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A comprehensive one-dimensional photochemical model extending from the middle atmosphere (50 km) to the exobase (432 km) has been used to study the escape of hydrogen and deuterium from the Earth's atmosphere. The model incorporates recent advances in chemical kinetics as well as atmospheric observations by satellites, especially the Atmosphere Explorer C satellite. The results suggest: (1) the escape fluxes of both H and D are limited by the upward transport of total hydrogen and total deuterium at the homopause (this result is known as Hunten's limiting flux theorem); (2) about one fourth of total hydrogen escape is thermal, the rest being nonthermal; (3) escape of D is nonthermal; and (4) charge exchange and polar wind are important mechanisms for the nonthermal escape of H and D, but other nonthermal mechanisms may be required. The efficiency to escape from the terrestrial atmosphere for D is 0.74 of the efficiency for H. If the difference between the D/H ratio measured in deep-sea tholeiite glass and that of standard sea water, delta D = -77%, were caused by the escape of H and D, we estimate that as much water as the equivalent of 36% of the present ocean might have been lost in the past.

Comparisons are undertaken between laboratory kinetics experiments and Voyager observations in order to shed light on possible chemical reaction pathways to the generation of cyanogen and dicyanoacetylene in Titan's upper atmosphere. The predicted concentrations of the simple nitrile compounds are found to be of a magnitude realistically corresponding to the Voyager observations.

Spacecraft and groundbased observations of the atmospheres of solar system objects have provided a definition of their present characteristics and have yielded clues about their past history. Table 1 presents a summary of our current knowledge of the atmospheric properties of all the planets, except Pluto, and several satellites. The masses of these atmospheres range from the very miniscule values for the Moon, Mercury, and Io, to the more substantial values for the Earth, Venus, Mars, and Titan, to the very large values for the giant planets, where the atmosphere constitutes a significant fraction of the total planetary mass. The compositions of these atmospheres encompass ones dominated by rare gases (the Moon and Mercury), ones containing highly oxidized compounds of carbon, nitrogen, and sulfur (the outer three terrestrial planets and Io), and ones with highly reduced gases (Titan and the giant planets). What factors account for this enormous diversity in properties?

Auroral emission originating at the foot of the Io-associated flux tube at Jupiter has been detected with a high-resolution spectrometer/telescope on board the Orbiting Astronomical Observatory Copernicus. The emission intensity at Ly-alpha is found to be greater than 100 kR, and the emission is located at zenographic latitudes greater than 65°.

The formal theory developed in Chapter 2 assumed the Stokes parameters to be additive. The sufficient condition for additivity is that the radiation fluxes in the atmosphere shall have no phase coherence. Thermal emission from independently excited molecules is necessarily incoherent with respect to phase. Atmospheric scattering centers are widely and randomly spaced, and they can be treated as independent and incoherent scatterers. The situation differs, however, when we consider details of the scattering process within a single particle, and in order to derive the extinction coefficient and the scattering matrix (see § 2.1.3) we must make use of a theoretical framework that involves the phase explicitly. The problem of the interaction between an electromagnetic wave and a dielectric particle can be precisely formulated using Maxwell’s equations. For a plane wave and a spherical particle, Mie’s theory provides a complete solution (see §7.6). But the general problem is complicated and our understanding is rendered more difficult by preconceptions based on the approximations of elementary optics. This chapter provides a brief survey of the important results and the underlying concepts. The geometry of the problem is illustrated in Fig. 7.1. An isolated particle is irradiated by an incident, plane electromagnetic wave. The plane wave preserves its character only if it propagates through a homogeneous medium; the presence of the scattering particle, with electric and magnetic properties differing from those of the surrounding medium, distorts the wave front. The disturbance has two aspects: first, the plane wave is diminished in amplitude; second, at distances from the particle that are large compared with the wavelength and particle size, there is an additional, outward-traveling spherical wave. The energy carried by this spherical wave is the scattered energy; the total energy lost by the plane wave corresponds to extinction; the difference is the absorption. The properties of the spherical wave in one particular direction (the line of sight) will be considered. This direction can be specified by the scattering angle 6 (see Fig. 7.1) in a plane containing both the incident and scattered wave normals (the plane of reference), and the azimuth angle ϕ) between the plane of reference and a plane fixed in space.

