Spherical Atmosphere Research Articles

Comparison of radiative transfer models for limb‐viewing scattered sunlight measurements

This study compares the limb scattered radiances calculated by six radiative transfer models for a variety of viewing conditions. Atmospheres that include molecular scattering, aerosol scattering, and ozone absorption are considered. All models treat single scattering accurately in full spherical geometry. Two “approximate spherical” models (CDI and LIMBTRAN) rely on the plane‐parallel atmosphere approximation to calculate the diffuse radiance field; the remaining four “spherical” models (Siro, MCC++, GSLS, and CDIPI) treat multiple scattering in a spherical atmosphere. Only three of the models (Siro, MCC++, and GSLS) have vector treatment with polarization. A brief comparison of vector radiances with the limb scattered radiances measured by the SOLSE and LORE instruments demonstrates agreement usually within 15% and always within 30%. The inclusion of polarization appears to have little effect on the level of agreement among the models (which agree to within 2% for this sample case). A more general comparison among calculated scalar radiances follows, including four solar zenith angles (20°, 60°, 80°, and 90°), three relative azimuth angles (20°, 90°, and 160°), and two surface albedos (0 and 0.95). The single scattered radiances agree to within 1% for almost every case. Comparisons of the total radiance show larger differences, with 2–4% spread among the results of the spherical models. The approximate spherical models show a positive radiance difference relative to the other models that increases with tangent height, reaching as much as 8% at 60 km. The rule used to divide the model atmosphere into discrete layers is shown to affect the calculated radiance, causing a height‐dependent difference of up to 1% for 1 km layer thickness.

Radiative transfer model MCC++ with evaluation of weighting functions in spherical atmosphere for use in retrieval algorithms

A linearized radiative transfer model MCC++ designed for use in retrieval algorithms was developed. It calculates the weighting functions with respect to the absorption in all atmospheric layers and the layer air mass factors simultaneously with the intensities. Multiple scattering radiance is calculated by the Monte Carlo methods for spherical atmosphere taking into account the polarization of light, aerosol loading of atmosphere and the Lambertian surface albedo. A validation of the MCC++ model against other radiative transfer models is presented. It includes a comparison of weighting function calculations, a comparison for the scattering limb geometry, a comparison for twilight ground-based observations. As an example, additional errors of Brewer Umkehr retrieval algorithms, when they use the weighting functions calculated for approximation of single-scattering, are evaluated.

Explaining the Observed Polarization from Brown Dwarfs by Single Dust Scattering

Recent observation of linear optical polarization from brown dwarfs confirms the dust hypothesis in the atmospheres of brown dwarfs with effective temperature higher than 1400 K. The observed polarization could arise due to dust scattering in the rotation induced oblate photosphere or due to the scattering by non-spherical grains in the spherical atmosphere or by the anisotropic distribution of dust clouds. Assuming single scattering by spherical grains in a slightly oblate photosphere consistent with the projected rotational velocity, the observed optical linear polarization is modeled by taking grains of different sizes located at different pressure height and of different number density. Minimum possible oblateness of the object due to rotation is considered in order to constrain the grain size. It is shown that the observed polarization from the L-dwarfs 2MASSW J0036+1821 and DENIS-P J0255-4700 can well be explained by several sets of dust parameters and with the minimum possible oblateness. Models for the observed polarization constrain the maximum size of grains. It is emphasized that future observation of polarization at the blue region will further constrain the grain size.

A forth-and-back implicit λ iteration in the solution of radiative transfer in spherical media

Forth-and-back implicit ?-iteration has been developed to solve radiative transfer (RT) problems with plane-parallel geometry in which there is a coupling of all RT equations by the scattering term included in the source function (Atanackovic-Vukmanovic, Crivellari and Simonneau 1997). Owing to the implicit representation of the source function in the computation of the mean intensities within a forth-and-back sequential treatment of the two intensities propagating in opposite directions, implicit ?-iteration (ILI) appears to be a very efficient method in the solution of linear as well as non-linear transfer problems. In this paper ILI method is generalized and applied to radiative transfer problems with spherical symmetry. The results for the monochromatic radiative transfer in a spherical atmosphere are presented and compared to those of other authors obtained by the other methods.

