Atmospheric Chemistry in Giant Planets, Brown Dwarfs, and Low-Mass Dwarf Stars: I. Carbon, Nitrogen, and Oxygen

The chemical species containing carbon, nitrogen, and oxygen in atmospheres of giant planets, brown dwarfs (T and L dwarfs), and low-mass stars (M dwarfs) are identified as part of a comprehensive set of thermochemical equilibrium and kinetic calculations for all elements. The calculations cover a wide temperature and pressure range in the upper portions of giant planetary and T-, L-, and M-dwarf atmospheres. Emphasis is placed on the major gases CH₄, CO, NH₃, N₂, and H₂O but other less abundant gases are included. The results presented are independent of particular model atmospheres, and can be used to constrain model atmosphere temperatures and pressures from observations of different gases. The influence of metallicity on the speciation of these key elements under pressure-temperature (P-T) conditions relevant to low-mass object atmospheres is discussed. The results of the thermochemical equilibrium computations indicate that several compounds may be useful to establish temperature or pressure scales for giant planet, brown dwarf, or dwarf star atmospheres. We find that ethane and methanol abundance are useful temperature probes in giant planets and methane dwarfs such as Gl 229B, and that CO₂ can serve as a temperature probe in more massive objects. Imidogen (NH) abundances are a unique pressure-independent temperature probe for all objects. Total pressure probes for warmer brown dwarfs and M dwarfs are HCN, HCNO, and CH₂O. No temperature-independent probes for the total pressure in giant planets or T-dwarf atmospheres are identified among the more abundant C, N, and O bearing gases investigated here.     

Theoretical brightness temperature profiles of atmospheric pure H2 rotational quadrupole lines: Jupiter and Uranus

With the advent of high-resolution instruments and their use high above most of the telluric water vapor, we can expect to observe the hydrogen pure rotational quadrupole lines at 28, 17, and 12 μm from the atmospheres of the outer planets. We have calculated the best values for the line strengths, pressure-broadening coefficients, diffusion constants, and pressure shifts for these rotational transitions. We have used the collisionally narrowed Galatry profile to calculate brightness temperature line profiles for these H₂ transitions for the outer planets Jupiter and Uranus. We have also included the effect of the H₂ rotational-translational continuum and the NH₃ν₂ band.     

Chemistry of atmospheres formed during accretion of the Earth and other terrestrial planets

We used chemical equilibrium and chemical kinetic calculations to model chemistry of the volatiles released by heating different types of carbonaceous, ordinary and enstatite chondritic material as a function of temperature and pressure. Our results predict the composition of atmospheres formed by outgassing during accretion of the Earth and other terrestrial planets. Outgassing of CI and CM carbonaceous chondritic material produces H₂O-rich (steam) atmospheres in agreement with the results of impact experiments. However, outgassing of other types of chondritic material produces atmospheres dominated by other gases. Outgassing of ordinary (H, L, LL) and high iron enstatite (EH) chondritic material yields H₂-rich atmospheres with CO and H₂O being the second and third most abundant gases. Outgassing of low iron enstatite (EL) chondritic material gives a CO-rich atmosphere with H₂, CO₂, and H₂O being the next most abundant gases. Outgassing of CV carbonaceous chondritic material gives a CO₂-rich atmosphere with H₂O being the second most abundant gas. Our results predict that the atmospheres formed during accretion of the Earth and Mars were probably H₂-rich unless the accreted material was dominantly CI and CM carbonaceous chondritic material. We also predict significant amounts of S, P, Cl, F, Na, and K in accretionary atmospheres at high temperatures (1500-2500 K). Finally, our results may be useful for interpreting spectroscopic observations of accreting extrasolar terrestrial planets.     

Hydrogen collisions in planetary atmospheres, ionospheres, and magnetospheres

Hydrogen is the most abundant element in the universe. Molecular hydrogen is the dominant chemical species in the atmospheres of the giant planets. Because of their low masses, neutral and ionized hydrogen atoms are the dominant species in the high atmospheres of many planets. Finally, protons are the principal heavy component of the solar wind.Here we present a critical evaluation of the current state of understanding of the chemical reaction rates and collision cross sections for several important hydrogen collision processes in planetary atmospheres, ionospheres, and magnetospheres. Accurate ab initio quantum theory will play an important role. The collision processes are grouped as follows:

(a)

H⁺+H charge transfer,

(b)

H⁺+H₂(v) charge transfer and vibrational relaxation, and

(c)

H₂(v,J)+H₂ vibrational, rotational, and ortho-para relaxation.

In each case we provide explicit representations as tabulations or compact formulas. Particularly important conclusions are that H⁺+H₂(v) collisions are more likely to result in vibrational relaxation than charge transfer and H₂ ortho-para conversion is at least an order-of-magnitude faster than previously assumed.     

On the sources of ultraviolet absorption in spectra of Titan and the outer planets

In response to the observations of the ultravioler deficiencies shown by all of the outer planets and Titan, models have been proposed to explain the low albedos by absorption by particles in the upper atmospheres of these objects. These particles are generally believed to be photochemically formed from gases in the upper atmospheres, primarily methane and hydrogen. Such processes may also be operative on Titan. The results of some laboratory experiments of the proton irradiation of mixtures of gases including CH₄ H₂, NH₃, etc., have shown that liquid and solid materials are produced that are strong ultraviolet absorbers. However, the material produced from the CH₄ + H₂ mixture was colorless, indicating that species containing elements other than carbon and hydrogen are necessary for the production of color. Two such elements are nitrogen (as NH₃ or N₂) and sulfur (as H₂S) and colored materials have been produced from such mixtures. None of these materials has spectral properties identical to those shown by the planets. Therefore it is necessary that mixtures (and/or cloud layers) of the photochemical materials be present.     