Results from the neutral mass spectrometer carried on the aeroshell of Viking 1 show evidence for NO in the upper atmosphere of Mars and indicate that the isotopic composition of carbon and oxygen is similar to that of Earth. Mars is enriched in ^(15)N relative to Earth by about 75 percent, a consequence of escape that implies an initial abundance of nitrogen equivalent to a partial pressure of at least 2 millibars. The initial abundance of oxygen present either as CO_2 or H_2O must be equivalent to an exchangeable atmospheric pressure of at least 2 bars in order to inhibit escape-related enrichment of ^(18)O.

Using the California Institute of Technology/Jet Propulsion Laboratory two-dimensional transport model, with transport coefficients taken from Yang and Tung (1989), we study the time evolution of excess carbon 14 in the stratosphere and the troposphere from October, 1963 to December, 1966. The model provides a satisfactory simulation of the observed data. Due to the impulsive nature of its source, initial distributions of excess carbon 14 exhibit large spatial gradients. This permits important constraints on the range of transport coefficients in the lower stratosphere to be derived. The standard model uses the circulation and eddy diffusivity of the year 1980. Large deviations (by factor of 2) from this standard transport are ruled out by our model. A self-consistently derived Kyy which is small (approximately 10(9) cm2 s-1) in tropical regions, but is larger (approximately 10(10) cm2 s-1) at higher latitudes is preferred. A Kzz as large as 1 x 10(4) cm2 s-1 would be inconsistent with the data. Excess carbon 14 is removed from the atmosphere with surface deposition velocities vS = 3 x 10(-3) cm s-1 and vN = 5 x 10(-3) cm s-1 in the southern and northern hemispheres, respectively. The last result is contrary to the current understanding that the oceans are the dominant sink for excess 14C.

An assessment is made of the ability of current theory to explain the phenomenology of upper atmospheric ozone as revealed by the sizeable body of measurements presently available. The chemistry of ozone in the mesosphere and lower thermosphere is closely coupled to the chemistries of other oxygen/hydrogen-containing species, which must be considered concurrently. To provide insight into the sensitivity of model calculations to the choice of values used for key chemical rate constants and climatological parameters, simple analytical expressions for ozone are derived for those situations when it is in photochemical steady state, the mesosphere during daylight hours and the lower thermosphere throughout the full diurnal period. The model is found to reproduce the detailed Aladdin 74 rocket measurements of ozone from 50 to 95 km, numerous other measurements of mid-latitude ozone in the lower mesosphere, the secondary maximum in the ozone vertical distribution at the mesopause, and the diurnal variability of ozone seen in the radio measurements of Wilson and Schwartz (1981) and other observations. The agreement with the Aladdin 74 data results from adjusting some key parameters within the uncertainties of laboratory measurements or known natural climatological variability. The variety of mid-latitude observations can be understood in terms of the estimated variability of environmental factors: diurnal, seasonal, and solar cycles in the solar illumination; the abundance of water vapor; and the details of the thermal profile of the atmosphere. The ozone secondary maximum results from the onset of the coupling between active-hydrogen and active-oxygen chemistry and its observed variability may be a consequence of secular changes in mesopause dynamics. Above ∼95 km, ozone observations are consistently higher than model results and cannot be accounted for by the set of reactions currently included in the model.

The surface of lo may be covered with a layer of ammonia ice containing trace amounts of sodium potassium, and calcium; and atmospheric nitrogen could be formed as a photochemical product of ammonia photolysis. Intense sporadic sodium emission from Io can be excited by collisions involving vibrationally excited nitrogen molecules. These metastable molecules may be formed by electron impact, with electrons energized by an auroral mechanism. In order to account for the intensity ratio of the sodium doublet, it is necessary to invoke scattering in a thick gaseous envelope ejected by Io.

