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.     

Trajectory Curvature As A Selection Criterion For valid Lagrangian Stochastic Dispersion Models

Among well-mixed multi-dimensional Lagrangian stochastic (LS) dispersion models, we observe that those in poorest agreement with observations produce spiralling trajectories, with an associated reduction in dispersion. We therefore investigate statistics of increments d ' to the orientation '= arctan(W'/U') of the Lagrangian velocity-fluctuation vector – as a possible means to distinguish the better LS models within the well-mixed class. Zero-spin models, having d' = 0, are found to provide best agreement with observations. It is not clear however, whether imposition of the zero-spin property selects (in conjunction with the well-mixed condition) a unique model.     

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.     

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     

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.     

Nitrate in the atmospheric boundary layer of the tropical South Pacific: Implications regarding sources and transport

Weekly bulk aerosol samples collected at Funafuti, Tuvalu (8°30S, 179°12E), American Samoa (14°15S, 170°35W), and Rarotonga (21°15S, 159°45W), from 1983 through most of 1987 have been analyzed for nitrate and other constituents. The mean nitrate concentration is about 0.11 g m^–3 at each of these stations: 0.107±0.011 g m^–3 at Funafuti; 0.116±0.008 at American Samoa; and 0.117±0.010 at Rarotonga. Previous measurements of mineral aerosol and trace metal concentrations at American Samoa are among the lowest ever recorded for the near-surface troposphere and indicate that this region is minimally affected by transport of soil material and pollutants from the continents. Consequently, the nitrate concentration of 0.11 g m^–3 can be regarded as the natural level for the remote marine boundary layer of the tropical South Pacific Ocean. In contrast, over the tropical North Pacific which is significantly impacted by the transport of material from Asia and North America, the mean nitrate concentrations are about three times higher, 0.29 and 0.36 g m^–3 at Midway and Oahu, respectively. The major sources of the nitrate over the tropical South Pacific are still very uncertain. A very significant correlation between the nitrate concentrations at American Samoa and the concentrations of ²¹⁰Pb suggests that transport from continental sources might be important. This continental source could be lightning, which occurs most frequently over the tropical continents. A near-zero correlation with ⁷Be indicates that the stratosphere and upper troposphere are probably not the major sources. A significant biogenic source would be consistent with the higher mean nitrate concentrations, 0.16 to 0.17 g m^–3, found over the equatorial Pacific at Fanning Island (3°55N, 159°20W) and Nauru (0°32S, 166°57E). The lack of correlation between nitrate and nss sulfate at American Samoa does not necessarily preclude an important role for marine biogenic sources.     

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     

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.     

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.     

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     

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.     

A Comparative Analysis of Transpiration and Bare Soil Evaporation

Transpiration E^v and bare soil evaporation E^b processes are comparatively analysed assuming homogeneous and inhomogeneous areal distributions of volumetric soil moisture content . For a homogeneous areal distribution of we use a deterministic model, while for inhomogeneous distributions a statistical-deterministic diagnostic surface energy balance model is applied. The areal variations of are simulated by Monte-Carlo runs assuming normal distributions of .The numerical experiments are performed for loam. In the experiments we used different parameterizations for vegetation and bare soil surface resistances and strong atmospheric forcing. According to the results theE^v()-^Eb() differences are great, especially in dry conditions. In spite of this, the available energy flux curves of vegetation A^v() and bare soil A^b() surfaces differ much less than the E^v() and ^Eb() curves. The results suggest that E^v is much more non-linearly related to environmental conditions than ^Eb. Both E^v and ^Eb depend on the distribution of , the wetness regime and the parameterization used. With the parameterizations, ^Eb showed greater variations than E^v. These results are valid when there are no advective effects or mesoscale circulation patterns and the stratification is unstable.     

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.     

Modelling of turbulence over low hills and varying surface roughness

Neutral surface layer flow over low hills and varying surface roughness is considered with emphasis on closure schemes in relation to the prediction of turbulence quantities. The equations are linearised, Fourier transformed in the two horizontal directions and solved by means of a finite difference method in the vertical. Three closure schemes are. employed, namely mixing length, E- and e-- closure where E, and indicate that differential equations are used for turbulent kinetic energy, dissipation rate and shear stress. Model calculations are compared with experimental data for the step in roughness problem and for the Askervein hill. The mean flow results turn out to be relatively insensitive to the closure scheme. The shear stress and the dimensionless shear, however, are much better predicted with the E- equations than with mixing length closure. In the outer layer of the hill problem, advection of shear stress becomes important. An equation for is needed here.     

