Mesoscale data assimilation and prediction of low stratus in the Alpine region

Summary A number of problems related to mesoscale numerical prediction of low stratus in the Alpine region are formulated, and addressed in a series of experiments for two wintertime cases. These problems include modelling aspects and issues of data assimilation which are relevant particularly in relation to the observation nudging technique. A focus is on the influence of orography.A comparison of operational optimum interpolation, and nudging of routine rawinsonde and surface-level data reveals that nudging often yields better analyses and forecasts of low stratus, and notably of the sharp vertical temperature and humidity gradients. However, the humidity advection scheme of the model and, near steep terrain, particularly the horizontal diffusion along the model's -levels are identified to contribute to spurious vertical smoothing which can result in erroneous cloud dissipation. On occasions, forecasts succeeding a nudging period are more sensitive to this process due to the sharper initial vertical gradients.Specific problems of representiveness arise when low-level rawinsonde information is spread laterally along the sloping -levels from low to high terrain. A new concept for -layer models is introduced by speading the observational information along isentropic surfaces, and this tends to improve the low stratus prediction over steep and even moderate orography. A partly successful attempt to take advantage of the steep Alpine orography is made by applying this concept to surface-level humidity data from a high-resolution network of Alpine surface stations which are distributed relatively uniformly in the vertical.With 19 Figures     

A Comparative Analysis of Transpiration and Bare Soil Evaporation

Transpiration E^v and bare soil evaporation E^b processes are comparatively analysed assuming homogeneous and inhomogeneous areal distributions of volumetric soil moisture content . For a homogeneous areal distribution of we use a deterministic model, while for inhomogeneous distributions a statistical-deterministic diagnostic surface energy balance model is applied. The areal variations of are simulated by Monte-Carlo runs assuming normal distributions of .The numerical experiments are performed for loam. In the experiments we used different parameterizations for vegetation and bare soil surface resistances and strong atmospheric forcing. According to the results theE^v()-^Eb() differences are great, especially in dry conditions. In spite of this, the available energy flux curves of vegetation A^v() and bare soil A^b() surfaces differ much less than the E^v() and ^Eb() curves. The results suggest that E^v is much more non-linearly related to environmental conditions than ^Eb. Both E^v and ^Eb depend on the distribution of , the wetness regime and the parameterization used. With the parameterizations, ^Eb showed greater variations than E^v. These results are valid when there are no advective effects or mesoscale circulation patterns and the stratification is unstable.     

Relative optical mass functions for air, water vapour, ozone and nitrogen dioxide in atmospheric models presenting different latitudinal and seasonal conditions

Summary A study of the dependence features of the relative optical mass functions for air, water vapour, ozone and nitrogen dioxide on the apparent solar zenith angle was performed by calculating these optical parameters by means of the well-known computer code LOWTRAN 7 at several values of and for nine atmospheric models characterized by different latitudes and seasons. Moreover, other investigations were performed on the dependence features of (i) the relative optical air mass on the thermal characteristics of the low troposphere, (ii) the relative optical water vapour mass on the vertical distribution characteristics of absolute humidity in the troposphere, and (iii) the relative optical mass function for ozone and nitrogen dioxide on the shape characteristics of the vertical profiles of the two gaseous concentrations and the concentration peak altitudes. The results are compared with the values given by the two simple formulas proposed by Kasten (1966) for air and water vapour and the formulas defined by Young (1969) and Staehelin et al. (1995) for ozone and nitrogen dioxide. From this comparison, a wide set of correction factors were obtained which can be conveniently used in the analysis of multispectral sun-radiometric measurements for calculating, with a very high precision, the values of the four optical mass functions at all the angles in the 0° to 87° range, corresponding to the various latitudinal and seasonal conditions described by the nine atmospheric models.With 9 Figures     

