Determination of the single-scattering albedo from polarization measurements of a rayleigh atmosphere

Exact analysis of a Rayleigh-scattering half space is used to solve the inverse problem whereby the single-scattering albedo can be determined from measurements of the polarized radiation emerging from the atmosphere.     

Effects of stepwise variation of single-scattering albedo on reflectivity and transmissivity of a linear-anisotropically scattering slab

Unsteady free-convection flows near an infinite vertical plate in a rotating medium in the presence of a constant transverse magnetic field are investigated under an arbitrary time-dependent heating of the plate. By using the Laplace transform technique, the Green's function of the problem is determined and exact solutions are obtained for special cases of the time-dependent heating effect. The thermal influence on skin friction at the plate and the displacement thickness of the boundary layer are determined, and the structure of the thermal wave trains is discussed.Formerly Kulshrestha.     

Deducing the age of the dense Venus atmosphere

We show how crater size-density counts may be used to help constrain the history of the Venus atmosphere, based on the predictions of simple but reasonable models for crater production, surface erosion, and the effects of atmospheric drag and breakup on incident meteors in the Venus atmosphere. If the atmosphere is old, we may also be able to determine the importance of breakup as a mechanism for destroying incident meteors in a dense fluid. In particular, if the atmosphere is young, the old (uneroded) surfaces will have crater densities upward of 10^?4 km^?2 and a ratio of small (4 km) craters to large (128 km) craters near 10³. If the atmosphere is old and the breakup mechanism is dominant, absolute crater densities on Venus surfaces will be diminished by several orders of magnitude relative to the young atmosphere case. If atmospheric drag is dominant and the atmosphere is old, the absolute crater density will be lowered by perhaps an order of magnitude relative to the young atmosphere case, and the ratio of small to large craters will be reduced to a value near 10^1.5 according to the models. The comparison of crater populations on young, as well as old, surfaces on Venus can help in distinguishing the young and old atmosphere scenarios, especially since the situation may be complicated by currently undetermined erosional and tectonic processes. Once a large fraction of Venus surface has been imaged at kilometer resolution, as the VOIR project promises to do, it could be possible to make an early determination of the age of the Venus atmosphere.     

Mean thermal and albedo behavior of the Mars surface and atmosphere over a Martian year

A Mars average data set (MADS) has been constructed from thermal and albedo measurements of the Viking Infrared Thermal Mapper; by merging information from all longitudes; and, ensuring reasonably complete longitudinal sampling, a representation of mean Mars behavior is obtained. Brightness temperatures at 7, 9, 11, 15, and 20 μm and albedo information in the band 0.3–3.0 μm have been binned using 2° latitude strips, 24 times of day, 3 emission angle intervals, and 23 nonoverlapping L_s periods covering 1.43 Mars years starting at L_s = 84°. The MADS is ideally suited to parametric study of latitudinal, diurnal, angular, and seasonal dependences. Data are presented for surface thermal and albedo behavior in clear and dusty atmospheric conditions; the thermal response of the atmospheric temperature to a major dust storm is found to be consistent with Mariner 9 data from the 1971 storm. Examples of use of the MADS, which is available through the Mars Consortium, indicate how averaged data reveal specific surface and atmospheric phenomena.     

Inorganic chemistry of O2 in a dense primitive atmosphere

A simple steady-state photochemical model is developed in order to determine typical molecular oxygen concentrations for a comprehensive range of primitive abiotic atmospheres. Carbon dioxide is assumed to be the dominant constituent in these atmospheres since CO2 photodissociation may potentially result in the enhancement of the O2 partial pressure. The respective effects of the H2O content, temperature, eddy diffusion coefficient and UV flux on the results are investigated. It is shown that for any pressure at the surface, the partial pressure of molecular oxygen does not exceed 10 mbar. The peculiar case of a runaway greenhouse which has possibly taken place on Venus is qualitatively envisaged. Although O2 is basically absent in the present Venus atmosphere, a transient presence in a primitive stage cannot be ruled out. Possible mechanisms for O2 removal in such an atmosphere are reviewed. At the present stage, we think that the detection of large O2 amounts would be at least a good clue for the presence of life on an extrasolar planet.     

