Incorporation of planetary boundary layer dynamics in a numerical model of long-range air-pollutant transport

In this paper, measurements of the first 150 m of the atmospheric boundary layer obtained by a high-frequency acoustic mini-sounder are compared with measurements obtained by a full complement of instruments including sonic anemometers mounted on the Boulder Atmospheric Observatory tower. The acoustic mini-sounder, starting as low as 6 m from the ground, measures in the monostatic mode the profiles of the vertical wind speed, w, and of the temperature structure parameter, C _T ² with enhanced height resolution of the order of 1 m and time resolution of the order of 30 s. The results of the comparison show that the high-frequency mini-sounder is an effective atmospheric boundary-layer profiler that is also portable and relatively inexpensive. Measurements of the spectrum of C _T ² are presented that provide information on the local isotropy of the temperature field. Statistics of the variability of C _T ² in both stable and unstable conditions are also given. The sounder's capabilities are further demonstrated by some detailed observations of the structure and time evolution of a thermal plume root at noon and of a nocturnal, stably stratified layer in which a dynamic instability develops. The plume starts at a height of less than 5 m, possesses substantial internal structure, and includes vertical velocities in excess of 2 m s^-1.     

Numerical experimentation with particles having non-zero terminal velocity in the atmospheric surface layer

Numerical solutions are obtained for a two-dimensional eddy diffusion equation describing aerosol particles in the atmospheric surface layer. Particles are assumed to be from either an elevated line source or a surface area source. Characteristics of the solutions are exhibited as a function of source type, lower boundary condition, and the ratio of terminal velocity () to friction velocity (u _*). This theory indicates that suspended particles tend to escape the near-surface layer, and are thus subject to long-range transport, when the ratio /u _* is less than von Karman's constant. This prediction is consistent with available data.     

Formulation of stability-dependent empirical relations for turbulent intensities from surface layer turbulence measurements for dispersion parameterization in a lagrangian particle dispersion model

Season- and stability-dependent turbulence intensity (σ _u /u _*, σ _v /u _*, σ _w /u _*) relationships are derived from experimental turbulence measurements following surface layer scaling and local stability at the tropical coastal site Kalpakkam, India for atmospheric dispersion parameterization. Turbulence wind components (u′, v′, w′) measured with fast response UltraSonic Anemometers during an intense observation campaign for wind field modeling called Round Robin Exercise are used to formulate the flux–profile relationships using surface layer similarity theory and Fast Fourier Transform technique. The new relationships (modified Hanna scheme) are incorporated in a Lagrangian Particle Dispersion model FLEXPART-WRF and tested by conducting simulations for a field tracer dispersion experiment at Kalpakkam. Plume dispersion analysis of a ground level hypothetical release indicated that the new turbulent intensity formulations provide slightly higher diffusivity across the plume relative to the original Hanna scheme. The new formulations for σ _u , σ _v , σ _w are found to give better agreement with observed turbulent intensities during both stable and unstable conditions under various seasonal meteorological conditions. The simulated concentrations using the two methods are compared with those obtained from a classical Gaussian model and the observed SF₆ concentration. It has been found that the new relationships provide comparatively higher diffusion across the plume relative to the model default Hanna scheme and provide downwind concentration results in better agreement with observations.     

Markov chain simulations of vertical dispersion from elevated sources into the neutral planetary boundary layer

A Lagrangian statistical-trajectory model based on a Markov chain relation is used to investigate vertical dispersion from elevated sources into the neutral planetary boundary layer. The model is fully two-dimensional, in that both vertical and longitudinal velocity fluctuations, and their correlation, are simulated explicitly. The best observational information currently available is used to characterize the mean and turbulent structure of the neutral boundary layer. In particular, a realistic vertical profile of the Lagrangian integral time scale is proposed, based partly on a review of direct measurements and partly on a comparison of the model predictions with published diffusion data. The model predictions are shown to agree well with a variety of dispersion observations. The model is used to study vertical diffusion as a function of release height H, friction velocity u* and surface roughness z ₀ for downwind distances up to 10 km from the source. The equivalent Gaussian dispersion parameter Σ _z is shown to decrease slightly with an increase in H, and to increase with increases in z ₀ or u*. It is demonstrated that relationships valid in a field of homogeneous turbulence can be applied to vertical dispersion in the atmosphere if the release occurs above the region of strongest gradients in the mean and turbulent parameters. Scaling in terms of the standard deviation in elevation angle of the wind at the release point leads to a universal curve which provides accurate estimates of Σ _z over a wide range of values of H, z ₀ and the meteorological parameters.     

