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.     

Diabatic wind speed profiles in coastal regions: Comparison of an internal boundary layer (IBL) model with observations

A model is presented to transform wind speed observations at a single height over sea or near the coast to any possible location and height in a topographic flat coastal region (up to distances of about 5 km from the coast and up to heights of 100 m). Only moderate and strong winds from the sea are considered, which are particularly important for wind energy applications. The model, called diabatic coast model, which is based on the well known internal boundary layer (IBL) concept and Monin-Obukhov similarity theory, describes the effects of the roughness transition from sea to land as well as the effect of stability on the shape of the profiles and the IBL growth. The predicted IBL heights are compared with published data.In the second part of this paper, the model is compared with measurements taken at the Maasvlakte location near the Dutch coast. It is shown that a neutral formulation of the IBL height is sufficient to model the overall mean wind speed with height, but that stability corrections are needed to describe the diurnal variations in wind speed properly. Finally, an application is given, where a single routine wind speed observation at the coast, combined with air-water temperature differences is used to predict the wind speed at 500m from the coast at heights of 10 and 53 m. The results are in good agreement with the measurements.     

Variability of Mixed-Layer Heights over the Indian Ocean and Central Arabian Sea during INDOEX, IFP-99

The upper air data collected from the balloon-borne GLASS Sondes launched from the Oceanic Research Vessel (ORV) Sagar Kanya during the Intensive Field Phase of the Indian Ocean experiment (INDOEX, IFP-99;SK-141 Cruise) are utilized forstudying the variability in the mixed-layer heights observed over the western tropical Indian Ocean and central Arabian Sea. During the entire cruise, typical daytime convective mixed-layer heights (roughly corresponding to 1400 LT) obtained from _V and q profiles, were observed to be in the range 200–900 m. Shallowmixed -layer heights are observed, in general, over the Inter-Tropical Convergence Zone (ITCZ). Over the central Arabian Sea, vertical profiles of _V and q demonstrate a double mixed-layer structure of the marine atmospheric boundary layer (MABL), which gradually disappears close to the Indian coastline.     

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.     

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     

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.     

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 Effect of Atmospheric Stability on the Surface-Layer Characteristics in a Low-Wind Area of Tropical West Africa

This study details the observed effects ofatmospheric stability on characteristics of thesurface layer in a low wind speed (U = 1.5 m s-1)regime of tropical West Africa. Theaerodynamic roughness length, z0, anddisplacement height, d, obtained from profilewind-speed data at our bush land site (height 2 m)have values of 0.24 ± 0.10 m and 1.54 ± 0.04 mrespectively. In the unstable range (-2.5 < Ri < -0.1; Riis gradient Richardson number), thestandard deviation in wind speed fluctuations, u, increased from 0.57 ± 0.19 m s-1 toa maximum of 0.7 ± 0.2 m s-1 in near-neutralconditions, and in the stable range, the parameterdecreased rapidly to 0.41 ± 0.15 m s-1 at Ri 0.2.In the same stability range, the horizontal winddispersion, , decreased withincreasing stability from 19 ± 8 deg. to 13 ± 5 deg.The surface-layer integral quantity, u/u*, when plottedas a function of stability, is in agreement with theempirical results. The ratio ofsensible heat flux (estimated) to the net radiationranged between 0.1 and 0.2 at nighttime,increasing to about 0.5 during the daytime, and showeda strong dependency on season.     

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     

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).     

The turbulent structure of the internal boundary layer near the shore

The mean structure within the internal boundary layer (IBL) near the shore, which develop from the coast in the presence of a sea breeze, has been described in Part I of this study (Ogawa and Ohara, 1984). This paper presents the results of the similarity and energy budget analysis for the purpose of parameterization of the turbulent structure within the IBL. The analysis of the turbulent kinetic energy balance, turbulent intensities and spectra show that the wind is strongly affected by mechanical turbulence in comparison with the past results in a fully developed convective layer where thermal convection dominated. The standard deviations of the wind velocities normalized by the friction velocity u _* (surface-layer scaling parameter) are functions only of the normalized height z/Z _i within 160 m of the shoreline, where Z _i is the IBL. On the other hand, the standard deviations of temperature normalized by _* (mixing-layer scaling parameter) have less scatter with distance than those normalized by T _* (surface-layer scaling parameter). The data showed that both u _* (not a mixed-layer parameter), and Z _i (not a surface-layer parameter) are necessary to describe the turbulent characteristics of the IBL near the shore.Deceased March, 1984.     

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.     

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     

Improving the diagnostic relation for the nocturnal boundary-layer height

A one-dimensional model of the nocturnal boundary layer (NBL) has been used to investigate the time variation of the NBL height for stationary and horizontally homogeneous synoptic conditions. The time variation of the well known quantity = hflu _* has been shown to be related to the wind variation at the top of the NBL. For the simple simulated conditions, this variation depends only on the roughness length and the Coriolis parameter. The value of averaged over the whole night is a function of the friction velocity. An expression is proposed for which is compared with observations. Under stationary external conditions, the new relation improves the determination of the NBL height if compared with the classical relation using a constant value of .     