Temperature distribution and current system in a convectively mixed lake

During spring and autumn, many lakes in temperate latitudes experience intensive convective mixing in the vertical, which leads to almost isothermal conditions with depth. Thus the regime of turbulence appears to be similar with that characteristic of convective boundary layers in the atmosphere. In the present paper a simple analytical approach, based on boundary-layer theory, is applied to convective conditions in lakes. The aims of the paper are firstly to analyze in detail the temperature distribution during these periods, and secondly to investigate the current system, created by the horizontal temperature gradient and wind action. For these purposes, simple analytical solutions for the current velocities are derived under the assumption of depth-constant temperatures. The density-induced current velocities are shown to be small, in the order of a few mm/sec. The analytical model of wind-driven currents is compared with field data. The solution is in good qualitative agreement with observed current velocities under the condition that the wind field is steady for a relatively long time and that residual effects from former wind events are negligible.The effect of the current system on an approximately depth-constant temperature distribution is then checked by using the obtained current velocity fields in the heat transfer equation and deriving an analytical solution for the corrected temperature field. These temperature corrections are shown to be small, which indicates that it is reasonable to describe the temperature distribution with vertical isotherms.Notation T temperature - t time - x, y, z cartesian coordinates - molecular viscosity - _h , _v horizontal and vertical turbulent viscosity - K _h ,K _v horizontal and vertical turbulent conductivity - Q heat flux through the water surface - D depth - u, v, w average current velocity components inx, y andz directions - f Coriolis parameter - p pressure - density - g gravity acceleration - a constant in the freshwater state equation - h _s deviation from the average water surface elevation - L _*,H _* length and depth scale - U _*,W _* horizontal and vertical velocity scale - T temperature difference scale - bottom slope - u _* friction velocity at the water surface - von Karman constant - L Monin-Obukhov length scale - buoyancy parameter - l turbulence length scale - C ₁,C ₂,C ₃ dimensionless constants in the expressions for the vertical turbulent viscosity - , dimensionless vertical coordinate and dimensionless local depth - angle between surface stress direction andx-axis - T _bx ,T _by bottom stress components - c bottom drag coefficient     

An application of the E-ε turbulence model for studying coupled air-sea boundary-layer structure

An E- turbulence model is used to study air-sea interaction characteristics and turbulence structure using a coupled model for air-sea boundary layers. The E- turbulence model consists of equations for the turbulent kinetic energy, the energy-dissipation, and for the turbulent exchange coefficient expressed in terms of turbulent kinetic energy and energy-dissipation. The energy-dissipation equations for the air-sea interface are solved analytically to obtain boundary conditions for energy-dissipation at the interface. The air-sea interaction and turbulence characteristics of the E- model are compared with those of the mixing-length model and with available observations.The simulations demonstrate that the air-sea interaction parameters obtained by the E- model agree well with observations. The numerical studies also show that the E- turbulence model with appropriate constants can give good results in modeling coupled air-sea boundary-layer flows.     

The behaviour of aerosol optical depth during clear summer days in Athens,Greece

Summary The integral aerosol optical depths (k ) at the hour of 08:20 Local Standard Time (LST), are compared with those calculated previously at 11:20 and 14:20 LST, for clear days during summer in Athens over the period 1962–1988. The mean values at 08:20 LST were consistently lower than the values at 11:20 and 14:20 LST. The influence of the vertical wind profile on the values ofk was also investigated. A comparison was made of the wind profiles at 02:00 and 14:00 LST, for days in which the 11:20 and 14:20 LST values ofk were 0.200 andk 0.350, respectively. The corresponding bulk wind shear s was also found for the period 1980–1988. The most significant results occurred with the first category of days. The resultant wind velocities from the surface to the 900 hPa level, in each hour were higher by 2–4 m·s^–1 with respect to the corresponding values for the second category. At 02:00 LST the bulk wind shear showed a considerable difference (1.8) between the two categories of days in the surface to 700 hPa layer at 02:00 LST. Finally, the associated weather conditions that appear to initiate a period of low values ofk (k 0.200) at 11:20 and 14:20 LST were examined for the period 1980–1988. Fifteen such cases were identified and it was found that they all occurred after the passage of weak cold fronts.With 6 Figures     

The source area influencing a measurement in the Planetary Boundary Layer: The “footprint” and the “distribution of contact distance”

