Properties of spatial temperature derivatives in the atmospheric surface layer

A pair of parallel cold wires separated in either the vertical or lateral direction was used to obtain the three components _x, _y, _z of the temperature derivative in the streamwise, lateral and vertical directions, respectively. The average absolute skewness values of _x and _z are nonzero and approximately equal, while the skewness of _y is approximately zero. These results appear to be consistent with the presence of a large, three-dimensional organised structure in the surface layer. There is an apparent low-frequency contamination in the spectral density of _y and _z due mainly to small errors in estimating the sensitivity of the cold wires. The temperature derivatives were high-pass filtered, the filter being set to remove possible contributions from the large structure and to minimise low-frequency sensitivity contamination. The filtered rms ratios \~_x/\~_y and \~_x/\~_z were in the range 0.7 to 0.9, a result in qualitative agreement with that obtained in the laboratory boundary layer by Sreenivasan et al. (1977). The skewness of filtered _x or _z is negligible, consistent with local isotropy of small-scale temperature fluctuations and in support of the high wavenumber spectral isotropy discussed in Antonia and Chambers (1978).     

A convectively-driven boundary layer in the monsoon trough

Characteristic features of the convectively driven monsoon-trough boundary layer have been explored using the conserved-variable method of analysis. Aerological observations during the Monsoon Trough Boundary Layer Experiment 1990 (MONTBLEX-90) during 18–20 August have been used to investigate the thermodynamic features of the Convective Boundary Layer (CBL). Thermodynamic parameters such as _e , _es have been used to study the dynamical aspects of the CBL. Also, mixed-layer heights at an inland station, in the monsoon trough region, obtained from SODAR, are used to document the saturation of the mixed layer after the onset of the monsoon.     

On Trajectory Curvature as a Selection Criterion for Valid Lagrangian Stochastic Dispersion Models

Recently Wilson and Flesch (Boundary-Layer Meteorology, 84, 411-426, 1997) suggested that the average increment d z to the orientation = arctan(w/u) of the Lagrangian velocity-fluctuation vector can be used to distinguish the better Lagrangian stochastic models within the well-mixed class. Here it is demonstrated that the specification of d z constitutes neither a sufficient or universally applicable criterion to distinguish the better Lagrangian stochastic models within the well-mixed class. The hypothesis made by Wilson and Flesch that Lagrangian stochastic models with /P_E irrotational are zero-spin models, having d z=0, is proven     

Numerical studies of heat island circulations

A two dimensional model has been set up to investigate the circulation induced by an urban heat island in the absence of synoptic winds. The boundary conditions need to be formulated carefully and due to difficulties arising here, we restrict our attention to cases of initially stable thermal stratification. Heat island circulations are allowed to develop from rest and prior to the appearance of the final symmetric double cell pattern, a transitional multi-cell pattern is observed in some cases. The influence on the steady state circulation of various parameters is studied, among which are eddy transfer coefficients, the heat island intensity, the initial temperature stratification and the heat island size. Some results are presented for a case in which differential surface cooling beneath an initially stable atmosphere produces a circulation and an unstable layer capped by an elevated inversion over the city. It is hoped that this case is vaguely representative of the night-time heat island with no geostrophic wind.Notation c_p Specific heat at constant pressure - g Acceleration due to gravity - H Top of integration region - K_z Vertical eddy transfer coefficient - K_x, K_xH, K_xm Horizontal eddy transfer coefficients for heat and momentum - l ixing length - p Pressure - p₀ Reference surface pressure (1000 mb) - P_H (x, t) Pressure at z = H - R Specific gas constant for dry air - t Time - u, w Horizontal and vertical velocities - x, z Horizontal and vertical coordinates - x₁, x₂ Positions of discontinuities in surface temperature field (see Figure 2) - x_a Heat island half-width - x_b Boundary of integration region - Parameter in formula for eddy coefficients (variable-K case) = 18.0 - _s Intensity of heat island - Potential temperature field - Reference absolute temperature (variable-K case) - _r Reference temperature (° C) - _s Surface temperature - Q Air density     