The effect of a dense atmosphere on the tidally induced potential of Titan

The effect of the dense atmosphere of Titan on the tidal variations of the external gravitational potential of degree two is quantified. The atmospheric tides perturb the external gravitational potential of Titan in two ways. First, the atmosphere itself contributes directly to the external gravitational potential with a period of 15.945 days. Second, the variable loading of the atmosphere induces mass redistribution within Titan, which also changes the external gravitational potential. It is shown that the relative atmospheric contributions to the tides are most likely less than 2% and vanish almost completely for the most plausible models with a subsurface ocean. This suggest that atmospheric tidal perturbations will contribute only negligibly to Cassini measurements of Titan's gravitational field so that the tidal Love numbers derived from these observations can be directly interpreted in terms of the satellite's interior.     

The continuous absorption coefficient of a stellar atmosphere

It is pointed out that, when calculating the continuous absorption coefficient in a stellar atmosphere, it is advantageous to use the coefficient per particle of the most abundant element instead of the usual coefficient per gram of matter. The sources of continuous opacity considered are 1) absorption by H^-, HI, H₂^-, H ₂⁺, HeI, HeII, CI, CII, CIII, NI, NII, OI, OII, NaI, MgI, MgII, AlI, AlII, SiI, SiII, ClI, KI, CaII; and 2) Rayleigh scattering by HI, HeI, CI, NI, OI, H₂, and 3) Thomson scattering of free electrons. The calculations are illustrated by the results for a solar-type photosphere.     

Optical depth of the Martian atmosphere and surface albedo from high-resolution orbiter images

In this paper we describe and evaluate the so-called shadow method. This method can be used to estimate the optical depth of the Martian atmosphere from the differences in brightness between shadowed and sunlit regions observed from an orbiter. We present elaborate and simplified versions of the method and analyze the capabilities and the sources of errors. It proves essential to choose shadowed and sunlit comparison regions with similar surface properties. Accurate knowledge of the observing geometry, including the slopes of the observed region, is important as well, since the procedure should be corrected for the non-horizontal surface. Moreover, the elaborate version of the shadow method can be sensitive to (i) the optical model of aerosols and (ii) the assumed bi-directional reflectance function of the surface. To obtain reliable estimates, the analyzed images must have a high spatial resolution, which the HiRISE camera onboard the MRO provides. We tested the shadow method on two HiRISE images of Victoria crater (TRA_0873_1780 and PSP_001414_1780) that were taken while this crater was the exploration site of the Opportunity rover. While the rover measured optical depth τ approximately in the ranges from 0.43 to 0.53 and from 0.53 to 0.59 by imaging the sun, our shadow procedure yielded τ about 0.50 and 0.575, respectively (from the HiRISE's red images). Thus, the agreement is quite good. The obtained estimates of the surface albedo are about 0.20 and 0.17, respectively.     

Emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo,II

For the evaluation of the effect of the non-uniform surface albedo on the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo is computed. This paper is the improved version of the previous paper (Takashima and Masuda, 1991). The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are (1) 0.25, 0.23, and 0.02, and (2) 0.75, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is calculated approximately by the contributions due to the multiple scattering in the atmosphere, and due to the diffusely or directly transmitted radiation through the atmosphere which is reflected by the surfaces once (4 interactive radiative modes between atmosphere and surface). Furthermore, to perform the hemispherical integration processing the radiative interaction, the transmission function based on the single scattering in the atmosphere is introduced and then the transmission function is averaged over the hemisphere with weighting function. The numerical simulation exhibits the extraordinary effect near the two half surface boundary of different albedoes. The effect decreases exponentially with the distance from the boundary. The effect depends on the atmospheric aerosol type, optical thickness, and surface albedo. The present version enables us to quantitatively discuss the radiative transfer trend near the boundary of two half surfaces. The upward radiance would simply be evaluated using the present scattering approximation method if the surface albedo is less than 0.3. The present method is thought of as a first step extending the one-dimensional radiative transfer model to two-dimensional using the doubling-adding method.     