This paper considers the ground area which affects the properties of fluid parcels observed at a given spot in the Planetary Boundary Layer (PBL). We examine two source-area functions; the footprint, giving the source area for a measurement of vertical flux: and the distribution of contact distance, the distance since a particle observed aloft last made contact with the surface. We explain why the distribution of contact distance extends vastly farther upwind than the footprint, and suggest for the extent of the footprint the inequalities: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9Lq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9W8qr0-vr% 0-viWZqaceaabiGaciaacaqabeaadaqaaqaaaOabaeqabaGaamyvam% aalaaabaGaamiAaaqaaiabeo8aZnaaBaaaleaacaWGxbaabeaakiaa% cIcacaWGObGaaiykaaaacqGH8aapcaWG4bGaeyipaWJaamyvaKazaa% iadaGabaqaamaaDaaajqwaacqaaiaadIgacaGGVaGabmOEayaacaGa% aiilaiaabccacaGGVbGaaiiDaiaacIgacaGGLbGaaiOCaiaacEhaca% GGPbGaai4CaiaacwgaaeaacaWGubWaaSbaaKazcaiabaGaamitaaqa% baqcKfaGaiaacIcacaWGObGaaiykaiaabYcacaqGGaGaaeiAaiaabc% cacaGGHbGaaiOyaiaac+gacaGG2bGaaiyzaiaabccacaGGZbGaaiyD% aiaackhacaGGMbGaaiyyaiaacogacaGGLbGaeyOeI0IaaiiBaiaacg% gacaGG5bGaaiyzaiaackhaaaaajqgaacGaay5EaaaakeaaaeaacaGG% 8bGaamyEaiaacYhacqGH8aapcqaHdpWCdaWgaaWcbaGaamODaaqaba% GccaGGOaGaamiAaiaacMcadaWcaaqaaiaadIhaaeaacaWGvbaaaaaa% aa!7877!\[\begin{array}{l} U\frac{h}{{\sigma _W (h)}} < x < U\left\{ {_{h/\dot z,{\rm{ }}otherwise}^{T_L (h){\rm{, h }}above{\rm{ }}surface - layer} } \right. \\ \\ |y| < \sigma _v (h)\frac{x}{U} \\ \end{array}\] where U is the mean streamwise (x) velocity, h is the observation height, _L is the Lagrangian timescale, _v and _w are the standard deviations of the cross-stream horizontal (y) and vertical (z) velocity fluctuations, and is the Lagrangian Similarity prediction for the rate of rise of the centre of gravity of a puff released at ground.Simple analytical solutions for the contact-time and the footprint are derived, by treating the PBL as consisting of two sub-layers. The contact-time solutions agree very well with the predictions of a Lagrangian stochastic model, which we adopt in the absence of measurements as our best estimate of reality, but the footprint solution offers no improvement over the above inequality.     

Wave-mean flow interactions in the upper atmosphere

The nature of internal gravity waves is described with special emphasis on their ability to transport energy and momentum. The conditions under which these fluxes interact with the mean state of the atmosphere are described and the results are applied to various problems of the upper atmosphere, including the quasi-biennial oscillation, the heat budget of the thermosphere, the general circulation of the mesosphere, turbulence in the mesosphere, and even the 4-day circulation of the Venusian stratosphere.Gravity waves have long been recognized as an important element in the dynamics of the upper atmosphere - largely due to their very large amplitudes in this region. It is the implied purpose of this paper to convey some of the thinking that has gone on about the role of gravity waves in the large-scale circulation of the upper atmosphere. Insofar as gravity waves are now being identified as important entities in the lower atmosphere as well, it is possible that mechanisms identified in the upper atmosphere will prove relevant to the troposphere.Alfred P. Sloan Foundation Fellow. Now at Harvard University.     

Measurements of solar radiation and estimation of optical depth in the high Andes of Peru

Summary During an expedition to the high Andes of Southern Peru in June–July 1977, measurements of direct solar radiation in four spectral bands (0.270–0.530–0.630–0.695–2.900 ) were conducted at six sites in elevations ranging from sea level to 5645 m. These measurements were evaluated in Langley plots to determine total optical depths () and irradiances at the top of the atmosphere. In addition, water vapor optical depths (_wv) were calculated from the mean radiosounding over Lima during the expedition, and Rayleigh (_ray) and ozone (_oz) optical depths were obtained from published tabulations. Subtracting _ray, _oz, and _wv from yielded estimates of aerosol optical depth _aer. The components _ray and _oz decrease from the shorter towards the longer wavelength bands and from the lower towards the higher elevation sites; _aer also decreases towards the higher elevations. Particularly pronounced is the decrease of _aer and from the lowlands of the Pacific coast to the highlands of the interior, reflecting the effect of a persistent lower-tropospheric inversion and the contrast from the marine boundary layer to the clear atmosphere of the high Andes.With 4 Figures     

