Pressure drag and effective roughness length with neutral stratification

A two-dimensional numerical mesoscale model is used to determine the pressure drag of sinoidal mountains and valleys in a neutral atmosphere. In the first part, pressure distributions and flow patterns for isolated obstacles are considered. For large aspect ratios, the pressure drag exerted by valleys becomes small compared to that of mountains. In the second part, interactions between several obstacles are investigated. For mountains, the drag on downstream obstacles is reduced considerably by the first obstacle when the obstacles are close together. For valleys there is a slight increase of the average drag exerted by each obstacle. In the limit for a large number of obstacles, average drag exerted by one mountain is equal to average drag for one valley. For smaller aspect ratios, this average drag can be entered into the resistence law from the Rossby number similarity theory to yield an effective roughness length.     

An improved calibration for tethered balloon wind measurements

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

Surface pressure distribution and pressure drag on mountains

Summary A mesoscale numerical model is used to compute the different components of the pressure drag on mountains, i.e.: form drag, wave drag, hydrostatic drag, and total pressure drag, for stable stratification. The Froude number is chosen so that non-breaking lee-waves evolve.The paper explains how the different parts of the drag are computed from the numerical results and how they form part of the horizontal momentum budget.For a single mountain the drag from the evolving stationary solution is compared to the wave drag from linear inviscid theory. Wave drag turns out to be about one third of the value expected from linear theory, and nonlinear interaction between wave and form drag is found. Wave drag is responsible for about 75% of the total drag if blocking is negligible.For two obstacles with varying distance the wave drag in the stationary solution varies between 5% and 30% of the value from linear theory due to partial cancellation between the lee-waves from the two mountains.Finally in an instationary simulation the passage of a cold air mass over a mountain and the respective drag components have been computed. 1500 m above the crestline of the obstacle wave drag is only 10% to 30% of the total drag.From the present results it seems realistic that wave drag from ALPEX experimental data was only a few percent of the value expected from the surface pressure distribution and from linear theory.With 7 Figures     

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

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

Similarity theory of diffusion and the observed vertical spread in the diabatic surface layer

The extension of Lagrangian similarity theory of diffusion to stratified flow is examined, to improve its prediction of the vertical spread of a passive substance. In the basic equation, where is the average height of a cluster of particles,u _* is the friction velocity andL is Monin-Obukhov length. It is shown theoretically, under the assumption of an equivalence between the diffusivities of heat and matter, that the unspecified function is the reciprocal of a more familiar meteorological parameter _n , the dimensionless temperature gradient. The universal constantb is found to be approximately equal to von Karman's constant for various stability conditions. The predicted effect of stability on vertical spread shows excellent agreement with that of the published data from the O'Neill experiments.     

Free convection scaling over the ocean derived from buoy measurements during gate

The structure of atmospheric turbulence in the surface layer over the open ocean is examined under conditions of local free convection. The raw data consist of profile and fluctuation measurements of wind and temperature as obtained from a meteorological buoy. For near neutral conditions and for waves running approximately along the wind direction, wave-induced wind fluctuations can be described by a simplified linear theory based on Miles (1957). In this case, the spectrum of wind velocity is given as the sum of two parts; for the turbulent part, the parameterization as obtained by Kaimal et al. (1972) applies, while the wave-induced part is parameterized using a simplification of Miles' linear theory. For cases of local free convection, the measurements of the vertical component of the wind velocity are well described by similarity theory; as expected, _w /(-uw)^1/2 is proportional to (- z/L)^1/3. In order to scale the longitudinal wind velocity component, it seems to be reasonable to extend the list of relevant parameters by the height of the mixed layer z _i. We obtain _u /(- uw)^1/2 (z/z _i)^1/3(- z/L)^1/3 with only a poor correlation coefficient of r = 0.6. Overall, the results of local free convection scaling obtained from direct measurements show good agreement with those obtained from profile measurements. A comparison between direct and indirect determination of turbulent fluxes of momentum shows an unexplained difference of about 20%. This discrepancy is mainly due to a gap in the uw-cospectrum at the swell frequency.     

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.     

Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index

Using a previous treatment of drag and drag partition on rough surfaces, simple analytic expressions are derived for the roughness length (z ₀) and zero-plane displacement (d) of vegetated surfaces, as functions of canopy height (h) and area index (). The resulting expressions provide a good fit to numerous field and wind tunnel data, and are suitable for applications such as surface parameterisations in atmospheric models.     

