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).     

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.     

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     

An improved calibration for tethered balloon wind measurements

A previously published technique for using tethered spherical balloons as anemometers for measuring light low-level winds has been further developed. Earlier data on the relationship between the aerodynamic drag coefficient and the Reynolds number of spherical rubber balloons were combined with a large number of new data and re-analysed; and the errors in the relationship were estimated. The results allowed a more accurate calculation of wind speed from the deflection of a tethered balloon from the vertical. When combined with a new technique for calculating the effects of the tether, this enabled light to moderate low-level winds at fixed heights up to 600 m or more to be measured with simple, cheap, and readily mobile equipment; and a slight modification of the technique allowed measurement of winds in and above fog. Wind speeds measured by the ballon technique showed reasonably good agreement with measurements by an anemometer carried beneath the balloon.Glossary of Symbols a, b, c Coefficients in the relationship between lnC _d and lnR - A Quantity under square root in solution for lnV whena0 - C _d Wind drag coefficient for balloon - C _dc Value ofC _d given by calibration curve of Table I - D Dynamic wind pressure force on balloon - F Buoyant free lift of balloon with load - Re Reynold's number of balloon (sphere) - R = Re/10⁵ - r Radius of sphere - T Tension in tether - V Wind speed - ₈₃() =(lnC _dc -lnC _d ) when 83° , or 0 for other - Error in lnC _d - Elevation of tether where attached to balloon - Elevation of balloon from ground tether point - Molecular viscosity of air - Ratio of circumference to diameter of circle - Density of air     

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     

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     

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.     

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.     

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.     

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.     

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.     

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 prediction of dust erosion by wind: An interactive model

We have devised a partial differential equation for the prediction of dust concentration in a thin layer near the ground. In this equation, erosion (detachment), transport, deposition and source are parameterised in terms of known quantities. The interaction between a wind prediction model in the boundary layer and this equation affects the evolution of the dust concentration at the top of the surface layer. Numerical integrations are carried out for various values of source strength, ambient wind and particle size. Comparison with available data shows that the results appear very reasonable and that the model should be subjected to further development and testing.Notation (x, y, z, t) space co-ordinates and time (cm,t) - u, v components of horizontal wind speed (cm s^–1) - u _g, v_g components of the geostrophic wind (cm s^–1) - V=(u²+v²)^1/2 (cm s^–1) - (û v)= 1/(h – k) _k ^h(u, v)dz(cm s^–1) - V _* friction velocity (cm s^–1) - z ₀ roughness length (cm) - k ₁ von Karman constant =0.4 - V _d deposition velocity (cm s^–1) - V _g gravitational settling velocity (cm s^–1) - h height of inversion (cm) - k height of surface layer (cm) - potential temperature (°K) - _gr potential temperature at ground (°K) - _K potential temperature at top of surface layer (°K) - P pressure (mb) - P ₀ sfc pressure (mb) - C _p/C_v - (t)= /z lapse rate of potential temperature (°K cm^–1) - A(z) variation of wind with height in transition layer - B(z) variation of wind with height in transition layer - Cd drag coefficient - C _HO transfer coefficient for sensible heat - C dust concentration (g m^–3) - C _K dust concentration at top of surface layer (g m^–3) - D(z) variation with height of dust concentration - u, v, w turbulent fluctuations of the three velocity components (cm s^–1) - A ₁ constant coefficient of proportionality for heat flux =0.2 - Ri Richardson number - g gravitational acceleration =980 cm s^–2 - Re Reynolds number = - D _s thickness of laminar sub-layer (cm) - v molecular kinematic viscosity of air - coefficient of proportionality in source term - dummy variable - t time step (sec) - n time index in numerical equations On sabbatical leave at University of Aberdeen, Department of Engineering, September 1989–February 1990.     

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     

Determination of similarity functions of the resistance laws for the planetary boundary layer using surface-layer similarity functions

Functional forms of the universal similarity functions A, B (for wind components parallel and normal to the surface stress), and C (for potential temperature difference) are determined based on the generalized theory of the resistance laws for the Planetary Boundary Layer (PBL). The similarity-profile functions for the surface layer are matched with the velocity and temperature-defect profiles that are assumed to have shapes modified by certain powers of nondimensional height z/h, where h is the PBL height. The powers of the outer-layer profile functions are determined, so that the functions become negligible in the surface layer. To close the temperature defect law, an assumption that the temperature gradient across the top of the PBL is continuous with the stratification of the overlying atmosphere is used. The result of this assumption is that nondimensional momentum and temperature profiles in the PBL can be described in terms of four basic ratios: (1) roughness ratio = /h (2) scale-height ratio =|f|h/u_*, (3) ambient stratification parameter =h/_*, and (4) stability parameter =h/L, where L is the Monin-Obukhov length, z₀ is the surface roughness, is the upper-air stratification, u _* is the friction velocity, and _* is the temperature scale at the surface. For stable conditions, the scale-height ratio can be related to the atmospheric stability and the upperair stratification, and the generalized similarity and Rossby number similarity theories become identical. Under appropriate boundary conditions, function A is explicitly dependent on the stability parameter , while B is a function of scale-height ratio , which in turn depends on the stability. Function C is shown to be dependent on the stability and the upper-air stratification, due to the closure assumption used for the temperature profile.The suggested functional forms are compared with other empirical approximations by several authors. The general framework used to determine the functional forms needs to be tested against good boundary-layer measurements.     

