The Askervein Hill Project: Mean wind variations at fixed heights above ground

This is one of a series of papers on the Askervein Hill Project. It presents results on the variations in mean wind speed at fixed heights (z) above the ground from linear arrays of anemometer posts and towers. Most of the data are for z = 10 m but some are for z = 3 m. Selected and directionally grouped data from the 55 Mean Flow runs are presented together with mean flow data from Askervein '83 Turbulence runs. Comparisons are made between the data and guideline estimates of fractional speed-up ratio at hilltop locations and between the data and MS3DJH/3 model predictions along the tower lines. There is good agreement in most cases.     

A reversing temperature-difference measurement system for Bowen ratio determination

The design and performance of a reversing temperature difference measurement system are reported. This system employs five-junction copper-constantan thermopiles for the measurement of T and T _w, while a linearized thermistor is used to measure T _w. Field performance has been checked against a precision lysimeter as well as against a second temperature difference measurement system in which diodes are used for temperature measurement. In both cases, the agreement between the systems is satisfactory for the measurement of hourly values of the Bowen ratio.     

A dynamical analysis of the drag conditions at the sea surface

When applied to a sea surface, shortcomings are noted for the ordinary classification of drag conditions at rigid underlying surfaces according to the Reynolds roughness number Re _s . It is shown that in the case of mobile underlying surfaces, it would be more natural to use the dynamical classification of drag conditions according to the order of magnitude of the ratio ( = /) of the momentum flux toward the waves ( _w) to the viscous momentum flux through the surface ( _w). The relevant estimates of for the main stages of development of the wind waves indicate that the observed values of the drag coefficient of the sea surface correspond to the case of underdeveloped roughness.     

Major wet interval in white mountains medieval warm period evidenced inδ 13C of bristlecone pine tree rings

A long ¹³C chronology was developed from bristlecone pine (Pinus longaeva) at the Methuselah Walk site in the White Mountains of California. The chronology represents cellulose from five-year ring groups pooled from multiple radii of multiple trees. The most dramatic isotopic event in the chronology appears from A.D. 1080–1129, when ¹³C values are depressed to levels ~ 2 below the mean for the period A.D. 925–1654. This isotopic excursion appears to represent a real event and is not an artifact of sampling circumstances; in fact, a similar excursion occurs in a previously-reported, independent ¹³C chronology from bristlecone pine. By carbon isotope fractionation models, the shift to low ¹³C values is consistent with abundant soil moisture, permitting leaf stomata to remain open, and allowing ready access of CO₂ from which carbon fixation may discriminate more effectively against¹³C in favor of¹²C. According to this model, the¹³C-depleted 50-yr isotopic excursion represents the wettest period in the White Mountains in the past 1000 yr, during which isotope-reconstructed July Palmer Drought Severity Indices averaged ~ +2.2.     

Temperature distribution and current system in a convectively mixed lake

During spring and autumn, many lakes in temperate latitudes experience intensive convective mixing in the vertical, which leads to almost isothermal conditions with depth. Thus the regime of turbulence appears to be similar with that characteristic of convective boundary layers in the atmosphere. In the present paper a simple analytical approach, based on boundary-layer theory, is applied to convective conditions in lakes. The aims of the paper are firstly to analyze in detail the temperature distribution during these periods, and secondly to investigate the current system, created by the horizontal temperature gradient and wind action. For these purposes, simple analytical solutions for the current velocities are derived under the assumption of depth-constant temperatures. The density-induced current velocities are shown to be small, in the order of a few mm/sec. The analytical model of wind-driven currents is compared with field data. The solution is in good qualitative agreement with observed current velocities under the condition that the wind field is steady for a relatively long time and that residual effects from former wind events are negligible.The effect of the current system on an approximately depth-constant temperature distribution is then checked by using the obtained current velocity fields in the heat transfer equation and deriving an analytical solution for the corrected temperature field. These temperature corrections are shown to be small, which indicates that it is reasonable to describe the temperature distribution with vertical isotherms.Notation T temperature - t time - x, y, z cartesian coordinates - molecular viscosity - _h , _v horizontal and vertical turbulent viscosity - K _h ,K _v horizontal and vertical turbulent conductivity - Q heat flux through the water surface - D depth - u, v, w average current velocity components inx, y andz directions - f Coriolis parameter - p pressure - density - g gravity acceleration - a constant in the freshwater state equation - h _s deviation from the average water surface elevation - L _*,H _* length and depth scale - U _*,W _* horizontal and vertical velocity scale - T temperature difference scale - bottom slope - u _* friction velocity at the water surface - von Karman constant - L Monin-Obukhov length scale - buoyancy parameter - l turbulence length scale - C ₁,C ₂,C ₃ dimensionless constants in the expressions for the vertical turbulent viscosity - , dimensionless vertical coordinate and dimensionless local depth - angle between surface stress direction andx-axis - T _bx ,T _by bottom stress components - c bottom drag coefficient     

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     

The use of σ T as a temperature scale in the atmospheric surface layer

The standard deviation of temperature _T is proposed as a temperature scale and as a velocity scale to describe the behaviour of turbulent flows in the Atmospheric Surface Layer (ASL), instead of _* andu _* of the Monin—Obukhov similarity theory, and ofT _f andU _f used for free convection stability conditions. On the basis of experimental evidence reported in the literature, it is shown that _T T _f andv _* U _f in the free convection region, and _{T *} andv _* U _* in nearneutral and stable conditions. This implies that the proposed scales can be applied for all stabilities. Furthermore, a new length scale is proposed and its relation with Obukhov length is given. Also, a simple semi-empirical expression is presented with which _T andv _* can be evaluated in a rather simple way. Some examples of practical applications are given, e.g., a stability classification for unstable conditions.     

