Roughness lengths for temperature and momentum over heterogeneous terrain

Measurements are presented describing the behaviour of roughness lengths for momentum and temperature for heterogeneous terrain of low fractional rough cover. The momentum roughness lengths were found to be up to several orders of magnitude larger than that for temperature, behaviour which is characteristic of a bluff-rough type of surface and which is consistent with previous experimental and theoretical studies. This contrasts with observations over uniform, vegetated surfaces, which show only an order-of-magnitude increase of momentum roughness length over that for temperature.     

Observations of fluxes over heterogeneous surfaces

This study analyzes data collected from repeated aircraft runs 30 m over alternating regions of irrigated and dry nonirrigated surfaces, each region on the order of 10 km across, during the California Ozone Deposition Experiment (CODE). After studying the scale dependence of the flow, the variables and their fluxes are decomposed into means for sublegs defined in terms of irrigated and nonirrigated regions and deviations from such subleg means. Since the repeated runs were flown over the same track, compositing the eight flight legs for each of the two days allows partial isolation of the influences of surface heterogeneity and transient mesoscale motions.A variance analysis is carried out to quantify the relative importance of surface heterogeneity and transient mesoscale motions on the variability of the turbulence fluxes. The momentum and ozone fluxes are more influenced by transient mesoscale motions while fluxes of heat, moisture and carbon dioxide are more influenced by surface heterogeneity. The momentum field is also influenced by a quasi-stationary mesoscale front and larger scale velocity gradients.For the present case, the mesoscale modulation of the turbulent flux is numerically more important than the direct mesoscale flux. This spatial modulation of the turbulent fluxes leads to extra Reynolds terms which act to reduce the area-averaged turbulent momentum flux and enhance the area-averaged turbulent heat flux.     

Observations of the barotropic Ekman layer over an urban terrain

Data from low-level soundings over Cambridge, U.S.A. were selected on the basis of an Ekman-like variation of the wind vector with altitude combined with evidence of a barotropic atmosphere. The method of geostrophic departure was used to determine the shear-stress distribution. The analysis yields the dimensionless properties of the barotropic Ekman layer under neutral and stable stratification. Some important results include: the geostrophic drag coefficient displays no dependence on the degree of static stability; the dimensionless height of the boundary layer decreases with increasing stability in agreement with the prediction of Zilitinkevich; the properties of the urban surface layer, where the roughness elements are multistory buildings, show no dependence on atmospheric stability under the moderate wind conditions which display the Ekman-like wind profile; and the directions of the horizontal shear stress and the vertical derivative of the velocity vector usually tend to be parallel only near the surface layer. Values of the two constants of the Rossby number similarity theory are found for the neutral barotropic Ekman layer at a surface Rossby number equal to 2 × 10⁵. The implications of the work with respect to wind-tunnel simulation of the flow over models of urban areas are discussed.     

The vertical transfer of momentum in the general circulation

Summary A simplified scheme of the transfer of zonal momentum in the general circulation is first summarised. Observational evidence in support of the pattern of vertical transfer is then provided from the relation between the fields of pressure and wind over the oceans in the Trades and westerlies, with large down-gradient motion in the former and very little cross-isobar motion in the latter. In neither case are the concepts of the classical (barotropic) friction layer valid. The vertical gradients of downwind and cross-wind shear stress are evaluated and from them climatological values of eddy viscosity are deduced for the surface layers. Values of eddy viscosity at levels of a few hundred metres are also deduced and found to be greater than at lower levels, consistent with the pattern of momentum transfer advanced. The transfer in the lower troposphere is probably mainly convective above the layer of mechanical turbulence. There is a concluding discussion on the nature of the vertical transfer of momentum in the middle and upper troposphere.

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Zusammenfassung Zunächst wird ein vereinfachtes Schema für den Transport der zonalen Bewegungsgröße in der allgemeinen Zirkulation skizziert. Hierauf werden auf Grund der Beziehungen zwischen Druck- und Windfeld über den Ozeanen in den Gebieten der Passatwinde und der Westströmung auf Beobachtungsmaterial beruhende Beweise für den Vertikaltransport entwickelt; dabei erweist sich der Winkel zwischen Isobaren und Windrichtung in den Passatgebieten als groß, in der Westströmung als klein. In keinem der beiden Fälle haben die Anschauungen über die klassische (barotrope) Reibungsschicht Gültigkeit. Die Vertikalgradienten der Schubspannung in Richtung wie auch senkrecht zum Winde werden berechnet und daraus klimatologische Mittelwerte der scheinbaren Viskosität (Austausch) für bodennahe Schichten abgeleitet. Werte der scheinbaren Viskosität werden auch für Niveaus von einigen 100 m berechnet und größer als in niedrigeren Schichten gefunden, was in Übereinstimmung mit der entwickelten Anschauung über das Schema der Fortpflanzung der Bewegungsgröße steht. Der Austausch in der unteren Troposphäre oberhalb der Schicht mechanischer Turbulenz ist wahrscheinlich in der Hauptsache konvektiv. Zum Schluß wird das Wesen des Vertikalaustausches der Bewegungsgröße in der mittleren und oberen Troposphäre diskutiert.