A Theoretical and Experimental Investigation of Energy-Containing Scales in the Dynamic Sublayer of Boundary-Layer Flows

The existence of universal power laws at low wavenumbers (K) in the energy spectrum (E_u) of the turbulent longitudinal velocity (u) is examined theoretically and experimentally for the near-neutral atmospheric surface layer. Newly derived power-law solutions to Tchen's approximate integral spectral budget equation are tested for strong- and weak-interaction cases between the mean flow and turbulent vorticity fields. To verify whether these solutions reproduce the measured E_u at low wavenumbers, velocity measurements were collected in the dynamic sublayer of the atmosphere at three sites and in the inner region of a laboratory open channel. The atmospheric surface layer measurements were carried out using triaxial sonic anemometers over tall corn, short grass, and smooth desert-like sandy soil. The open channel measurements were performed using a two-dimensional boundary-layer probe above a smooth stainless steel bed. Comparisons between the proposed analytical solution for E_u, the dimensional analysis by Kader and Yaglom, and the measured Haar wavelet E_u spectra are presented. It is shown that when strong interaction between the mean flow and turbulent vorticity field occurs, wavelet spectra measurements, predictions by the analytical solution, and predictions by the dimensional analysis of Kader-Yaglom (KY) are all in good agreement and confirm the existence of a -1 power law in E_u(= C_uuu² _* K^-1, where C_uu is a constant and u_* is the friction velocity). The normalized upper wavenumber limit of the -1 power law (Kz = 1, where z is the height above the zero-plane displacement) is estimated using two separate approaches and compared to the open channel and atmospheric surface-layer measurements. It is demonstrated that the measured upper wavenumber limit is consistent with Tchen's budget but not with the KY assumptions. The constraints as to whether the mean flow and turbulent vorticity strongly interact are considered using a proposed analysis by Panchev. It is demonstrated that the arguments by Panchev cannot be consistent with surface-layer turbulence. Using dimensional analysis and Heisenberg's turbulent viscosity model, new constraints are proposed. The new constraints agree with the open channel and atmospheric surface-layer measurements, Townsend's inactive eddy motion hypothesis, and the Perry et al. analysis.     

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.     

Note on turbulent scaling parameters for the convective planetary boundary layer

Scaling velocities relevant for turbulent flows in the planetary boundary layer are discussed. It is suggested that the scaling parameters should be determined by integrated bulk properties of the respective turbulent production terms. According to this concept, a new velocity scale, replacing the friction velocityu*, is proposed depending on bothu* and the geostrophic windu _g . The convective velocity scalew* can be determined by the integral of the buoyancy production term and is therefore an appropriate velocity scale. Examination of Minnesota and Kansas data shows that these data do not give the possibility of verifying whether the new scaling velocity is more appropriate thanu*. This is because the range of variability of atmospheric stability during the field measurements is too small. However, theoretical considerations based on integrated properties of the turbulence, through the depth of the planetary boundary layer, are given in support of the new scaling velocity.     

Measurements of Turbulence and Dispersion in Three Idealized Urban Canopies with Different Aspect Ratios and Comparisons with a Gaussian Plume Model

Water-tunnel measurements of velocity, turbulence and scalar concentration for three model urban canopies with aspect ratios A _r of building height-to-width of 0.25, 1 and 3 are presented. The measurements for the canopies with A _r = 1 and 3 are new, while the measurements for A _r = 0.25 were previously published. A passive scalar was continuously released from a near-ground point source, and the concentration was measured at several distances from the source and at different heights above the ground. Plume spreads, concentration and distance from the source were non-dimensionalized using length, time and velocity scales reflecting the geometry of the buildings. The scaling collapses the data for all aspect ratios and is valid when the vertical extent of the plume is smaller than the canopy height. The observed plume spreads are compared with analytical relations, which predict linear growth in both transverse and vertical directions. The observed mean concentration is compared with a Gaussian dispersion model that predicts a ?2 power-law decay with distance from the source.     