The source function for scattering, (2.32), is more complicated than a thermal source function on two accounts: it is not a function of local conditions alone, but involves conditions throughout the atmosphere, through the local radiation field, and the phase function, Pij(s, d), may be an extremely complex function of the directions, s and d, and the states of polarization, i and j. The general solution, (2.87), is still valid, but it is now an integral equation, involving the intensity both on the left-hand side and under the integral on the right-hand side. Successive approximations, starting with the first-order scattering term [third term on the right-hand side of (2.116)], are an obvious approach, and would lead to a solution, but there are more efficient and more accurate ways to solve the problem. Many methods are available because their fundamental theory has proved to be mathematically interesting and because there are important applications in neutron diffusion theory and astrophysics. These motivations are extraneous to atmospheric science, but the availability of the methodology has led to its adoption and extension to atmospheric problems. Many methods are available because their fundamental theory has proved to be mathematically interesting and because there are important applications in neutron diffusion theory and astrophysics. These motivations are extraneous to atmospheric science, but the availability of the methodology has led to its adoption and extension to atmospheric problems. Solutions to scattering problems can be elaborate and mathematically elegant; they can also be numerically onerous but, with access to modern computers, “exact” solutions are feasible, given the input parameters τv, av (=sv/ev), and Pi j. For monochromatic calculations with simple phase functions, numerical solutions present few difficulties. Nevertheless, the combination of unfamiliar formalism with inaccessible and undocumented algorithms can be daunting for those with only a peripheral interest in radiation calculations. It is, therefore, relevant to note that available data are imprecise and virtually never require the accuracy available from exact methods. Easily visualized two-stream approximations, combined with similarity relations to handle complex phase functions (see §§8.4.4 and 8.5.6), are often more than adequate, and some angular information can be added, if required, from the use of Eddington’s second approximation (§ 2.4.5).

The direct collisional interaction of magnetospheric particles with Io will lead to sputtering of atoms and molecules from the satellite into circum-Jovian space. The ∼520-eV S (and ∼260-eV O) ions composing the Io torus are the most effective agents for net sputter removal of matter from the satellite. An incident flux of ∼10^(10) cm^(−2) s^(−1) is estimated to provide ∼5 × 10^(10) S atoms cm^(−2) s^(−1) from sputtering of a (dayside) atmosphere with an exobase at a few hundred kilometers and up to ∼10^(12) S atoms cm^(−2) s^(−1) from an atmosphere at 1500°K with an exobase at ∼2.2 R_(Io). The supply of S (and O) required to stabilize the torus has been estimated by others to be from 10^(10) to 10^(12) cm^(−2) s^(−1). If Na and K are present in the atmosphere at a concentration level of 1%, the corresponding sputtering rates are calculated to be a few times 10^8 cm^(−2) s^(−1) for an exobase at several hundred kilometers. These numbers are large enough to supply the 10^7 cm^(−2) s^(−1) fluxes required to maintain the Na and K clouds. Sputtering can also remove heavy molecules, like Sn, from the atmosphere. At night, direct S sputtering of the unprotected surface is calculated to eject S and Na (1% concentration) at rates given approximately by ∼10^(10) and ∼10^8 cm^(−2) s^(−1), respectively. All atomic species residing on the surface must be ejected into circum-Jovian space at a rate approximately proportional to their (surface) abundances, if direct surface sputtering occurs, so that the particle content of the inner Jovian magnetosphere should map rather faithfully all species present on Io's surface. The processes of plume sputtering, avalanche cascading, and ionic saltation may lead to spatial and temporal variations in the number of ejected particles.

Carbon monoxide, produced in the Venus atmosphere by photolysis of CO_2, is removed mainly by reaction with OH. The radical OH is formed in part by photolysis of H_2O_2, in part by reaction of O with HO_2. Photolysis of HCl provides a major source of H radicals near the visible clouds of Venus and plays a major role in the overall photochemistry. The mixing ratio of O_2 is estimated to be approximately 10^(−7), about a factor of 10 less than a recent observational upper limit reported by Traub and Carleton. A detailed model, which accounts for the photochemical stability of Venus CO_2, is presented and discussed.

In this chapter we discuss radiative equilibrium models of the earth’s atmosphere and the closely related radiative—convective models, for which small-scale convection is included in a highly parameterized form. In both cases, heat transports by planetary-scale motions are neglected. Despite their limitations, radiative equilibrium and radiativeconvective studies have provided stimuli for many of the fundamental ideas discussed in this book. Their value is principally heuristic. The radiative equilibrium state is one conceivable state of a planetary atmosphere that may be analyzed so that the implications of parameteric changes can be understood in simple terms (e.g., changes in atmospheric composition, earth orbital elements, solar emission, etc.). The same cannot yet be said of any dynamic model. While numerical solutions are available from general circulation models, their behavior is often no easier to interpret than that of the atmosphere itself. For studies that are not based on the existence of day-to-day observations, radiative equilibrium considerations provide the irreplaceable first step in a number of fields: the atmospheres of other planets, stellar atmospheres, the earth’s primitive atmosphere; and much of the progress in studies of climate change has been based on the simplest energy balance models. In addition to their value in examining general principles, there is a recurrent, although disputed theme that radiative equilibrium has direct relevance to the observed atmospheric structure. This proposition embraces a number of instructive ideas but, before examining them, we consider some of the observational evidence that motivates them. From the earliest days following the discovery of the stratosphere, theoretical workers assumed that the stratosphere, unlike the troposphere, was in radiative equilibrium. The reasoning was that no forms of heat transport, other than radiative, could be important in a highly stable atmosphere. Since nothing was known about planetary-scale motions at that time, this conclusion was premature. If we turn to modern data, Fig. 9.1a presents the observed climatological temperatures in the middle atmosphere, to be compared with radiative equilibrium calculations shown in Fig. 9.1b. Agreement between theory and observation is fairly good except in the region of the polar winter.

