La forme rotationnelle des équations de la dynamique atmosphérique et les invariants du mouvement de l'air

Résumé Après avoir rappelé quelques notions de calcul tensoriel et les équations de la dynamique atmosphérique en coordonnées généralisées, l'auteur établit l'équation fondamentale de la rotationnelle absolue de l'air. Diverses formes de cette équation sont mentionnées. La première de ces formes est celle d'un bilan qui permet de définir le transport et le taux de production de la rotationnelle absolue de l'air. De la forme particulière de ce transport, il résulte que ce bilan se réduit à un bilan dans un espace à deux dimensions. Deux exemples illustrent les formules générales, le premier, en coordonnées sphériques (, ,r), le second, en coordonnées (, , ) où est un scalaire quelconque (pression atmosphérique, température potentielle, ...). Une autre forme de l'équation fondamentale est celle qui donne le taux d'accroissement individuel d'une composante de la rotationnelle absolue. Cette forme conduit à l'équation d'Ertel. En terminant, l'auteur généralise l'invariant d'Ertel-Rossby.

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Summary Having recalled some results of the tensor analysis and the equations of atmospheric motion in general coordinates, the writer establishes the fundamental equation of the absolute vorticity. Different forms of this equation are mentioned. One of these is the equation of balance from which it is possible to deduce the definition of transport and production of vorticity. It is shown that the equation of balance of the absolute vorticity may be reduced to an equation of balance in two-dimensional space. Two examples illustrate the general equations and formulas: the first example, in spherical coordinates (, ,r), the second one in the coordinates (, , ) where is an arbitrary single-valued scalar quantity (pressure, potentiel temperature, ...). Another form of the absolute vorticity equation expresses the individual change of an arbitrary component of the absolute vorticity. This form leads toErtel's equation. Finally, the writer generalizes theErtel-Rossby invariant.

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Zusammenfassung Nach einer Rekapitulation einiger Resultate der Tensorrechnung und der atmosphärischen Bewegungsgleichungen in generalisierten Koordinaten wird die absolute Wirbelgleichung aufgestellt und es werden verschiedene Formen dieser Gleichung erwähnt. Eine derselben ist die Bilanzformel, aus der die Definition des Wirbeltransports und der Anteil der Wirbelbildung abgeleitet werden können. Es wird gezeigt, daß die Bilanzgleichung des absoluten Wirbels auf eine Bilanzgleichung im zweidimensionalen Raum reduziert werden kann. Die allgemeinen Formeln werden durch zwei Beispiele erläutert: das erste in Kugelkoordinaten (, ,r), das zweite in den Koordinaten (, , ), wo eine beliebige skalare Größe (luftdruck, potentielle Temperatur usw.) darstellt. Eine andere Form der absoluten Wirbelgleichung gibt die individuelle Zunahme einer beliebigen Komponente der absoluten Wirbelstärke wieder; diese Form führt zurErtelschen Gleichung. Zum Schlusse wird dieErtel-Rossbysche Invariante verallgemeinert.

     

Eddy energy dissipation rate and puff diffusion during calms

The paper considers a puff diffusion in its inertial stage when particle separation obeys the laws of the inertial subrange and depends only on eddy energy dissipation rate . The can be determined in the surface layer by the turbulent kinetic energy equation. Similarity equations connect with diffusion measure .A simple analytical model has been deduced to estimate pollutants diffusion during calms.     

Analytical solutions for the Ekman layer

The PBL equation that governs the transition from the constant-stress surface layer to the geostrophic wind in a neutrally stratified atmosphere for which the eddy viscosityK(z) is assumed to vary smoothly from the surface-layer value U _*z (0.4,U _*=friction velocity,z=elevation) to the geostrophic asymptoteK _GU _*d forzd is solved through an expansion in fd/U _*1 (f=Coriolis parameter). The resulting solution is separated into Ekman's constant-K solution an inner component that reduces to the classical logarithmic form forzd and isO() relative to the Ekman component forzd. The approximationKU _*d is supported by the solution of Nee and Kovasznay's phenomenological transport equation forK(z), which yieldsK–U _*d exp(–z/d), where is an empirical constant for which observation implies, 1. The parametersA andB in Kazanskii and Monin's similarity relation forG/U _* (G=geostrophic velocity) are determined as functions of . The predicted values ofG/U _* and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value ofB based on the assumption of asymptotically constantK is 4.5, while that based on the Nee-Kovasznay model is 5.1; these compare with the observed value of 4.7 for the Leipzig profile. A thermal wind correction, an asymptotic solution for arbitraryK(z) and 1, and an exact (unrestricted ) solution forK(z)=U _*d[1–exp(–z/d)] are developed in appendices.     