Equilibrium evaporation beneath a growing convective boundary layer

Expressions for the equilibrium surface Bowen ratio ( _s ) and equilibrium evaporation are derived for a growing convective boundary layer (CBL) in terms of the Bowen ratio at the top of the mixed layer _i and the entrainment parameter A _R . If A_R is put equal to zero, the solution for _s becomes-that previously obtained for the zero entrainment or closed box model. The Priestley-Taylor parameter is also calculated and plotted in terms ofA _R and _i . Realistic combinations of the atmospheric parameters give values of in the range 1.1 to 1.4.     

Numerical simulation of turbulent convective flow over wavy terrain

By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude up to 0.15H and wavelength ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz _o=10^–4 H. The mean wind is varied between zero and 5w _*, wherew _* is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with /H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w _*>2.     

Near-field dispersion from instantaneous sources in the surface layer

This paper considers the near-field dispersion of an ensemble of tracer particles released instantaneously from an elevated source into an adiabatic surface layer. By modelling the Lagrangian vertical velocity as a Markov process which obeys the Langevin equation, we show analytically that the mean vertical drift velocity w(t) is w()=bu _*(1–e ^–(1+)), where is time since release (nondimensionalized with the Lagrangian time scale at the source), b Batchelor's constant, and u _*, the friction velocity. Hence, the mean height and mean depth of the ensemble are calculated. Although the derivation is formally valid only when 1, the predictions for w, mean height and mean depth are consistent in the downstream limit ( 1) with surface-layer Lagrangian similarity theory and with the diffusion equation. By comparing the analytical predictions with numerical, randomflight solutions of the Langevin equation, the analytical predictions are shown to be good approximations at all times, both near-field and far-field.     

Diskussionsbeitrag zur Frage der Sicht in Wolken

Summary The discrepancy between measured (or estimated) visual range (V _g) and the one calculated from the drop size distribution (V _b), stated byTrappenberg on the basis of the measurements ofRittberger, is discussed. It is assumed that in the measurement of the drop size distribution the small droplets are discriminated. If the distributions are extrapolated to drop diameters of 2 or 1 ,V _b turns out to be in agreement withV _g.

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Diskussionsbeitrag zur Frage der Sicht in Wolken

Zusammenfassung Die vonTrappenberg auf Grund der Messungen vonRittberger festgestellte Diskrepanz zwischen gemessener (oder geschätzter) SichtweiteV _g und der aus der Tropfengrößenverteilung berechnetenV _b wird diskutiert. Es wird angenommen, daß bei der Messung der Tropfengrößenverteilung die kleinen Tropfen nicht genügend zur Geltung kommen. Extrapoliert man die Verteilungen in zwangloser Weise bis zu Tropfendurchmessern von 2 oder 1 , so ergibt sich eine gute Übereinstimmung vonV _b mitV _g.

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Résumé L'auteur discute la discrépance existant entre la visibilité mesurée (ou estimée)Vg et la visibilité calculéeV _b au moyen de la répartition de la grosseur des gouttes, discrépance établie parTrappenberg en partant des mesures deRittberger. On admet alors que, lors de la mesure de la répartition de la grosseur des gouttes, les plus petites d'entre elles n'ont pas suffisament de poids. Si l'on extrapole cette répartition jusqu'à un diamètre des gouttes de 2 ou 1 , on constate alors une bonne concordance entreV _b etV _g.

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Mit 1 Textabbildung     

Estimates of diabatic wind speed profiles from near-surface weather observations

In this paper we analyse diabatic wind profiles observed at the 213 m meteorological tower at Cabauw, the Netherlands. It is shown that the wind speed profiles agree with the well-known similarity functions of the atmospheric surface layer, when we substitute an effective roughness length. For very unstable conditions, the agreement is good up to at least 200 m or z/L–7(z is height, L is Obukhov length scale). For stable conditions, the agreement is good up to z/L1. For stronger stability, a semi-empirical extension is given of the log-linear profile, which gives acceptable estimates up to ~ 100 m. A scheme is used for the derivation of the Obukhov length scale from single wind speed, total cloud cover and air temperature. With the latter scheme and the similarity functions, wind speed profiles can be estimated from near-surface weather data only. The results for wind speed depend on height and stability. Up to 80 m, the rms difference with observations is on average 1.1 m s^–1. At 200 m, 0.8 m s^–1 for very unstable conditions increasing to 2.1 m s^–1 for very stable conditions. The proposed methods simulate the diurnal variation of the 80 m wind speed very well. Also the simulated frequency distribution of the 80 m wind speed agrees well with the observed one. It is concluded that the proposed methods are applicable up to at least 100 m in generally level terrain.     