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Résumé Un schéma simplifié du transport, dans la circulation générale, de la quantité de mouvement zonal est d'abord esquissé. Des arguments en faveur du transport vertical proposé sont alors fournis par les relations des champs de pression et du vent au-dessus des océans dans les zones des alizés et du courant d'ouest; dans la première, l'angle entre l'isobare et la direction du vent est grande, dans la seconde il est petit. Dans aucun des deux cas, la conception de la couche de friction classique (barotropique) n'est valable. Les gradients verticaux des tensions internes sont évalués dans la direction et normalement à la direction du vent et des valeurs climatologiques de la viscosité apparente due à la turbulence en sont déduites pour les couches voisines du sol. Les valeurs de la viscosité apparente calculées pour des niveaux de quelques centaines de mètres sont plus grandes que celles des niveaux bas, concordant ainsi avec le transport vertical proposé. Dans la basse troposphère le transport est probablement surtout convectif au-dessus de la couche de turbulence. En conclusion l'auteur discute la nature du transport vertical de la quantité de mouvement dans la troposphère moyenne et supérieure.

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With 1 Figure.     

Observations of complex terrain flows using acoustic sounders: Echo interpretation

We examine methods for the interpretation of sodar facsimile records obtained in the study of complex terrain flows. Acoustic scattering theory is presented first and then interpreted using a simpolified second-order turbulence closure scheme. The use of this theory suggests the strong sensitivity of acoustic scatter to changes in the wind shear. With this introduction, detailed sodar facsimile records, temperature and wind profiles, and model calculations follow. Characteristic scattering patterns are described for simple drainage jets, complex basin flows, convection with a capping inversion, stratus, and dynamical instabilities. Examples are also shown of bistatic facsimile records detailing the strong temporal and spatial variability in small-scale turbulence.     

Estimation of surface heat and momentum fluxes using the flux-variance method above uniform and non-uniform terrain

Eddy-correlation measurements above an uneven-aged forest, a uniform-irrigated bare soil field, and within a grass-covered forest clearing were used to investigate the usefulness of the fluxvariance method above uniform and non-uniform terrain. For this purpose, the Monin and Obukhov (1954) variance similarity functions were compared with direct measurements. Such comparisons were in close agreement for momentum and heat but not for water vapor. Deviations between measured and predicted similarity functions for water vapor were attributed to three factors: 1) the active role of temperature in surface-layer turbulence, 2) dissimilarity between sources and sinks of heat and water vapor at the ground surface, and 3) the non-uniformity in water vapor sources and sinks. It was demonstrated that the latter non-uniformity contributed to horizontal gradients that do not scale with the vertical flux. These three factors resulted in a turbulence regime that appeared more efficient in transporting heat than water vapor for the dynamic convective sublayer but not for the dynamic sublayer. The agreement between eddy-correlation measured and flux-variance predicted sensible heat flux was better than that for latent heat flux at all three sites. The flux-variance method systematically overestimated the latent heat flux when compared to eddy-correlation measurements. It was demonstrated that the non-uniformity in water vapor sources reduced the surface flux when compared to an equivalent uniform terrain subjected to identical shear stress, sensible heat flux, and atmospheric water vapor variance. Finally, the correlation between the temperature and water vapor fluctuations was related to the relative efficiency of surface-layer turbulence in removing heat and water vapor. These relations were used to assess critical assumptions in the derivation of the flux-variance formulation.     

The influence of stratification on heat and momentum turbulent transfer in antarctica

Data from the Antarctic winter at Halley Base have been used in order to evaluate qualitatively and quantitatively how the stratification in the low atmosphere (evaluated with the gradient Richardson number, Ri) influences the eddy transfers of heat and momentum. Vertical profiles of wind and temperature up to 32 m, and turbulent fluxes ( , and ) measured from three ultrasonic thermo-anemometers installed at 5, 17 and 32 m are employed to calculate Ri, the friction velocity (u _*) and the eddy diffusivities for heat (K _h ) and momentum (K _m ). The results show a big dependence of stability onK _m ,K _h andu _*, with a sharp decrease of these turbulent parameters with increasing stability. The ratio of eddy diffusivities (K _h /K _m ) is also analyzed and presents a decreasing tendency as Ri increases, reaching values even less than 1, i.e., there were situations where the turbulent transfer of momentum was greater than that of heat. Possible mechanisms of turbulent mixing are discussed.     

