis parameter, and h is the boundary-layer depth). Using the geostrophic drag coefficient found here and the results of surface drag coefficient studies, a relationship between geostrophic windspeed and surface windspeed is obtained which shows good agreement with empirical data.     

Impact of terrain complexity on the turbulence drag coefficient: A case study from the Indian Himalayan region

The aerodynamic drag coefficient (C_D) is conjectured to change (or remains almost uniform) with the horizontal wind speed (U) over a flexible (or fixed) surface element, which is represented with the surface roughness (z₀). This conjecture is tested for the near neutral atmospheric turbulence (i.e. when surface stability z/L is almost equal to 0, where z is the measurement height and L is Obukhov length) of monsoon and winter season at an on-slope and a ridge-top site in the Indian Himalaya, wherein the ridge-top site is associated with a higher degree of sensitivity to the roughness element and terrain attributes. This hypothesis is successfully verified for two conditions, (i) the monsoon period observations of ridge-top site are found to have higher z₀ due to vegetative growth than the winter period for flows having similar terrain signature, and (ii) the monsoon and winter period observations of on-slope site are noted to have similar z₀ for flows having signature of steep terrain. Subsequently, constants (i.e. a and b) of the power-law relationships between C_D and U (i.e. C_D = aU^b), as a function of z₀, are optimized. It is noted that the relationship between C_D and U has higher sensitivity towards the terrain slope than the vegetative growth.     

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.     

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375?C395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u _*/u _*R , where u _* is the friction velocity and u _*R is the friction velocity from the uniform building height case, is expressed well as an algebraic function of ?? and ?? _h /h _m , where ?? is the frontal area index, ?? _h is the standard deviation of the building height, and h _m is the mean building height. The simulations also resulted in a simple algebraic relation for z ₀/z _0R as a function of ?? and ?? _h /h _m , where z ₀ is the aerodynamic roughness length and z _0R is z ₀ found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.     

The impact of the PBL scheme and the vertical distribution of model layers on simulations of Alpine foehn

Summary This paper investigates the influence of the planetary boundary-layer (PBL) parameterization and the vertical distribution of model layers on simulations of an Alpine foehn case that was observed during the Mesoscale Alpine Programme (MAP) in autumn 1999. The study is based on the PSU/NCAR MM5 modelling system and combines five different PBL schemes with three model layer settings, which mainly differ in the height above ground of the lowest model level (z ₁). Specifically, z ₁ takes values of about 7 m, 22 m and 36 m, and the experiments with z ₁ = 7 m are set up such that the second model level is located at z = 36 m. To assess if the different model setups have a systematic impact on the model performance, the simulation results are compared against wind lidar, radiosonde and surface measurements gathered along the Austrian Wipp Valley. Moreover, the dependence of the simulated wind and temperature fields at a given height (36 m above ground) on z ₁ is examined for several different regions. Our validation results show that at least over the Wipp Valley, the dependence of the model skill on z ₁ tends to be larger and more systematic than the impact of the PBL scheme. The agreement of the simulated wind field with observations tends to benefit from moving the lowest model layer closer to the ground, which appears to be related to the dependence of lee-side flow separation on z ₁. However, the simulated 2 m-temperatures are closest to observations for the intermediate z ₁ of 22 m. This is mainly related to the fact that the simulated low-level temperatures decrease systematically with decreasing z ₁ for all PBL schemes, turning a positive bias at z ₁ = 36 m into a negative bias at z ₁ = 7 m. The systematic z ₁-dependence is also observed for the temperatures at a fixed height of 36 m, indicating a deficiency in the self-consistency of the model results that is not related to a specific PBL formulation. Possible reasons for this deficiency are discussed in the paper. On the other hand, a systematic z ₁-dependence of the 36-m wind speed is encountered only for one out of the five PBL schemes. This turns out to be related to an unrealistic profile of the vertical mixing coefficient. Correspondence: Günther Z?ngl, Meteorologisches Institut der Universitat München, 80333 München, Germany     

Estimating the baroclinic Rossby radius of deformation in the Sea of Okhotsk

The first baroclinic Rossby radius of deformation (R ₁) in the Sea of Okhotsk is estimated using the hydrological datasets from the World Ocean Atlas (WOA) 2001 and WOA 2013. It is established that the maximum values of R ₁ are observed over the Kuril Basin (18–20 km), and its minimum values (1.5–2 km), over the northern shelf of the Sea of Okhotsk. In the central part of the sea R1 varies from 8 to 10 km. The seasonal variability of R1 for both datasets is characterized by the minima in winter and by the maxima in summer. It was found that on the eastern shelf of Sakhalin Island R ₁ reaches the maximum both in November (～6 km) and in April (～4-5 km). According to the obtained estimates of R ₁, the model grid resolution of 3 to 8 km should be used for the eddy-permitting numerical simulation of circulation in the Sea of Okhotsk, and the model grid resolution from 1.5 to 2 km, for the explicit simulation of mesoscale variability.     

Variability of surface roughness and turbulence intensities at a coastal site in India

Surface-layer features with different prevailing wind directions for two distinct seasons (Southwest Monsoon and Northeast Monsoon) on the west coast of India are studied using data obtained from tower-based sensors at a site located about 500 m from the coast. Only daytime runs have been used for the present analysis. The surface boundary-layer fluxes have been estimated using the eddy correlation method. The surface roughnessz ₀ obtained using the stability-corrected wind profiles (Paulson, 1970) has been found to be low for the Southwest monsson season. For the other season,z ₀ is relatively high. The drag coefficientC _D varies with height in the NE monsoon season but not in the season with lowz ₀. This aspect is reflected in the wind profiles for the two seasons and is discussed in detail. The scaling behaviour of friction velocityu _* and the turbulence intensity of longitudinal, lateral and vertical winds _u, _v and _w, respectively) are further examined to study their dependence on fetch. Our study shows that for the non-dimensional case, _u/u_* and _v/u_* do not show any surface roughness dependence in either season. On the other hand, for _w/u_* for the season with lowz ₀, the values are seen to agree well with that of Panofskyet al. (1977) for homogeneous terrain whereas for the other season with highz ₀, the results seem to conform more to the values observed by Smedman and Högström (1983) for coastal terrain. The results are discussed in the light of observations by other investigators.     

Turbulent Flow at 190 m Height Above London During 2006–2008: A Climatology and the Applicability of Similarity Theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ _i /u _* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.