Final results of the CONDORS convective diffusion experiment

TheConvectiveDiffusionObserved byRemoteSensors (CONDORS) field experiment conducted at the Boulder Atmospheric Observatory used innovative techniques to obtain three-dimensional mappings of plume concentration fields, /Q, of oil fog detected by lidar and chaff detected by Doppler radar. It included extensive meteorological measurements and, in 1983, tracer gases measured at a single sampling arc. Final results from ten hours of elevated and surface release data are summarized here. Many intercomparisons were made. Oil fog /Q measured 40m above the arc are mostly in good agreement withSF ₆ values, except in a few instances with large spacial inhomogeneities over short distances. After a correction scheme was applied to compensate for the effect of its settling speed, chaff dy/Q agreed well with those of oil except in two cases of oil fog hot spots. Mass or frequency distribution vs. azimuth or elevation angle comparisons were made for chaff, oil, and wind, with mostly good agreements. Spacial standard deviations, _y and _z, of chaff and oil agree overall and are consistent at short range with velocity standard deviations _vand _w 0.6w^* (the convective scale velocity), as measured atz>100m. Surface release _y is enhanced up to 60% at smallx, consistent with the Prairie Grass measurements and with larger _v and reduced wind speed measured near the surface. Decreased _y at small dimensionless average times is also noted. Finally, convectively scaled dy, C _y, were plotted versus dimensionlessx andz for oil, chaff, and corrected chaff for each 30–60 min period. Aggregated CONDORSC _y fields compare well with laboratory tank and LES numerical simulations; surface-released oil fog compares expecially well with the tank experiments. However, large deviations from the norm occurred in individual averaging periods; these deviations correlated strongly with anomalies in measured distributions.On assignment to the US Environmental Protection Agency, Atmospheric Research and Exposure Assessment Laboratory, RTP, NC.     

Modifications of the structure of cold fronts over the foreland and in a mountain valley

Summary The investigations during the German Frontal Experiment 1987 show the modification of structure and movement of cold fronts in the vicinity of the Alps and in an Alpine valley. The two cold fronts that moved nearly parallel to the mountains were modified at the mountain barrier by the channelling effect. In those cases the postfrontal air flowed into the Inn valley from the valley's exit up-valley. The upper and lower parts of the fronts became detached, and the structure of the lower part changes on its way from the foreland to the mountain barrier.In contrast the fourth cold front, which moved from north-west to south-east, crossed the mountains without appreciable deformation although it suffered some degree of blocking and retardation.With 7 Figures     

The prediction of dust erosion by wind: An interactive model

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

Eddy flux measurements over the ocean and related transfer coefficients

Eddy correlation measurements of vertical turbulent fluxes made during AMTEX 1975 are used to assess the reliability of flux prediction from established bulk transfer relations, using both surface-layer and planetary boundary-layer formulations. The surface-layer formulae predict momentum and latent heat fluxes to an accuracy comparable to the direct eddy correlation method, using transfer coefficients of C _DN (at 10m and in neutral conditions) increasing with wind speed, and a constant C _EN - 1.5 × 10 ^–3 . The data suggest C _CHN , for sensible heat, increases significantly with wind speed and is on average 30% lower than C _CEN The boundary-layer drag coefficient, C _GD , agrees within about 40% of recently published values using a vertically averaged geostrophic wind to the height of the lowest temperature inversion, corrected for trajectory curvature. Values of _* / from which C _CGH is derived, are in excellent agreement if the published values are modified to account for inappropriate surface temperatures used in their derivation. Preliminary values of C _GE are also presented.     