Numerical modeling of the nocturnal urban boundary layer

A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate , and turbulence intensities u ² and w ² increase rapidly at the upwind edge of the urban area. The Reynolds stress uw displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux w had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.     

A radiation and energy balance study of mature forest and clear-cut sites

Components of the radiation and energy balances were measured over a clear-cut area and a mature, mixed forest during the summer of 1981 at the Petawawa National Forestry Institute, Chalk River, Ontario. The work concentrated on the clear-cut site which supported a canopy layer composed primarily of bracken fern and logging remnants.Forty days of radiation data were collected at the clear-cut site. After the first four weeks of measurements (the green season), most of the ferns quickly died, and their foliage changed appearance from a green to brownish colour (the brown season). The daily mean reflection coefficient of solar radiation determined over the green season was 0.20 and decreased to 0.13 for the brown season. The corresponding value for the forest was 0.13, based on a limited amount of data. The clear-cut site received 11% and 21% less net radiation than the forest on a 24-hr and daylight-hours basis, respectively, as a consequence of the higher reflection coefficient and larger daytime longwave radiation emission.A reversing temperature difference measurement system (RTDMS), incorporating ten-junction thermopiles was employed at each site in order to determine Bowen ratios () via differential psychrometry. Both systems performed well, especially the RTDMS over the forest which was capable of resolving very small differences of temperature, typically less than 0.2 °C over a height of 3 m. The mean hourly Bowen ratio, calculated from values from 0800 to 1600 hr, varied from 0.2 to 1.0 for the forest and from 0.4 to 0.8 for the clear-cut site in the green season.A significant canopy heat storage component of the energy balance, Q _S , was found at the clear-cut site. In the early morning, a portion of the available energy was used to heat the biomass materials and air within the canopy layer. The stored heat within the canopy was released later in the day, increasing the available energy total.The daily mean value of the Priestley-Taylor coefficient (Priestley and Taylor, 1972) for the green season at the clear-cut site was 1.14, and individual values tended to increase during wet surface conditions and decrease when the surface dried. The daylight mean value during dry canopy conditions at the forest was 1.05, and much higher values occurred when the canopy was wet. The enhancement of for the wet forest was a result of the evaporation of intercepted rain (which is not limited by stomatal resistance) and the concomitant transfer of sensible heat to the forest.     

Calculation of velocity skewness in real and artificial plant canopies

Wind velocities within a plant canopy are much more strongly skewed than those of the air flow above. We have examined the governing Eulerian equations for the velocity products u _i, u _j u_k using data from a wind tunnel study with an artificial canopy consisting of an array of 5 cm lengths of monofilament fishing line, and from measurements in corn (Zea mays L).Simple parameterizations for pressure-velocity correlations, and for the quadruple velocity products allowed reasonably accurate calculations of the third moments using measured profiles of the mean velocity, variance and covariance fields. Comparisons of individual terms in the rate equations for ovu _i, u _j u _krevealed that diffusion (from above) and mean shear were most important in creating large skewness in the canopy. A drag term also contributed but was of lesser importance. These terms were balanced by return-to-isotropy and a turbulence interaction term. A quasi-Gaussian approximation considerably underestimated the magnitude of the fourth moments within the canopy.     