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 model study of the structure and similarity scaling of the nocturnal boundary layer (NBL)

A one-dimensional numerical model based on the equations of mean motion and turbulent kinetic energy (TKE), with Delage's (1974) mixing-length parameterization has been used to simulate the mean and turbulent structure of the evolving stably stratified nocturnal boundary layer (NBL). The model also includes a predictive equation for the surface temperature and longwave radiational cooling effects.In the absence of advective and gravity wave effects, it is found that the model-simulated structure, after a few hours of evolution, could be ordered fairly well by a similarity scaling (u _*0, _*0, L ₀, and h) based on surface fluxes and the NBL height. Simple expressions are suggested to describe the normalized profiles of momentum and heat fluxes, TKE, eddy-viscosity and energy dissipation. A good ordering of the same variables is also achieved by a local scaling (u _*0, _* and L) based on the height-dependent local fluxes. The normalized TKE, eddy viscosity and energy dissipation are unique functions of z/L and approach constant values as z/L , where L is the local Monin-Obukhov length. These constants are close to the values predicted for the surface layer as z/L , thus suggesting that the Monin-Obukhov similarity theory can be extended to the whole NBL, by using the local (height-dependent) scales in place of surface-layer scales. The observed NBL structure has been shown to follow local similarity (Nieuwstadt, 1984).     

Propeller anemometers as sensors of atmospheric turbulence

Even though propeller anemometers are found to give outputs which deviate from the desired cosine relationship by an amount which varies with wind speed, their overall performance is consistent with many atmospheric requirements. Their output per unit wind speed is a function of angle of attack, such that when used as sensors of the vertical or horizontal cross-wind components in the atmosphere, calibration factors may differ by as much as 30 % from those obtained in a normal wind-tunnel calibration procedure (in which wind velocity is parallel to the anemometer shaft). These characteristics are sufficiently important that great care should be taken in using these devices inu-v-w orthogonal arrays.For use in eddy-correlation equipment, it appears that it is best to vane-mount the horizontal sensor to ensure that the appropriate calibration factor is employed.The response lengths of propeller anemometers also vary with angle of attack. Near=0 °, the axially-referred response length appears to depend linearly on cos, but near=90 ° a dependence on cos^1/2 fits the data. No strong effect of wind speed is found.Due to their limited response characteristics, these anemometers give rise to underestimates of the Reynolds stress measured near the surface. The extent of the loss is about 8 % when anemometers in good condition are employed at a height of 5m. Operation at a greater height would allow this error to be reduced. After exposure in the atmosphere for some time, the anemometers tend to respond more slowly and greater losses (of the order 25 %) can occur. Some improvement in performance is possible by the choice of a suitable spatial separation of the sensors.     

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.     

Observational Evidence And Modelling Of An Internal Hydraulic Jump At The Atmospheric Boundary-Layer Top During A Tramontane Event

A hydraulic jump has been observed with the airborne backscatter lidar LEANDRE 1 (Lidar embarqué pour l'Etude des Aérosols, des Nuages, des interactions Dynamique-Rayonnement etdu cycle de l'Eau) at the top of the atmospheric boundary layer (ABL) during a Tramontane event in the framework of the Pyréneés experiment. An analytical fluid mechanics model is used to interpret lidar observations in connection with in situ measurements andto study the sensitivity of the hydraulic jump triggering to the boundary conditions. This model, which generalizes the reduced-gravity shallow-water theory for two-dimensional stratified flows over a topograpy, is diagnostic (i.e., the reduced gravity g' = g _{v v} is prescribed) and uses boundary conditions defined in terms of Riemann invariants. Using inflow and outflow boundary conditions as well as the reduced gravity prescribed from in situ measurements, the model is able to diagnose the presence of a hydraulic jump at the location suspected from the lidar observations. The wind speed, ABL height and Froude number derived from the model are in good agreement with the observations (within about 20–30%).     

Turbulence in a Katabatic Flow

Turbulence measurements performed in a stable boundary layer over the sloping ice surface of the Vatnajökull in Iceland are described. The boundary layer, in which katabatic forces are stronger than the large-scale forces, has a structure that closely resembles that of a stable boundary layer overlying a flat land surface, although there are some important differences. In order to compare the two situations the set-up of the instruments on an ice cap in Iceland was reproduced on a flat grass surface at Cabauw, the Netherlands. Wind speed and temperature gradients were calculated and combined with flux measurements made with a sonic anemometer in order to obtain the local stability functions _m and _h as a function of the local stability parameter z/L. Unlike the situation at Cabauw, where _m was linear as a function of z/L, in the katabatically forced boundary layer, the dependence of _m on stability was found to be non-linear and related to the height of the wind maximum. Thermal stratification and the depth of the stable boundary layer however seem to be rather similar under these two different forcing conditions.Furthermore, measurements on the ice were used to construct the energy balance. These showed good agreement between observed melt and components contributing to the energy balance: net radiation (supplying 55% of the energy), sensible heat flux (30%) and latent heat flux (15%).Local sources and sinks in the turbulent kinetic energy budget are summed and indicate a reasonable balance in near-neutral conditions but not in more stable situations. The standard deviation of the velocity fluctuations _u, _v, and _w, can be scaled satisfactorily with the local friction velocity u_* and the standard deviation of the temperature fluctuation with the local temperature scale _*.