Effects of Topographical Slope Angle and Atmospheric Stratification on Surface-Layer Turbulence

The effect of topographical slope angle and atmospheric stratification on turbulence intensities in the unstably stratified surface layer have been parameterized using observations obtained from a three-dimensional sonic anemometer installed at 8 m height above the ground at the Seoul National University (SNU) campus site in Korea for the years 1999–2001. Winds obtained from the sonic anemometer are analyzed according to the mean wind direction, since the topographical slope angle changes significantly along the azimuthal direction. The effects of the topographical slope angle and atmospheric stratification on surface-layer turbulence intensity are examined with these data. It is found that both the friction velocity and the variance for each component of wind normalized by the mean wind speed decrease with increase of the topographical slope angle, having a maximum decreasing rate at very unstable stratification. The decreasing rate of the normalized friction velocity (u _* /U) is found to be much larger than that of the turbulence intensity of each wind component due to the reduction of wind shear with increase in slope angle under unstable stratification. The decreasing rate of the w component of turbulence intensity (σ _w /U) is the smallest over the downslope surface whereas that of the u component (σ _u /U) has a minimum over the upslope surface. Consequently, σ _w /u _* has a maximum increasing rate with increase in slope angle for the downslope wind, whereas σ _u /u _* has its maximum for the upslope wind. The sloping terrain is found to reduce both the friction velocity and turbulence intensity compared with those on a flat surface. However, the reduction of the friction velocity over the sloping terrain is larger than that of the turbulence intensity, thereby enhancing the turbulence intensity normalized by the friction velocity over sloping terrain compared with that over a flat surface.     

The Control Of Coherent Eddies In Vegetation Canopies: Streamwise Structure Spacing, Canopy Shear Scale And Atmospheric Stability

An analogy has been established between a plane mixing layer and the atmospheric flow near the top of a vegetation canopy. It is based on a common feature, a strong inflection in the mean velocity profile, responsible for hydrodynamical instabilities that set the pattern for the coherent eddies and determine the turbulence length scales. In an earlier study, this analogy was tested using a small data set from thirteen experiments, all in near-neutral conditions. It provided a good prediction of the streamwise spacing _w of the dominant canopy eddies (evaluated from time series of vertical velocity) that appears to depend on a shear length scale L_s = U(h)/U'(h), where h is canopy height, U is mean velocity and U' the vertical gradient dU/dz. The present analysis utilizes an extensive data set of approximately 700 thirty-minute runs, from six experiments on two forest sites and a maize crop, with a large range of stability conditions. _w was estimated for each run using the wavelet transform as an objective, automated detection method. First, the variations of _w and L_s with atmospheric stability are discussed. Neutral and unstable values exhibit a large scatter whereas in stable conditions both variables decrease with increasing stability. It is subsequently found that _w is directly related to L_s, in a way close to the neutral prediction _w /h = 8.1L_s/h.The Strouhal number S_tr = L_s /_w is then shown to vary with atmospheric stability, weakly in unstable conditions, more significantly in stable conditions. Altogether these results suggest that, to some extent, the plane mixing-layer analogy can be extended to non-neutral conditions. It is argued that the primary effect of atmospheric stability, at least in stable conditions, is to modify the shear length scale L_s through changes in U(h) and U'(h), which in turn determines the streamwise spacing of the active, coherent motions.     

Mixed-layer heat advection and entrainment during the sea breeze

A model is developed to simulate the potential temperature and the height of the mixed layer under advection conditions. It includes analytic expressions for the effects of mixed-layer conditions upwind of the interface between two different surfaces on the development of the mixed layer downwind from the interface. Model performance is evaluated against tethersonde data obtained on two summer days during sea breeze flow in Vancouver, Canada. It is found that the mixed-layer height and temperature over the ocean has a small but noticeable effect on the development of the mixed layer observed 10 km inland from the coast. For these two clear days, the subsidence velocity at the inversion base capping the mixed layer is estimated to be about 30 mm s^–1 from late morning to late afternoon. When the effects of subsidence are included in the model, the mixed-layer height is considerably underpredicted, while the prediction for the mean potential temperature in the mixed layer is considerably improved. Good predictions for both height and temperature can be obtained when values for the heat entrainment ratio,c, 0.44 and 0.68 for these two days respectively for the period from 1000 to 1300 LAT, were used. These values are estimated using an equation including the additional effects on heat entrainment due to the mechanical mixing caused by wind shear at the top of the mixed layer and surface friction. The contribution of wind shear to entrainment was equal to, or greater than, that from buoyant convection resulting from the surface heat flux. Strong wind shear occurred near the top of the mixed layer between the lower level inland flow and the return flow aloft in the sea breeze circulation.Symbols c entrainment parameter for sensible heat - c _p specific heat of air at constant pressure, 1010 J kg^–1 K^–1 - d ₁ the thickness of velocity shear at the mixed-layer top, m - Q _H surface sensible heat flux, W m^–2 - u _m mean mixed-layer wind speed, m s^–1 - u _* friction velocity at the surface, m s^–1 - w subsidence velocity, m s^–1 - W subsidence warming,^oC s^–1 - w _e entrainment velocity, m s^–1 - w _* convection velocity in the mixed layer, m s^–1 - x downwind horizontal distance from the water-land interface, m - y dummy variable forx, m - Z height above the surface, m - Z _i height of capping inversion, m - Z _m mixed-layer depth, i.e.,Z _i–Z_s, m - Z _s height of the surface layer, m - lapse rate of potential temperature aboveZ _i, K m^–1 - potential temperature step atZ _i, K - u _h velocity step change at the mixed-layer top - _m mean mixed-layer potential temperature, K     