Experiments On Buoyant Plume Dispersion In A Laboratory Convection Tank

Plume dispersion in the convective boundary layer (CBL) is investigated experimentally in a laboratory convection tank. The focusis on highly-buoyant plumes that loft near or become trapped in the CBL capping inversion and resistdownward mixing. Such plumes are defined by dimensionless buoyancy fluxes F_* 0.1, where F_* = F_b/(U w_* ² z_i), F_b is the stack buoyancy flux,U is the mean wind speed, w_* is the convective velocity scale, and z_i is the CBL depth. The aim is to obtain statistically-reliable mean (C) and root-mean-square (rms, _c) concentration fields as a function of F_* and the dimensionless distance X = w_*x/(U z_i), where x is the distance downstream of the source.The experiments reveal the following mainresults: (1) For 3 X 4and F_* 0.1, the crosswind-integrated concentration (CWIC) fields exhibit distinctly uniform profiles below z_i with a CWIC maximum aloft, in contrast to the nonuniform profiles obtained earlier by Willis and Deardorff. (2) The lateral dispersion (_y) variation with X is consistent with Taylor's theory for _* 0.1 and a buoyancy-enhanced dispersion, _y/z_i F_* ^1/3X^2/3, forF_* = 0.2 and 0.4. (3) The entrapment, the plume fraction above z_i, has a mean (E) that follows a systematic variationwith X and F_*, and a variability (_e/E) that is broad ( 0.3 to 2) near the source but subsides to 0.25 far downstream. (4) Vertical profiles of the concentration fluctuation intensity (c/C) are uniform for z < z_i and X > 1.5, but exhibit significant increases: (a) at the surface and close to the source (X 1.5), and(b) in the entrainment zone. (5) The cumulative distribution functions (CDFs) of the scaled concentration fluctuations (c/_c) separate into mixed-layer and entrainment-layer CDFs for X 2, with the mixed-layer group collapsing to a single distribution independent of z.These are the first experiments to obtain all components of the lateral and vertical dispersion parameters (rms meander, relative dispersion, total dispersion) for continuous buoyant releases in a convection tank. They also are the first tank experiments to demonstrate agreement with field observations of: (1) the scaled ground-level concentration along the plume centreline, and (2) the dimensionless lateral dispersion _y/z_i of buoyant plumes.     

Seasonal variation of Σθ with wind speed,direction and stability

For an airport site near Visakhapatnam, India, and based on 10 years of data for the months of January, April, August and October, values of are given as a function of wind speed, wind direction and Pasquill diffusion category.     

Observed variations of σθ and σΦ in the nocturnal drainage flow in a deep valley

The variations of and in the drainage flow in the Brush Creek valley of western Colorado are investigated using data from Doppler acoustic sodars and instrumented towers. The data were obtained on two experimental nights during the 1984 ASCOT field study. There is good agreement between the variations derived from low-level observations of the sodars and those derived from the towers located throughout the valley. The observed hourly average and in the nocturnal drainage flow are about 20 ° to 25 ° and 5 °, respectively; these values are much larger than those generally observed over flat terrain during nighttime stable conditions. After sunrise (about 0600 MST), as the valley warms and the flow direction changes to up-valley, these parameters increase sharply to their peak values at about 0800 MST and then decrease to their normal daytime values after about two hours.In the drainage flow, the hourly average varies inversely with wind speed according to the relation u 0.7ms^-1. The vertical standard deviation is much less enhanced by complex terrain than the horizontal standard deviation. The observed values are predicted fairly well by the local similarity theory.Oak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 andOak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 and     

Turbulent mixing of reactive gases in the convective boundary layer

We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯, ¯w¯ ¯ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.     

Observation of lake breeze penetration and subsequent development of the thermal internal boundary layer for the Nanticoke II Shoreline Diffusion Experiment

The turbulent structure of the lake breeze penetration and subsequent development of the thermal internal boundary layer (TIBL) was observed using a kytoon-mounted ultrasonic anemometer-thermometer. The lake breeze penetrated with an upward rolling motion associated with the upward flow near the lake breeze front. After the lake breeze front passed, the behaviors of the velocity and temperature at the top of the lake breeze layer were similar to those found in convective boundary layers (CBL). Comparing _gq/_*, _u /w _* and _w /w _* between the present observation of TIBL development after the passage of the lake breeze front and CBL data from the literature, the /_* values showed reasonable agreement; however, _u /w _* and _w /W_* had smaller values in the TIBL than in the CBL at higher altitudes. This is due to the differences in the mean velocity profiles. While the CBL has a uniform velocity profile, the TIBL has a peak at lower elevation due to the lake breeze penetration; the velocity then decreases with height.Present address: The Institute of Behavioral Science, 1-35-7 Yoyogi, Tokyo 151, Japan.     

