Turbulence mechanisms at an agricultural site

An extensive set of turbulence data from the 3- and 12-m heights taken over an agricultural site (Marsta, Sweden) are analyzed and compared with data from ideal sites.In unstable air, Monin-Obukhov similarity is found to be valid for the non-dimensional gradients of wind, _m , temperature, _h , and humidity, _e , for (only a few data), for _T /|T _*|,/ _E /|E _*| and for the non-dimensionalized inertial subrange spectra of temperature and humidity. Where comparison is possible, the unstable data also agree with those found in the Kansas study, with one remarkable exception, the inertial subrange constant of the temperature spectrum, ₁, being only 0.39, compared to the value 0.80 found at the Kansas site.On the stable side, most similarity predictions break down, with most of the data differing systematically from the corresponding Kansas results, the only exception being . The inertial subrange constants for temperature, ₁, and for humidity, ₁ are found to have the same values, 0.39 and 0.30, respectively, as they do on the unstable side. Remarkable similarity is found for the shape of the stable u- and - and e-spectra. In addition, this shape is found to be identical with that found in Kansas. The peak wavelength of the stable u-, and -spectra is found to be about four times larger than it is for the corresponding Kansas spectra. This is interpreted to be a result of the increased macro-roughness at the Marsta site as compared with that at the Kansas site. A possible explanation for the low ₁-value is discussed, suggesting that ₁ is not a universal constant, but instead dependent on the turbulent structure.     

Airflow above changes in surface heat flux,temperature and roughness; an extension to include the stable case

A numerical model of airflow above changes in surface roughness and thermal conditions is extended to include cases with stable thermal stratification within the internal boundary-layer. The model uses a mixing-length approach with empirical forms for M and H.Results are presented for some basic cases and an attempt is then made to compare results given by the model with the experimental results of Rider, Philip and Bradley. Tolerable agreement is achieved. The importance of roughness change and thermal stability effects in the diffusion of heat and moisture near a leading edge is emphasised.Notation A Refers to Taylor (1970) - B Businger-Dyer constant (= 16.0) in forms for _M and _H - C Constant in form for in stable case - c _p Specific heat at constant pressure - E Scaled absolute humidity - g Acceleration due to gravity - H Upward vertical heat flux - H ₀, H ₁ Surface heat fluxes for x <0, x0 - H _E Upward latent heat flux - k Von Kármán's constant (= 0.4) - K _H K _W Eddy transfer coefficients for heat and water vapour - L Monin-Obukhov length - L _H Latent heat of evaporation for water - m Ratio of roughness lengths ( = z ₁/z ₀) - RPB Refers to Rider et al. (1964) - RL* Non-dimensional parameter (see Equations (9), (20a), (22a), (24a)) - R* Net radiation less ground heat flux (see Equations (15), (16)) - T Scaled temperature - T ₁ Downstream scaled surface temperature - u ₀ u ₁(x) Surface friction velocities for x <0, x0 - U, W Horizontal and vertical mean velocities - x, z Horizontal and vertical co-ordinates - Z _i Local roughness length - z ₀, z _i Roughness lengths for x < 0, x 0 - Temperature - ₀, ₁ Surface temperatures for x<0, x0 - _E Non-dimensional absolute humidity gradient - _H Non-dimensional temperature gradient of heat flux - _M Non-dimensional wind shear - = _M = _H = _E an assumption used in stable conditions - Air density - Absolute humidity - _w Density of water - Kinematic shear stress - Logarithmic height scale (= ln(z+z ₁)/z ₁)     

Surface-Layer Fluxes in Stable Conditions

Micrometeorological tower data from the Microfronts experiment are analyzed. Scale-dependencies of the flux and flux sampling error are combined to automatically determine Reynolds turbulence cut-off time scales for computing fluxes from time series. The computed downward heat flux at the 3 m height averaged over nine nights with 7.3 hours each night is 20% greater than the downward heat flux computed at the 10 m height. In contrast, there is only a 1.2% difference between 3 m and 10 m heat fluxes averaged over daytime periods, and there is less than a 2% difference between 3 m and 10 m momentum fluxes whether averaged over nighttime or daytime periods.Stability functions, M(z/L) and H(z/L) are extended to z/L up to 10, where z is the observational height and L is the Obukhov length. For 0.01 < z/L < 1 the estimated functions generally agree with Businger-Dyer formulations, though the H estimates include more scatter compared to the M estimates. For 1 < z/L < 10, the flux intermittency increases, the flux Richardson number exceeds 0.2, and the number of flux samples decreases. Nonetheless the estimates of the stability function M based on 3-m fluxes are closer to the formula proposed by Beljaars and Holtslag in 1991 while the M functions based on 10-m fluxes appears to be closer to the formula proposed by Businger et al. in 1971. The stability function H levels off at z/L = 0.5.     

