Scaling turbulence in the planetary boundary layer

Two different approaches to scaling turbulence in the planetary boundary layer over Lake Ontario are investigated. The height up to the inversion was found to be the appropriate scaling height while u. for near‐neutral and w* for unstable conditions were the appropriate scaling velocities. The results were in general agreement with the numerical models of Deardorff (1972) and Wyngaard, Cote, and Rao (1974).     

Radiation,evaporation and the maintenance of turbulence under stable conditions in the lower atmosphere

An expression is derived relating the critical flux Richardson number with the critical (gradient) Richardson number. In contrast to an earlier analysis by Townsend (1958), which is restricted to the atmosphere well outside the earth's boundary layer, the present treatment is intended specifically for turbulent flow in the lower atmosphere and it takes account of the effect of evaporation on the stability. The effect of radiation on the rate of destruction of the mean square of the temperature fluctuations is obtained by considering the radiative flux divergence in a stratified atmosphere and by using a simple functional relationship to represent empirical emissivity data.It was found that evaporation and radiation increase the critical Richardson number by a sensible amount depending on the atmospheric conditions, mainly temperature, humidity and the gradients. There is no definite critical Richardson number but rather a range between 0.25, below which turbulence is very likely, and somewhat higher than 0.5, above which turbulence is improbable. The value of the critical Richardson number can be expressed in terms of evaporation, radiation and the ratio ( _w /u _*) which also appears not to have a definite critical value. Evaporation and radiation cause the ratio ( _w /u ^*) to be larger than unity under neutral conditions. These results, based on the assumption of Reynolds' analogy,K ^H =K ^M , are consistent with the available experimental evidence.     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

Intermittent wind close to the ground within a grass canopy

Wind speed was measured at a height of 1 cm above the ground and at several other heights in and above a canopy of tall fescue grass (Festuca arundinacea) using single hot-wire and triple hot-film anemometers. The plant area density in the canopy was concentrated close to the ground, with 75% of the plant area standing belowz=15 cm, wherez is height above the ground. The frequency distributions of horizontal wind speeds,s, were sharply skewed towards positive values at all measurement heights, but were most highly skewed near the ground where the coefficient of skewness ranged from 1.6 to 2.9. Above mid-canopy height, the frequency distribution ofs was described reasonably well by a Gumbel extreme value distribution. Average wind speed,S, decreased exponentially with depth into the canopy with an exponential scale length of abouth/2.8, whereh is the height of the canopy. Atz=1 cm, the value ofS was about 11% of the surface-layeru _*. The standard deviation of the fluctuations of the vertical and horizontal components of the wind speed also decreased exponentially with depth inside the canopy with a scale length of abouth/2.5.Inside the canopy, the Eulerian integral time scales for the vertical ( _w ) and horizontal ( _u ) components of wind speed were about 0.1 s and 1.0 s, respectively, and were approximately constant with height. Above the canopy, these time scales increased sharply and, atz=2.25h, _w and _u were approximately 1.0 and 3.0s, respectively. Turbulence length scales in the vertical and downwind directions, _u and _w ·U, respectively, were approximately 1 cm for heights between 1 to 10 cm above the ground inside the canopy, while atz=2.25h, they were about 55 cm and 277 cm. Relatively quiescent periods (lulls) in the air close to the ground were interrupted frequently by gusts. The frequency of occurrence of gusts appears to be correlated with the value of the local shear near the top of the canopy.     

Deriving characteristic parameters of the convective boundary layer from sodar measurements of the vertical velocity variance

This paper deals with the derivation of the convective mixing height and the characteristic convective velocity w _* from profiles of _w measured by sodar. The parameters were obtained by fitting an analytical profile to the observed data. Results were compared with values obtained by the meteorological preprocessor of a dispersion model and from noon radiosoundings. In addition, a Monte Carlo method was applied to study the influence of measurement errors. It turned out that it is inherently difficult to determine the depth of deep mixed layers from sodar measurements with a limited range, although the determination of w _* should be possible. However, a significant underestimation of _w , and thus w _*, was found, which is probably due to disproportional sampling of updrafts and downdrafts.     