Field measurements of snow-drift threshold and mass fluxes,and related model simulations

Field measurements were carried out to calculate the threshold friction velocity for snow saltation, and mass fluxes during snow drift. The wind was measured in three components by an ultrasonic anemometer, and the mass fluxes were determined using an optical sensor (snow particle counter), acoustic sensors (Flowcapt) and mechanical traps. The threshold friction velocity was found to be correlated to the grain size (R²=0.75). The mass flux measurements were compared with numerical simulations of snow drift, and it was demonstrated that the maximum snow transport takes place at shear stress values of roughly two times the average shear stress over 20 min. By implementing a probability distribution for the shear stress the mass flux was simulated with only the mean measured value of the shear stress as input. This procedure enables the future use of the numerical model for operational applications.     

Shear convection

The paper discusses convection in the presence of wind shear, a condition analysed previously by Zilitinkevich (1971). This region (between the forced and fully developed convective layers) was also considered by Betchov and Yaglom (1971). In the present paper the author endeavors to develop a consistent analysis from the basic hypothesis of a very weak interaction between the vertical convective motions and mechanical turbulence, employing a new similarity model of the turbulent regime. Additional experimental data are introduced. Unlike the notation used in the references quoted above, this regime is termed shear convection rather than free convection. The latter is traditionally regarded as synonymous with the terms pure or fully developed convection.     

Occurrence of roll circulations in a shallow boundary layer

Meteorological measurements taken at the Näsudden wind turbine site during slightly unstable conditions have been analyzed. The height of the convective boundary layer (CBL) was rather low, varying between 60 and 300 m. Turbulence statistics near the ground followed Monin-Obukhov similarity, whereas the remaining part of the boundary layer can be regarded as a near neutral upper layer. In 55% of the runs, horizontal roll vortices were found. Those were the most unstable runs, with -z _i/L > 5. Spectra and co-spectra are used to identify the structures. Three roll indicators were identified: (i) a low frequency peak in the spectrum of the lateral component at low level; (ii) a corresponding increase in the vertical component at mid-CBL; (iii) a positive covariance {ovvw} together with positive wind shear in the lateral direction (V/z) in the CBL. By applying these indicators, it is possible to show that horizontal roll circulations are likely to be a common phenomenon over the Baltic during late summer and early winter.     

Applications of the transilient turbulence parameterization to atmospheric boundary-layer simulations

An improved first-order closure approximation is developed for the non-local transilient turbulence parameterization. Instead of using Richardson numbers, this improved approach uses non-local approximations to the shear, buoyancy, storage, and dissipation terms of the turbulence kinetic energy equation to parameterize the turbulent mixing potential between every combination of grid points in a 1-D model of the atmosphere. The original (n ² – n) degrees of freedom associated with the independent transilient matrix coefficients for a model of n grid points is thus reduced to four degrees of freedom associated with the four free parameters.The resulting parameterization is applied to three consecutive case-study days of boundary-layer data acquired near the Cabauw tower in The Netherlands. The first day is used for sensitivity tests to select the best values of the four free parameters. The remaining two days, used as independent tests, demonstrate that realistic entraining mixed layers and nocturnal boundary layers form in the model without explicitly parameterizing such boundary layers. Simulations are also presented for two idealized cases: dry stratocumulus-induced convection and a neutral boundary layer.Work performed while a visiting scientist at the Royal Netherlands Meteorological Institute.     

A coupled ocean-atmosphere climate model: temperature versus salinity effects on the thermohaline circulation