On Trajectory Curvature as a Selection Criterion for Valid Lagrangian Stochastic Dispersion Models

Recently Wilson and Flesch (Boundary-Layer Meteorology, 84, 411-426, 1997) suggested that the average increment d z to the orientation = arctan(w/u) of the Lagrangian velocity-fluctuation vector can be used to distinguish the better Lagrangian stochastic models within the well-mixed class. Here it is demonstrated that the specification of d z constitutes neither a sufficient or universally applicable criterion to distinguish the better Lagrangian stochastic models within the well-mixed class. The hypothesis made by Wilson and Flesch that Lagrangian stochastic models with /P_E irrotational are zero-spin models, having d z=0, is proven     

Effects of heat and water vapor transport on eddy covariance measurement of CO2 fluxes

Flux densities of carbon dioxide were measured over an arid, vegetation-free surface by eddy covariance techniques and by a heat budget-profile method, in which CO₂ concentration gradients were specified in terms of mixing ratios. This method showed negligible fluxes of CO₂, consistent with the bareness of the experimental site, whereas the eddy covariance measurements indicated large downward fluxes of CO₂. These apparently conflicting observations are in quantitative agreement with the results of a recent theory which predicts that whenever there are vertical fluxes of sensible or latent heat, a mean vertical velocity is developed. This velocity causes a mean vertical convective mass flux (= _cw for CO₂, in standard notation). The eddy covariance technique neglects this mean convective flux and measures only the turbulent flux _c w. Thus, when the net flux of CO₂ is zero, the eddy covariance method indicates an apparent flux which is equal and opposite to the mean convective flux, i.e., _c w = – _c w. Corrections for the mean convective flux are particularly significant for CO₂ because _cw and _c w are often of similar magnitude. The correct measurement of the net CO₂ flux by eddy covariance techniques requires that the fluxes of sensible and latent heat be measured as well.     

A review of flux-profile relationships

Flux-profile relationships in the constant flux layer are reviewed. The preferred relationships are found to be those of Dyer and Hicks (1970), namely, _H = _W =(1–16(z/L))^–1/2, _M =(1–16(z/L))^–1/4 for the unstable region, and _H = _W = _M = 1+5(z/L) for the stable region.The carefully determined results of Businger et al. (1971) remain a difficulty which calls for considerable clarification.     

Modelling radiation quantities and photolysis frequencies in the troposphere

STAR (System for Transfer of Atmospheric Radiation) was developed to calculate accurately and efficiently the irradiance, the actinic flux, and the radiance in the troposphere. Additionally a very efficient calculation scheme to computer photolysis frequencies for 21 different gases was evolved. STAR includes representative data bases for atmospheric constituents, especially aerosol particles. With this model package a sensitivity study of the influence of different parameter on photolysis frequencies in particular of O₃ to Singlet D oxygen atoms, of NO₂, and of HCHO was performed. The results show the quantitative effects of the influence of the solar zenith angle, the ozone concentration and vertical profile, the aerosol particles, the surface albedo, the temperature, the pressure, the concentration of NO₂, and different types of clouds on the photolysis frequencies.Notation I _A(, ) actinic flux - I _H(, ) irradiance - L(, , , ) radiance - wavelength - azimuth angle - cosine of zenith angle - _s cosine of solar zenith angle - optical depth - _s scattering coefficient - _c extinction coefficient - _o single scattering albedo - p _mix mixed phase function - g _mix mixed asymmetry factor - J _gas photolysis frequency     

Three-dimensional modeling of synthetic cold fronts interacting with northern Alpine foehn