Inequality of eddy transfer coefficients for vertical transport of sensible and latent heats during advective inversions

Similarity of transport of water vapour and sensible heat was investigated within an advective inversion layer by measuring eddy fluxes together with gradients of temperature and humidity. The experimental site was a field of rice, grown under flood irrigation, which was situated in a semi-arid region. The fetch was about 300 m and local stabilities (z/L) over the rice ranged from 0 to 0.1. Results were expressed as the ratio of eddy transfer coefficients for sensible heat (K _H) and water vapour (K _w). Near neutral stability, K _H/K_W approached 1, but the ratio decreased to about 0.65 with increasing stability. Existing theory predicts the result qualitatively but accounts for only about one fifth of the decrease in K _H/K_W with stability.     

The Height Correction of Similarity Functions in the Stable Boundary Layer

Empirical similarity functions of the Richardson number, obtained from bin-averaged data in the lower part of the stable boundary layer, show an undesired dependence on height at which the observations are collected. A correction of this flaw is proposed and tested by employing the neutral mixing length l _o as a similarity scale for height. The function of height describing l _o is assumed to be linear in the surface layer, and approaching a specified value with increasing height. The modification does not alter the dependence of similarity functions on the Richardson number, and is shown to be supported by the Cooperative Atmospheric-Surface Exchange Study-1999 (CASES-99) data.     

Dispersion of Heavy Particles Emitted from Area Sources in the Unstable Atmospheric Boundary Layer

Reliable predictions of the daytime dispersal of heavy particles in the unstable atmospheric boundary layer are important in a variety of disciplines. For many applications, particles disperse from area sources near the ground, and corresponding theoretical solutions are desired to reveal insight into the physical processes. Here, theoretical solutions recently developed for neutral conditions are modified to include the effects of atmospheric instability. The Obukhov length L _O and convection velocity w _? are introduced to characterize the patterns of particle dispersion, in additional to friction velocity u _? and settling velocity w _s used in the neutral case. The major effects of atmospheric instability are accounted for by modifying the vertical velocity variance profile and considering the ratio of velocity scales w _?/u _?. Theoretical predictions including the mean concentration profile, plume height, and horizontal transport above the source, and ground deposition flux downwind from the source agree well with large-eddy simulation results while the particle plume is within the atmospheric surface layer. The deposition curve is characterized by a power-law decay whose exponent depends on u _?, w _s, and w _?. A second steeper power-law develops once the plume extends into the mixed layer. This effect is enhanced with increasing atmospheric instability, implying that particles disperse farther from the source.     

An approximate analytical solution for the deposition of heavy particles released from an elevated line source

This work re-examines and further develops an analytical solution for the deposition swath of heavy particles released in the atmosphere from an elevated source over uniform terrain, correcting the particle diffusivity for the crossing trajectory effect. The revised (approximate) analytical solution proves to be accurate within 20% over a wide range of micrometeorological conditions and particle size, despite its neglect of the turbulence component of the deposition flux. It compares very satisfactorily with experimental data and with the simulations of a Lagrangian stochastic model, provided the variable U(H)/w _g ≤7 (ratio of the mean horizontal wind speed at source height to the particle settling velocity). In this domain of validity, simple formulae relating the statistics of the deposition swath to U(H)/w _g are derived.     

A 35-GHz Polarimetric Doppler Radar and Its Application for Observing Clouds Associated with Typhoon Nuri

Millimeter-wavelength radar has proved to be an effective instrument for cloud observation and research. In this study, 8-mm-wavelength cloud radar (MMCR) with Doppler and polarization capabilities was used to investigate cloud dynamics in China for the first time. Its design, system specifications, calibration, and application in measuring clouds associated with typhoon are discussed in this article. The cloud radar measurements of radar reflectivity (Z), Doppler velocity (Vr), velocity spectrum width (Sw) and the depolar-ization ratio (LDR) at vertical incidence were used to analyze the microphysical and dynamic processes of the cloud system and precipitation associated with Typhoon Nuri, which occurred in southern China in August 2008. The results show the reflectivity observed using MMCR to be consistent with the echo height and the melting-layer location data obtained by the nearby China S-band new-generation weather radar (SA), but the Ka-band MMCR provided more detailed structural information about clouds and weak precipitation data than did the SA radar. The variation of radar reflectivity and LDR in vertical structure reveals the transformation of particle phase from ice to water. The vertical velocity and velocity spectrum width of MMCR observations indicate an updraft and strong turbulence in the stratiform cloud layer. MMCR provides a valuable new technology for meteorological research in China.     

