Spectra of temperature derivatives in the atmospheric surface layer

Measured spectra ofθ _x,θ _y,θ _z, the derivatives of temperature in streamwise, lateral and vertical directions, respectively, indicate that the spectral densities ofθ _z andθ _y are nearly similar but significantly different from the spectral density ofθ _x. The high-frequency parts of the three spectra satisfy, in a qualitative sense, local isotropy requirements. In the high-frequency end of the inertial subrange, the relative behaviour of spectra ofθ _x,θ _y andθ _z is also consistent with local isotropy.     

Spectral scaling in a high reynolds number laboratory boundary layer

Spectra and co-spectra of the streamwise (u) and normal or vertical (w) velocity fluctuations have been measured in the inner region of a large Reynolds number laboratory boundary layer over a rough wall. There is reasonable evidence of ak ₁ ^–1 range in theu spectrum (wherek ₁ is the streamwise wavenumber). Such a range results from an overlap between a spectral region dominated by largescale, inactive motion, which scales on the boundary-layer thickness, and a region dominated by smaller-scale, active motion which scales on the distance from the wall. Spectra ofw, anduw cospectra, scale in a manner consistent with the dominance by active motion. The present spectral data do not support local isotropy over the inertial subrange. A comparison between measuredw spectra and calculations based on isotropy indicates that the inertial subrange anisotropy is only slightly affected by the magnitude of the non-dimensional mean shear.     

Large-Eddy Simulation of Flow and Pollutant Transports in and Above Two-Dimensional Idealized Street Canyons

A large-eddy simulation (LES) model, using the one-equation subgrid-scale (SGS) parametrization, was developed to study the flow and pollutant transport in and above urban street canyons. Three identical two-dimensional (2D) street canyons of unity aspect ratio, each consisting of a ground-level area source of constant pollutant concentration, are evenly aligned in a cross-flow in the streamwise direction x. The flow falls into the skimming flow regime. A larger computational domain is adopted to accurately resolve the turbulence above roof level and its influence on the flow characteristics in the street canyons. The LES calculated statistics of wind and pollutant transports agree well with other field, laboratory and modelling results available in the literature. The maximum wind velocity standard deviations σ _i in the streamwise (σ _u ), spanwise (σ _v ) and vertical (σ _w ) directions are located near the roof-level windward corners. Moreover, a second σ _w peak is found at z ≈ 1.5h (h is the building height) over the street canyons. Normalizing σ _i by the local friction velocity u _*, it is found that σ _u /u _* ≈ 1.8, σ _v /u _* ≈ 1.3 and σ _w /u _* ≈ 1.25 exhibiting rather uniform values in the urban roughness sublayer. Quadrant analysis of the vertical momentum flux u′′w′′ shows that, while the inward and outward interactions are small, the sweeps and ejections dominate the momentum transport over the street canyons. In the x direction, the two-point correlations of velocity R _v,x and R _w,x drop to zero at a separation larger than h but R _u,x (= 0.2) persists even at a separation of half the domain size. Partitioning the convective transfer coefficient Ω _T of pollutant into its removal and re-entry components, an increasing pollutant re-entrainment from 26.3 to 43.3% in the x direction is revealed, suggesting the impact of background pollutant on the air quality in street canyons.     

Drag coefficients and turbulence spectra within three boreal forest canopies

Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C _d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C _d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.     

Methodological Considerations Regarding the Measurement of Turbulent Fluxes in the Urban Roughness Sublayer: The Role of Scintillometery

We address some of the methodological challenges associated with the measurement of turbulence and use of scintillometers in the urban roughness sublayer (RSL). Two small-aperture scintillometers were located near the roof interface in a densely urbanized part of Basel, Switzerland, as part of the Basel Urban Boundary-Layer Experiment (BUBBLE) in the summer of 2002. Eddy correlation instruments were co-located near the mid-point of each scintillometer path for data verification purposes. The study presents the first values of the inner length scale of turbulence (l ₀) and the refractive index structure parameter of air for a city and demonstrates the influence of mechanical driven turbulence on dissipation. Comparison of dissipation values determined from the two approaches show large scatter that is possibly due to the spatial inhomogeneity of the turbulence statistics within the RSL. Velocity and temperature spectra display a −2/3 slope in the inertial subrange, although the spectral ratio is less than the theoretical prediction of 4/3 expected for isotropy. Conventional Monin–Obukhov equations used to calculate fluxes from the scintillometer were replaced with urban forms of the equations. The results suggest that the scintillometer may be an appropriate tool for the measurement of sensible heat flux (Q _H ) above the rooftops given a suitable determination of the effective measurement height.     

Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China

We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels.     

Time series analyses of concentration and wind fluctuations

Analyses of concentration fluctuation (C) spectra from boundary-layer smoke plume experiments at six separate locations show that the spectra from these experiments generally exhibit an inertial subrange at high frequencies with a slope of -5/3 and indicate peak energy at a time period of about 50 to 100 s. These periods of peak energy are a factor of two to five less than those for the peak of the wind speed fluctuation (u or v) spectra. A general spectral formula fits normalized spectra from the U.S. and Australia, where the frequency, n, is made dimensionless by multiplying by the plume dispersion parameter, _y , and dividing by the wind speed, u. Peak energy occurs at a dimensionless frequency of n _y/u equal to about 0.15. The Kolmogorov constant in the inertial subrange is estimated from a set of averaged spectra. Cross-spectra indicate little relation between concentration and wind fluctuations. However, most of the correlation that exists is due to periods larger than about 10 or 20 s.     

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.     

Statistics of atmospheric turbulence within a natural black spruce forest canopy

Turbulence statistics were measured in a natural black-spruce forest canopy in southeastern Manitoba, Canada. Sonic anemometers were used to measure time series of vertical wind velocity (w), and cup anemometers to measure horizontal wind speed (s), above the canopy and at seven different heights within the canopy. Vertical profiles were measured during 25 runs on eight different days when conditions above the canopy were near-neutral.Profiles of s and of the standard deviation ( _w ) of w show relatively little scatter and suggest that, for this canopy and these stability conditions, profiles can be predicted from simple measurements made above the canopy. Within the canopy, a negative skewness and a high kurtosis of the w-frequency distributions indicate asymmetry and the persistence of large, high-velocity eddies. The Eulerian time scale is only a weak function of height within the canopy.Although w-power spectra above the canopy are similar to those in the free atmosphere, we did not observe an extensive inertial subrange in the spectra within the canopy. Also, a second peak is present that is especially prominent near the ground. The lack of the inertial subrange is likely caused by the presence of sources and sinks for turbulent kinetic energy within our canopy. The secondary spectral peak is probably generated by wake turbulence caused by form drag on the wide, horizontal spruce branches.     

On the Scaling Laws of the Velocity-Scalar Cospectra in the Canopy Sublayer Above Tall Forests

The scaling laws of the vertical (F _wc ) and longitudinal (F _uc ) velocity-scalar cospectra within the inertial subrange are explored using dimensional arguments and a simplified cospectral budget in the canopy sublayer above three distinct forested ecosystems. The cospectral budget was shown to be consistent with plausible scaling laws originating from dimensional considerations. Using the analytical solution to the novel cospectral budget, it was shown that F _wc (k) and F _uc (k) are governed by the linear superposition of two terms that scale as k ^−2/3−α and k ^−β , where k is the wavenumber, −α is the exponent of the velocity spectrum, and β( ≥ 7/3) depends on the ratio of the similarity constants for the pressure-scalar covariance and the flux transport terms. It was also demonstrated that, when the magnitude of the mean scalar concentration gradient is large, the k ^−2/3−α term dominates the velocity-scalar cospectral budget. For such a case, correcting for biases emerging from high frequency losses in eddy-covariance scalar flux measurements can be readily formulated by using the measured velocity spectral exponent in the inertial subrange.     

A Study in Search of Interconnection between Surface Parameters and Surrounding Synoptic And Subsynoptic Features

The paper reveals that the variations in parameters like u*, the scaling velocity and θ*. The scaling tempera-ture during the various phases of monsoon might be linked with subsynoptic features. The rise in u* is mainly connected with the presence of lower tropospheric cyclonic vorticity over a subsynoptic scale of the site. However the variations in θ* is mainly linked with the various phases of monsoon and θ* shows a sharp rise in presence of low level convective cloud.Besides the correlation studies of u and u*, θv and θv* , θv-θv0 and θv* are undertaken. The correlation be?tween θv and θv* is poor. In other two cases correlations are good. Besides u/u* , has shown good coefficient of variation values within the ζ range.     