Neutrino oscillation mechanism for pulsar kicks reexamined

Anisotropic neutrino emission during neutron star formation can be the origin of the observed proper motions of pulsars. We derive a general expression for the momentum asymmetry in terms of the neutrino energy flux gradient, and show that a nonvanishing effect is induced at the lowest order by a deformed neutrinosphere. In particular, this result is valid for a neutrino flux transported through a spherical atmosphere with constant luminosity.

Normal modes of deep atmospheres. II: f–F‐plane geometry

AbstractNumerical results have shown that, for a rotating spherical atmosphere with terrestrial parameters, making the shallow‐atmosphere approximation has only a very small impact on the frequency of linear, unforced normal modes, compared with those obtained from the full, unapproximated equations. In nearly all cases the normal‐mode frequencies are smaller in magnitude when the shallow‐atmosphere approximation is relaxed. Relaxing the approximation was also found to have only a small impact on the structures of normal modes, with the exception of long‐zonal‐wavelength internal acoustic modes. These results are particularly surprising in the tropics where the inclusion of the F = 2Ω cosϕ Coriolis terms (which are dropped in the shallow‐atmosphere approximation) might be expected to dominate the usual f=2Ωsinϕ Coriolis terms. The complexity of the full equations, however, prevents analysis of why this insensitivity to the extra terms arises.In this paper normal modes are examined under the f–F‐plane approximation and compared with those on the more usual f‐plane. The resulting equations are more amenable to analysis than the full equation set, and analytic expressions for the dispersion relation and for the normal‐mode structures are obtained for the particular case of an isothermal reference profile. This simplified geometry allows the effects of the F Coriolis terms to be examined while eliminating the geometrical effects of relaxing the shallow‐atmosphere approximation, giving some insight into the relative importance of the two types of effect as well as the physical mechanisms at work. The F Coriolis terms are found to be responsible for the structural changes to long‐zonal‐wavelength internal acoustic modes, and can also affect extremely shallow and extremely deep gravity modes. However, these terms are found to have only a small effect on normal‐mode frequencies, and geometrical effects, rather than these Coriolis terms, are responsible for the systematic reduction in the magnitude of normal‐mode frequencies in a deep spherical atmosphere.In planar geometry the inclusion of the F terms gives rise to a new kind of normal mode in addition to the usual Rossby, gravity, and acoustic modes. The new modes are inertial in character, have frequency very close to f, and have extremely strong vertical tilt. © Royal Meteorological Society, 2002. N. Wood's and A. Staniforth's contributions are Crown copyright.

RADIATIVE TRANSFER IN A SCATTERING SPHERICAL ATMOSPHERE

We have written a code called QDM_sca, which numerically solves the problem of radiative transfer in an anisotropically scattering, spherical atmosphere. First we formulate the problem as a second order differential equation of a quasi-diffusion type. We then apply a three-point finite differencing to the resulting differential equation and transform it to a tri-diagonal system of simultaneous linear equations. After boundary conditions are implemented in the tri-diagonal system, the QDM_sca radiative code fixes the field of specific intensity at every point in the atmosphere. As an application example, we used the code to calculate the brightness of atmospheric diffuse light(ADL) as a function of zenith distance, which plays a pivotal role in reducing the zodiacal light brightness from night sky observations. On the basis of this ADL calculation, frequent uses of effective extinction optical depth have been fully justified in correcting the atmospheric extinction for such extended sources as zodiacal light, integrated starlight and diffuse galactic light. The code will be available on request.