Summary The effect of the Alpine orography on prototype cold fronts approaching from the west is investigated by three-dimensional numerical model simulations. The numerical experiments cover a range of parameter constellations which govern the prefrontal environment of the front. Especially, the appearance and intensity of prefrontal northern Alpine foehn varies from case to case.The behaviour of a cold front north of the Alps depends much on the prefrontal condition it encounters. It is found that prefrontal foehn can either accelerate or retard the approaching front.An important feature is the pressure depression along the northern Alpine rim that results from the southerly foehn flow. In cases where this depression compensates the eastward directed pressure gradient associated with the largescale flow, the front tends to accelerate and the foehn breaks down as soon as the front passes. In contrast, the foehn prevents the front from a rapid eastward propagation if it is connected with a strong southerly wind component.No-foehn experiments are performed for comparison, where either the mountains are removed, or the static stability is set to neutral. Also shown are effects of different crossfrontal temperature contrasts.List of Symbols c _F propagation speed of a front - x, y horizontal grid spacing (cartesian system) - , horizontal grid spacing (geographic system) - t time step - z vertical grid spacing (cartesian system) - cross-frontal potential temperature difference - _i potential temperature step at an inversion - E turbulent kinetic energy - f Coriolis parameter - FGP frontogenesis parameter (see section 2.2) - g gravity acceleration (g=9.81 m s^–2) - vertical gradient of potential temperature - h terrain elevation (above MSL) - h _i height of an inversion (h _i =1000 m MSL) - H height of model lid (H=9000 m MSL) - K _M exchange coefficient of momentum - K _H exchange coefficient of heat and moisture - longitude - N Brunt-Väisäla-frequency - p pressure - Exner function (=T/) - latitude - q _v specific humidity - R _d gas constant of dry air (R _d =287.06 J kg^–1 K^–1) - density of dry air - t time - T temperature - potential temperature - TFP thermal front parameter (see section 2.2) - u, v, w cartesian wind components - u _g ,v _g geostrophic wind components - horizontal wind vector - x, y, z cartesian coordinates Abbreviations GND (above) ground level - MSL (above) mean sea level - UTC universal time coordinated With 20 Figures     

Reactions of alkoxy radicals under atmospheric conditions: The relative importance of decomposition versus reaction with O2

The reactions of alkoxy radicals determine to a large extent the products formed during the atmospheric degradations of emitted organic compounds. Experimental data concerning the decompositions, 1,5-H shift isomerizations and reactions with O₂ of several classes of alkoxy radicals are inconsistent with literature estimations of their absolute or relative rate constants. An alternative, although empirical, method for assessing the relative importance under atmospheric conditions of the reactions of alkoxy radicals with O₂ versus decomposition was derived. This estimation method utilizes the differences in the heats of reaction, (H)=(H_{decomposition}–H_{O 2 reaction}), between these two reactions pathways. For (H)[22–0.5(H_{O 2 reaction})], alkoxy radical decomposition dominates over the reaction with O₂ at room temperature and atmospheric pressure of air, while for (H)[25-0.5(H_{O 2 reaction})], the O₂ reaction dominates over decomposition (where the units of H are in kcal mol^–1). The utility and shortcomings of this approach are discussed. It is concluded that further studies concerning the reactions of alkoxy radicals are needed.     

Analysis and trends of atmospheric turbidity parameters over Cairo

Summary This work deals with the Linke turbidity factor, based on total spectrum observations of the direct solar beam and aerosol turbidity parametersa _a , , and based on observations in broad spectral bands. Diurnal and seasonal variations of these turbidity parameters were analyzed for the period 1975 to 1991.Annual variations of these parameters show low values in winter and high values in both spring and summer. The extinction coefficients decrease with increase of both wavelength and optical airmass. Trend analysis shows an increase in aerosol extinction coefficient below 0.63 m, and a slight decrease for longer wave-lengths.Linear regression relations are also constructed to estimate botha _a and whenT _L is available. The relations show thata _a can be estimated with errors below 20%. The relation with the parameter, may give better results when it is estimated by assigning a fixed value of .Nomenclature AV Monthly and total average of the measured parameter - a Atmospheric optical thicknes - a _a Aerosol optical thickness - a _r Mean value of optical thickness of. Rayleigh atmosphere over all wavelengths - a _o Ozone optical thickness - a _o Ozone absorption coefficient - a _w Water vapor optical thickness - COR Correlation coefficient of the linear relation in percentage - Ex₁, Ex₂, Ex₃ Aerosol extinction coefficients in the bands .2–.53, .53–.63, .63–.695, respectively - I _(o) Normal incident direct solar radiation, under clear sky condition - I _o Extraterrestrial insolation at normal incidence - m _r Relative (optical) air mass - NO Number of the observations used in either making the relation or the verification - RMSE Root mean square error of the linear relation - RMSE% Percentage value of the root mean square error relative to the average measured value AV - T _L Linke turbidity factor - T Dry bulb temperature in °C - u _o Ozone layer thickness, cm - Z Zenith angle - Ångström wavelength exponent - Ångström turbidity coefficient - Wavelength - Y The year number after 1975 With 5 Figures     

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.     