Momentum Absorption in Rough-Wall Boundary Layers with Sparse Roughness Elements in Random and Clustered Distributions

A wind-tunnel experiment has been used to investigate momentum absorption by rough surfaces with sparse random and clustered distributions of roughness elements. An unusual (though longstanding) method was used to measure the boundary-layer depth δ and friction velocity u _* and thence to infer the functional relationship z ₀/h = f(λ) between the normalised roughness length z ₀/ h and the roughness density λ (where z ₀ is the roughness length and h the mean height of the roughness elements). The method for finding u _* is based on fitting the velocity defect in the outer layer to a functional form for the dimensionless velocity-defect profile in a canonical zero-pressure-gradient boundary layer. For the conditions investigated here, involving boundary layers over sparse roughness with strong local heterogeneity, this velocity-defect-law method is found to be more robust than several alternative methods for finding u _* (uw covariance, momentum integral and slope of the logarithmic velocity profile).The experimental results show that, (1) there is general agreement in the relationship z ₀/h = f(λ) between the present experiment with random arrays and other wind-tunnel experiments with regular arrays; (2) the main effect of clustering is to increase the scatter in the z ₀/h = f(λ) relationship, through increased local horizontal heterogeneity; (3) this scatter obscures any trend in the z ₀/h = f(λ) relationship in response to clustering; and (4) the agreement between the body of wind-tunnel data (taken as a whole) and field data is good, though with scatter for which it is likely that a major contribution stems from local horizontal heterogeneity in the field.     

Turbulent Kinetic Energy Dissipation in the Surface Layer

We estimated the turbulent kinetic energy (TKE) dissipation rate for thirty-two 1-h intervals of unstable stratification covering the stability range 0.12 ≤ −z/L ≤ 43 (z/L is the ratio of instrument height to the Obukhov length), by fitting Kolmogorov’s inertial subrange spectrum to streamwise spectra observed over a desert flat. Estimated values are compatible with the existence of local equilibrium, in that the TKE dissipation rate approximately equalled the sum of shear and buoyant production rates. Only in the neutral limit was the turbulent transport term in the TKE budget measured to be small.     

Waves to the lee of a meso-scale elliptic orographic barrier

Summary ?The paper considers a meso-scale, adiabatic, inviscid and Boussisnesq flow of a stably stratified fluid over a three-dimensional (3-D) meso-scale orographic barrier with elliptic contour, with special reference to a part of the Western ghats mountain along west coast of India and on the Khasi-Jayantia hill in the northeast India. The airstream characteristics are simplified by assuming that the upstream wind velocity (U) and buoyancy frequency (N) are constant with height. Solutions for perturbation vertical velocity (w′) and streamline displacement (η′) are expressed in terms of double integrals. These integrals cannot be evaluated exactly, hence they have been approximated by asymptotic expansion method. Side by side solutions using numerical method have also been obtained. The results of the study indicate that the updraft regions in the asymptotic solution are crescent shaped, symmetrical about the axis y = 0, tilting upwind and spreading laterally with height. The study also shows that in both asymptotic solution and numerical solution w′ and η′ fall off down wind of the barrier in the central plane (y = 0), further more in the asymptotic solution w′ and η′ fall off as x ⁻¹. The study also indicates that the discrete updraft regions obtained in the numerical solution, when joined, take a crescent shape. Received November 26, 2001; accepted February 27, 2002     

Can Water Vapour Raman Lidar Resolve Profiles of Turbulent Variables in the Convective Boundary Layer?