Torques exerted by a shallow fluid on a non-spherical, rotating planet

A general derivation is given for the torque exerted on a non-spherical planet by a shallowfluid, presenting in a unified form a number of results which are currently scattered throughthe literature, and deriving those results in a new way. This shows how the sum of gravitationaland pressure torques can be rewritten as a “centrifugal” torque plus a topographic torque dueto pressure acting on topography measured relative to the geoid. This clarifies the physicsbehind the use of spherical coordinate atmosphere and ocean models for calculating torqueson the earth. It also shows why the total torque due to the earth’s equatorial bulge can becalculated as if it were a pressure torque on an “effective bulge” of approximately 11 km, thegravitational torque partially offsetting the actual pressure torque on the earth’s 21 km bulge.

Parametrization of atmospheric muon angular flux underwater

The analytical expression for angular integral flux of atmospheric muons in matter with the explicit relation of its parameters with those of the sea level spectrum is obtained. The fitting formula for the sea level muon spectrum at different zenith angles for spherical atmosphere is proposed. The concrete calculations for pure water are presented. Fluctuations of muon energy losses are taken into account by means of parametrized correction factor calculated using survival probabilities resulted from Monte Carlo simulations. Parametrizations of all continuous energy losses are obtained with using the most recent expressions for muon interaction cross-sections. The corresponding parametrization errors and field of method application are comprehensively discussed. The proposed formulae could be useful primarily for experimentalists processing data of arrays located deep under water or under ice.

Atmospheric refraction effects in Earth remote sensing

Just as refraction moves the apparent positions of stars from their true ones, it slightly distorts the view of Earth from space, as well as affecting the angle at which sunlight or moonlight illuminates its surface. The astronomer's problem is to correct the apparent position of a star for refraction, relating the position as observed from Earth to the true position. By contrast, the space observer's problem is to obtain the true (refracted) surface zenith angle z′ of illumination or of viewing, when the zenith angle z 0 of the ray in space is known, and to correct for the apparent horizontal displacement of the surface point being viewed. This paper solves the problem of the refraction angle for a spherical atmosphere by a simple, analytic solution, depending only on the surface index of refraction μ 0 namely: sin( z 0)= μ 0 sin( z′). The problem of the apparent horizontal displacement of the point viewed is also solved analytically, but approximately, because the result depends weakly on an assumed vertical structure of the atmosphere. The results are useful primarily in cases where observation must be done at large zenith angle, or low Sun angle.

Spectral remote sensing of the atmosphere by the occultation of stars: Retrieval of the constituents and evaluation of the refraction effect

Abstract The spectral inversion method was used for retrieval of the contents of atmospheric gases and aerosols in an application to ozone monitoring by the stellar light occultation technique. This method is focused on the aerosols contribution, and based upon a priori information about the spectral cross-sections of the atmospheric gases. A smooth filtration approach enables one to separate the gases and aerosols contribution to the optical depth. For an estimation of the aerosol effective radius, the Angstrom parametrization of the aerosol cross-section at visible wavelengths was used. The regular refraction effect in the case of limb measurements was accurately evaluated and an additional error caused by sunlight scattering was estimated using the solution of the ray tracing equations for a spherical atmosphere.

Transfer of diffuse astronomical light and airglow in scattering Earth atmosphere

To understand an observed distribution of atmospheric diffuse light (ADL) over an entire meridian, we have solved rigorously, with the quasi-diffusion method, the problem of radiative transfer in an anisotropically scattering spherical atmosphere of the earth. In addition to the integrated starlight and the zodiacal light we placed a narrow layer of airglow emission on top of the scattering earth atmosphere. The calculated distribution of the ADL brightness over zenith distance shows good agreement with the observed one. The agreement can be utilized in deriving the zodiacal light brightness at small solar elongations from the night sky brightness observed at large zenith distances.