Transport-Dissipation Analytical Solutions to the E-∈Turbulence Model and their Role in Predictions of the Neutral ABL

E- turbulence model predictions of the neutralatmospheric boundary layer (NABL) are reinvestigated to determine thecause for turbulence overpredictions found in previous applications. Analytical solutions to the coupled E and equations for the case of steady balance between transport and dissipation terms, the dominant balance just below the NABL top, are derived. It is found that analytical turbulence profiles laminarizeat a finite height only for values of closure parameter ratio c ₂ /_e equal toor slightly greater than one, with laminarization as z for greater . The point = 2 is additionally foundthat where analytical turbulent length scale (l) profilesmade a transition from ones ofdecreasing ( < 2) to increasing ( > 2)values with height. Numerically predicted profiles near the NABL topare consistent with analytical findings. The height-increasingvalues of l predicted throughout the NABL with standard values ofclosure parameters thus appear a consequence of 2.5(> 2), implied by these values (c ₂ = 1.92, _{= 1.3}, _{e = 1}). Comparison of numericalpredictions with DNS data shows that turbulence overpredictions obtained with standard-valued parameters are rectifiedby resetting and _e to 1.1 and 1.6, respectively, giving, with c ₂ = 1.92, 1.3, and laminarization of the NABL's cappingtransport-dissipation region at a finite height.     

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.     

Flux Footprints Within and Over Forest Canopies

The characteristics of turbulence within a forest arespatially heterogeneous and distinct from thoseassociated with the surface boundary layer. Consequently, the size and probability distribution offlux footprints emanating from sources below aforest canopy have the potential to differ from thoseobserved above forests.A Lagrangian random walk model was used toinvestigate this problem since no analytical solutionof the diffusion equation exists. Model calculations suggest that spatialcharacteristics of flux footprint probabilitydistributions under forest canopies are muchcontracted, compared to those evaluated in the surfaceboundary layer. The key factors affecting thestatistical spread of the flux footprint, and theposition of the peak of its probability distribution,are horizontal wind velocity and the standarddeviations of vertical and horizontal velocityfluctuations. Consequently, canopies, which attenuatemean horizontal wind speed, or atmospheric conditions,which enhance vertical velocity fluctuations, willcontract flux footprint distributions mostly near thefloor of a forest. It was also found that theprobability distributions of the flux footprint arenarrower when horizontal wind velocity fluctuationsare considered, instead of the simpler case that considers only vertical velocity fluctuations and meanhorizontal wind velocity.     

A first-order closure scheme to describe counter-gradient momentum transport in plant canopies

The gradient diffusion parameterization of the Reynolds stress is modified by adding a bulk momentum transport term. Comparisons to available data indicate that this term accounts for the gusts or downsweeps of higher momentum fluid into the canopy and ejections of lower momentum fluid out of the canopy. This term results in realistic mean wind speed profiles.     

Diurnal variation of horizontal wind direction fluctuations in complex terrain at Geysers,Cal.

Horizontal diffusion in the surface layer is dependent on the standard deviation of wind direction fluctuations . Diurnal variation of this parameter in complex terrain was studied for the July 1979 Geysers, Cal., experiment using data from a network of 11 short meteorological towers in the 25 km² Anderson Creek watershed Valley side slopes are roughly 20 ° and maximum terrain difference is about 1 km.Values of for wind directions sampled for one hour at a height of 10 m are about 35 ° during the daytime. They slowly decrease to about 20 ° by 8 to 10 p.m. as stability increases but wind speeds are still relatively high. After 10 p.m. the drainage flow sets in at most stations, with speeds of 1 to 2 m s^-1, and average increases to about 30° during the period 11 p.m. to 6 a.m. In general, highest values of at night are associated with lowest values of wind speed and greatest static stability. This enhancement of by the terrain suggests that horizontal diffusion at night always conforms to that expected during nearly neutral stabilities. That is, Pasquill class D diffusion applies to the horizontal component all night in complex terrain.     

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.     

Northern hemisphere atmospheric response to changes of atlantic ocean SST on decadal time scales: a GCM experiment

