A new parameterization of eddy diffusivities for nocturnal boundary-layer modeling

Exchange coefficients and mixing lengths under stable stratification have been studied through measurements of mean wind velocity and temperature in the nocturnal boundary layer. For values of the gradient Richardson number lower than 0.15, our measurements fit well the relation of Delage (1974). Beyond Ri = 0.15, the decrease of mixing length is much slower. So a new parameterization of turbulent exchanges is suggested. When introduced in a model of the nocturnal boundary layer, it results in a thickening of the turbulent and inversion layers.     

Determination of the convective boundary-layer height with laser remote sensing

Different methods to determine the height of the convective boundary layer from lidar measurements are described and compared. The differences in either aerosol backscatter or in humidity between the boundary layer and the free troposphere are used, and either the variance or the gradient profile of the parameter under study is evaluated. On average the different methods are in very good agreement. Temporal resolution of the gradient methods is very high, on the order of seconds, but often there is an ambiguity in the choice of the “relevant” minimum in the gradient that corresponds to the boundary-layer height. This is avoided by combining the variance and the gradient methods, using the result of the variance analysis as an indicator for the region where the minimum of the gradient is sought. The combined method is useful for automated determination of the boundary-layer height at least under convective conditions. Aerosol backscatter is found to be as good an indicator for boundary-layer air as humidity, so a relatively simple backscatter lidar is sufficient for determination of the boundary-layer height.     

A comparative evaluation of the coastal internal boundary-layer height equations

A parabolic shaped Thermal Internal Boundary Layer (TIBL) develops at the coast because of the temperature discontinuity between land and water. The TIBL is shown to play a significant role in determining where a coastal elevated plume fumigates to the ground. Six TIBL models available in the literature were identified and statistically compared. Two data bases obtained from the TIBL experiments, one at eastern Long Island, the other at the Kashimaura area of Japan, were used for statistical comparisons. Statistical methods of t, F and R were used to determine bias, scatter and correlation. The data were also classified according to wind speed (low and high) and stability (unstable, neutral, isothermal and stable onshore flow) to determine whether some models worked better under certain conditions. These limited data indicated that a formulation which included heat flux and wind speed together with overwater lapse rate, all raised to the half power, performed the best. Classifications according to wind speed and thermal stability also showed that the heat flux type of equation worked reasonably well.     

Evaluation and model impacts of alternative boundary-layer height formulations

We study bulk formulations for the boundary-layer height which are currently in use for atmospheric modelling. The formulations are based on various forms of the Richardson number, and these are evaluated with Cabauw field data in stable conditions. Results for both a large-eddy simulation model and anE-ε turbulence closure model for neutral boundary layers are also utilised. An updated formulation is introduced, which combines the effects of shear in the outer region of the boundary layer with surface friction. The updated formulation has a better performance for neutral boundary layers with upper level stratification. The findings are illustrated with a single-column model for a case with relatively high winds over the tropical ocean including shallow cumulus convection, and for a case with fair weather over land. We also show that for stable conditions, the updated formulation performs better than estimates on the basis of surface friction alone.     

On the inner-layer scale height of boundary-layer flow over low hills

Jackson and Hunt's (1975) equation for the depth of the inner layer of flows over low hills does not depend on any closure assumption as contrarily supposed in literature. This equation contains a constant which can arbitrarily be specified. It is suggested that this inner-layer constant should be determined from experimental data. A preliminary check with some data from the Askervein experiment suggests that Jackson and Hunt's equation fits these data almost as well as Jensen's equation provided that fitted inner-layer constants are used.     

On the inner-layer scale height of boundary-layer flow over low hills

The scaling properties of the depth of the inner-layer of flow over low hills are studied by means of numerical solution of the equations. Two closure schemes are applied: the mixing-length model and the E- formulation. It is shown that the scale relation for the inner-layer depth lies between two formulations proposed in literature. It is also shown that the scale relation depends on the closure scheme.Presently at the European Centre for Medium-Range Weather Forecasts, Shinficld Park, Reading, Berkshire RG2 9AX, England.     