Damage from the impacts of small asteroids

Previous work is extended by using a model spherical atmosphere with a fitted density profile to find the damage done by an asteroid entering it at various zenith angles. At zenith angle 0° and a typical impact: velocity at the top of the atmosphere of V = 17.5 km s −1, the atmosphere absorbs more than half the kinetic energy of stony meteoroids with diameters, D M<230 m and iron meteoroids with D M<50 m. At zenith angle 45° the corresponding figures are 360 and 70 m while at 60° they are 500 and 100 m. For comets with V = 50 km s −1 the values are D M<1900 and 3000 m for 45 and 60°, respectively, using typical values of ablation, but they are much smaller if ablation is reduced. Only impactors with D M above these critical values are effective in producing ground impact damage: craters, earthquakes, and tsunami. Smaller impactors can still produce atmospheric blast waves. It is found that the area of destruction around the impact point in which the overpressure in the blast wave exceeds 4p.s.i. = 2.8 × 10 5 dyn cm −2, which is enough to knock over trees and destroy buildings. It is found that for chondritic asteroids entering at zenith angle 45° and an impact velocity at the top of the atmosphere of 17.5 km s −1 that it increases rapidly from zero for those less than 50 m in diameter (13.5 megatons) to about 2000 km 2 for those 76 m in diameter (31 megatons). If we assume that a stony asteroid 100 m in diameter hits land about every 1000 years, we find that a 50 m diameter one (causing some blast damage) hits land every 125 years while a Tunguska size impactor occurs about every 400 years. If iron asteroids are about 3.5 per cent of the frequency of stony ones of the same size, they constitute most of the impactors that produce areas of blast damage of less than 300 km 2. While the optical flux from a small asteroid such as Tunguska is enough to ignite pine forests, the blast from it goes beyond the radius within which the fire starts. The blast tends to blow out the fire, so it is likely that the impact will char the forest (as at Tunguska), but it will not produce a sustained fire.

C 4N 2 ice in Titan's north polar stratosphere

The 478 cm −1 ν 8 band of condensed dicyano-acetylene (C 4N 2) associated with Titan's north polar hood has been modeled using a radiative transfer program developed for tangent viewing in spherical atmospheres. Absence of the associated 471 cm −1 band of gaseous C 4N 2 leads to an upper limit of 4 × 10 −10 for the vapor mole fraction, and a corresponding upper limit of 90 km for the cloud top. The condensate/vapor abundance ratio ranges between 50 and 200 at the cloud top, depending on the cloud scale height. Corresponding cloud optical thicknesses are ∼0.1 and 0.006, respectively, while the majority of particles appear to have radii between 5 and 10 μm. Because of delayed response to the changing seasons, Titan's polar stratosphere appears to be cooling down as it becomes more illuminated by sunlight during the progression of winter into spring. As a result, photolytic decomposition of C 4N 2 vapor occurs above the advancing sunlight/shadow boundary at the same time that condensation increases below the boundary. This time-dependent cyclic process appears to give rise to a C 4N 2 condensate/vapor ratio approximately two orders of magnitude greater than that expected under steady-state conditions.

Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview

Remote sensing from satellite or airborne platforms of land or sea surfaces in the visible and near infrared is strongly affected by the presence of the atmosphere along the path from Sun to target (surface) to sensor. This paper presents 6S (Second Simulation of the Satellite Signal in the Solar Spectrum), a computer code which can accurately simulate the above problems. The 6S code is an improved version of 5S (Simulation of the Satellite Signal in the Solar Spectrum), developed by the Laboratoire d'Optique Atmospherique ten years ago. The new version now permits calculations of near-nadir (down-looking) aircraft observations, accounting for target elevation, non lambertian surface conditions, and new absorbing species (CH/sub 4/, N/sub 2/O, CO). The computational accuracy for Rayleigh and aerosol scattering effects has been improved by the use of state-of-the-art approximations and implementation of the successive order of scattering (SOS) algorithm. The step size (resolution) used for spectral integration has been improved to 2.5 nm. The goal of this paper is not to provide a complete description of the methods used as that information is detailed in the 6S manual, but rather to illustrate the impact of the improvements between 5S and 6S by examining some typical remote sensing situations. Nevertheless, the 6S code has still limitations. It cannot handle spherical atmosphere and as a result, it cannot be used for limb observations. In addition, the decoupling the authors are using for absorption and scattering effects does not allow to use the code in presence of strong absorption bands.