A variety of models for Io's atmosphere, ionosphere, surface, and environment are developed and discussed in the context of recent observational data. The sodium emission detected by Brown appears to require a collisional excitation process in Io's atmosphere, and the extended sodium emission measured by Trafton et al. may require scattering of the planetary radiation by an extended sodium cloud. The sodium is presumably present initially in bound form on Io's surface and may be released by the sputtering mechanism suggested by Matson et al. The ionosphere detected by the radio occultation experiment on Pioneer 10 could be attributed to photoionization of atmospheric sodium if Io's atmosphere could sustain significant vertical motions, of order 1 s^(-1) directed up during the day, down at night. Vertical motions of this magnitude could be driven by condensation of atmospheric NH_3. The total density of gas at Io's surface appears to lie in the range 10^(10)-10^(12) molecules cm^(-3). Corpuscular ionization could play an additional role for the Ionosphere. In this case the satellite should exhibit an exceedingly bright, ~ 10 kR, airglow at Lɑ. The incomplete hydrogen torus observed by Judge and Carlson in the vicinity of Io requires a large supply of hydrogen from the satellite's atmosphere. The escape flux should be of order 10^(11) cm^(-2) s^(-1) and could be maintained by photolysis of atmospheric NH_3. The observed geometry of the hydrogen torus appears to require a surprisingly short lifetime, ~ 10^5 s, for neutral hydrogen near Io's orbit, and may indicate the presence of a large flux, ~ 10^9 cm ^(-2) s^(-1), of low-energy protons in Jupiter's magnetosphere. Implications of the hydrogen torus for the energy and mass balance of Jupiter's magnetosphere are discussed briefly, and observational programs are identified which might illuminate present uncertainties in our understanding of Io.

The carbon monoxide cycle is studied by incorporating the known and hypothetical sources and sinks in a tracer model that uses the winds generated by a general circulation model. Photochemical production and loss terms, which depend on OH radical concentrations, are calculated in an interactive fashion. The computed global distribution and seasonal variations of CO are compared with observations to obtain constraints on the distribution and magnitude of the sources and sinks of CO, and on the tropospheric abundance of OH. The simplest model that accounts for available observations requires a low latitude plant source of about 1.3 x 10 to the 15th g/yr, in addition to sources from incomplete combustion of fossil fuels and oxidation of methane. The globally averaged OH concentration calculated in the model is 750,000/cu cm. Models that calculate globally averaged OH concentrations much lower than this nominal value are not consistent with the observed variability of CO. Such models are also inconsistent with measurements of CO isotopic abundances, which imply the existence of plant sources.

International audience; The Voyager Ultraviolet Spectrometer (UVS) is an objective grating spectrometer covering the wavelength range of 500–1700 Å with 10 Å resolution. Its primary goal is the determination of the composition and structure of the atmospheres of Jupiter, Saturn, Uranus and several of their satellites. The capability for two very different observational modes have been combined in a single instrument. Observations in the airglow mode measure radiation from the atmosphere due to resonant scattering of the solar flux or energetic particle bombardment, and the occultation mode provides measurements of the atmospheric extinction of solar or stellar radiation as the spacecraft enters the shadow zone behind the target. In addition to the primary goal of the solar system atmospheric measurements, the UVS is expected to make valuable contributions to stellar astronomy at wavelengths below 1000 Å.