A simple nonlinear three-box ocean model of the North Atlantic Ocean including the rudiments of eddy mixing, vertical stratification and thermohaline circulation is first presented. It is subject to uniform latitudinal differential heating, q, and net evaporation m _e , and includes a linear equation of state. Two quite different limiting steady-state solutions exist. The first has a warm saline surface water and a cold, low-salinity deep ocean; deep water is primarily formed in higher latitudes by the prevalence of differential heating. A second limiting solution consists of a warm saline deep ocean underlying a cool, low-salinity surface ocean; deep water is formed primarily in lower latitudes as a consequence of large differential evaporation. A coupled ocean-atmosphere model, in which the oceanic surface heat fluxes are determined internally but with differential evaporation at the ocean surface m _e remaining an external parameter, is next presented. The atmosphere component is a simple energy balance model that emphasizes the vertical fluxes of radiative, sensible and latent heat fluxes but does not include temperature-albedo feedback. Model response depends on the external parameters m _e and , controlling the magnitude of the thermohaline-driven circulation, and on the magnitudes of the eddy mixing coefficients and the solar constant. For small m _e , a steady-state solution corresponding to a cold fresh deep ocean is found, qualitatively similar to the modern ocean. For large m _e , a steady-state solution with a warm saline deep ocean occurs; this solution resembles conceptual models that have been proposed for the warm saline Cretaceous ocean. There exists an intermediate region of values of m _e for which the solutions are more complex. On the lower end of this region, both the cold fresh deep-ocean and warm saline deep-ocean circulations coexist as stable equilibria. On the upper end, the cold-deep ocean becomes unstable, manifesting oscillations with growing amplitude, and ultimately reaches the warm saline deep-ocean solution. In the neighborhood of a cusp on the , m _e plane, that is, for relatively small , more complex behaviour occurs, which has not yet been fully analyzed. The model response in the region of complexity is not sensitive to changes in the solar constant but is sensitive to the eddy mixing coefficients.     

On the mean monthly equivalent potential temperature and rainfall in West Africa

Summary Rainfall in West Africa is examined in relation to monthly mean equivalent potential temperature ( _e )at the earth's surface. The study revealed that monthly mean equivalent potential temperature ( _e ) and monthly rainfall (R) generally decreased northwards from the equator.A good relationship existed betweenR and _e in the northern zone of West Africa (i.e., north of 7.5° N). No definite relationship existed in the southern zone. In the northern zone, the departure of _e from its annual mean ( ) first became positive about a month before the onset of the rains. Positive departures from ) generally resulted in more than normal (or average) rainfall in this zone. In general, little or no rainfall occurred in West Africa whenever _e was less than 320 K.

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Zusammenfassung Der Niederschlag (MonatssummeR) in Westafrika wird in Zusammenhang mit der mittleren monatlichen Äquivalent-temperatur ( _e ) an der Erdoberfläche untersucht. Es zeigte sich, daß die Monatswerte beider Elemente im allgemeinen vom Äquator nach Norden abnehmen.ZwischenR und _e ergab sich für das nördliche Westafrika (nördlich von 7.5° N) eine gute, für die südliche Zone jedoch keine beweisbare Übereinstimmung. In der nördlichen Zone übertraf _e das Jahresmittel erstmals etwa einen Monat vor Beginn der Regenzeit. Positive Abweichungen vom mittleren _e hatten immer übernormalen Niederschlag in dieser Zone zur Folge. Dagegen gab es wenig oder keinen Niederschlag in Westafrika, wenn _e unter 320 K lag.

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With 7 Figures     

Limitations of the Eddy-correlation technique for the determination of turbulent fluxes near the surface

Recent measurements of turbulent fluxes by Desjardins and Lemon (1973) probably involve underestimates in these fluxes of 40 % or more, because of poor sensor response to high frequency fluctuations. Indications are that use of the Gill propeller anemometer as a sensor of vertical velocity fluctuations should be confined to heights greater than 5 m over land, and greater than 10 m over the sea.     

A numerical modeling study of the marine boundary layer over the Gulf Stream during cold air advection