Three-dimensional simulations of air flow and momentum transfer in partially harvested forests

In order to predict wind loading on trees (canopy height h) in partially harvested forests, it is necessary to characterize air flow and momentum transfer in progressively more complex patterns where groups of trees (or aggregates) are retained. In this study, we used large-eddy simulation to explore the effects of aggregate size, inter-aggregate spacing, and the ratio between the aggregate size and inter-aggregate spacing on air flow and momentum transfer. Forty-five grid points across an aggregate were needed to achieve an adequate level of turbulence. Using grid sizes of h/15 throughout was too viscous for the smaller aggregates. Vertical and horizontal flow deflection by the leading aggregates sheltered some of the downstream aggregates to varying degrees where turbulence increased for subsequent rows. The number of rows of protected aggregates decreased as aggregate dimensions and the space between aggregates increased. A theoretical treatment of time-dependent wind is presented for the lead aggregate and a simulation case is presented for the case of a gust of reduced wind passing through the aggregate pattern. The leading aggregate responded with decreasing moment for decreasing ambient wind speed as predicted by theory. However, downwind aggregates experienced substantial increases in bending moment. The overall results of the disruptive aspects of time dependence agrees with arguments regarding the role of irrotational (potential) flow to this problem. Our treatment of retention pattern design is only a first step and further research suggestions are presented.     

Turbulence intensity and turbulent kinetic energy parameters over a heterogeneous terrain of Loess Plateau

A deep understanding of turbulence structure is important for investigating the characteristics of the atmospheric boundary layer, especially over heterogeneous terrain. In the present study, turbulence intensity and turbulent kinetic energy (TKE) parameters are analyzed for different conditions with respect to stability, wind direction and wind speed over a valley region of the Loess Plateau of China during December 2003 and January 2004. The purpose of the study is to examine whether the observed turbulence intensity and TKE parameters satisfy Monin-Obukhov similarity theory (MOST), and analyze the wind shear effect on, and thermal buoyancy function of, the TKE, despite the terrain heterogeneity. The results demonstrate that the normalized intensity of turbulence follows MOST for all stability in the horizontal and vertical directions, as well as the normalized TKE in the horizontal direction. The shear effect of the wind speed in the Loess Plateau region is strong in winter and could enhance turbulence for all stability conditions. During daytime, the buoyancy and shear effect together constitute the generation of TKE under unstable conditions. At night, the contribution of buoyancy to TKE is relatively small, and mechanical shearing is the main production form of turbulence.     

Observations of complex terrain flows using acoustic sounders: Drainage flow structure and evolution

This paper presents an analysis of nocturnal drainage flows in a mountainous coastal environment where the elevation of the terrain is comparable with the elevation of the marine temperature inversion. The analysis traces the initiation, evolution, and breakup of the drainage flow using acoustic sounder facsimile data and tethered sonde measurements of wind and temperature. Conditions addressed include (1) opposing seabreeze flow ranging from 2 to 8m s^-1, (2) aiding flow, and (3) large-scale and drainage-induced subsidence. The effect of deep marine temperature inversions pervades the observations, as seen in deeper, more stratified echo layers, weaker drainage, and delayed destruction of the inversion in the morning.     

Heat and momentum transfer characteristics of adjacent fields of soybeans and maize

Measurements made as part of studies of the evolution of the planetary boundary layer (the Sangamon experiments of 1975 and 1976) are used to compare the surface eddy fluxes of heat and momentum over adjacent fields of soybeans and maize. Although the maize canopy was much taller and rougher than that of the soybeans, daytime eddy fluxes of momentum over the maize exceeded those over the soybeans by only about 35%, in good agreement with predictions based on PBL similarity theory. Heat flux was about 10% greater over the maize, probably as a consequence of greater evaporation over the soybeans. Infrared surface temperatures generally differed by less than 0.4 °C and net radiation by less than 10%. For the soybean canopy, the momentum displacement height was found to be located at approximately 90% of the crop height, and the roughness length was about 5%. The roughness length for sensible heat transfer was found to be 2–3% of the soybean canopy height. For the maize canopy, the momentum displacement height was about 60% of the crop height, and the roughness length about 7%.Work supported under the auspices of the U.S. Department of Energy.     