Flux-profile Relationships for Wind Speed and Temperature in the Stable Atmospheric Boundary Layer

Wind and temperature profiles in the stable boundary layer were analyzed in the context of MoninObukhov similarity. The measurements were made on a 60-m tower in Kansas during October 1999 (CASES-99). Fluxprofile relationships, obtained from these measurements in their integral forms, were established for wind speed and temperature. Use of the integral forms eliminates the uncertainty and accuracy issues resulting from gradient computations. The corresponding stability functions, which were nearly the same for momentum and virtual sensible heat, were found to exhibit different features under weakly stable conditions compared to those under strongly stable conditions. The gradient stability functions were found to be linear, namely _m = 1+ 5.8 and _h = 1 + 5.4 up to a limit of the MoninObukhov stability parameter = 0.8; this is consistent with earlier findings. However, for stronger stabilities beyond a transition range, both functions were observed gradually to approach a constant, with a value of approximately 7. To link these two distinct regimes, a general but pliable functional form with only two parameters is proposed for the stability functions, covering the entire stability range from neutral to very stable conditions.     

The atmospheric tide as a continuous spectrum: Lunar semidiurnal tide in surface pressure

Summary The standard equations for the theory of atmospheric tides are solved here by an integral representation on the continuous spectrum of free oscillations. The model profile of back-ground temperature is that of the U.S. Standard Atmosphere in the lower and middle atmosphere, and in the lower thermosphere, above which an isothermal top extends to arbitrarily great heights. The top is warm enough to bring both the Lamb and the Pekeris modes into the continuous spectrum.Computations are made for semidiurnal lunar tidal pressure at sea level at the equator, and the contributions are partitioned according to vertical as well as horizontal structure. Almost all the response is taken up by the Lamb and Pekeris modes of the slowest westward-propagating gravity wave. At sea level, the Lamb-mode response is direct and is relatively insensitive to details of the temperature profile. The Pekeris mode at sea level has an indirect response-in competition with the Lamb mode-and, as has been known since the time of its discovery, it is quite sensitive to the temperature profile, in particular to stratopause temperature. In the standard atmosphere the Lamb mode contributes about +0.078 mb to tidal surface pressure at the equator and the Pekeris mode about –0.048 mb.The aim of this investigation is to illustrate some consequences of representing the tide in terms of the structures of free oscillations. To simplify that task as much as possible, all modifying influences were omitted, such as background wind and ocean or earth tide. Perhaps the main defect of this paper's implementation of the free-oscillation spectrum is that, in contrast to the conventional expansion in the structures of forced oscillations, it does not include dissipation, either implicity or explicity, and thus does not satisfy causality. Dissipation could be added implicity by means of an impedance condition, for example, which would cause up-going energy flux to exceed downgoing flux at the base of the isothermal top layer. To achieve complete causality, however, the dissipation must be modeled explicity. Nevertheless, since the Lamb and Pekeris modes are strongly trapped in the lower and middle atmosphere, where dissipation is rather weak (except possibly in the surface boundary layer), more realistic modeling is not likely to change the broad features of the present results.Symbols a earth's mean radius; expansion coefficient in (5.3) - b recursion variable in (7.4); proximity to resonance in (9.2) - c sound speed in (2.2); specific heatc _p in (2.2) - f Coriolis parameter 2sin in (2.2) - g standard surface gravity - h equivalent depth - i ; discretization index in (7.3) - j index for horizontal structure - k index for horizontal structure; upward unit vectork in (2.2) - m wave number in longitude - n spherical-harmonic degree; number of grid layers in a model layer - p tidal pressure perturbation; background pressurep ₀ - q heating function (energy per mass per time) - r tidal state vector in (2.1) - s tidal entropy perturbation; background entropys ₀ - t time - u tidal horizontal velocityu - w tidal vertical component of velocity - x excitation vector defined in (2.3); vertical coordinate lnp _*/p ₀ [except in (3.8), where it is lnp /p ₀] - y vertical-structure function in (7.1) - z geopotential height - A constant defined in (6.2) - C spherical-harmonic expansion coefficient in (3.6) - D vertical cross section defined in (5.6) and (5.9) - E eigenstate vector - F vertical-structure function for eigenstate pressure in (3.2) [re-defined with WKB scaling in (7.2)] - G vertical-structure function for eigenstate vertical velocity in (3.2) [re-defined with WKB scaling in (7.2)] - H pressure-scale height - I mode intensity defined in (8.1) - K quadratic form defined in (4.4) - L quadratic form defined in (4.4); horizontal-structure magnification factor defined in (5.11) - M vertical-structure magnification factor defined in (4.6) - P eigenstate pressure in (3.2); tidal pressure in (6.2) - R tidal state vector in (5.1) - S eigenstate entropy in (3.2); spherical surface area, in differential dS - T background molecular-scale (NOAA, 1976) absolute temperatureT ₀ - U eigenstate horizontal velocityU in (3.2); coefficient in (7.3) - V horizontal-structure functionV for eigenstate horizontal velocity in (3.2); recursion variable in (7.3) - W eigenstate vertical velocity in (3.2) - X excitation vector in (5.1) - Y surface spherical harmonic in (3.7) - Z Hough function defined in (3.6) - +dH/dz - (1––)/2 - Kronecker delta; Dirac delta; correction operator in (7.6) - equilibrium tide elevation - (square-root of Hough-function eigenvalue) - ratio of specific gas constant to specific heat for air=2/7 - longitude - - - background density ₀ - eigenstate frequency in (3.1) - proxy for heating functionq =c _P/t - latitude - tide frequency - operator for the limitz - horizontal-structure function for eigenstate pressure in (3.2) - Hough function defined in (6.2) - earth's rotation speed - horizontal gradient operator - ()₀ background variable - ()_* surface value of background variable - () value at base of isothermal top layer - Õ state vector with zerow-component - , energy product defined in (2.4) - | | energy norm - ()^* complex conjugate With 10 Figures     

