Disagreements between gradient-diffusion and Lagrangian stochastic dispersion models,even for sources near the ground

It is well known that if turbulent mass convection is modelled as diffusion, errors result unless trajectories from the source (ath) to the point of observation (z _p ) comprise many statistically-independent segments (Taylor, 1921). We show that this is not guaranteed merely by the Lagrangian timescale () at the source being small (e.g., source at ground), but that a better criterion istmax[(h), (z _p )], wheret is a typical travel time toz _p .     

Second-order closure study of the covariance between chemically reactive species in the surface layer

A second-order modelling technique is used to investigate the influence of turbulence on chemical reactions. The covariance and variance equations for the NO-O₃-NO₂ system are developed as a function of the ratio of the timescale of turbulence ( _t ) and the timescale of chemistry (_Ch): the first Damköhler number ( _t /_Ch). Special attention is given to the calculation of the covariance between NO and O₃ normalized by the product of their means, the so-called intensity of segregation (I _S ). This parameter quantifies the state of mixing of two chemical species.The intensity of segregation is calculated as a function of the flux of NO and the first Damköhler number. The model results presented illustrate the importance of taking the effect of turbulence on chemical reactions into account for higher values of the NO flux, for values of the ratio O₃/NO larger than 12.5 and for values of the ratio _t /_CH larger than 0.1. For such cases, the effective reaction rates are slower than if the chemical species are assumed to be uniformly mixed.     

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     

Wind stress over water waves: Field experiments on lake of Geneva

Summary A fixed platform (Fig.3), installed 100 m from the shoreline in 3 m water depth, was instrumented with velocity, temperature and wave-height sensors. 132 data (10 minutes averages) were analysed to calculate the wind stress; from these, 99 data were used to investigate the vertical distribution of the wind stress; all data are presented with Table 1.It was postulated that the total stress, _t being constant with height, is made up additively of two components, the wave-supporting stress, _w , and the turbulent stress, _c ; see Eq. 1. The vertical distribution of these two components is shown schematically in Fig. 1.The total stress, _t , evaluated outside the zone of wave influence, is given in the classical way with Fig. 4. The wave-supporting stress, _w (z), was evaluated from the data according to a relation proposed by Kitaigorodskii et al. (1984); it is given with Fig. 5. A height-dependency is clearly evident. The turbulent stress _c (z), was evaluated with data of the velocity gradient; it is given with Fig. 6. A height-dependency is not evident.The field data from the lake of Geneva give evidence that the additive relation of Eq. 1 seems to be justified.With 6 Figures     

Direct Measurement Of Shear Stress During Snow Saltation

Wind-tunnel experiments were carried out to measure the shear stressduring snow saltation. Shear stress acting on the snow surface, measured directly with a newly developed drag meter system, revealedthat the shear stress increased with the development ofsaltation. This result supports Owen's hypothesis that the saltationlayer acts as an increased roughness to the flow above the saltationlayer, leading to an increase in surface shear stress. To investigate the contribution of the grain borne shear stress_g and the fluid shear stress _f to the increment of the total shear stress _total, _g was calculated from the loss of horizontal momentum of saltating snowparticles. Since _g is the largest contribution to theincrement of _total, the collision of thesaltating particles is dominant for the shear stressmodification. The results qualitatively support the numericalsimulation reported by McEwan and Willetts.     

On the temperature coefficient of PCO 2 in seawater

The commonly reported temperature coefficient of P. the equilibrium partial pressure of CO₂, is (P/T) _A,C ,which is about 15 ppm/°C, or 5% of the atmospheric partial pressure of CO₂. This coefficient, however, applies only to deep water, not to surface water which can exchange CO₂ with the atmosphere. The coefficient (P/T) _A,C ,, where designates constancy of the sum of atmospheric and surface-ocean CO₂, is the appropriate value for air-sea exchange. Numerical values are mass-dependent because the depth of the exchanging ocean layer must be specified. For a 100-m surface layer, the value is ca. 1.5 ppm/°C, or 0.5% of ambient CO₂. Editor's Note:In view of the interdisciplinary importance of the carbon dioxide-climate problem, this note on seawater chemistry should be of interest to specialists beyond the discipline of ocean chemistry.     

