Temperature structure parameter measurements using differential temperature sensors

The comparison of C _infT ^sup2 estimates in the atmospheric boundary layer, from spectral and differential temperature (T) measurements, is discussed. Measurements of C _infT ^sup2 using these two methods are compared and the differences between the two are shown to be due to low-frequency enhancement of the T spectrum. Possible explanations for this effect are considered and attention is drawn to the significance of the resulting errors in boundary-layer turbulence measurements.Now at Department of Electrical and Electronic Engineering, Portsmouth Polytechnic, Anglesea Road, Portsmouth, U.K.Now at Department of Meteorology, University of Athens, Greece.     

Interaction between the atmospheric and oceanic boundary layers

The two-layer system of an atmosphere over water bodies is reduced to a single-layer problem. Values of the interfacial quantities, such as the friction velocity, the surface velocity, the angles, and , between the surface shear stress and the geostrophic wind velocity and the surface wind velocity, respectively, and the surface roughness, all of which depend upon external parameters, such as the geostrophic wind and stratifications, are obtained. The geostrophic drag coefficient C _d, the geostrophic wind coefficient C _f, and the angles , and , of the turbulent flow at the sea-air interface are functions of a dimensionless number, mfG/kg, with S ₁ and S ₂ as two free stratification parameters. The surface roughness is uniquely determined from the geostrophic wind rather than from the wind profile in the boundary layer.Formerly Visiting Research Associate, Applied Physics Branch, Earth Observations Division, NASA-Manned Spacecraft Center, Houston, Texas.     

The structure of the stably stratified internal boundary layer in offshore flow over the sea

Observations obtained mainly from a research aircraft are presented of the mean and turbulent structure of the stably stratified internal boundary layer (IBL) over the sea formed by warm air advection from land to sea. The potential temperature and humidity fields reveal the vertical extent of the IBL, for fetches out to several hundred of kilometres, geostrophic winds of 20–25 m s^–1, and potential temperature differences between undisturbed continental air and the sea surface of 7 to 17 K. The dependence of IBL depth on these external parameters is discussed in the context of the numerical results of Garratt (1987), and some discrepancies are noted.Wind observations show the development of a low-level wind maximum (wind component normal to the coast) and rotation of the wind to smaller cross-isobar flow angles. Potential temperature () profiles within the IBL reveal quite a different structure to that found in the nocturnal boundary layer (NBL) over land. Over the sea, profiles have large positive curvature with vertical gradients increasing monotonically with height; this reflects the dominance of turbulent cooling within the layer. The behaviour is consistent with known behaviour in the NBL over land where curvature becomes negative (vertical gradients of decreasing with height) as radiative cooling becomes dominant.Turbulent properties are discussed in terms of non-dimensional quantities, normalised by the surface friction velocity, as functions of normalised height using the IBL depth. Vertical profiles of these and the normalised wavelength of the spectral maximum agree well with known results for the stable boundary layer over land (Caughey et al., 1979).     

étude expérimentale de la couche limite de montagne

The characteristics of the boundary layer over complex terrain (Lannemezan - lat.: 43.7° N and, long.: 0.7 ° E) are analyzed for various scales, using measurements obtained during the COCAGNE Experiment. In this first part, the dynamic characteristics of the flow are studied with respect to atmospheric stability and the relief at small (~20 km) and medium scales (~100 km). These relief scales depend on the topographical profile of the Lannemezan Plateau along the dominant axis of the wind (E-W) and the Pyrénées Mountains located at the south of the experimental site. The terrain heterogeneities have a standard deviation of ~48 m and a wavelength of ~2 km.The averaged vertical profiles of wind speed and direction over the heterogeneous terrain are analyzed. The decrease of wind speed within the boundary layer is greater than over flat terrain (WANGARA Experiment). However, a comparison between ETTEX (complex terrain) and COCAGNE vertical wind speed profiles shows good agreement during unstable conditions. In contrast, during neutral conditions a more rapid increase with normalized height is found with COCAGNE than with ETTEX and WANGARA data. The vertical profiles of wind direction reveal an influence of the Pyrénées Mountains on the wind flow. The wind rotation in the BL is determined by the geostrophic wind direction-Pyrénées axis angle (negative deviation) as the geostrophic wind is connected with the Mountain axis.When the geostrophic wind does not interact with the Pyrénées axis, the mean and turbulent wind flow characteristics (drag coefficient C _D, friction velocity u _*) depend on the topography of the plateau. When the wind speed is strong (>6 m s ^-1), an internal boundary layer is generated from the leading edge of the Plateau.     

The influence of the geostrophic wind advection approximation on a well-mixed layer

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.     