Numerical study of wind energy characteristics over heterogeneous terrain — Central Israel case study

A numerical mesoscale meteorological model has been applied over the heterogeneous terrain of central Israel in order to study wind energy characteristics of three typical synoptic situations. The supportive nature of this method for observationally oriented wind energy studies has been emphasized. Mesoscale forcing effects on the availability of wind energy and on the exponent, p, in the vertical wind power law are evaluated.     

The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer

Using an incomplete third-order cumulant expansion method (ICEM) and standard second-order closure principles, we show that the imbalance in the stress contribution of sweeps and ejections to momentum transfer (ΔS _o ) can be predicted from measured profiles of the Reynolds stress and the longitudinal velocity standard deviation for different boundary-layer regions. The ICEM approximation is independently verified using flume data, atmospheric surface layer measurements above grass and ice-sheet surfaces, and within the canopy sublayer of maturing Loblolly pine and alpine hardwood forests. The model skill for discriminating whether sweeps or ejections dominate momentum transfer (e.g. the sign of ΔS _o ) agrees well with wind-tunnel measurements in the outer and surface layers, and flume measurements within the canopy sublayer for both sparse and dense vegetation. The broader impact of this work is that the “genesis” of the imbalance in ΔS _o is primarily governed by how boundary conditions impact first and second moments.     

LLM – a nonhydrostatic model applied to high-resolving simulations of turbulent fluxes over heterogeneous terrain

Summary ?At the Deutscher Wetterdienst (DWD) an internal project named LITFASS was running to determine the representative turbulent fluxes of heat and momentum over heterogeneous land surfaces by observation and simulation. The project took advantage of the infrastructure of the Research Division at the DWD, where model research capacity is combined with the measurements made at and around the Meteorological Observatory Lindenberg. The paper describes the simulation component of the LITFASS-project. It consists of a high-resolving model, derived from the new operational non-hydrostatic, compressible Lokal-Modell (LM), which is denoted LLM (LITFASS-Lokal-Modell). The integration area covers the lower atmosphere in the vertical up to 3000 m with 39 model layers. The horizontal size of the integration area with 145 × 145 grid points (horizontal mesh width Δs = 96.5 m) corresponds to a typical grid box of a meso-scale model. The LLM has to operate under real meteorological conditions. Therefore, the LLM is driven by time-dependent measured vertical profiles of wind, temperature and humidity and surface-based measurements (of radiation, precipitation, soil properties) supported by satellite information. The profiles are available for a great variety of weather situations occurring during the simulation period (1–20 June 1998). First model results from extended 24 hour-integrations against different kinds of measurements are discussed. They reveal the LLM to become a promising validation instrument, from which a systematic, sustainable validation system can be established beyond LITFASS for improving parameterization schemes in the NWP models of the DWD. Received July 18, 2001; revised March 15, 2002; accepted May 30, 2002     

Estimation of turbulent sensible heat and momentum fluxes over a heterogeneous urban area using a large aperture scintillometer

The accurate determination of surface-layer turbulent fluxes over urban areas is critical to understanding urban boundary layer (UBL) evolution. In this study, a remote-sensing technique using a large aperture scintillometer (LAS) was investigated to estimate surface-layer turbulent fluxes over a highly heterogeneous urban area. The LAS system, with an optical path length of 2.1 km, was deployed in an urban area characterized by a complicated land-use mix (residential houses, water body, bare ground, etc.). The turbulent sensible heat (Q H) and momentum fluxes (τ) were estimated from the scintillation measurements obtained from the LAS system during the cold season. Three-dimensional LAS footprint modeling was introduced to identify the source areas ("footprint") of the estimated turbulent fluxes. The analysis results showed that the LAS-derived turbulent fluxes for the highly heterogeneous urban area revealed reasonable temporal variation during daytime on clear days, in comparison to the land-surface process-resolving numerical modeling. A series of sensitivity tests indicated that the overall uncertainty in the LAS-derived daytime Q H was within 20%-30% in terms of the influence of input parameters and the non-dimensional similarity function for the temperature structure function parameter, while the estimation errors in τ were less sensitive to the factors of influence, except aerodynamic roughness length. The 3D LAS footprint modeling characterized the source areas of the LAS-derived turbulent fluxes in the heterogeneous urban area, revealing that the representative spatial scales of the LAS system deployed with the 2.1 km optical path distance ranged from 0.2 to 2 km2 (a "micro-α scale"), depending on local meteorological conditions.     