On Modelling the One-Dimensional Atmospheric Boundary Layer

Several commonly used turbulence closure schemes forthe atmospheric boundarylayer (ABL) are applied to simulate neutral, nocturnal and diurnal cyclesituations in a one-dimensional ABL. Results obtained with the differentschemes, E-, E- and its modified versions, and twoversions ofthe q ² Level 2.5, are compared and discussed.     

Examination of ‘global atmospheric temperature monitoring with satellite microwave measurements’: 2. Analysis of satellite data

Using Microwave Sounding Unit (MSU) channel 2 (Ch. 2, 53.74 GHz) data, Spencer and Christy (1992a) determined that the earth exhibits no temperature trend in the period 1979–90, while other authors find a temperature increase of roughly 0.1 K. Based on a theoretical analysis Prabhakara et al. (1995) showed that the information about the global atmospheric temperature deduced from MSU Ch. 2 observations has a small contamination, T ₂, as a result of the attenuation due to hydrometeors in the atmosphere. A method is developed in this study, that utilizes coincident measurements made by MSU in Ch. 1 (50.3 GHz), to estimate this T ₂ over the global oceans. The magnitude of T ₂ is found to be about 1 K over significant parts of the tropical oceanic rain belts and about 0.25 K over minor portions of the mid-latitude oceanic storm tracks. Due to events such as El Niôo, there is variability from year to year in the rain areas and rain intensity leading to significant change in the patterns of T ₂. The patterns of T ₂ derived for March 82 and March 83 reveal such a change. When averaged over the global oceans, from 50° N to 50° S, T ₂ has a value of 0.25 and 0.29 K for March 1982 and 1983, respectively. Due to these reasons the interannual temperature change derived by Spencer and Christy from MSU Ch. 2 will contain a residual hydrometeor effect. Thus in evaluating decadal trend of the global mean temperature of the order of 0.1 K from MSU Ch. 2 data one has to take into account completely the contamination due to hydrometeors.     

Markov-chain simulation of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerian velocity variance

The Langevin equation is used to derive the Markov equation for the vertical velocity of a fluid particle moving in turbulent flow. It is shown that if the Eulerian velocity variance _wE is not constant with height, there is an associated vertical pressure gradient which appears as a force-like term in the Markov equation. The correct form of the Markov equation is: w(t + t) = aw(t) + b _wE + (1 – a)T _L ( _wE ²)/z, where w(t) is the vertical velocity at time t, a random number from a Gaussian distribution with zero mean and unit variance, T _L the Lagrangian integral time scale for vertical velocity, a = exp(–t/T _L), and b = (1 – a ²)^1/2. This equation can be used for inhomogeneous turbulence in which the mean wind speed, _wE and T _L vary with height. A two-dimensional numerical simulation shows that when this equation is used, an initially uniform distribution of tracer remains uniform.     

Carbon dioxide and the δ18O record of late-Quaternary climatic change: a global model

A dynamical model for the late-Quaternary global variations of ¹⁸O, mean ocean surface tempeature , ice mass I, deep ocean temperature , and atmospheric carbon dioxide concentration , is constructed. This model consists of two diagnostic equations (for ¹⁸O and ), and three prognostic equations (for I, , and ) of a form studied extensively in previous articles. The carbon dioxide equation includes forcing by a representation of the Milankovitch earth-orbital radiation effects, and contains a basic instability that drives a free oscillation of period near 100,000 years. The system is constrained to conserve mass and energy, contain physically plausible feedbacks including a system time constant no greater than 10.000 years, and be robust (i. e., structurally stable in the presence of expected noise levels and uncertainties in values of coefficients). Within the limits of these constraints, coefficients are chosen such that (i) the solution gives a good fit to the observed SPECMAP ¹⁸O variations, and (ii) the ice mass variations are qualitatively similar to the ¹⁸O variations. The predicted long term variations of sea surface temperature and atmospheric carbon dioxide are in reasonably good agreement with the limited observational evidence available for these quantities, while the predicted variations of deep ocean temperature remain to be verified when paleoclimatic estimates of this quantity become available. The relative contributions of ice mass changes and surface water temperature changes to the variations of ¹⁸O at any time are given by the model.     

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.