Analyses indicate that the Atlantic Ocean seasurface temperature (SST) was considerably colder at the beginning than in the middle of the century. In parallel, a systematic change in the North Atlantic sea-level pressure (SLP) pattern was observed. To find out whether the SST and SLP changes analyzed are consistent, which would indicate that the SST change was real and not an instrumental artifact, a response experiment with a low-resolution (T21) atmospheric GCM was performed. Two perpetual January simulations were conducted, which differ solely in the Atlantic Ocean (40° S-60° N) SST: the cold simulation utilizes the SSTs for the period 1904–1913; the warm simulation uses the SSTs for the period 1951–1960. Also, a control run with the model's standard SST somewhat between the cold and warm SST was made. For the response analysis, a rigorous statistical approach was taken. First, the null hypothesis of identical horizontal distributions was subjected to a multivariate significance test. Second, the level of recurrence was estimated. The multivariate statistical approaches are based on hierarchies of test models. We examined three different hierarchies: a scale-dependent hierarchy based on spherical harmonics (S), and two physically motivated ones, one based on the barotropic normal modes of the mean 300 hPa flow (B) and one based on the eigenmodes of the advection diffusion operator at 1000 hPa (A). The intercomparison of the cold and warm experiments indicates a signal in the geostrophic stream function that in the S-hierarchy is significantly nonzero and highly recurrent. In the A-hierarchy, the low level temperature field is identified as being significantly and recurrently affected by the altered SST distribution. The SLP signal is reasonably similar to the SLP change observed. Unexpectedly, the upper level stream-function signal does not appear to be significantly nonzero in the B-hierarchy. If, however, the pairs of experiments warm versus control and cold versus control are examined in the B-hierarchy, a highly significant and recurrent signal emerges. We conclude that the cold versus warm response is not a small disturbance that would allow the signal to be described by eigenmodes of the linear system. An analysis of the three-dimensional structure of the signal leads to the hypothesis that two different mechanisms are acting to modify the model's mean state. At low levels, local heating and advection are dominant, but at upper levels the extratropical signal is a remote responce to modifications of the tropical convection.This paper was presented at the International Conference on Modelling of Global Climate Change and Variability, held in Hamburg 11–15 September 1989 under the auspices of the Meteorological Institute of the University of Hamburg and the Max Planck Institute for Meteorology. Guest Editor for these papers is Dr. L. Dilmenil.AWI Publication no. 254     

Effects of water vapour on the structure parameter of the refractive index for near-infrared radiation

The refractive index of air (n) mainly depends on temperature andwater vapour content. For near-infrared radiation, temperature isthe main determining factor. To determinethe structure parameter of temperature ( ) fromthe structure parameter of the refractive index( ), the influence ofwater vapour content on n needs to be taken into account as acorrection. Three levels of approximation are presented. The firstinvolves the standard deviations of T and q (_T and_q) as well as the correlation coefficient betweenT and q (R_Tq). The second approximation involvesR_Tq and the Bowen ratio (), and the last uses only the Bowen ratio.The latter is the classical Bowen ratio correction.Evaluation of the validity of the assumptions used in the derivationreveals that a large error may be introduced (for situations withR_Tq < 0.8) by replacing _T/_qwith the Bowen ratio.Consequently, estimating from using the Bowen ratiocan contain errors of 5–40% for || < 1. Adding R_Tqas extra information reduces the errors only marginally. For || > 1,the correction is small, and all three approximations give errors of lessthan 1% in . When is used to compute the sensible heat flux,the influence of the quality of the correction forwater vapour fluctuations on the measured energy balance is small: forsmall ||, the correction is large, but the absolute value ofthe heat flux is small, whereas for large ||, the correctionis insignificant.     

On the representation of frequency spectra in meteorology

The common representation of frequency spectra in meteorology and climatology is discussed. It is pointed out that this representation is misleading since spectral peaks and spectral gaps are obtained even when the spectrum density is monotonously decreasing in the whole frequency range. A plea is made for using the spectrum distribution function, F() which gives an unambiguous picture of the distribution of variance with frequency.     

Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface

Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.     

Observed variations of σθ and σΦ in the nocturnal drainage flow in a deep valley

The variations of and in the drainage flow in the Brush Creek valley of western Colorado are investigated using data from Doppler acoustic sodars and instrumented towers. The data were obtained on two experimental nights during the 1984 ASCOT field study. There is good agreement between the variations derived from low-level observations of the sodars and those derived from the towers located throughout the valley. The observed hourly average and in the nocturnal drainage flow are about 20 ° to 25 ° and 5 °, respectively; these values are much larger than those generally observed over flat terrain during nighttime stable conditions. After sunrise (about 0600 MST), as the valley warms and the flow direction changes to up-valley, these parameters increase sharply to their peak values at about 0800 MST and then decrease to their normal daytime values after about two hours.In the drainage flow, the hourly average varies inversely with wind speed according to the relation u 0.7ms^-1. The vertical standard deviation is much less enhanced by complex terrain than the horizontal standard deviation. The observed values are predicted fairly well by the local similarity theory.Oak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 andOak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 and     