Notes on an Internal Boundary-Layer Height Formula

The derivation of the Panofsky–Dutton internal boundary-layer(IBL) height formula has been revisited. We propose that the upwindroughness length (rather than downwind) should be used in theformula and that a turbulent vertical velocity (_w) ratherthan the surface friction velocity (u_*) should be considered asthe appropriate scaling for the rate of propagation ofdisturbances into the turbulent flow. A published set ofwind-tunnel and atmospheric data for neutral stratification hasbeen used to investigate the influence of the magnitude ofroughness change on the IBL height.     

Estimating the convective velocity scale for diffusion applications

A simple mixed layer model is used to derive the following expressions for the maximum (daily) convective velocity scale. w _*m = AQ _m ^1/2; w _*m = Bz _im The variables A and B are shown to vary within narrow limits thus allowing them to be treated as constants. This is very useful for routine computation of w _*m , an important variable for dispersion under unstable conditions, from estimates of either the kinematic surface heat flux Q _m (m^-1) or the maximum mixed layer height z _im .Analysis of observations made during the Minnesota boundary layer experiment shows that there is ample justification for assigning typical values to A and B in estimating w _*m.     

Monin-Obukhov Functions for Standard Deviations of Velocity

The origins of Monin-Obukhov similarity theory (MOST) are briefly reviewed, as a context for the analysis of signals from sonic anemometers operating in the surface layer over a Utah salt flat. At this site (over the interval of these measurements) the neutral limit for the normalized vertical velocity standard deviation (σ _w /u _*) deviates markedly from what has generally been regarded as the standard value (i.e. about 1.3), suggesting (since others have also reported such deviations) that this Monin-Obukhov constant is not, in fact, universal. New (but tentative) formulae are suggested for σ _w and for the longitudinal standard deviation σ _u .     

Calculation of particle trajectories in the presence of a gradient in turbulent-velocity variance

Recent papers by Wilson et al. (1981b) and Legg and Raupach (1982) give methods for the calculation of particle trajectories in turbulence with a gradient in vertical velocity variance ² _w. However the two methods seem contradictory.This paper demonstrates that in systems in which l(d _w /dz) (where / is the length scale) varies only slowly with height z, the two methods give similar predictions, and indicates why this is the case. For a particular system in which the restriction on l(d _w /dz) is not satisfied, it is shown that neither method is correct but that a simple modification of the method of Wilson et al. (1981b) gives reasonable predictions.     

Large-Eddy Simulations on the Effects of Surface Geometry of Building Arrays on Turbulent Organized Structures

Turbulent organized structures (TOS) above building arrays were investigated using a large-eddy simulation (LES) model for a city (LES-CITY). Square and staggered building arrays produced contrasting behaviour in terms of turbulence that roughly corresponded to the conventional classification of ‘D-type’ and ‘K-type’ roughness, respectively: (1) The drag coefficients (referred to the building height) for staggered arrays were sensitive to building area density, but those for square arrays were not. (2) The relative contributions of ejections to sweeps (S₂/S₄) at the building height for square arrays were sensitive to building area density and nearly equalled or exceeded 1.0 (ejection dominant), but those for staggered arrays were insensitive to building area density and were mostly below 1.0 (sweep dominant). (3) Streaky patterns of longitudinal low speed regions (i.e., low speed streaks) existed in all flows regardless of array type. Height variations of the buildings in the square array drastically increased the drag coefficient and modified the turbulent flow structures. The mechanism of D-type and K-type urban-like roughness flows and the difference from vegetation flows are discussed. Although urban-like roughness flows exhibited mixed properties of mixing layers and flat-wall boundary layers as far as S₂/S₄ was concerned, the turbulent organized structures of urban-like roughness flows resembled those of flat-wall boundary layers.     