From Near-Neutral to Strongly Stratified: Adequately Modelling the Clear-Sky Nocturnal Boundary Layer at Cabauw

The performance of an atmospheric single-column model (SCM) is studied systematically for stably-stratified conditions. To this end, 11 years (2005–2015) of daily SCM simulations were compared to observations from the Cabauw observatory, The Netherlands. Each individual clear-sky night was classified in terms of the ambient geostrophic wind speed with a \(1\hbox { m} \hbox { s}^{-1}\) bin-width. Nights with overcast conditions were filtered out by selecting only those nights with an average net radiation of less than \(-\,30\hbox { W }\hbox {m}^{-2}\). A similar procedure was applied to the observational dataset. A comparison of observed and modelled ensemble-averaged profiles of wind speed and potential temperature and time series of turbulent fluxes showed that the model represents the dynamics of the nocturnal boundary layer (NBL) at Cabauw very well for a broad range of mechanical forcing conditions. No obvious difference in model performance was found between near-neutral and strongly-stratified conditions. Furthermore, observed NBL regime transitions are represented in a natural way. The reference model version performs much better than a model version that applies excessive vertical mixing as is done in several (global) operational models. Model sensitivity runs showed that for weak-wind conditions the inversion strength depends much more on details of the land-atmosphere coupling than on the turbulent mixing. The presented results indicate that in principle the physical parametrizations of large-scale atmospheric models are sufficiently equipped for modelling stably-stratified conditions for a wide range of forcing conditions.     

On the extension of the wind profile over homogeneous terrain beyond the surface boundary layer

Analysis of profiles of meteorological measurements from a 160 m high mast at the National Test Site for wind turbines at Høvsøre (Denmark) and at a 250 m high TV tower at Hamburg (Germany) shows that the wind profile based on surface-layer theory and Monin-Obukhov scaling is valid up to a height of 50–80 m. At higher levels deviations from the measurements progressively occur. For applied use an extension to the wind profile in the surface layer is formulated for the entire boundary layer, with emphasis on the lowest 200–300 m and considering only wind speeds above 3 m s^?1 at 10 m height. The friction velocity is taken to decrease linearly through the boundary layer. The wind profile length scale is composed of three component length scales. In the surface layer the first length scale is taken to increase linearly with height with a stability correction following Monin-Obukhov similarity. Above the surface layer the second length scale (L _MBL ) becomes independent of height but not of stability, and at the top of the boundary layer the third length scale is assumed to be negligible. A simple model for the combined length scale that controls the wind profile and its stability dependence is formulated by inverse summation. Based on these assumptions the wind profile for the entire boundary layer is derived. A parameterization of L _MBL is formulated using the geostrophic drag law, which relates friction velocity and geostrophic wind. The empirical parameterization of the resistance law functions A and B in the geostrophic drag law is uncertain, making it impractical. Therefore an expression for the length scale, L _MBL , for applied use is suggested, based on measurements from the two sites.     

On the solution of the stationary,baroclinic Ekman-layer equations with a finite boundary-layer height

The stationary, Ekman-layer equations have been solved in closed form for two expressions of the eddy viscosity as a function of height, z: v _τ=cu*z(1?z/h)and v _τ=cu*z(1?z/h) ², where u* is the friction velocity, h the boundary-layer height and c a constant. The main difference between both solutions is that the quadratic K-profile leads to a velocity discontinuity at the top of the boundary layer, while the solution for the cubic profile approaches the geostrophic wind at z=h smoothly. We discuss the characteristics of the solutions in terms of a dimensionless parameter C=fh/cu*, where f is the Coriolis parameter. The dependence on C can be interpreted in terms of a varying boundary-layer height or in terms of stability. The results for C ~ 1 are related to a neutral boundary layer. They agree well with results of a second-order model. The limit C → 0 is investigated in detail. We find that the stress profile becomes linear. The velocity profile shows different characteristics depending on whether we consider a shallow or a very unstable boundary layer. The results agree with observations. Finally we consider the influence of baroclinicity on the wind and stress profiles.     

Models for estimating offshore winds from onshore meteorological measurements

To understand and estimate wind speed differences across the coastal zone, two models, one theoretical and another semi-empirical, have been developed and verified by available data sets. Assuming that: (1) mean horizontal motion exists across the coastal zone; and (2) the geostrophic wind does not change appreciably at the top of the planetary boundary layer (PBL), the equation of motion in the direction of the wind can be reduced so that 341-01, where U, H, and C _D are wind speed, height of PBL, and drag coefficient over the sea and land, respectively. For practice, C _D SEA has been modified from a formula with U _LAND as the only input. H _SEA may be estimated routinely from known H _{D LAND LAND} and the temperature difference between land and sea, which can be provided by such means as remote sensing from meteorological satellites. For a given coast, Cmay be estimated also. This formula is recommended for weather forecasters. The semiempirical formula is based mainly on the power law wind distribution with height in the PBL. The formula states that 341-02. Simultaneous offshore and onshore wind measurements made at stations ranging from Somalia, near the equator, to the Gulf of Alaska indicated that values of a and b are 2.98 and 0.34 with a correlation coefficient of -0.95. For oceanographic applications, a simplified equation, i.e., 341-03, is also proposed.     