Robust estimation of background noise and signal detection in climatic time series

We present a new technique for isolating climate signals in time series with a characteristic red noise background which arises from temporal persistence. This background is estimated by a robust procedure that, unlike conventional techniques, is largely unbiased by the presence of signals immersed in the noise. Making use of multiple-taper spectral analysis methods, the technique further provides for a distinction between purely harmonic (periodic) signals, and broader-band (quasiperiodic) signals. The effectiveness of our signal detection procedure is demonstrated with synthetic examples that simulate a variety of possible periodic and quasiperiodic signals immersed in red noise. We apply our methodology to historical climate and paleoclimate time series examples. Analysis of a 3 million year sediment core reveals significant periodic components at known astronomical forcing periodicities and a significant quasiperiodic 100 year peak. Analysis of a roughly 1500 year tree-ring reconstruction of Scandinavian summer temperatures suggests significant quasiperiodic signals on a near-century timescale, an interdecadal 16–18 year timescale, within the interannual El Niño/Southern Oscillation (ENSO) band, and on a quasibiennial timescale. Analysis of the 144 year record of Great Salt Lake monthly volume change reveals a significant broad band of significant interdecadal variability, ENSO-timescale peaks, an annual cycle and its harmonics. Focusing in detail on the historical estimated global-average surface temperature record, we find a highly significant secular trend relative to the estimated red noise background, and weakly significant quasiperiodic signals within the ENSO band. Decadal and quasibiennial signals are marginally significant in this series.     

A Green Planet Versus a Desert World: Estimating the Maximum Effect of Vegetation on the Land Surface Climate

We quantify the maximum possible influence of vegetation on the global climate by conducting two extreme climate model simulations: in a first simulation (desert world), values representative of a desert are used for the land surface parameters for all non glaciated land regions. At the other extreme, a second simulation is performed (green planet) in which values are used which are most beneficial for the biosphere's productivity. Land surface evapotranspiration more than triples in the presence of the green planet, land precipitation doubles (as a second order effect) and near surface temperatures are lower by as much as 8 K in the seasonal mean resulting from the increase in latent heat flux. The differences can be understood in terms of more absorbed radiation at the surface and increased recycling of water. Most of the increase in net surface radiation originates from less thermal radiative loss and not from increases in solar radiation which would be expected from the albedo change. To illustrate the differences in climatic character and what it would imply for the vegetation type, we use the Köppen climate classification. Both cases lead to similar classifications in the extra tropics and South America indicating that the character of the climate is not substantially altered in these regions. Fundamental changes occur over Africa, South Asia and Australia, where large regions are classified as arid (grassland/desert) climate in the desert world simulation while classified as a forest climate in the green planet simulation as a result of the strong influence of maximum vegetation on the climate. This implies that these regions are especially sensitive to biosphere-atmosphere interaction.     

Turbulence characteristics and organized motion in a suburban roughness sublayer

To investigate tubulence characteristics and organized motion within and above an urban canopy, field observations were conducted in July 1991 and November 1992 in Sapporo, Japan. The measurement heights were 5.4, 10.3, 18, 35 and 45 m above ground; the canopy height was 7 m. The profiles of _u peaked slightly above the canopy, while _v and _w had nearly uniform profiles. Vertical profiles of Reynolds stress - peaked slightly at 1.5 times the canopy height and decreased slowly with height thereafter. A four-quadrant analysis showed that sweep and ejection motions caused high-velocity fluid from above moves downward toward the surface and low-velocity fluid from below moves upward. An ensemble-averaging technique was used to isolate typical features of the flow and temperature fields. A time-height cross-section of velocity vectors and temperature contours showed details of the flow structures associated with temperature ramps. It has been noted that the organized motions play important roles in the transport of heat near the urban canopy, where the sweep motion causes negative temperature fluctuations and the ejection motion causes positive temperature fluctuations.