Extreme ultra-violet absorption cross-sections in the Earth's upper atmosphere

Relative absorption cross-sections between 180 Å and 304 Å, and between 584 Å and 304 Å are obtained for atomic oxygen in the upper atmosphere, by observing the attentuation of solar radiation using a satellite instrument.     

A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite

The purpose of this paper is to present a model for the radiation pressure acceleration of a spherical satellite, due to the radiation reflected by a planet with a uniform albedo. A particular choice of variables allows one to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimensional integrals. Exact analytical expressions are found for the integrals corresponding to the case where the spacecraft does not "see" the terminator. The other integrals can be computed either numerically, or analytically in an approximate form. The results are compared with those of Lochry (1966). The model is applied to Magellan, a spacecraft orbiting Venus.     

Estimates of quasipolar absorption by methane in the atmosphere of Titan

The basis for “quasipolar” absorption (QPA) by CH₄ is the existence of a small electric dipole moment in its ground state. The integrated intensity α_QPA at a temperature of 90K is calculated to be between 4.8 × 10^?5 and 1.9 × 10^?2 cm^?2 atm^?1. With an assumed mean pressure of 0.1 atm and a relative abundance of $\text{[}\text{CH}{}_4\text{]}\text{[}\text{H}{}_2\text{]}\text{= 1}$, it is estimated that the ratio of quasipolar to pressure-induced absorption (PIA) is 0.05 ? α_QPA/α_PIA ? 18 for the spectral range from 0 to 300 cm^?1. This result suggests that quasipolar absorption may contribute to a weak, CH₄-induced greenhouse in the atmosphere of Titan.     

On the level of h2 quadrupole absorption in the Jovian atmosphere

The hydrogen quadrupole absorption lines are uniquely characterized by the property of being collision narrowed. For the 3-0 and 4-0 bands the lines continue to narrow to below the pressure levels in the Jovian atmosphere where they appear to be formed. Since the collision narrowing is the reverse of the case for ordinary molecular absorptions the use of the Curtis-Godson approximation must be reconsidered. We have done this using the line shape for this process derived by Galatry and find that the Curtis-Godson approximation represents the absorption very well through the inhomogeneous Jovian atmosphere. The hydrogen quadrupole absorptions, 3-0 S (l) and 4-0 S (l), have been analysed by a procedure which has been shown to give self-consistent results for the methane 3v3 manifolds. The 3-0 S(1) line is strongly saturated and even the weak 4-0 S(l) line (equiv width ～ 8mÅ) exhibits a 10% saturation. We derive a mixing ratio (by volume) of approx 7 x 10^?4 for methane to hydrogen in agreement with earlier results.     

On the nature of the blue and ultraviolet absorption in the Jovian atmosphere

Spatially resolved reflectivities from 3000 to 6600 Å of three positions from the center to the limb of the Jovian Equator, North Equatorial Belt, and North Tropical Zone are analyzed to determine the vertical distribution and wavelength dependence of various sources of blue and uv absorption. Six different models of the distribution of absorbing dust particles are examined. In each model, the variation of dust optical depth and cloud single-scattering albedo are determined. Only those models having dust above the upper NH₃ cloud layer will fit the data. The high altitude dust distribution is approximately uniform over the three regions examined. The contrast in reflectivity of the belts and zones may be modeled by a different cloud single-scattering albedo in the different regions.     