Estimation of abl Parameters Using the Vertical Velocity Measurements of an Acoustic Sounder

The friction velocity, the surface heat flux and the height of the Atmospheric Boundary Layer (ABL) are important parameters. In this work, vertical velocity variance ( _w ² ) and wind velocity structure parameter (C _v ² ) profiles estimated by acoustic sounder measurements are used, along with similarity relations, to estimate these parameters in the unstable Atmospheric Boundary Layer and the friction velocity in the stable one. The data were collected by two acoustic sounders with different height range and resolution under various atmospheric conditions (stability) and at two experimental sites in different terrain. The C _v ² profiles are estimated using gate difference of the vertical velocity measurements and the assumption of local isotropy. The vertical velocity data are corrected for the significant effects of noisy measurements and sampling volume averaging on the _w ² and C _v ² estimations using original techniques that are presented in this work. The results of the similarity method using acoustic sounder data are compared against estimates of the corresponding atmospheric parameters obtained from direct measurements. The comparison confirms the ability of the method to provide reasonably accurate estimates of these parameters especially in the middle of the day.     

Analysis of sky conditions using 40 year records of solar radiation data in China

Summary Forty years of daily global and diffuse radiation data have been used to characterize the atmospheric optical conditions at 14 premium radiation stations in China. The clearness index (K _T ), diffuse ratio (K _D ), and diffuse coefficient (K _C ) have been analyzed for long-term and seasonal variations, correlations of relative sunshine (R _S ) versus clearness index and diffuse coefficient, respectively. Two polynomial models have been developed to simulate clearness index and diffuse ratio by using relative sunshine data and have been shown to be reasonable at most of the 14 stations. The results show that there are significant declining trends in clearness index and increasing trends in diffuse ratio at most of the 14 premium radiation stations, but there are no significant trends for diffuse coefficient. The seasonal variations of clearness index are determined by the regional climate and changes with relative sunshine.     

Simultaneous measurements of turbulence over land and water

Turbulence and mean flow variables under unstable conditions are examined with special emphasis on the consequences of roughness and surface elevation change. An interpolation formula for _w ², between neutral and free convection, is shown to bring order to the data. The spectral distribution of vertical wind variance is found to be in good agreement with results over horizontal homogeneous terrain, both with respect to form and position. In particular, the length scale _m corresponding to the maximum of nS _w(n) is unchanged. Another turbulent length scale, (k/)z, is found to be substantially reduced in the disturbed zone of the internal boundary layer. To a first approximation, the flow-acceleration effect on the non-dimensional wind shear can be separated from the diabatic effect.     

Regional roughness of the landes forest and surface shear stress under neutral conditions

Mean wind velocity profiles were measured by means of radio-windsondes over the Landes region in southwestern France, which consists primarily of pine forests with scattered villages and clearings with various crops. Analysis of neutral profiles indicated the existence of a logarithmic layer between approximately z – d ₀ = 67(±18)z ₀ and 128(+-32)z ₀ (z is the height above the ground, z ₀ the surface roughness and d ₀ the displacement height). The upper limit can also be given as z – d ₀ = 0.33 (±0.18)h, where h is the height of the bottom of the inversion. The profiles showed that the surface roughness of this terrain is around 1.2 m and the displacement height 6.0 m. Shear stresses derived from the profiles were in good agreement with those obtained just above the forest canopy at a nearby location with the eddy correlation method by a team from the Institute of Hydrology (Wallingford, England).     

Cloud drop spectra at different levels and with respect to cloud thickness and rain

Measurements on drop size were made in cumulus clouds over Pune (inland region) during the summer monsoon seasons. In this paper, the measurements of the cloud drop spectra made in non-raining clouds at different levels and for different thickness have been studied. Also, those on the days with rain and with no rain (the rain being observed within the clouds) have been compared. The average spectra broadened with height. The concentration of drops >50 μm (N_L), liquid water content (LWC), mean volume diameter (MVD) and dispersion increased with height. The concentration of drops <20 μm (N_S) and total concentration (N_T) decreased with height. The spectra were broader, while N_S and N_T are smaller and the other parameters are greater for thicker clouds as compared to those for thinner. The spectra were broader, while N_S and N_T are smaller and the other parameters are greater on the days with rain with respect to those on the days with no rain. The distributions were bimodal at higher levels, for thicker clouds and on the days with rain, while they were unimodal at lower levels, for thinner clouds and on the days with no rain. The variations of the cloud drop spectra, preceding rain, at initial stage of rain and following rain are discussed.