The stably stratified internal boundary layer for steady and diurnally varying offshore flow

A two-dimensional numerical mesoscale model is used to investigate the internal structure and growth of the stably stratified internal boundary layer (IBL) beneath warm, continental air flowing over a cooler sea. Two situations are studied — steady-state and diurnally varying offshore flow. In the steady-state case, vertical profiles of mean quantities and eddy diffusion coefficients (K) within the IBL show small, but significant, changes with increasing distance from the coast. The top of the IBL is well defined, with large vertical gradients within the layer and a maximum in the coast-normal wind component near the top. Well away from the coast, turbulence, identified by non-zero K, decreases to insignificant levels near the top of the IBL; the IBL itself is characterised by a critical value of the layer-flux Richardson number equal to 0.18. The overall behaviour of the mean profiles is similar to that found in the horizontally homogeneous stable boundary layer over land.A simple physical model is used to relate the depth of the layer h to several relevant physical parameters viz., x, the distance from the coast and U, the large-scale wind (both normal to the coastline) and g/, being the temperature difference between continental mixed-layer air and sea surface, is the mean potential temperature and g is the acceleration due to gravity. Excellent agreement with the numerical results is found, with h = 0.014x ^1/2 U (g/)^–1/2.In the diurnally varying case, the mean profiles within the IBL show only small differences from the steady-state case, although diurnal variations, particularly in the wind maximum, are evident within a few hundred kilometres of the coast. A mesoscale circulation normal to the coast, and superimposed upon the mean offshore flow, develops seawards of the coastline with maximum vertical velocities about sunset, of depth about 2 km and horizontal scale 500 km. The circulation is related to the advection, and subsequent decay, of daytime convective turbulence over the sea.     

Diurnal variation of horizontal wind direction fluctuations in complex terrain at Geysers,Cal.

Horizontal diffusion in the surface layer is dependent on the standard deviation of wind direction fluctuations . Diurnal variation of this parameter in complex terrain was studied for the July 1979 Geysers, Cal., experiment using data from a network of 11 short meteorological towers in the 25 km² Anderson Creek watershed Valley side slopes are roughly 20 ° and maximum terrain difference is about 1 km.Values of for wind directions sampled for one hour at a height of 10 m are about 35 ° during the daytime. They slowly decrease to about 20 ° by 8 to 10 p.m. as stability increases but wind speeds are still relatively high. After 10 p.m. the drainage flow sets in at most stations, with speeds of 1 to 2 m s^-1, and average increases to about 30° during the period 11 p.m. to 6 a.m. In general, highest values of at night are associated with lowest values of wind speed and greatest static stability. This enhancement of by the terrain suggests that horizontal diffusion at night always conforms to that expected during nearly neutral stabilities. That is, Pasquill class D diffusion applies to the horizontal component all night in complex terrain.     

Estimation of the Monin-Obukhov similarity functions from a spectral model

From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function _m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - _m nondimensional mean shear - _H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - _D nondimensional divergence of vertical transports of turbulent linetic energy     

The dynamical range of global circulations — II

The dynamical range of global atmospheric circulations is extended to specialized parameter regions by evaluating the influence of the rotation rate () on axisymmetric, oblique, and diurnally heated moist models. In Part I, we derived the basic range of circulations by altering for moist and dry atmospheres with regular and modified surfaces. Again we find the circulations to be composed of only a few elementary forms. In axisymmetric atmospheres, the circulations consist of a single jet in the rotational midrange (^*=1/2–1) and of double jets in the high range (^*=2–4), together with one or two pairs of Hadley and Ferrel cells; where (^*=/ _E ) is the rotation rate normalized by the terrestrial value. These circulations differ from those predicted by firstorder symmetric-Hadley (SH₁) theory because the moist inviscid atmosphere allows a greater nonlinearity and prefers a higher-order meridional mode. The axisymmetric circulations do, however, resemble the mean flows of the natural system — but only in low latitudes, where they underlie the quasi-Hadley (QH) element of the MOIST flows. In midlatitudes, the axisymmetric jets are stronger than the natural jets but can be reduced to them by barotropic and baroclinic instablities. Oblique atmospheres with moderate to high tilts ( _P =25°–90°) have the equator-straddling Hadley cell and the four basic zonal winds predicted by the geometric theory for the solstitial-symmetric-Hadley (SSH) state: an easterly jet and a westerly tradewind in the summer hemisphere, and a westerly jet and an easterly tradewind in the winter hemisphere. The nonlinear baroclinic instability of the winter westerly produces a Ferrel cell and the same eddy fluxes as the quasi-geostrophic QG element, while the instability of the summer easterly jet produces a QG-Hadley (QGH) element with a unique, vertically bimodal eddy momentum flux. At high _P and low ^*, the oblique atmospheres reach a limiting state having global easterlies, a pole-to-pole Hadley cell, and a warm winter pole. At low tilts _P <10°, the oblique circulations have a mix of solstitial and equinoctial features. Diurnal heating variations exert a fundamental influence on the natural-Hadley (NH) circulations of slowly rotating systems, especially in the singular range where the zonal winds approach extinction. The diurnality just modifies the NH element in the upper singular range (1/45^*1/16), but completely transforms it into a subsolar-antisolar Halley circulation in the lower singular range (0^*<1/45). In the modified NH flows, the diurnality acts through the convection to enhance the generation of the momentum-transferring planetary waves and, thereby, changes the narrow polar jets of the nondiurnal states into broad, super-rotating currents. Circulation theory for these specialized flows remains rudimentary. It does not explain fully how the double jets and the multiple cells arise in the axisymmetric atmospheres, how the QGH element forms in the oblique atmospheres, or how waves propagate in the slowly rotating diurnal atmospheres. But eventually all theories could, in principle, be compared against planetary observation: with Mars testing the QGH elements; Jupiter, the high-range elements; Titan, the equinoctial and solstitital axisymmetric states; and Venus, the diurnally modified NH flows.     