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 .     

The impact of soil moisture on dispersion-related characteristics

This study investigates the impact of soil moisture availability on dispersion-related characteristics: surface fric-tion velocity (u*), characteristic scales of temperature and humidity (T* and q*), the planetary boundary layer height (h) and atmospheric stability classified by Monin-Obukhov length (L), Kazanski-Monin parameter (μ) and convective velocity scale (w*) during daytime convective condition using a one-dimensional primitive equation with a refined soil model.     

Turbulence Structure of the Unstable Atmospheric Surface Layer and Transition to the Outer Layer

We present a new model of the structure of turbulence in the unstable atmospheric surface layer, and of the structural transition between this and the outer layer. The archetypal element of wall-bounded shear turbulence is the Theodorsen ejection amplifier (TEA) structure, in which an initial ejection of air from near the ground into an ideal laminar and logarithmic flow induces vortical motion about a hairpin-shaped core, which then creates a second ejection that is similar to, but larger than, the first. A series of TEA structures form a TEA cascade. In real turbulent flows TEA structures occur in distorted forms as TEA-like (TEAL) structures. Distortion terminates many TEAL cascades and only the best-formed TEAL structures initiate new cycles. In an extended log layer the resulting shear turbulence is a complex, self-organizing, dissipative system exhibiting self-similar behaviour under inner scaling. Spectral results show that this structure is insensitive to instability. This is contrary to the fundamental hypothesis of Monin--Obukhov similarity theory. All TEAL cascades terminate at the top of the surface layer where they encounter, and are severely distorted by, powerful eddies of similar size from the outer layer. These eddies are products of the breakdown of the large eddies produced by buoyancy in the outer layer. When the outer layer is much deeper than the surface layer the interacting eddies are from the inertial subrange of the outer Richardson cascade. The scale height of the surface layer, z _s, is then found by matching the powers delivered to the creation of emerging TEAL structures to the power passing down the Richardson cascade in the outer layer. It is z _s = u _* ³ /k_s, where u _* is friction velocity, k is the von Kármán constant and _s is the rate of dissipation of turbulence kinetic energy in the outer layer immediately above the surface layer. This height is comparable to the Obukhov length in the fully convective boundary layer. Aircraft and tower observations confirm a strong qualitative change in the structure of the turbulence at about that height. The tallest eddies within the surface layer have height z _s, so z _s is a new basis parameter for similarity models of the surface layer.     

The limitations on stress parameterization imposed by intermittency in turbulent flow

The indirect dissipation technique is used to estimate 1-min averages of friction velocity u _*in the surface layer over the tropical ocean. These estimates are compared to estimates of u _*obtained using a drag coefficient and the relative difference between the two is examined in relation to stability and averaging time. Plumes and downdrafts are found to be responsible for an anomalous behavior of the drag coefficient estimates. Certain factors relating to plume properties, derived using conditional sampling as described in Khalsa (1980), are shown to be related to the variance between the two estimates of friction velocity. An investigation into the effects of increasing the averaging time reveals that plume spacing, which is dependent on stability, and the mean wind speed determine the minimum time for smoothing the influence of plumes and downdrafts.Department of Atmospheric Sciences contribution number 513.     