Calculation of single-scattering albedos: Comparison of Mie results with Hapke approximations

The grain size of water ice can be determined from its near-infrared spectrum, which has numerous diagnostic absorption bands of different opacities. Models that have been used to determine water ice grain size from infrared spectra of icy outer Solar System objects have shown discrepancies in modeled grain size of a factor of two or more. Here the single-scattering albedo calculated using the commonly used Hapke model given by Roush [Roush, T.L., 1994. Icarus 108, 243-254] is compared with the exact calculation for spheres from a Mie series. An earlier approximation of single-scattering albedo called the Hapke “slab” model is also used in the comparison. All three models are implemented using the same optical constants for water ice at ∼110 K. Results are displayed for a large range of grain sizes from 1 μm to 1 mm. In general neither Hapke model can mimic the Rayleigh effects from particles sized near the wavelength of light that the Mie model predicts. For 10 μm particles, the slab model matches the Mie calculation quite well, but larger sizes are more discrepant. The Hapke/Roush model grain size needs to be ∼2.5 times larger to mimic the Mie results, and there are additional discrepancies in the continuum levels and band strengths. The Mie calculation for spheres is recommended for analysis of unknown remote sensing measurements, as it can mimic the spectra of oblate, prolate, and hollow particles given by equivalent sphere theories.     

The microwave absorption of SO2 in the Venus atmosphere

Sulfur dioxide has a strong and complex rotational spectrum in the microwave and far infrared regions. The microwave absorption due to SO₂ in a CO₂ mixture is calculated for conditions applicable to the Venus atmosphere. It is shown that at the concentrations detected by Pioneer-Venus in situ measurements, SO₂ may be expected to contribute significantly to the microwave opacity of the Venus atmosphere. In particular, SO₂ might provide the major source of opacity in the atmospheric region immediately below the main sulfuric acid cloud deck. The spectrum is largely nonresonant at the pressures where SO₂ is expected to occur, however.     

A comparison of Martian albedo features with topography

Martian albedo features photographed from the Earth are compared with the topography observed by Mariner 9. We present three Lambert azimuthal equal-area charts prepared to facilitate the comparison. No correlation between large-scale albedos and topography can be generalized, but several different kinds of relationships seem to be indicated in particular regions. Examples of these are discussed.     

On the albedo of the interplanetary dust

The zodiacal light brightness and measured spatial density of the interplanetary dust lead to a mean geometric albedo of 0.24 for the dust particles near 1 AU; whereas the composition of collected micrometeroids suggests a geometric albedo ?0.1. The data do not support the very low albedo (?0.01) proposed by A. F. Cook [Icarus33 (1978), 349–360]. The evidence is against a change in the mean particle albedo between 0.1 and 2 AU. Beyond 2 AU the data are unclear and a change in albedo is not ruled out.     

Multiple scattering in the atmosphere with a rough surface

In the present paper, the intensity of radiation emergent from the atmosphere bounded by a rough surface is discussed with the aid of the superposition method derived by Mukai (1973). The merit of this method is to express the laws of diffuse reflection and transmission for the planetary problem with a rough surface in terms of a scattering and a transmission function for the standard problem.Here the bottom surface is assumed to reflect light in accordance with the slope distribution given by Cox and Munk (1954a, b). The results are discussed in terms of the optical properties and roughness of the bottom surface.     

On the effects of a sudden change in the albedo of the Earth

Acquisition by the upper atmosphere of some 10¹⁴ gm of cometary dust would have major implications on the Earth's climate. Pluvial activity would increase dramatically as temperature differences between sea and land widened. Global distribution of precipitation would be controlled by the density of the dust in the atmosphere; for a partially reflective blanket, a fraction of solar energy would still reach ground level creating new climatic zones. The totally undecomposed state of the interiors of Siberian Mammoths and the curious distribution, often uphill, of erratic boulders point to unbelievably sudden and severe conditions at the onset and possibly end of a glacial period. We suggest that a reflective blanket of particles could produce such conditions.