Properties of spatial temperature derivatives in the atmospheric surface layer

A pair of parallel cold wires separated in either the vertical or lateral direction was used to obtain the three components _x, _y, _z of the temperature derivative in the streamwise, lateral and vertical directions, respectively. The average absolute skewness values of _x and _z are nonzero and approximately equal, while the skewness of _y is approximately zero. These results appear to be consistent with the presence of a large, three-dimensional organised structure in the surface layer. There is an apparent low-frequency contamination in the spectral density of _y and _z due mainly to small errors in estimating the sensitivity of the cold wires. The temperature derivatives were high-pass filtered, the filter being set to remove possible contributions from the large structure and to minimise low-frequency sensitivity contamination. The filtered rms ratios \~_x/\~_y and \~_x/\~_z were in the range 0.7 to 0.9, a result in qualitative agreement with that obtained in the laboratory boundary layer by Sreenivasan et al. (1977). The skewness of filtered _x or _z is negligible, consistent with local isotropy of small-scale temperature fluctuations and in support of the high wavenumber spectral isotropy discussed in Antonia and Chambers (1978).     

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     

Über die mittlere lineare sukzessive Differenz und ihre Anwendung auf die Untersuchung meteorologischer Beobachtungsreihen

Zusammenfassung Eine endliche Reihe (Sequenz) wird als eine der möglichen Permutationen ihrer Glieder aufgefaßt. Es wird gezeigt, daß die Summe der absoluten Differenzen der aufeinanderfolgenden Glieder gleich ist , wo die natürliche Zahlen sind und nur von der Rangordnung der Glieder der Reihe (von der Permutation) abhängen; die _j sind von der Reihenfolge unabhängig und werden durch die Dispersion der Reihenglieder bestimmt. Die _j und die _j werden separat untersucht; der Erwartungswert der erwähnten Differenzsumme wird abgeleitet. Verschiedene bereits bekannte und auch erstmalig hier vorgeschlagene Maßzahlen werden geprüft. An Reihen jährlicher Regenmengen wird die Rolle der _j und der _j und das Verhalten der besprochenen Maßzahlen veranschaulicht.