The thermodynamic equation for an ideal gas is where ρcv6 is the internal energy per unit volume and hR is the radiative heating rate. For the sake of clarity we omit diabatic terms additional to the radiative heating. We may expand the left-hand side of (10.1) and write it in the form of an enthalpy equation, and cp is the specific heat at constant pressure. The left-hand side of includes both internal and potential energy, d is the dynamic heating. If the vertical coordinate is pressure, ∂p/∂t = 0 and all terms in d tend to zero as the velocities tend to zero. Solutions to (10.2) in conjunction with the equations of motion, the equation of continuity, and the gas law are the matter of dynamic meteorology. In this chapter, we look at a single aspect, namely the coupling between radiation and dynamics as expressed by the thermodynamic equation, (10.2). We shall use the methods of perturbation theory. Assume the existence of a basic, steady-state (suffix 0) for which This basic state could be a state of radiative equilibrium or a state dominated by dynamic transports.

Digital archives offer the investigator an up-to-date analysis of an extensive and specialized literature. Periodic revisions are reported in the open literature and it seems unlikely that future investigators will attempt to use any other source where archives can provide the required data. For this reason, we shall confine our comments on permitted vibration-rotation transitions to describing the AFGL tape contents, but we shall add two areas not contained in it: first, electronic bands, and second, the related topics of forbidden transitions, collision-induced transitions, and polymer spectra. The AFGL tape lists data on one important set of electronic transitions, those giving rise to the near-infrared atmospheric bands of molecular oxygen. These bands behave in the same way as vibration rotation bands, except for the frequency displacement caused by the change in electronic energy and the symmetry conditions imposed by the electronic wave functions. Other electronic transitions usually involve larger differences between energy levels and cannot be understood as completely as the lower energy, vibrational and rotational transitions. Fortunately, visible and ultraviolet bands of importance for atmospheric problems are less complicated than vibration—rotation bands and they are usually less affected by state parameters. Atmospheric absorption calculations in the visible and ultraviolet spectrum are commonly made on the basis of empirical data without requiring the level of understanding developed in Chapters 3 and 4 for vibration-rotation bands. The altitude of unit optical depth for ultraviolet atmospheric bands is illustrated in Fig. 5.1. The intensity of solar radiation falls off rapidly with decreasing wavelength in the spectral region shown (the irradiance at 2000 Å compared to that at 3000 Å is 10-2 whereas at 1000 Å it is 10-5, see Appendix 9). For heating rate calculations at altitudes less than 100km, only O2 and O3 are important, except under special conditions when the atmosphere contains large amounts of volcanic aerosols, or polar stratospheric clouds at high latitudes. All of the absorptions shown in Fig. 5.1 are important for other reasons that do not directly concern us here.

It is proposed that Saturn's satellite Titan is covered by an ocean one to several kilometers deep consisting mainly of ethane. If the ocean is in thermodynamic equilibrium with an atmosphere of 3 percent (mole fraction) methane, then its composition is roughly 70 percent ethane, 25 percent methane, and 5 percent nitrogen. Photochemical models predict that ethane is the dominant end product of methane photolysis so that the evolving ocean is both the source and sink for continuing photolysis. The coexisting atmosphere is compatible with Voyager data.

Viking measurements of the Martian upper atmosphere indicate thermospheric temperatures below 200°K, temperatures much colder than those implied by remote sensing experiments on Mariner 6, 7, and 9 and Mars 3. The variability in thermospheric temperature may reflect an important dynamical coupling of upper and lower regions of the Martian atmosphere. Absorption of extreme ultraviolet solar radiation can account for observed features of the ionosphere and provides an important source of fast N and O atoms which may escape the planet's gravitational field. Isotopic measurements of oxygen and nitrogen impose useful constraints on models for planetary evolution. It appears that the abundance of N_2 in Mars' past atmosphere may have exceeded the abundance of CO_2 in the present atmosphere and that the planet also has copious sources of H_2O. The planet acquired its nitrogen atmosphere early in its history. The degassing rate for nitrogen in the present epoch must be less than the time-averaged degassing rate by at least a factor of 20.

The physical and chemical processes that lead to the preferential escape of hydrogen over deuterium in the Martian atmosphere are studied in detail using a one-dimensional photochemical model. Comparison of our theory with recent observations of HDO suggests that, averaged over the planet, Mars contains 0.2 m of crustal water that is exchangeable with the atmosphere. Our estimate is considerably lower than recent estimates of subsurface water on Mars based on geomorphological analysis of Viking images. The estimate can be reconciled if only a small fraction of crustal water can exchange with the atmosphere.