Internal boundary-layer height formulae — A comparison with atmospheric data

The height of the internal boundary layer (IBL) downwind of a step change in surface roughness is computed using formulae of Elliott (1958), Jackson (1976) and Panofsky and Dutton (1984). The results are compared with neutral-stratification atmospheric data extracted from the set of wind-tunnel and atmospheric data summarized by Jackson (1976) as well as neutral-stratification data presented by Peterson et al. (1979) and new data measured at Cherrywood, Ontario. It is found that the Panofsky-Dutton formulation gives the least root-mean-square (RMS) absolute errors for atmospheric applications.     

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.     

Matching classical boundary-layer solutions toward a geostrophic drag coefficient relation

The relationship between geostrophic, Ekman-layer, and surface-layer flow is explored. Formalized limit solutions for each layer are developed; together they form a continuous solution for the semi-infinite flow over a surface. These classical solutions are re-derived and related, to prepare for a two-layer composite boundarylayer solution with patching criteria. The patching process yields a resistance law which indicates a correspondence between the stress and the geostrophic flow deviation involving a similarity relation with two arbitrary parameters.     

大气边界层重力流与局地强降水的关系

本文利用测雨雷达、325米气象专用塔以及常规气象资料,分析了北京锋面暴雨产生前后的边界层结构。指出:随着锋面过境,低层出现了重力流的多次浪涌,每次浪涌前沿有强上升运动,最大可达35厘米/秒,每次重力流浪涌都伴有一阵强降水。重力流可以激发出周期为几分钟至20分钟的重力内波。     

On the evolution of the height and temperature difference across the nocturnal stable boundary layer

Evidence is furnished which indicates that in some cases the height of the stable boundary layer (SBL) and the magnitude of the temperature difference across the SBL may be more appropriately described by an error function erf(t/) rather than the generally accepted square root time dependence. The time constant was observed to have values of one to three hours. The discovery has been found to be site dependent, however, as data from other sites follow the usual square root time evolution.     

Nocturnal boundary-layer height: Observations by acoustic sounders and predictions in terms of surface-layer parameters

Acoustic sounder measurements of the stable boundary-layer height taken during the EPRI Plume Model Validation and Development Project experiment are examined. Comparison of simultaneous measurements by two sodars located 15 km apart shows good agreement. Several widely used diagnostic formulas for estimation of the boundary-layer height, based on wind speed and surface-layer parameters, such as friction velocity and Monin-Obukhov length, are tested against the sodar data. Of these, best performance is found using a simple linear relationship with friction velocity or, alternatively, wind speed at 10 m height. No evidence is found to support the more often used Zilitinkevich (1972) formula. Tests using selected data from the Cabauw site in the Netherlands confirm the results found on the basis of EPRI data.     

Estimation of surface stress over a forest from sodar measurements and its use to parameterize the stable boundary-layer height

Sodar observations from three nights of the HAPEX-MOBILHY experiment have been used to compute covariances between single measurements of the three velocity components. From these, estimates of a low frequency friction velocityu _* are derived which show better correlation with observed values of the stable boundary layer (SBL) height,h, than directu _*-measurements by an ultrasonic anemometer. On the contrary, interdiurnal variability ofh is better correlated with directu _*-measurements. These findings should be mainly due to the problem of different spectral and spatial representativity of the twou _*-values.     

A method for solving the planetary boundary-layer equations

A method for solving the nonlinear three-dimensional steady-state equations which govern planetary boundary layer flow is described. The method is applicable to air motions over terrain with horizontally varying surface roughness, temperature and moisture. It can also be applied to a physical system consisting of the air and the sea (or earth) boundary layers taken together. Examples of calculations for selected cases of terrain variations are presented. Convergence of the method has been assessed by determining the degree to which the solutions satisfy the set of equations.The results of the calculations show that the method produces qualitatively realistic distributions of the different meteorological variables.Contribution No. 1251 from the University of Miami, Rosenstiel School of Marine and Atmospheric Sciences.     