On the relationship between meridional eddy transfer of angular momentum and meridional circulations in the earth's atmosphere

Summary Recent investigations have shown that the poleward flux of angular momentum across latitutde 30° N can be regarded essentially as an edey flux due to macroturbulence. Since the principal source region of atmospheric angular momentum is the frictional layer in the trade-wind zone it is necessary to have a mechanism which explains the transport of the angular momentum up to the upper troposphere and the tropopause level and into the planetary jet stream aroundlatitude 30° N. In the present paper it is shown that this transport can easily be explained by assuming the existence of a mean meridional circulation between the Equator and latitude 30°N. The mass transport in this meridional circulation cell can be computed from the empirical data for the poleward eddy flux of angular momentum presented byY. Mintz. The same data can then also be used to estimte the excess of precipitation over evaporation in the equatorial zone of the ascending branch of the circulation.

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Zusammenfassung Neuere Untersuchungen haben gezeigt, daß der Polwärtstransport des Rotationsimpulses über Breite 30° N hinaus im wesentlichen als Austauschströmung durch Makroturbulenz aufgefaßt werden kann. Da dase Hauptquellgebieet des atmosphärischen Rotationsimpulses die Reibungs-schicht der Passatzone ist, ist es notwendig, einen Mechanismus zu finden, der die Verlagerung des Rotationsimpulses bis in die obere Troposphäre und das Tropenpasausenniveau und in den planetarischen jet stream rund um den Brietenkreis 30° N erklärt. In der vorliegenden Arbiet wird gezeigt, daß diese Verlagerung durch die Annahme ener mittleren Meridionalzirkulation zwischen dem Äquator und 30° N leicht erklärt werden kann. Der Massentransport in dieser Meridionalzirkulationszelle kann aus den Empirischen Daten berechnet werden, dieY. Mintz für den turbulenten Polwärtstransport des Rotationsimpulses angegeben hat. Dieselben Werten können auch benützt werden, um den überschuß des Niederschlags über die Verdungstung in der Äquatorialzone des aufsteigenden Zirkulationszweiges zu berechnen.

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Résumé De récentes recherches ont montré que le flux du moment cinétique dirigé vers le pôle à travers la région de 30° lat. N peut être considéré comme étant essentiellement unflux dû à la macroturbulence. Etant donné que la source principale du moment cinétique atmosphérique est située dans la couche de friction dans la zone des vents alizés, il est nécessaire de trouver un mécanisme qui expliquerait le transport du moment cinétique vers la haute troposphère et le niveau de la tropopause ainsi que dans le jet stream planétaire autour du 30ème degré de latitude nord. Dans l'article suivant l'auteur montre comment il est possible d'expliquer facilement ce transport en admettant l'existence d'une circulation méridienne moyenne entre l'équateur et 30° lat. N. Le transport de masse dans cette cellule de circulation méridienne peut être calculé à partir des données empiriques indiquées parY. Mintz concernant le flux du moment cinétique dû à la turbulence et dirigé vers de pôle. Les mêmes données peuvent aussi être employées pour estimer l'excès des précipitations sur l'évaporation dans la zone équatoriale de la branche ascendante de la circulation.

     

A note on the analogy between momentum transfer across a rough solid surface and the air-sea interface

The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re _s =h _s u _*/, whereh _s is the effective roughness height, -viscosity,u _*-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the sea roughness cannot be explained only on the basis of the classification of aerodynamic conditions of the sea surface proposed by Kitaigorodskii and Volkov (1965) and Kitaigorodskii (1968) even though the latter approach gains some support from recent experimental studies (see for example Geernaertet al. 1986). In this paper, an attempt is made to explain some of the recently observed features of the variability of surface roughness (Toba and Ebuchi, 1991; Donelanet al., 1993). The fluctuating regime of the sea surface roughness is also described. It is shown that the contribution from the dissipation subrange to the variability of the sea surface can be very important and by itself can explain Charnock's (1955) regime.     

Observational results on the influence of stability and wind-wave coupling on momentum transfer and turbulent fluctuations over ocean waves

Turbulence data obtained over ocean waves during the BOMEX experiment of 1969 are presented. Procedures in measurement and analyses are described which include adjustments for possible platform, R/V FLIP, motion. Momentum transfer is shown to have been influenced by both stability and wind-wave coupling. The wind-wave coupling influence is separated from the stability influence and is described in terms of a linear dependence of the deviation from the logarithmic profile on C/u _*, where C is the phase speed corresponding to the wave spectrum peak. As observed by others, a value of C/u _* near 25 is associated with minimal wind-wave coupling influence. For C/u _* greater than 25, momentum transfer is decreased relative to the neutral profile prediction. Expressions are also presented for the wind-wave coupling influence on relative intensities, _u /u _*, _u /u _* and _w/u _*. Values of the relative intensities approximate neutral overland values when the expressions are written such that the wave influence is zero near a C/u _* value of 25.