This chapter is concerned with the requirements of numerical weather prediction and general circulation models. These numerical models always assume a stratified atmosphere and utilize a limited number of grid points in the vertical direction. Computations are repeated at many horizontal grid points and at frequent time intervals; a premium is placed on computational economy. The nested integrals involved in radiative flux and heating calculations, particularly the frequency integration, can create an unacceptable computational burden unless approximated. In this chapter we limit attention to clear-sky conditions, i.e., to absorbing constituents and a thermal source function (§2.2). For a Planck function, the formal solution, (2.86), is a definite integral involving measurable quantities, temperatures, and gaseous densities. Scattering problems, on the other hand, involve the intensity in the source function and cannot be solved by a single application of this integral. Scattering calculations will be discussed further in Chapter 8; it will be shown that scattering can be neglected if the volume scattering coefficient is not very much larger than the volume absorption coefficient. This is usually the case for aerosols in the thermal region of the spectrum. As regards boundary conditions, it is usual for clear-sky calculations to assume that the earth’s surface and the upper and lower surfaces of clouds can be treated as black surfaces in the thermal spectrum. Equations (2.86) and (2.87) are stated in terms of general boundary conditions. In the flux and heating integrals, (2.106) and (2.110), these conditions are specialized to a black surface at ground level, but they can be generalized without difficulty to include a black surface at any level or partial reflection from these surfaces, if appropriate. The equations for which efficient algorithms are required are the flux equations, (2.107) and (2.108), the heating equations, (2.110) or (2.111), and the solar flux equations, (2.115). The nested integrals are 1. the vertical integral, (2.92), for the optical depth; 2. the integral, (2.86), along the optical path; 3. the angular integral, (2.102); 4. an integral over all frequencies. We may introduce the issues by considering a restricted example, that of the intensity recorded outside the atmosphere by a downward pointing satellite spectrometer.

A value of 1.7 × 10^(−3) has been reported for the ratio of CH_3D to CH_4 in the stratosphere of the saturnian moon Titan. A lower value of 6 × 10^(−4) for this ratio in the deeper part of Titan's atmosphere was reported by de Bergh et al. For comparison we note that the CH_3D to CH_4 ratio on Saturn and Jupiter is 8.7 × 10^(−5) and 6.7 × 10^(−5), respectively (see Table 1). We estimate the uncertainties in all these observations and data reduction to be about a factor of 2. Despite these uncertainties it appears that Titan's atmosphere is enriched in deuterium by a factor of ≥3 relative to Jupiter and Saturn. Potential causative factors examined here for this enrichment are condensation to form tropospheric methane clouds, fractionation occurring over a hypothetical CH_4–C_2H_6 ocean and between the ocean and the clathrate crust beneath, fractionation which occurred during the formation of Titan and fractionation occurring as a result of the evolution of Titan's atmosphere. We conclude that the greater part of the observed fractionation is probably derived from the formation of Titan and the subsequent evolution of Titan's atmosphere driven by photochemistry.

Methane and ammonia abundances in the coma of Halley are derived from Giotto IMS data using an Eulerian model of chemical and physical processes inside the contact surface to simulate Giotto HIS ion mass spectral data for mass-to-charge ratios (m/q) from 15 to 19. The ratio m/q = 19/18 as a function of distance from the nucleus is not reproduced by a model for a pure water coma. It is necessary to include the presence of NH3, and uniquely NH3, in coma gases in order to explain the data. A ratio of production rates Q(NH3)/Q(H20) = 0.01-0.02 results in model values approximating the Giotto data. Methane is identified as the most probable source of the distinct peak at m/q = 15. The observations are fit best with Q(CH4)/Q(H2O) = 0.02. The chemical composition of the comet nucleus implied by these production rate ratios is unlike that of the outer planets. On the other hand, there are also significant differences from observations of gas phase interstellar material.

In common with astrophysical usage the word intensity will denote specific intensity of radiation, i.e., the flux of energy in a given direction per second per unit frequency (or wavelength) range per unit solid angle per unit area perpendicular to the given direction. In Fig. 2.1 the point P is surrounded by a small element of area dπs, perpendicular to the direction of the unit vector s. From each point on dπs a cone of solid angle dωs is drawn about the s vector. The bundle of rays, originating on dπs, and contained within dωs, transports in time dt and in the frequency range v to v + dv, the energy . . . Ev = Iv(P,S) dπs dωs dv dt, (2.1). . . where Iv(P, s) is the specific intensity at the point P in the s-direction. If Iv is not a function of direction the intensity field is said to be isotropic ; if Iv is not a function of position the field is said to be homogeneous.