Evaluation of the pseudo‐spherical approximation for backscattered ultraviolet radiances and ozone retrieval

The pseudo‐spherical approximation for solving the radiative transfer equation has been used for many years in an attempt to account for the sphericity of the atmosphere. However, even with this “correction” there has been some uncertainty about the accuracy of the radiances calculated by using this method at large solar zenith angles. With a new model for numerically solving the radiative transfer equation in a spherical atmosphere the accuracy of the pseudo‐spherical approximation can now be evaluated. The comparisons between the pseudo‐spherical and spherical models presented in this paper for backscattered ultraviolet (BUV) radiances show virtually no difference for the nadir direction. The off‐nadir radiances, however, show large differences (±8%) for a solar zenith angle of 85° and depend on the solar zenith angle and azimuth angle as well as the view angle. These differences increase rapidly at larger solar zenith angles to nearly 20% at 88°. This disagreement is primarily caused by the incorrect attenuation of the solar radiation along the observers' line of sight in the pseudo‐spherical method. Differences are also exhibited in the multiple‐scatter component but are generally much smaller than the solar attenuation term. In general, the resultant error in total ozone estimation can be as large as 6% but is less than 1% for the Nimbus 7 total ozone mapping spectrometer.

The sphericity effects in model atmospheres of central stars of Planetary Nebulae

The model atmospheres of central stars of planetary nebulae are often calculated under the assumption of the plane-parallel geometry. This assumption seems to be reasonable for stars with relatively thin atmospheres like white dwarfs, where the thickness of the atmosphere is only few kilometers while the corresponding radius is about several thousands of kilometers. Nevertheless, calculations of a grid of pure hydrogen model atmospheres of hot white dwarfs demonstrated that this assumption may fail even for thin atmospheres (Kubát 1995). We found small differences between line profiles (about 1%) calculated under the assumption of plane-parallel and spherically symmetric atmospheres. Such differences are detectable by contemporary observational technique, and, consequently, may not be neglected. In addition, sphericity effects are important also in stars of other types (Kubát 1996). We decided to test the assumption of the plane parallel geometry also for sample model atmospheres of central stars of planetary nebulae. We assumed static atmospheres in radiative, hydrostatic, and statistical equilibrium (NLTE) consisting of hydrogen and helium. We calculated spherically symmetric and plane parallel model atmospheres of two central stars, namely LoTr4 and K1-27. Basic atmospheric parameters of these stars were adopted from Rauch et al. (1996, 1994), respectively. The atmospheric parameters for LoTr4(Teff = 120000K, log g = 5.5, M = 0.65M⊙, n(H)/n(He) = 0.5 yield a model with an extension (r(τR = 10–5)/r(τR = 2/3)) of 1.028. For K1-27, the atmospheric parameters (Teff = 100000K, log g = 6.5, M = 0.52M⊙, n(H)/n(He) = 0.2 produce only a small extension of 1.0035. The differences in temperature structure of our model atmospheres are more pronounced for a star with lower gravity and, consequently, larger extension. Continuum flux is lower for spherical atmospheres. This difference is larger for LoTr4, i.e. a star with more extended atmosphere, and almost negligible for K1-27. Paschen and Pickering He ii lines also show differences. These differences are quite large (several per cent) for α lines, and they decrease towards higher series members. Using plane-parallel model atmospheres instead of spherically symmetric ones introduces a systematic error into results. This error is present also in highly sophisticated NLTE line blanketed models. Due to the above mentioned differences one should avoid using lower series members (e.g. He ii 4686 å) for determination of atmospheric parameters (Teff, log g, abundances,…) from plane-parallel atmospheres. Details of our calculations will be presented in Astronomy and Astrophysics.