A two-dimensional mesoscale model has been developed to simulate the air flow over the Gulf Stream area where typically large gradients in surface temperature exist in the winter. Numerical simulations show that the magnitude and the maximum height of the mesoscale circulation that develops downwind of the Gulf Stream depends on both the initial geostrophic wind and the large-scale moisture. As expected, a highly convective Planetary Boundary Layer (PBL) develops over this area and it was found that the Gulf Stream plays an important role in generating the strong upward heat fluxes causing a farther seaward penetration as cold air advection takes place. Numerical results agree well with the observed surface fluxes of momentum and heat and the mesoscale variation of vertical velocities obtained using Doppler Radars for a typical cold air outbreak. Precipitation pattern predicted by the numerical model is also in agreement with the observations during the Genesis of Atlantic Lows Experiment (GALE).List of Symbols u east-west velocity [m s^–1] - v north-south velocity [m s^–1] - vertical velocity in coordinate [m s^–1] - w vertical velocity inz coordinate [m s^–1] - gq potential temperature [K] - q moisture [kg kg^–1] - scaled pressure [J kg^–1 K^–1] - U _g the east-south component of geostrophic wind [m s^–1] - V _g the north-south component of geostrophic wind [m s^–1] - vertical coordinate following terrain - x east-west spatial coordinate [m] - y north-south spatial coordinate [m] - z vertical spatial coordinate [m] - t time coordinate [s] - g gravity [m² s^–1] - E terrain height [m] - H total height considered in the model [m] - q _s saturated moisture [kg kg^–1] - p pressure [mb] - p ₀₀ reference pressure [mb] - P precipitation [kg m^–2] - vertical lapse rate for potential temperature [K km^–1] - L latent heat of condensation [J kg^–1] - C _p specific heat at constant pressure [J kg^–1 K^–1] - R gas constant for dry air [J kg^–1 K^–1] - R _v gas constant for water vapor [J kg^–1 K^–1] - f Coriolis parameter (2 sin ) [s^–1] - angular velocity of the earth [s^–1] - latitude [^o] - K _H horizontal eddy exchange coefficient [m² s^–1] - t integration time interval [s] - x grid interval distance inx coordinate [m] - y grid interval distance iny coordinate [m] - adjustable coefficient inK _H - subgrid momentum flux [m² s^–2] - subgrid potential temperature flux [m K s^–1] - subgrid moisture flux [m kg kg^–1 s^–1] - u _* friction velocity [m s^–1] - _* subgrid flux temperature [K] - q _* subgrid flux moisture [kg kg^–1] - w _* subgrid convective velocity [m s^–1] - z ₀ surface roughness [m] - L Monin stability length [m] - _s surface potential temperature [K] - k von Karman's constant (0.4) - v air kinematic viscosity coefficient [m² s^–1] - K _M subgrid vertical eddy exchange coefficient for momentum [m² s^–1] - K subgrid vertical eddy exchange coefficient for heat [m² s^–1] - K _q subgrid vertical eddy exchange coefficient for moisture [m² s^–1] - z _i the height of PBL [m] - h _s the height of surface layer [m]     

Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer

The relation between the turbulence Reynolds numberR and a Reynolds numberz* based on the friction velocity and height from the ground is established using direct measurements of the r.m.s. longitudinal velocity and turbulent energy dissipation in the atmospheric surface layer. Measurements of the relative magnitude of components of the turbulent kinetic energy budget in the stability range 0 >z/L 0.4 indicate that local balance between production and dissipation is maintained. Approximate expressions, in terms of readily measured micrometeorological quantities, are proposed for the Taylor microscale and the Kolmogorov length scale .     

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.     

The spectral velocity tensor for homogeneous boundary-layer turbulence

We have postulated a simple model for the spectral tensor _ij (k) of an anisotropic, but homogeneous turbulent velocity field. It is a simple generalization of the spectral tensor _inf ^{ij piso}(k) for isotropic turbulence and we show how in the limit of isotropy, _ij (k) becomes equal to _inf ^{ij piso}(k). Whereas _inf ^{ij piso}(k) is determined entirely by one scalar function of k = ¦k¦, namely the energy spectrum, we need three independent scalar functions of k to specify _ij (k). We show how it is possible by means of the three stream-wise velocity component spectra to determine the three scalar functions in _ij (k) by solving two uncoupled, ordinary linear differential equations of first and second order. The analytic form of the component spectra each has a set of three parameters: the variance and the integral length scale of the velocity component and a dimensionless parameter, which governs the curvature of the spectrum in the transition domain from the inertial subrange towards lower wave numbers. When the three sets of parameters are the same, the three spectra correspond to isotropic turbulence and they are all interrelated and related to the energy spectrum. We show how it is possible to obtain these spectral forms in the neutral surface layer and in the convective boundary layer from data reported in the literature. The spectral tensor is used to predict the lateral coherences for all three velocity components and these predictions are compared with coherences obtained in two experiments, one using three masts at a horizontally homogeneous site in Denmark and one employing two aircraft flying in formation over eastern Colorado. Comparison shows reasonable agreement although with considerable experimental scatter.The National Center for Atmospheric Research is sponsored by the National Science Foundation.