Observations of the Daytime Boundary Layer in Deep Alpine Valleys

Mixing depth structure and its evolution have been diagnosed from radar wind profiler data in the Chamonix and the Maurienne valleys (France) during summer 2003. The behaviour of refractive index structure parameter C _n ² peaks coupled with the vertical velocity variance σ _w ² was used to estimate the height of the mixed layer. Tethersonde vertical profiles were carried out to investigate the lower layers of the atmosphere in the range of approximately 400–500 m above ground level. The tethersonde device was especially useful to study the reversal of the valley wind system during the morning transition period. Specific features such as wind reversal and the convective mixed layer up to approximately the altitude of the surrounding mountains were documented. The wind reversal was observed to be much more sudden in the Maurienne valley than in the Chamonix valley     

A sodar study of the temperature structure parameter in the convective boundary layer

From sodar measurements gathered during the Voves experiment (France, summer 1977), the variations of the temperature structure parameter C _T ² were studied in the morning planetary boundary layer. Dimensionless profiles of C _T ² are consistent with the mixed-layer scaling of Kaimal et al. (1976); however, for z < 0,5 z _i, the decrease of C _T ² as z ^4/3 should be weighted according to Frisch and Ochs (1975).When the final breakup of the nocturnal inversion is achieved, the variations of the maximum of the C _T ² profile are in good agreement with those predicted by Wyngaard and Le Mone (1980). Discrepancies are observed mainly when the mixed layer is shallow and mechanical turbulence is important compared with buoyancy-driven turbulence.     

Some aspects of determining the stable boundary layer depth from sodar data

The question of estimating the height of the stable boundary layer (SBL) based on digitalized vertical profiles of sodar signal intensity has been re-examined. A simple one-dimensional numerical boundary-layer model is used to compute vertical profiles of the temperature structure parameterC _T ² . It is shown that especially at the beginning of the night (when stratification is weak) one can not expect any significant profile structure in the upper part of the SBL if its depth is determined in terms of common turbulent height scales. From this it is concluded that the SBL-height will be underestimated early in the night when derived from the maximum gradient in the signal intensity profiles. Later in the night in contrast, the computations often show elevated maxima or even zones with reduced, and above them enhanced, vertical gradients ofC _T ² , from which a SBL-height can be deduced that compares well with other common height scales. The computed profiles ofC _T ² are shown to be in qualitative agreement with observed profiles of sodar signal intensity for several analysed cases from the HAPEX-MOBILHY experiment.Comparing different SBL-depth scales with sodar observations, it is demonstrated that most of them are often closely related to a sodar-derived SBL-height only during certain phases of the night. Thus the sodar-SBL-height can, after a transition period, be perhaps associated with the lower turbulent layer of the growing surface inversion during the first part and with the height of the low-level wind maximum during the second part of the night.     

Similarity scaling applied to sodar observations of the convective boundary layer above an irregular hill

Nine profiles of the temperature structure parameter C _T ² and the standard deviation of vertical velocity fluctuations ( _w) in the convective boundary layer (CBL) were obtained with a monostatic Doppler sodar during the second intensive field campaign of the First ISLSCP Field Experiment in 1987. The results were analyzed by using local similarity theory. Local similarity curves depend on four parameters: the height of the mixed layer (z _i ), the depth of the interfacial layer (), and the temperature fluxes at the top of the mixed layer (Q _i ) and the surface (Q _o). Values of these parameters were inferred from sodar data by using the similarity curve for C _T ² and observations at three points in its profile. The effects of entrainment processes on the profiles of C _T ² and _wnear the top of the CBL appeared to be described well by local similarity theory. Inferred estimates of surface temperature flux, however, were underestimated in comparison to fluxes measured by eddy correlation. The measured values of _wappeared to be slightly smaller than estimates based on available parmeterizations. These discrepancies might have been caused by experimental error or, more likely, by the distortion of turbulence structure above the site by flow over the nonuniform terrain at the observation site.     