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Summary A series ofn members can be considered as one of the possible permutations of its members. It is shown that the sum of the linear successive differences is equal to the expression , where the _j are positive integers, dependent only upon the rank-order (the permutation) of the members, while the _j are independent of the order of the succession and are determined by the dispersion of the members of the series. The factors _j and _j are separately investigated; the expected value of the sum of the linear successive differences is established. Various related statistical measures, already in usage and new ones suggested here, are discussed. Series of yearly rainfall amounts are used to show the effects of the _j and _j and to discuss the behaviour of the various measures.

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Résumé Une série, constituée parn valeurs, est regardée comme une des possibles permutations de ces valeurs. L'auteur montre que la somme des différences absolues, qui se présentent entre les valeurs consécutives de la série, est égale à l'expression . Les _j sont des nombres entiers positifs et ne dépendent que de l'ordre des membres de la série, tandis que les _j, indépendants de l'ordre, sont déterminés par la dispersion des membres. Les facteurs _j et _j sont étudiés séparément; l'espérance mathématique de la somme mentionnée est dérivée. Des paramètres statistiques déjà connus ou proposés ici pour la première fois, sont discutés. Le rôle des _j et des _j et le comportement des divers paramètres sont montrés à l'aide de séries de totaux annuels de pluies.

     

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.     

On the cumulative frequency distributions ofk-day period amounts of precipitation for any station in The Netherlands,while k≧30

Summary A simple method of representing cumulative frequency distributions ofk-day period amounts of precipitation (30k1800), deduced from observations at Hoofddorp during 87 years and from observations at Winterswijk during 73 years, by means of cumulative Poisson distributions, had been developed. Poisson's constant appeared to depend linearly onk only, while the Poisson unitq appeared to be only proportional to the annual variation.In this paper it is shown that the representation of observed cumulative frequency distributions with the aid of Poisson distributions is true for any station in The Netherlands in the interval 30k1800. A map with isopleths of -values fork=360 presents a simple picture, so that for any station an -value fork=360 can be estimated. For the process of representation the meank-day period amount of precipitation is also necessary. This value may be obtained from a map for each of the 12 months, each map covered with isohyetal lines, which give a distribution of the monthly precipitation.

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Zusammenfassung Es wurde eine Methode entwickelt, um in einfacher Weise Summenfunktionen vonk-tägigen Niederschlagsmengen (30k1800), welche aus Beobachtungen in Hoofddorp während 87 Jahren und in Winterswijk während 73 Jahren angestellt worden sind, durch kumulative Poissonsche Häufigkeitsverteilungen darzustellen. Dabei ergab sich, daß die Poissonsche Konstante nur linear vonk abhängig ist, während die Poissonsche Einheitq sich als proportional zum Jahresgang erwies.In der vorliegenden Untersuchung wird nun gezeigt, daß die Darstellung der beobachteten kumulativen Häufigkeitsverteilungen mit Hilfe von Poisson-Verteilungen für irgendeine Station in den Niederlanden im Bereich von 30k1800 gültig ist. Eine Karte mit Isoplethen der -Werte fürk=360 ergibt ein einfaches Bild, aus dem für jede beliebige Station ein -Wert fürk=360 abgelesen werden kann. Für eine solche Darstellung muß auch die Niederschlagsmenge derk-tägigen Perioden bekannt sein; diese Werte erhält man aus monatlichen Isohyeten-Karten, die die monatliche Niederschlagsverteilung wiedergeben.

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Résumé On avait développé une méthode pour représenter d'une façon simple les distributions des sommes cumulées dek jours (30k1800) des quantités de précipitations déduites des observations faites à Hoofddorp pendant 87 ans et à Winterswijk pendant 73 ans. On avait démontré que la constante de Poisson ne dépend dek que linéairement et que l'unité de Poissonq est proportionnelle à la variation annuelle.De la présente étude ressort que, dans l'intervalle de 30k1800, la représentation des distributions des fréquences cumulées observées au moyen des formules de Poisson est valable pour une station quelconque aux Pays-Bas. Une carte d'isoplèthes de la valeur pourk=360 donne une image suffisamment simple pour que la valeur d'une station quelconque aux Pays-Bas puisse être déterminée sans difficulté. Pour une telle représentation il faut connaître également les moyennes des quantités des périodes dek jours de la précipitation. Ces valeurs peuvent se déduire de cartes mensuelles des isohyètes moyennes.

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With 1 Figure

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Dedicated to Dr.Anders K. Ångström on the occasion of his 70th birthday.     

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.