Modelling the equilibrium and transient responses of global temperature to past and future trace gas concentrations

Recent works with energy balance climate models and oceanic general circulation models have assessed the potential role of the world ocean for climatic changes on a decadal to secular time scale. This scientific challenge is illustrated by estimating the response of the global temperature to changes in trace gas concentration from the pre-industrial epoch to the middle of the next century. A simple energetic formulation is given to estimate the effect on global equilibrium temperature of a fixed instantaneous radiative forcing and of a time-dependent radiative forcing. An atmospheric energy balance model couple to a box-advection-diffusion ocean model is then used to estimate the past and future global climalic transient response to trace-gas concentration changes. The time-dependent radiative perturbation is estimated from a revised approximate radiative parameterization, and the recent reference set of trace gas scenarios proposed by Wuebbles et al. (1984) are adopted as standard scenarios. Similar computations for the past and future have recently been undertaken by Wigley (1985), but using a purely diffusive ocean and slightly different trace gas scenarios. The skill of the socalled standard experiment is finally assessed by examining the model sensitivity of different parameters such as the equilibrium surface air temperature change for a doubled CO₂ concentration [T _ae (2×CO₂)], the heat exchange with the deeper ocean and the trace gas scenarios. For T _ae (2×CO₂) between 1 K and 5 K, the following main results are obtained: (i) for a pre-industrial CO₂, concentration of 270 ppmv, the surface air warming between 1850 and 1980 ranges between 0.4 and 1.4 K (if a pre-industrial CO₂ concentration of 290 ppmv is chosen, the range is between 0.3 and 1 K); (ii) by comparison with the instantaneous equilibrium computations, the deeper ocean inertia induces a delay which amounts to between 6 years [for lower T _ae (2×CO₂)] and 23 years [for higher Tae(2×CO₂)] in 1980; (iii) for the standard future CO₂ and other trace gas scenarios of Wuebbles et al., the surface air warming between 1980 and 2050 is calculated to range between 0.9 and 3.4 K, with a delay amounting to between 7 years and 32 years in 2050 when compared to equilibrium computations.     

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.     

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     

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.     

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.     

On the determination of the height of the Ekman boundary layer

The heighth of the Ekman turbulent boundary layer determined by the momentum flux profile is estimated with the aid of considerations of similarity and an analysis of the dynamic equations. Asymptotic formulae have been obtained showing that, with increasing instability,h increases as ¦¦^1/2 (where is the non-dimensional stratification parameter); with increasing stability, on the other hand,h decreases as ^–1/2. For comparison, a simple estimate of the boundary-layer heighth _u determined by the velocity profile is given. As is shown, in unstable stratification,h _u behaves asymptotically as ¦¦^–1, i.e., in a manner entirely different from that ofh .     

A comparison of airborne eddy correlation and bulk aerodynamic methods for ocean-air turbulent fluxes during cold-air outbreaks

Four bulk schemes (LKB, FG, D and DB), with the flux-profile relationships of Liuet al. (1979), Francey and Garratt (1981), Dyer (1974), and Dyer and Bradley (1982), are derived from the viscous interfacial-sublayer model of Liuet al. These schemes, with stability-dependent transfer coefficients, are then tested against the eddy-correlation fluxes measured at the 50 m flight level above the western Atlantic Ocean during cold-air outbreaks. The bulk fluxes of momentum (), sensible heat (H), and latent heat (E) are found to increase with various von Kármán constants (k _M for k _H forH, andk _E forE). Except that the LKB scheme overestimates by 28% (46Wm^–2), on the average, the fluxes estimated by the four bulk schemes appear to be in fairly good agreement with those of the eddy correlation method (magnitudes of biases within 10% for , 17% forH, and 13% forE). The results suggest that the overall fluxes and surface-layer scaling parameters are best estimated by FG and thatk _H <k _E . On the average, the FG scheme underestimates by 10% (0.032N m^–2) andE by 4% (12Wm^–2), and overestimatesH by 0.3% (0.5W m^–2). The equivalent neutral transfer coefficients at 10 m height of the FG scheme compare well with some schemes of those tested by Blanc (1985).The relative importance of various von Kármán constants, dimensionless gradients and roughness lengths to the oceanic transfer coefficients is assessed. The dependence of transfer coefficients on wind speeds and roughness lengths is discussed. The transfer coefficients for andE agree excellently between LKB and FG. However, the ratio of the coefficient forH of LKB to that of FG, increasing with decreasing stability, is very sensitive to stability at low winds, but approaches the neutral value of 1.25 at high winds.     

Mechanisms of shrubland expansion: land use,climate or CO2?