     

Stable Isotope Ratios: Hurricane Olivia

The oxygen and hydrogen isotopic compositions of rains from HurricaneOlivia (1994) in the eastern Pacific were measured. The rains werecollected on 24 and 25 September during airplane flights conducted at anelevation of 3 km. Hurricane Olivia peaked in intensity to a category-4storm between the two dates. Isotope ratios of rains from HurricaneOlivia were markedly lower ( ¹⁸O = –13.9to –28.8) than that of rain collected from a thunderstormat an elevation of 2.3 km outside the influence of Olivia (¹⁸O = –3.8). A distinct decrease in isotoperatios from the first day to the next ( ¹⁸O =–18.4 to –21.9) in Hurricane Olivia wasattributed to decreased updraft velocities and outflow aloft. Thisshifted the isotopic water mass balance so that fewer hydrometeors werelifted and more ice descended to flight level. A decrease in the averagedeuterium excess from the first day to the next (d = 15.5 to 7.1)was attributed to an increase in the relative humidity of the watervapor `source' area. We hypothesize that the `source' region for therain was in the boundary layer near the storm center and that becausethe hurricane was at peak intensity prior to the second day the relative humidity was higher.     

A study of the sensitivity of bare soil evaporation schemes to soil surface wetness,using the coupled soil moisture and surface temperature prediction model,BARESOIL

Summary The performance of evaporation schemes with and approach and their combination within resistance representation of evaporation from bare soil surface is discussed. For this purpose nine schemes, based on different functions of or , on the ratio of the volumetric soil moisture content and its saturated value are used.The quality of the chosen schemes has been evaluated using the results of time integration by the coupled soil moisture and surface temperature prediction model, BARESOIL, using in situ data. A sensitivity analysis was made using two sets of data derived from the volumetric soil moisture content of the top soil layer. One with values below the wilting point (0.17 m³m^–3) and the second with values above 0.20m³m^–3. Data sets were obtained at the experimental site Rimski anevi, Yugoslavia, from the bare surface of a chernozem soil.With 4 Figures     

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.     

A Wind Tunnel Model for Quantifying Fluxes in the Urban Boundary Layer

Transport of pollution and heatout of streets into the boundary layer above is not currently understood and so fluxes cannot be quantified. Scalar concentration within the street is determined by the flux out of it and so quantifying fluxes for turbulent flow over a rough urban surface is essential. We have developed a naphthalene sublimation technique to measure transfer from a two-dimensional street canyon in a wind tunnel for the case of flow perpendicular to the street. The street was coated with naphthalene, which sublimes at room temperature, so that the vapour represented the scalar source. The transfer velocity w_T relates the flux out of the canyon to the concentration within it and is shown to be linearly related to windspeed above the street. The dimensionless transfer coefficient w_T/U represents the ventilation efficiency of the canyon (here, w_T is a transfer velocity,U is the wind speed at the boundary-layer top). Observed values are between 1.5 and 2.7 ×10^-3 and, for the case where H/W0 (ratio of buildingheight to street width), values are in the same range as estimates of transfer from a flat plate, giving confidence that the technique yields accurate values for street canyon scalar transfer. w_T/U varies with aspect ratio (H/W), reaching a maximum in the wake interference regime (0.3 < H/W < 0.65). However, when upstream roughness is increased, the maximum in w_T/U reduces, suggesting that street ventilation is less sensitive to H/W when the flow is in equilibrium with the urban surface. The results suggest that using naphthalene sublimation with wind-tunnel models of urban surfaces can provide a direct measure of area-averaged scalar fluxes.     

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.     

AN E – ε – ℓ TURBULENCE CLOSURE SCHEME FOR PLANETARY BOUNDARY-LAYER MODELS: THE NEUTRALLY STRATIFIED CASE

The standard E – model generates aplanetary boundary layerthat appears to be much too deep. The cause of theproblem is traced to the equation for the dissipationrate () of turbulent kinetic energy (E), specifically theparameterization of dissipation production anddestruction. In the context of atmosphericboundary-layer modelling, we argue that a part of thedissipation production should be modelled as the inputto the spectral cascade from the energy-containingpart of the spectrum, with a characteristic length , while the equilibrium imbalancebetween local production and destruction ofdissipation is modelled as proportional toE2/E, as in the standard model. Wepropose an E – – turbulence closurescheme, in which both the mixing length, m, and are prescribed. The importance ofthe equation is diminished, though itstill determines the dissipation rate in the Eequation.     

The wind-induced shaping and migration of an isolated dune: A numerical experiment

Numerical experiments are carried out to simulate the development and migration of a barchan dune starting with a conical pile of sand. Such an experiment is done in three steps: (1) computation of the steady-state wind field over and around a barchan using the numerical meso-scale simulation model FITNAH, whereby the horizontal variation of the friction velocity is also calculated; (2) computation of the sand transport using the friction velocity in the transport formula by Lettau and Lettau (1978); (3) computation of the erosion and deposition rates as the divergence of the sand transport, where a special treatment is used for the slip-face of the barchan dune. Adding these rates to the height field leads to a different shape of the dune after a time step t _h . Then this procedure has to be repeated for the next time step t _h .The results are in good agreement with observations: the initial pile of sand develops wings (horns) and a slip-face between them. In addition, flow separation over the lee-side can be simulated. Finally, the tendency to form a barchan in equilibrium is considered.