Inferring the thermal-infrared hemispheric emission from a sparsely-vegetated surface by directional measurements

The thermal-infrared (longwave) emission from a vegetated terrain is generally anisotropic, i.e., the emission temperature varies with the view direction. If a directional measurement of temperature is considered to be equal to the effective temperature of the hemispheric emission, then the estimate of the latter can be significantly in error. The view-direction (zenith angle _eq ) at which the emission equivalence does hold is determined in our modeling study. In a two-temperature field-of-view (soil and plants), _eq falls in a narrow range depending on plant density and canopy architecture. _eq does not depend on soil and (uniform) plant temperatures nor on their ratio, even though the pattern of emission vs. the view direction depends crucially on this ratio. For a sparse canopy represented as thin, vertical cylindrical stalks (or vertical blades uniformly distributed in azimuth) with horizontal facets, _eq ranges from 48 to 53° depending on the optical density of the vertical elements alone. When plant elements are modeled as small spheres, _eq lies between 53 to 57° (for the same values of the canopy optical density). Only for horizontal leaves (a truly planophile canopy) is the temperature measured from any direction equal to the temperature of the hemispheric emission. When the emission temperature changes with optical depth within the canopy at a specified rate, _eq depends to some extent on that rate. For practically any sparsely vegetated surface, a directional measurement at the zenith angle of 50° offers an appropriate evaluation of the hemispheric emission, since the error in the estimate will, at most, only slightly exceed 1% (around 4 W m^–2). Estimates of the hemispheric emission through a nadir measurement, on the other hand, can be in error in some cases by about 10%, i.e., on the order of 40 W m^–2....by a small sample we may judge the whole piece... Miguel de Cervantes, 1605, inDon Quixote de la Mancha, Pt. I, Ch. 4     

Estimates of sensible heat flux from observations of temperature fluctuations

Comparisons between sensible heat flux measured using eddy correlation instrumentation and estimated using the temperature fluctuation method are presented for four types of surface in West Africa. Agreement between measured and estimated values is good. Regression of estimated on measured sensible heat flux gave a mean slope of 0.98 with a mean r ² of 0.94 for bare soil, mature millet, fallow savannah and tiger bush. Estimates of heat flux from temperature fluctuations measured by an instrument mounted beneath a tethered balloon are also shown to be in close agreement with eddy correlation measurements made at the surface (regression slope = 0.98, r ² = 0.84). The results provide evidence that the ratio /_×is indeed a universal function of z/L for all the surface types considered.     

The use of σ T as a temperature scale in the atmospheric surface layer

The standard deviation of temperature _T is proposed as a temperature scale and as a velocity scale to describe the behaviour of turbulent flows in the Atmospheric Surface Layer (ASL), instead of _* andu _* of the Monin—Obukhov similarity theory, and ofT _f andU _f used for free convection stability conditions. On the basis of experimental evidence reported in the literature, it is shown that _T T _f andv _* U _f in the free convection region, and _{T *} andv _* U _* in nearneutral and stable conditions. This implies that the proposed scales can be applied for all stabilities. Furthermore, a new length scale is proposed and its relation with Obukhov length is given. Also, a simple semi-empirical expression is presented with which _T andv _* can be evaluated in a rather simple way. Some examples of practical applications are given, e.g., a stability classification for unstable conditions.     

Local similarity of spectral and cospectral characteristics in the stable-continuous boundary layer

The local similarity theory, presented in the recent papers of Sorbjan (1986a, b), is extended by taking into consideration spectral (u, v, w, ) and cospectral (uw, w, u) densities in the stable-continuous boundary layer. The resulting universal expressions for spectra, cospectra and the reduced frequencies of their peaks are in agreement with empirical data from the Kansas 1968 surface-layer and Minnesota 1973 boundary-layer experiments. In addition, the universal functions for the structure parameters and the dissipation rates are also derived and shown to fit the empirical data well.On leave from Institute of Environmental Engineering, Warsaw Polytechnic University, 00653 Warsaw, Poland.     

An observational aircraft-based study of sea-breeze frontogenesis

In the summer of 1988/89 flights were carried out in the Coorong coastal area of South Australia to investigate sea-breeze fronts. The flights yielded data sets of the structure of the fronts in the cross-frontal direction with a spatial resolution of approximately 3 m. The study is focused on the budgets of sensible and latent heat in the vicinity of the front and on frontogenesis/frontolysis processes which are closely related to budget considerations.The frontogenesis relationships and the budgets were established on a 2 km length scale by low-pass filtering of the space series. As the wind components were measured with high accuracy, all processes which determine frontogenesis could be evaluated and are displayed in x,z-cross-sections: these are the confluence, shear and diabatic effects, all of which play a role in q/x-, q/z-, /x- as well as /z-frontogenesis. A detailed analysis is given for two different states of frontal development. The presented results shed much light on the governing physical processes in the frontal region with strong emphasis on the effects of confluence-generated updrafts, on shear instabilities causing bulges and clefts in the frontal surface as well as producing the elevated frontal head, and on processes related to differential heating and moistening.