Growth Of The Summer Daytime Convective Boundary Layer At Anand

The heights of the daytime convective boundary layer (CBL), computed by a one-dimensional model for a bare soil surface at a semi-arid station,Anand, during the dry and hot summer month of May 1997, are presented. As input, the model requires surface heat flux, friction velocity and air temperature as functions of time. Temperature data at the one-metre level from a tower and sonic anemometer data at 9.5 m collected during the period 13–17 May 1997 in the Land Surface Processes Experiment (LASPEX-97) are used to compute hourly values of surface heat flux, friction velocity and Obukhov length following the operational method suggested by Holtslag and Van Ulden [J. Climate Appl. Meteorol. 22,517–529 (1983)]. The model has been tested with different values for the potential temperature gradient ( ) above the inversion. The model-estimated CBL heights comparefavourably with observed heights obtained from radiosonde ascents.     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.     

Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface

Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.     

Atmospheric estimates of power-law exponents Μ and Μθ

Measurements in the atmospheric surface layer of sixth-order velocity structure functions and of sixth-order mixed velocity-temperature structure functions support values of and previously obtained in the laboratory at moderate turbulence Reynolds numbers.     

The estimation of the surface-layer parameters from wind velocity,temperature and humidity profiles by least-squares methods

The estimation of the surface-layer parameters u _* (friction velocity), _* and q _* (temperature and humidity scales), _r and q _r (temperature and humidity reference values), z _o (roughness length) and d (zero-displacement) from vertical profiles of wind velocity, temperature and humidity by least-squares methods is described. The estimation is based on the flux-gradient relationships and the constant flux assumption for the transfer of momentum, sensible heat and matter near the Earth's surface.Test calculations were carried out with the vertical profile data from the GREIV I 1974 experiment and the Great Plains Turbulence Project.     

An observational study of the vertical profile of the high frequency fluctuations of the wind in the atmospheric boundary layer

This paper summarizes some measurements of high-frequency turbulence made at Cardington during the years 1968, 1969 and 1970 at heights up to 900 m. It discusses the statistical distribution of the data which appears to be closely log-normal. Also it is shown how the mean profiles of the derived dissipation of turbulent kinetic energy () can be rationalized to some extent in terms of atmospheric stability and low-level wind speed. A close correlation between and the mean wind and temperature profiles up to 900 m is illustrated and some discussion of the turbulent energy budget throughout the boundary layer is presented. The use and limitations of the constant flux layer relations in calculatingz ₀ andL from the estimates of, at the lower heights, is brought out.     

Trajectory Curvature As A Selection Criterion For valid Lagrangian Stochastic Dispersion Models

Among well-mixed multi-dimensional Lagrangian stochastic (LS) dispersion models, we observe that those in poorest agreement with observations produce spiralling trajectories, with an associated reduction in dispersion. We therefore investigate statistics of increments d ' to the orientation '= arctan(W'/U') of the Lagrangian velocity-fluctuation vector – as a possible means to distinguish the better LS models within the well-mixed class. Zero-spin models, having d' = 0, are found to provide best agreement with observations. It is not clear however, whether imposition of the zero-spin property selects (in conjunction with the well-mixed condition) a unique model.