Analytical investigations of horizontal meso-scale momentum equations with Newtonian nudging

Summary This study presents an analytical investigation of the local behaviour of the solution to a mesoscale model with Newtonian nudging when observed winds are time varying. The analysis examines each Fourier component of the time series of observed winds. Unlike the case with a constant observed wind, the nudged wind vector does not asymptotically approach the observed wind. In response to sinusoidal oscillation of the observed wind, the nudged wind vector is always on a half circle connecting the vector ends of the observed and un-nudged modelled winds. When nudging parameter 0, the nudged wind vector approaches the un-nudged wind; when , the nudged wind vector approaches the observed wind. For commonly used values of nudging parameter , the modelled wind field always carries errors.A target nudging scheme is devised in this study in order to ensure the model result is identical to observed winds with sinusoidal oscillation. Investigation shows that such a target wind exists for a finite value of , and the magnitude of the target-nudging term is about the same as that of a normal nudging term if f, wheref is the Coriolis parameter and is the frequency of the wind oscillation.With 7 Figures     

Measurements of solar radiation and estimation of optical depth in the high Andes of Peru

Summary During an expedition to the high Andes of Southern Peru in June–July 1977, measurements of direct solar radiation in four spectral bands (0.270–0.530–0.630–0.695–2.900 ) were conducted at six sites in elevations ranging from sea level to 5645 m. These measurements were evaluated in Langley plots to determine total optical depths () and irradiances at the top of the atmosphere. In addition, water vapor optical depths (_wv) were calculated from the mean radiosounding over Lima during the expedition, and Rayleigh (_ray) and ozone (_oz) optical depths were obtained from published tabulations. Subtracting _ray, _oz, and _wv from yielded estimates of aerosol optical depth _aer. The components _ray and _oz decrease from the shorter towards the longer wavelength bands and from the lower towards the higher elevation sites; _aer also decreases towards the higher elevations. Particularly pronounced is the decrease of _aer and from the lowlands of the Pacific coast to the highlands of the interior, reflecting the effect of a persistent lower-tropospheric inversion and the contrast from the marine boundary layer to the clear atmosphere of the high Andes.With 4 Figures     

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.     

Periodicity of annual precipitation in different climate regions of Croatia

Summary The periodicity of a 100-year series of annual precipitation over Croatia has been studied by means of power spectrum analysis at 3 stations representing the different climatic regions of Croatia. The annual precipitation variance spectra in the continental lowland (Osijek) and at the north East Adriatic coast (Crikvenica) can be fitted by Markov white noise continuum, but in the transitional region between the Dinaric Alps and the Pannonian lowland (Zagreb-Gri) a non-white noise continuum is necessary. Quasi-periodic oscillations appear in two spectra ranges: short (2.2 and 4.7 years) and medium (25.0 and 33.3 years). These results are compared with those of other authors for other parts of the Europe.With 2 Figures     

Scavenging Efficiency of ‘Aerosol Carbon’ and Sulfate in Supercooled Clouds at Mt. Sonnblick (3106 m a.s.l., Austria)

Cloud water and interstitial aerosol samples collected at Mt. Sonnblick (SBO) were analyzed for sulfate and aerosol carbon to calculate in-cloud scavenging efficiencies. Scavenging efficiencies for sulfate (_SO) ranged from 0.52 to 0.99 with an average of 0.80. Aerosol carbon was scavenged less efficiently with an average value (_AC) of 0.45 and minimum and maximum values of 0.14 and 0.81, respectively. Both _SO and _AC showed a marked, but slightly different, dependence on the liquid water content (LWC) of the cloud. At low LWC, _SO increased with rising LWC until it reached a relatively constant value of 0.83 above an LWC of 0.3 g/m³. In the case of aerosol carbon, we obtained a more gradual increase of _AC up to an LWC of 0.5 g/m³. At higher LWCs, _{_} remained relatively constant at 0.60. As the differences between _SO and _A varied across the LWC range observed at SBO, we assume that part of the aerosol carbon was incorporated into the cloud droplets independently from sulfate. This hypothesis is supported by size classified aerosol measurements. The differences in the size distributions of sulfate and total carbon point to a partially external mixture. Thus, the different chemical nature and the differences in the size and mixing state of the aerosol particles are the most likely candidates for the differences in the scavenging behavior.     

PHYSICAL IMPACTS OF CLIMATIC CHANGE ON DELTAIC COASTAL SYSTEMS (II): DRIVING TERMS

The evaluation of the impact of climatic change on deltaic coastal systems requires establishing a reference situation. As deltaic coastal zones are highly dynamic areas, it is necessary to define the reference situation as a function of their present evolutive stage. This implies characterizing coastal processes as a complex system defined by the links between driving or forcing terms and the coastal response at different temporal and spatial scales (long/large, medium and episodic scales). Starting from classical previous works on deltaic systems and including all available field and conceptual knowledge to properly consider present conditions (largely regulated rivers, subsidence, etc.) a detailed methodology to analyse forcing or driving agents at the three mentioned scales is presented. This methodology which developed the general approach presented in a companion paper, will be followed by a future paper focusing on the analysis of the coastal response.