Modelling of the twilight sky brightness using a numerical solution of the radiation transfer equation

A model of solar light scattering in the terrestrial spherical atmosphere is developed on the basis of a numerical solution of the radiation transfer equation. It allows us to model the twilight sky brightness. This brightness for the range of solar zenith angles of 92–106 degrees and wavelength 530 tun has been compared with the experimental data and with other calculated results. Modelling has been carried out for standard altitude distributions of the molecular number density and ozone absorption coefficient and for the aerosol model of Toon and Pollack (1976). The different layers' contribution and the contribution of different orders of scattering from'some altitudes to the zenith intensity have been obtained. The role of multiple scattering in the twilight sky brightness and a hypothesis on the high turbidity of the upper atmosphere are discussed.

Hybrid Fluid/Kinetic Approach to Planetary Atmospheres: an Example of an Intermediate-Mass Body

view Abstract Citations (20) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Hybrid Fluid/Kinetic Approach to Planetary Atmospheres: an Example of an Intermediate-Mass Body Marconi, M. L. ; Dagum, L. ; Smyth, William H. Abstract The atmosphere of an intermediate mass planetary body is calculated in a self-consistent fashion by the use of a hybrid fluid/kinetic theory approach on massively parallel computers. Assuming a spherical atmosphere and a heating layer, this technique is used to obtain the atmosphere from the collisional hydrodynamic regime, through the quasi-collisional nonlinear kinetic regime, and into the self-collisionless linear kinetic regime. The results display significant nonequilibrium phenomena in both macroscopic variables such as temperature and microscopic variables such as the velocity distribution. Comparison with a standard hydrodynamic model demonstrates substantial differences. This method which is valid for all Knudsen numbers can be easily generalized to more complex problems and should be a powerful tool to study the structure, dynamics, and evolution of planetary atmospheres. Publication: The Astrophysical Journal Pub Date: September 1996 DOI: 10.1086/177789 Bibcode: 1996ApJ...469..393M Keywords: HYDRODYNAMICS; PLANETS AND SATELLITES: GENERAL full text sources ADS |

熱帯に局在した加熱による波動励起と中層大気への伝播

Response of a resting spherical atmosphere to transient localized heating in the tropics is studied theoretically with linearized primitive equations. The method of separation of variables is used to solve the problem, and time-integrations of the full nonlinear equations are also done to assess the linearity of the response. The linearity of the response is good for some realistic values of the heating. The dominant responses are equatorially-trapped vertically propagating waves whose vertical scale matches that of the heating and global normal (or free) modes. In the middle atmosphere, the equatorially trapped waves respond effectively if the angular frequency is the order of 10 × [damping rate]. If the frequency is greater than this order, the response is suppressed in a stochastic sense; while if the frequency is less than this order, it is suppressed by the damping. Spatial pattern of the response is obtained for a realization of idealized stochastic heating with a Gaussian form in space and time. For the heating, of which the time scale is a few days or longer, horizontal cross sections of the response show the Gill pattern at the beginning and then the response disperses zonally in low latitudes. For short-lived heating, on the other hand, the gravity wave response expands concentrically at the beginning and then the response spreads zonally in low latitudes. Energy and momentum spectra to various kinds of wave are calculated for the stochastic heating. As the time scale of the heating events decreases, gravity-wave responses increase relatively to Rossby-wave responses. As the zonal scale of the heating events decreases, on the other hand, Rossby-wave responses slightly increase relatively to the gravity-wave responses. Heating just on the equator is less effective to excite Rossby waves than that off the equator. Energy and momentum of these vertically propagating waves are of comparable orders to those of the real atmosphere if the heating has an appropriate spectrum with a realistic amount comparable to the total latent heat release in the tropics; and so does the energy of global normal modes. Wave energy propagation into the middle atmosphere has to be taken into account even for the calculation of the transient response in the troposphere if the dominant frequency is larger than the damping rate.