A maritime boundary-layer model for the prediction of fog

A two-dimensional boundary-layer model is described. The model is designed to predict and study the effects of meteorological changes on the formation and dissipation of fog and stratus. Radiational heat loss along with the transport of static energy, moisture and momentum are treated. Cloud droplet distributions are parameterized using a gamma distribution from which radiative properties and droplet fall velocities are computed. Turbulent exchange coefficients are calculated using the Monin-Obukhov theory of similitude which accounts for variations in atmospheric stability. Although the boundary-layer depth depends only on turbulent intensity during stable atmospheric conditions, its growth during unstable conditions is determined from the capping inversion's intensity and the amount of turbulence generated at the surface.Several experiments are presented which demonstrate the effects of various meteorological parameters on the formation and duration of stratus and fog. Energy-budget analyses show the importance of each of the physical processes being modeled.Although not new, radiative transfer processes are shown to be extremely important in the transfer of heat from the boundary layer and in the process of fog formation. Fog formation location is highly sensitive to the moisture content upstream, whereas changes in wind speed had much less effect in the variance of fog location.Numerical experiments with other processes such as back radiation from the atmosphere, haze and cloud droplet population, are described and shown to have smaller effects.     

The steady-state height and resistance laws of the nocturnal boundary layer: Theory compared with cabauw observations

An expression is derived for the height of the stationary boundary layer during stable lapse rate conditions. It satisfies the conventional limits for neutral conditions and for large values of stability. Comparison with acoustic sounder observations near the meteorological mast at Cabauw (the Netherlands) shows that the steady-state height is not attained for large stability values. The observations are also used to investigate how the similarity functions A and B in the resistance laws depend on the stability parameters ₀ = u _*/f L and = h/L. The function B shows a clear trend as a function of stability, which can be described in terms of . The dependence of A is masked by scatter in the data points. The general conclusion leads to the concept of a non-steady boundary layer during stable lapse rate conditions.     

Numerical simulations of stratiform boundary-layer clouds on the meso-γ-scale. Part I: The influence of terrain height differences

A higher order closure mesoscale model is used to study the influence of terrain height differences on the meso--scale on stratiform boundary-layer clouds. The model is hydrostatic, has a terrain-following coordinate system and a sub-grid scale condensation scheme. It also has a radiation parameterisation for shortwave and longwave radiation in order to calculate radiative cooling/heating. The simulations show that the cloud base height variations induced by the terrain can be much larger than motivated by terrain height variations alone. It is also shown how this behavior is dependent on upstream boundary-layer conditions and/or changes in the turbulence field. Other features studied include the wave in the lee of a ridge/hill and the associated lifting of the cloud base. The results are compared with some simpler physical models, and limitations in those models are demonstrated.     

Measurement of the atmospheric boundary-layer resistance law for water vapor

Information is presented regarding the function D(h/L) which appears in the expression for the atmospheric boundary-layer resistance law for water vapor. Using a data set which includes directly measured evapotranspiration and utilizing the conventional definition of D(h/L), this function is found to resemble the analogous C(h/L) function, which appears in the expression for the heat transfer coefficient. There is no evidence of systematic differences between these two functions for the unstable case. On the stable side, the scatter was so great that no conclusions could be drawn except that D(h/L) is negative.     

An ice breeze mechanism for boundary-layer jets

The existence of a low-level (z=~1000 m) jet adjacent to a sea-ice boundary is investigated with a two-dimensional numerical model. A thermally-direct ice breeze circulation is induced by specifying an ice-sea surface temperature gradient, with the mean geostrophic wind parallel to the ice edge. Pressure changes associated with over-water mixed-layer development create an increase in geostrophic velocity that accounts for most of the increase in wind speed. A change in initial geostrophic wind direction has significant effects on location and intensity of the low-level jet; geostrophic winds parallel to the ice edge result in stronger jets than occur with cross-ice geostrophic winds. An inertial oscillation simulated by the model in 1-D makes a negligible contribution to the low-level jet.