Effects of local accelerations and baroclinity on the mean structure of the atmospheric boundary layer over the sea

Substitution of the geostrophic wind by the actual upper wind in the equations of motion for the boundary layer implies less sensitivity of the mean wind to inertial effects. This is confirmed by observations, although the problem of computing time or spatial derivatives from scattered data reduces the accuracy and the clarity of the results. It is found that acceleration (deceleration) increases (decreases) the cross-isobar angle whereas the geostrophic drag coefficient is a minimum (maximum) for crosswind acceleration (deceleration). On the other hand, cold air advection increases the cross-isobar angle whereas the geostrophic drag coefficient is a maximum when the thermal wind is parallel to the surface wind. The universal functions A _m and B _m based on vertically averaged winds are also rather insensitive to inertial influences.     

A numerical study of boundary-layer dynamics in a mountain valley

The characteristics of dynamics and thermodynamics of the atmospheric boundary layer in a part of the Colorado River Valley, centered around Lake Mohave, have been investigated by analysis of measurements conducted during a field program in late spring and early summer of 1986 and a series of numerical simulations by a three-dimensional second-moment turbulence-closure model. The model was validated against measurements described in a companion article (Engeret al., 1993). According to airsonde measurements performed on eight nights, the depth of the surface inversion was around 200 m with an average temperature gradient of about 30 K km^–1. Analysis of acoustic sounder data collected during one month revealed significant diurnal variations ofU andV wind-speed components related to slope and valley flows, respectively. Some of the dynamics properties have been explained by the simulation results. It has been shown that the appearance of supergeostrophic southerly valley flow is associated with the westerly component of the geostrophic flow. Since a westerly component of the geostrophic wind is quite common for this area in summer, this effect also explains the frequently observed southerly valley flow in summer. Elevated minima of the measured wind speed around valley ridges appear to be related to the interaction of conservation of momentum in theX andY directions. The critical direction of the geostrophic wind relevant for reversal of up-valley flow to down-valley flow has also been studied. The critical direction is about 300° for one of the measurement sites and, depending on the angle between valley axis and south-north direction, the critical direction is expected to vary by about 15–20°. The scale analysis of the simulated equations of motion and turbulence kinetic energy emphasizes the strong impact of meandering of the flow due to actual topographic complexity.     

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 .     

On nocturnal wind shear with a view to engineering applications

Wind shear data from 14 clear nights with low-level jet development are analysed up to heights of 200 m. Temporal variations of the magnitude of the shear vector and of the power-law exponent p are shown. The frequencies of occurrence of maximum shear and of p are examined and the effect of the product of geostrophic surface wind speed and mean layer temperature gradient on the shear is investigated.     

Nocturnal boundary layer height prediction from surface routine meteorological data

Summary A number of well known diagnostic equations for the determination of the height,h, of the nocturnal boundary layer. with minimum data requirements of at most surface wind speed, air temperature and total cloud cover, have been tested as to their effectiveness. The computed values have been compared with direct estimation ofh, from temperature or wind profiles of rawinsonde ascents available at 00Z (02h LST). The comparison between computed and observed values shows that best agreement is found when the nocturnal boundary layer height is determined through wind profiles. The ratio of the computed to the observed values reveals a strong dependence on stability, resulting in overestimation by the models for very low stability and underestimation for strong stability. The simple expressions involving the wind speed rather than other stability parameters resulted in a better overall fit to the observed values. A simple prognostic model is shown to provide the best estimates of the NBL height compared to both wind and temperature profile definition.With 5 Figures     

In the Core of the Night-Effects of Intermittent Mixing on a Horizontally Heterogeneous Surface

Intermittent breakdowns that accompany wind gusts at the surface are responsible for a large fraction of the turbulent exchange between the surface and the upper boundary layer in the core of clear nights. Vertical and horizontal structure of the breakdowns are investigated using data from a network of 26 stations in an area of 30 km × 30 km. Surface heterogeneity in the area includes complex terrain with different types of land cover. We treat the fine-scale landscape structure near sensors (sheltering) as a separate component of heterogeneity. These features have important consequences on the spatial distribution of mean variables and surface fluxes. We found that breakdowns connect the surface layer to a higher level (level H_C). Weak wind gusts below a threshold (approximately 1.5 m s^-1) mix the air down to the colder ground, cooling the surface layer. On the other hand, wind gusts above this threshold promote mixing with upper levels, warming the surface layer. The spatial maximum of surface temperature over the network can be used as an estimate of the temperature at H_C, allowing vertical gradients and stability to be approximated. Minimum temperature is a function of topography and sheltering. Appreciable surface fluxes at night occur primarily at high, open locations, and can be large enough there to influencearea-averaged values. Surface-fluxparameterizations currently used in mesoscale models were tested first by estimating fluxes at each station and aggregating, and then by formingarea-averages before estimating fluxes. Results show that these formulations underestimate the average surface fluxes over a region for most of the nights.     

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

Although the bulk aerodynamic transfer coefficients for sensible (C _H ) and latent (C _E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C _H and C _E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C _E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s^–1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10^–3 and 1.5 × 10^–3.