High-resolution water vapour measurements made by the Atmospheric Radiation Measurement (ARM) Raman lidar operated at the Southern Great Plains Climate Research Facility site near Lamont, Oklahoma, U.S.A. are presented. Using a 2-h measurement period for the convective boundary layer (CBL) on 13 September 2005, with temporal and spatial resolutions of 10 s and 75 m, respectively, spectral and autocovariance analyses of water vapour mixing ratio time series are performed. It is demonstrated that the major part of the inertial subrange was detected and that the integral scale was significantly larger than the time resolution. Consequently, the major part of the turbulent fluctuations was resolved. Different methods to retrieve noise error profiles yield consistent results and compare well with noise profiles estimated using Poisson statistics of the Raman lidar signals. Integral scale, mixing-ratio variance, skewness, and kurtosis profiles were determined including error bars with respect to statistical and sampling errors. The integral scale ranges between 70 and 130 s at the top of the CBL. Within the CBL, up to the third order, noise errors are significantly smaller than sampling errors and the absolute values of turbulent variables, respectively. The mixing-ratio variance profile rises monotonically from ≈0.07 to ≈3.7 g² kg⁻² in the entrainment zone. The skewness is nearly zero up to 0.6 z/z _i , becomes −1 around 0.7–0.8 z/z _i , crosses zero at about 0.95 z/z _i , and reaches about 1.7 at 1.1 z/z _i (here, z is the height and z _i is the CBL depth). The noise errors are too large to derive fourth-order moments with sufficient accuracy. Consequently, to the best of our knowledge, the ARM Raman lidar is the first water vapour Raman lidar with demonstrated capability to retrieve profiles of turbulent variables up to the third order during daytime throughout the atmospheric CBL.     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Relating Urban Surface-layer Structure to Upwind Terrain for the Salford Experiment (Salfex)

Profiles of wind and turbulence over an urban area evolve with fetch in response to surface characteristics. Sodar measurements, taken on 22 April 2002 during the Salford Experiment in the UK (Salfex), are here related to upstream terrain. A logarithmic layer up to z = 65m was observed in all half-hour averaged profiles. Above this height the profile showed a different vertical gradient, suggesting a change in surface cover upstream. The drag coefficient varied by a factor of two over only a 20° direction change. Turbulence intensity (σ _x ) for each wind component (x) decreased with height, but the ratio suggested an underestimate of σ _u compared to previous results. Mean urban and suburban cover fraction within the source area for each height decreased sharply between z = 20 and 50m, increasing slightly above. The near-convergence of cover fractions thus occured for source areas of minimum length ≈ 2,200 m. In comparison, the mean length scale of heterogeneity L _P was calculated from surface cover data to be 1,284 m, and the corresponding mean blending height h _b was 175 m. Finally, the mean streamline angle, α, was negative and the magnitude decreased with height. An exponential fit to α for z ≤ 65m gave an e-folding height scale of 159 m. A simple relationship between this height scale and L _P was assumed, giving L _P ≈ 1,080 m, which is in reasonable agreement with the estimate from surface cover type. The results suggest that more emphasis is required on modelling and measuring surface-layer flow over heterogeneous urban canopies.     

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     

The Fallacy of Drifting Snow

A common parametrization over snow-covered surfaces that are undergoing saltation is that the aerodynamic roughness length for wind speed (z ₀) scales as au_*²/g{\alpha u_\ast^2/g}, where u _* is the friction velocity, g is the acceleration of gravity, and α is an empirical constant. Data analyses seem to support this scaling: many published plots of z ₀ measured over snow demonstrate proportionality to u_*²{u_\ast^2 }. In fact, I show similar plots here that are based on two large eddy-covariance datasets: one collected over snow-covered Arctic sea ice; another collected over snow-covered Antarctic sea ice. But in these and in most such plots from the literature, the independent variable, u _*, was used to compute z ₀ in the first place; the plots thus suffer from fictitious correlation that causes z ₀ to unavoidably increase with u _* without any intervening physics. For these two datasets, when I plot z ₀ against u _* derived from a bulk flux algorithm—and thus minimize the fictitious correlation—z ₀ is independent of u _* in the drifting snow region, u _* ≥ 0.30 ms⁻¹. I conclude that the relation z₀ = au_*²/g{z_0 = \alpha u_\ast^2/g} when snow is drifting is a fallacy fostered by analyses that suffer from fictitious correlation.     

A Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u _*/w _*, where u _* and w _* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/z _i , where z _i is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.