The characteristics of a laboratory produced turbulent Ekman layer

The characteristics of the atmospheric turbulent Ekman boundary layer have been qualitatively simulated in an annular rotating wind tunnel. Observed velocity spirals found to exist within the wind tunnel resembled qualitatively those found in the atmosphere in that a two-layer structure was evident, consisting of a log-linear portion topped by an outer spiral layer. The magnitude of the friction velocity u _* obtained from the log-linear profile agreed with that measured directly, i.e., that obtained from the relation: u _* = (u′w′)^1/2. Also, the effects of surface roughness on the characteristics of the boundary layer agreed with expected results. In cases where the parametric behaviour predicted by theory departed from the observed behaviour, the probable cause was the inherent size limitations of the wind tunnel. The ability to maintain dynamic similarity is constrained by the limited radius of curvature of the wind tunnel. The vertical distribution of turbulent intensity in the wind tunnel was found to agree qualitatively with an observed atmospheric distribution. Also, a vertical distribution of eddy diffusivity was calculated from tunnel data and found to give qualitatively what one might expect in the atmosphere.     

Turbulence characteristics in the atmospheric surface layer during summer monsoon of 1997 over a semi-arid location in India

A land surface processes experiment (LASPEX) was conducted in the semi-arid region of Northwest India during January 1997–February 1998. Analysis of turbulent components of wind and air temperature collected in the surface layer (SL) at Anand (22°35′N, 72°55′E) during the Indian summer monsoon season from June to September 1997 is presented. Turbulent fluctuation of wind components and air temperature observed at Anand varied as a function of terrain features and stability of the surface layer. Under neutral conditions, the standard deviation of vertical velocity (σ _w ) and temperature (σ _T ) were normalized using respective surface layer scaling parameter u _* and T _* which fitted the expressions σ _w /u _* = 1.25 and σ _T /T _* ≈ 4. Micrometeorological spectrum of wind and temperature at 5 m above ground level (AGL) at Anand showed peaks at time scale of 1–3 min at the low-frequency end. The inertial sub-range characteristics (?2/3 slope) of the spectrum are exhibited mostly. However, in some occasions, slope of ?1 denoting brown noise was depicted by the wind and temperature spectrum, which indicated anisotropy in turbulence.     

On equilibrium profiles of suspended particles

A power law is often used to represent the vertical profile of uniform suspended particles above a horizontally homogeneous surface. It serves as an analytical solution representing an equilibrium between vertical turbulent diffusion and gravitational settling, andcan be used to extract settling velocity information from observed particle number density profiles. In this note, we analyse this situation and use a numerical model to investigate the temporal change of particle number density and of the net vertical flux due to turbulent diffusion and gravitational settling. The results show that the net flux approaches zero very slowly for small particles (w_s/ u_* < 1), and show that the power law does not hold for small particles. If the power law is used to extract settling velocities from observed vertical distributions of particle number density in these cases, the estimated settling velocity may be unrealistically large.     

A note on the height dependence of the skewness and the kurtosis of the vertical turbulent velocity in the neutral surface layer

Several experimental results indicate that S _w (the skewness of the vertical turbulent velocity) increases with height, and K _w (the kurtosis) decreases with height in the neutral surface layer. The measured behavior of S _w and K _w with height under neutral conditions is shown to be consistent with available models for the gradient-diffusion and the pressure-velocity correlation. In addition, an estimate of the mode of the probability density distribution turns out to be helpful in interpreting the height dependence of K _w.     

Comparing Estimates of Turbulence Based on Near-Surface Measurements in the Nocturnal Stable Boundary Layer

Tethered Lifting System (TLS) estimates of the dissipation rate of turbulent kinetic energy (e){(\varepsilon)} are reasonably well correlated with concurrent measurements of vertical velocity variance (s_w²){(\sigma_{w}^{2})} obtained from sonic anemometers located on a nearby 60-m tower during the CASES-99 field experiment. Additional results in the first 100 m of the nocturnal stable boundary layer confirm our earlier claim that the presence of weak but persistent background turbulence exists even during the most stable atmospheric conditions, where e{\varepsilon} can exhibit values as low as 10⁻⁷ m² s⁻³. We also present a set of empirical equations that incorporates TLS measurements of temperature, horizontal wind speed, and e{\varepsilon} to provide a proxy measurement for s_w²{\sigma_{w}^{2}} at altitudes higher than tower heights.