Our knowledge of Io has progressed dramatically in the past year. Prior to 1973, observations of Io made at optical, IR and radio wavelengths have revealed that this innermost Galilean satellite of Jupiter is unusual in a number of ways. A list would include post-eclipse brightening, high near-IR albedo, puzzling features (or lack of features) in the reflection spectrum, discordant brightness temperatures measured at 10 and 20 μm, and modulation of Jovian decametric activity. We now understand that Io has an atmosphere and an ionosphere. Their presence and interaction with the Jovian magnetosphere may account for much of the unusual behavior of the enigmatic satellite.

A sharp stratospheric emission feature at 667 cm^(−1) in the Voyager infrared spectra of Titan is associated with the ν_2 Q branch of CO_2. A coupling of photochemical and radiative transfer theory yields an average mole fraction above the 110 mbar level of ƒCO_2 = 1.5 ± ^(1.5)_(0.8) x 10^(-9), with most of the uncertainty being due to imprecise knowledge of the vertical distribution. CO_2 is found to be in a steady state, with its abundance being regulated principally by the ∼72 K cold trap near the tropopause and secondarily by the rate at which water-bearing meteoritic material enters the top of the atmosphere. An influx of water about 0.4 times that at the top of the terrestrial atmosphere is consistent with a combination of the observed CO_2 abundance and a steady state CO mole fraction of 1.1×10^(−4); the theoretical value for CO is close to the value observed by Lutz et al. (1983), although there are large margins for error in both numbers. If steady state conditions for CO prevail, little information is available regarding the evolution of Titan's atmosphere.

The greenhouse effect due to nitrous oxide in the present atmosphere is about 0.8°K. Increase in atmospheric N_2O due to perturbation of the nitrogen cycle by man may lead to an increase in surface temperature as large as 0.5°K by 2025, or 1.0°K by 2100. Other climatic effects of N_2O are briefly discussed.

Titan’s geometric albedo varied noticeably from 1972 to 1978, in phase with variations in solar activity [Lockwood and Thompson, 1979]. We carry out a series of radiative transfer and aerosol formation calculations in order to demonstrate the feasibility of the following scenario for these secular brightness changes: solar activity changes, especially in the UV output of the Sun, result in alterations to the mass production rate of aerosols in Titan’s atmosphere, which lead to modifications of their microphysical properties. The latter, in turn, cause the albedo to vary. Current estimates of the change in the solar UV radiation below the dissociation limit of methane imply alterations to the mean radius of the aerosols over an 11-yr solar cycle that are consistent in sign and magnitude with those required to explain the observed secular brightness changes.

The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. Our analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the inter-connection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems are provided.

A combined experimental study of the fluorescence spectrum of H_2 at wavelengths of 1200-1700 A by electron impact and its application to modeling the Jovian aurora have been carried out. Our laboratory data suggest that at 100 eV the relative cross sections for direct excitation of Lyɑ, Lyman bands (B^1Σ_u^+-X^1Σ_g^+), and Werner bands (C^1π_u-X^1Σ_g^+) are 1, 2.3±0.6, and 2.6±0.5, respectively, in conflict with Stone and Zipfs (1972) results for the Werner bands. Cascade from E,F^1Σ_g^+ states contributes an additional 31% to the B^1Σ_u^+ state population. It is shown that the most likely fate for the metastable H(2^2S) atoms produced in the Jovian aurora is collisional quenching to H(2^2P), and this could add as much as 60% to the predicted Lyɑ emission. On the basis of detailed atmospheric and radiative transfer modeling, we conclude that the recent IUE and Voyager observations are consistent with precipitation of electrons with energy in the range of 1-30 keV or other energetic particles that penetrate to number densities of 4 X 10^(10)-5 X 10^(13) cm^(-3) or column densities of 5 X 10^(17)-2 X 10^(20) cm^(-2) in the atmosphere. The globally averaged energy flux and production of hydrogen atoms are 0.5-2 ergs cm^(-2) s^(-1) and 1-4 X 10^(10) atoms cm^(-2) s^(-1), respectively.