Turbulent fluxes of momentum,heat and water vapor in the atmospheric surface layer at sea during ATEX

The vertical turbulent fluxes have been determined during the Atlantic Trade Wind Experiment (ATEX) both by direct and profile methods. The drag coefficient obtained from direct measurements was c _D = 1.39 × 10^–3. A distortion of the wind profile due to wave action could be demonstrated, this produced an increased drag coefficient estimated by the profile method. The dissipation technique using the downwind spectrum gave a lower drag coefficient of 1.26 × 10^–3, probably due to non-isotropic conditions (the ratio of vertical to downwind spectrum at high frequencies scattered considerably with an average of 1 instead of 4/3).From direct measurements, the sensible heat flux showed a poor correlation with the bulk parameter product U, contrary to the heat flux obtained from profiles. It is shown that this is due to the higher frequency part of the cospectrum, say above 0.25 Hz, which contributes more than 50 % of the total flux. Determination of the heat flux from temperature fluctuations by the dissipation method would be in agreement with the direct determination only if the corresponding Kolmogoroff constant were 2.1 instead of 0.8.For the vertical flux of water vapor obtained from profiles, the bulk transfer coefficient was 1.28 × 10^–3.This work was supported by the Deutsche Forschungsgemeinschaft, Schwerpunktprogramm Meeresforschung and later the Sonderforschungsbereich Meeresforschung Hamburg.     

Microwave vegetation optical depth and inverse modelling of soil emissivity using Nimbus/SMMR satellite observations

Summary A radiative transfer model has been used to determine the large scale effective 6.6 GHz and 37 GHz optical depths of the vegetation cover. Knowledge of the vegetation optical depth is important for satellite-based large scale soil moisture monitoring using microwave radiometry. The study is based on actual observed large scale surface soil moisture data and observed dual polarization 6.6 and 37 GHz Nimbus/SMMR brightness temperatures over a 3-year period. The derived optical depths have been compared with microwave polarization differences and polarization ratios in both frequencies and with Normalized Difference Vegetation Index (NDVI) values from NOAA/AVHRR. A synergistic approach to derive surface soil emissivity from satellite observed brightness temperatures by inverse modelling is described. This approach improves the relationship between satellite derived surface emissivity and large scale top soil moisture fromR ²=0.45 (no correction for vegetation) toR ²=0.72 (after correction for vegetation). This study also confirms the relationship between the microwave-based MPDI and NDVI earlier described and explained in the literature.List of Symbols f frequency [Hz] - f _i(p) fractional absorption at polarizationp - h surface roughness - h h cos² - H horizontal polarization - n _i complex index of refraction - p polarization (H orV) - R _s microwave surface reflectivity - T _B(p) brightness temperature at polarizationp - T ^* normalized brightness temperature - T polarization difference (T _v-T _H) - T _s temperature of soil surface - T _c temperature of canopy - T _max daily maximum air temperature - T _min daily minimum air temperature - V vertical polarization - soil moisture distribution factor; also used for the constant to partition the influence of bound and free water components to the dielectric constant of the mixture - empirical complex constant related to soil texture - microwave transmissivity of vegetation (=e ^–) - ^* effective transmissivity of vegetation (assuming =0) - microwave emissivity - _s emissivity of smooth soil surface - _rs emissivity of rough soil surface - _vs emissivity of vegetated surface - soil moisture content (% vol.) - K dielectric constant [F·m^–1] - K _fw dielectric constant of free water [F·m^–1] - K _ss dielectric constant of soil solids [F·m^–1] - K _m dielectric constant of mixture [F·m^–1] - K _o permittivity of free space [8.854·10^–12 F·m^–1] - high frequency limit ofK _wf [F·m^–1] - wavelength [m] - incidence angle [degrees from nadir] - polarization ratio (T _H/T _V) - b soil bulk density [gr·cm^–3] - s soil particle density [gr·cm^–3] - R surface reflectivity in red portion of spectrum - NIR surface reflectivity in near infrared portion of spectrum - _eff effective conductivity of soil extract [mS·cm^–1] - vegetation optical depth - _6.6 vegetation optical depth at 6.6 GHz - ₃₇ vegetation optical depth at 37 GHz - ^* effective vegetation optical depth (assuming =0) - single scattering albedo of vegetation With 12 Figures     

On similarity laws in regional climatology

Summary Starting with a linear theory of the flow around and over mountains a similarity hypothesis of the wind field over complex terrain is formulated and tested by simulations with the numerical mesoscale model KAMM (Karlsruhe Atmospheric Mesoscale Model) and applied to observations of the orographically induced phenomenon Moehlin-Jet, which were performed and analysed by Dütsch (1985). Because this hypothesis combines parameters describing the state of the large scale flow with form parameters of the orography it can be used to regionalize large scale climatological informations to smaller scale. It allows to generalize observations of typical mesoscale phenomena like channeling in broad valleys or orographically induced jet-like currents.With 9 Figures