Encroachment of trees and shrubs into grasslands and the thicketization of savannas has occurred worldwide over the past century. These changes in vegetation structure are potentially relevant to climatic change as they may be indicative of historical shifts in climate and as they may influence biophysical aspects of land surface-atmosphere interactions and alter carbon and nitrogen cycles. Traditional explanations offered to account for the historic displacement of grasses by woody plants in many arid and semi-arid ecosystems have centered around changes in climatic, livestock grazing and fire regimes. More recently, it has been suggested that the increase in atmospheric CO₂ since the industrial revolution has been the driving force. In this paper we evaluate the CO₂ enrichment hypotheses and argue that historic, positive correlations between woody plant expansion and atmospheric CO₂ are not cause and effect.Please direct all correspondence to the senior author.     

A non-linear climate oscillator controlled by biogeochemical cycling in the ocean: an alternative model of Quaternary ice age cycles

A new, biogeochemical model of ice age cycles is developed and applied which explains major features of climate variations in the late Quaternary —rapid ice age terminations, large glacial-interglacial amplitudes and 100-kyr cycles — in a way consistent with the paleorecord. Existing models which invoke non-linear, ice-sheet-earth-crust dynamics to explain ice age cycles are not consistent with simultaneous terminations in both hemispheres and other phase relationships implied by the paleorecord. The present model relates climate change to oscillations of oceanic primary (new) production controlled by the availability of inorganic nitrogen. Large oscillations follow shelf erosion events triggered by small sea-level drops. These drops are due to glacial buildup associated with a minimum in Northern Hemisphere insolation. Rapid global warming at terminations is initiated by open ocean denitrification events leading to new production crashes and rapid modification of atmospheric trace gas concentrations (CO₂, DMS, N₂O). Other feedbacks of the land-ice-atmosphere-ocean system control the rest of the climate cycle. 100-kyr cycles derive from orbital pacemaking of the strong, low-frequency model response. Results suggest that the climate regime transition near 800 kyr B.P. may be related to changes in the continental shelf slope, that existing chronologies based on orbital tuning may need to be revised and that temporary increases in atmospheric N₂O concentrations at terminations, due to the denitrification events, may have caused significant greenhouse warming. A spike of elevated N₂O concentration at terminations may be recorded in polar ice.     

A Simple Mixing Length Formulation for the Eddy-Diffusivity Parameterization of Dry Convection

In this paper a simple mixing length formulation for the eddy-diffusivityparameterization of dry convection is suggested. The new formulation relates the mixinglength to the square root of the turbulent kinetic energy (e) and a time scale ( ):l = e. To close the parameterization the time scale is calculated as a functionof the boundary-layer height (h) and the convective velocity scale (w_*), h/w_*. Thesimpler approach of a constant time scale is also studied. The simulation of a case of dry atmosphericconvection with a one-dimensional boundary-layer model shows that the model with the new formulationreproduces quite well the main properties of the convective boundary layer. In particular,the entrainment is realistically represented by the new mixing length, which has the advantage of naturallydecreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapserate, in the context of a simplified situation, show the robustness of the new formulation.     

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     

Carbonyl sulfide emissions from biomass burning in the tropics

Carbonyl sulfide emissions from biomass burning have been studied during field experiments conducted both in an African savanna area (Ivory Coast) and rice fields, central highland pine forest and savanna areas in Viet-Nam. During these experiments CO₂, CO and C₂H₂ or CH₄ have also been also monitored. COS values range from 0.6 ppbv outside the fires to 73 ppbv in the plumes. Significant correlations have been observed between concentrations of COS and CO (R ²=0.92,n=25) and COS and C₂H₂ (R ²=0.79,n=26) indicating a COS production during the smoldering combustion. COS/CO₂ emission factors (COS/CO₂) during field experiments ranged from 1.2 to 61×10^–6 (11.4×10^–6 mean value). COS emission by biomass burning was estimated to be up to 0.05 Tg S/yr in tropics and up to 0.07 Tg S/yr on a global basis, contributing thus about 10% to the global COS flux. Based on the S/C ratio measured in the dry plant biomass and the COS/CO₂ emission factor, COS can account for only about 7% of the sulfur emitted in the atmosphere by biomass burning.     

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.     

On geoengineering and the CO2 problem

The problem of CO₂ control in the atmosphere is tackled by proposing a kind of fuel cycle for fossil fuels where CO₂ is partially or totally collected at certain transformation points and properly disposed of.CO₂ is disposed of by injection into suitable sinking thermohaline currents that carry and spread it into the deep ocean that has a very large equilibrium capacity.The Mediterranean undercurrent entering the Atlantic at Gibraltar has been identified as one such current; it would have sufficient capacity to deal with all CO₂ produced in Europe even in the year 2100.