A study is made of the UV reflection spectrum of Jupiter as measured by the International Ultraviolet Explorer. Detailed modeling reveals the mixing ratios of C_2H_2, C_2H_6, and C_4H_2 to be (1.0 ± 0.1) x 10^(-1), (6.6 ± 5.3) x 10^(-6), and (2.9 ± 2.0) x 10^(-10), respectively, in the pressure region between ~3 and 40 mbar. Upper limits in this pressure region for the mixing ratios of C_2H_4 and NH_3 were determined to be (3.9^(+4.9)_(-3.9))x10^(-10) and (4.2^(+6.7)_(-4.2))x10^(-9), respectively. An upper limit to the optical depth of dust above the tropopause, assuming it is well mixed, is 0.2^(+0.3)_(-1.4), and an upper limit on the dayglow emission by the Lyman bands of H_2 is 1.4^(+2.4)_(-1.4) kR. Comparison with Voyager results suggests that the scale height of C_2H_2 in the region 150-10 mbar is approximately twice that of the bulk atmosphere, consistent with the IUE observation of cosine-like limb darkening in the north-south direction on Jupiter in this spectral range. These results are of use in the photochemical modeling of the upper atmosphere of Jupiter.

In the upper stratosphere, an altitude range in which ozone should be in photochemical steady-state, calculated ozone abundances that are derived from a one-dimensional photochemical model with updated chemistry are up to 60% smaller than mean observed values. On the other hand, the model results for the key free radicals (HO_x, NO_x, and ClO_x species) in the catalytic destruction of ozone are shown to be in reasonable agreement with available measurements. The general validity of the model simulation of ClO_x chemistry is confirmed through a detailed intercomparison between the computed ClO diurnal variation and recently published ground-based microwave observations. Since many field measurements are performed near sunrise or sunset, the uncertainties in the model results arising from the details of the radiation field calculations at large zenith angles are discussed. Although the calculated ozone discrepancy could be the result of a number of errors in adopted photochemical parameters, a sensitivity analysis shows that no reasonable change in any one or two parameters can resolve this problem. The limited available observations regarding the ratio of atomic oxygen to ozone suggest a possible discrepancy in that quantity, which could be responsible for a large part of the ozone problem.

Observations of the temporal and spatial distribution of N_2O in solution are not yet sufficient to permit quantitative assessment of the role of the ocean in the budget of atmospheric N_2O. Consideration of the global nitrogen cycle suggests that the land should be the primary source of N_2O. The gas is removed in the atmosphere by photolysis and by reaction with O(¹D), and there may be additional sinks in the ocean.

A photochemical theory is proposed for producing complex polymers in a methane atmosphere. It is argued that the polyacetylenes (C_(2n)H_2) are the most likely precursor molecules for the formation of the stratospheric haze layer on Titan. The production of polyacetylenes involves a strong positive feedback, leading to more production of polyactylenes. The thermosphere of Titan may undergo substantial expansion and contraction over a solar cycle, with important consequences for the chemistry of the upper atmosphere.

A candidate explanation for Early Mars rivers is atmospheric warming due to surface release of H$_2$ or CH$_4$ gas. However, it remains unknown how much gas could be released in a single event. We model the CH$_4$ release by one mechanism for rapid release of CH$_4$ from clathrate. By modeling how CH$_4$-clathrate release is affected by changes in Mars' obliquity and atmospheric composition, we find that a large fraction of total outgassing from CH$_4$ clathrate occurs following Mars' first prolonged atmospheric collapse. This atmosphere-collapse-initiated CH$_4$-release mechanism has three stages. (1) Rapid collapse of Early Mars' carbon dioxide atmosphere initiates a slower shift of water ice from high ground to the poles. (2) Upon subsequent CO$_2$-atmosphere re-inflation and CO$_2$-greenhouse warming, low-latitude clathrate decomposes and releases methane gas. (3) Methane can then perturb atmospheric chemistry and surface temperature, until photochemical processes destroy the methane. Within our model, we find that under some circumstances a Titan-like haze layer would be expected to form, consistent with transient deposition of abundant complex abiotic organic matter on the Early Mars surface. We also find that this CH$_4$-release mechanism can warm Early Mars, but special circumstances are required in order to uncork 10$^{17}$ kg of CH$_4$, the minimum needed for strong warming. Specifically, strong warming only occurs when the fraction of the hydrate stability zone that is initially occupied by clathrate exceeds 10%, and when Mars' first prolonged atmospheric collapse occurs for atmospheric pressure > 1 bar., Accepted by Planetary and Space Science