The significance of pressure shifts for the interpretation of H2 quadrupole lines in planetary spectra

The effects of pressure shifts on the formation of H₂ quadrupole absorption lines in the atmospheres of the major planets have not previously been considered. It is shown that, although pressure shifts have not been measured for the 3-0 and 4-0 H₂ bands, they can be estimated from existing experimental and theoretical knowledge. Using these estimates, it is shown that the effect of pressure shifts is negligible for Jupiter and small for Saturn, but quite large for Uranus. Consideration of the shifts reduces H₂ abundances determined for Uranus by from 25% to 50% as compared to calculations in which the shifts are ignored. The effect may be even larger for Neptune.     

Volatiles on Earth and Mars: A comparison

Based on our new and previous determinations of halogens in SNC meteorites, the bulk concentrations of halogens in the SPB, which is thought to be Mars, are estimated. The two-component model for the formation of terrestrial planets as proposed byA. E. Ringwood (Geochem. J. 11, 111–135 (1977) andOn the Origin of the Earth and Moon, Springer-Verlag, New York, 1979) andH. Wa¨nke (Philos. Trans. Roy. Soc. London, Ser. A 303, 287–302 (1981) is further substantiated. It is argued that almost all of the H₂O added to Mars during its homogeneous accretion was converted on reaction with metallic Fe to H₂, which escaped. By comparing the solubilities of H₂O and HCl in molten silicates, the amount of H₂O left in the mantle of Mars at the end of accretion can be related to the abundance of Cl. In this way an H₂O content in the Martian mantle of 36 ppm is obtained, corresponding to an ocean covering the whole planet to a depth of about 130 m.The huge quantities of H₂ produced by the reaction of H₂O with metallic iron should also have removed other volatile species by hydrodynamic escape. Thus it is postulated that the present atmospheres of Venus, Earth, and Mars were formed by degassing the interiors of the planets, after the production of H₂ had ceased, i.e., after metallic iron was no longer available. It is also postulated that the large differences in the amounts of primordial rare gases in the atmospheres of Venus, Earth, and Mars are due mainly to different loss factors.Except for gaseous species, Mars is found to be richer in volatile (halogens) and moderately volatile elements than the Earth. The resulting low release factor of⁴⁰Ar for Mars is attributed to a low degree of fractionation, leading to a relatively small crustal enrichment of even the most incompatible elements like K.     

Core formation in giant gaseous protoplanets

Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 MSaturn to 10 MJupiter. Giant protoplanets with masses of 5 MJupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼0.25 M_⊕ and ∼0.5 M_⊕, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M_⊕. Saturn's core mass is found to be ∼8 M_⊕.     

Oxygen airglow emission on Venus and Mars as seen by VIRTIS/VEX and OMEGA/MEX imaging spectrometers

Imaging spectrometers are highly effective instruments for investigation of planetary atmospheres. They present the advantage of coupling the compositional information to the spatial distribution, allowing simultaneous study of chemistry and dynamics in the atmospheres of Venus and Mars. In this work, we summarize recent results about the O₂(a¹Δ_g) night and day glows, respectively obtained by VIRTIS/Venus Express and OMEGA/Mars Express, the imaging spectrometers currently in orbit around Venus and Mars. The case of the O₂(a¹Δ_g - X³Σ_g⁻) IR emission at 1.27 μm on the night side of Venus and the day side of Mars is analyzed, pointing out dynamical aspects of these planets, like the detection of gravity waves in their atmospheres. The monitoring of seasonal and daily airglow variations provides hints about the photochemistry on these planets.     

Origin and evolution of the atmospheres of early Venus,Earth and Mars

We review the origin and evolution of the atmospheres of Earth, Venus and Mars from the time when their accreting bodies were released from the protoplanetary disk a few million years after the origin of the Sun. If the accreting planetary cores reached masses \(\ge 0.5 M_\mathrm{Earth}\) before the gas in the disk disappeared, primordial atmospheres consisting mainly of H\(_2\) form around the young planetary body, contrary to late-stage planet formation, where terrestrial planets accrete material after the nebula phase of the disk. The differences between these two scenarios are explored by investigating non-radiogenic atmospheric noble gas isotope anomalies observed on the three terrestrial planets. The role of the young Sun’s more efficient EUV radiation and of the plasma environment into the escape of early atmospheres is also addressed. We discuss the catastrophic outgassing of volatiles and the formation and cooling of steam atmospheres after the solidification of magma oceans and we describe the geochemical evidence for additional delivery of volatile-rich chondritic materials during the main stages of terrestrial planet formation. The evolution scenario of early Earth is then compared with the atmospheric evolution of planets where no active plate tectonics emerged like on Venus and Mars. We look at the diversity between early Earth, Venus and Mars, which is found to be related to their differing geochemical, geodynamical and geophysical conditions, including plate tectonics, crust and mantle oxidation processes and their involvement in degassing processes of secondary \(\hbox {N}_2\) atmospheres. The buildup of atmospheric \(\hbox {N}_2\), \(\hbox {O}_2\), and the role of greenhouse gases such as \(\hbox {CO}_2\) and \(\hbox {CH}_4\) to counter the Faint Young Sun Paradox (FYSP), when the earliest life forms on Earth originated until the Great Oxidation Event \(\approx \) 2.3 Gyr ago, are addressed. This review concludes with a discussion on the implications of understanding Earth’s geophysical and related atmospheric evolution in relation to the discovery of potential habitable terrestrial exoplanets.     

Detection of new hydrocarbons in Uranus' atmosphere by infrared spectroscopy

Ethane (C₂H₆), methylacetylene (CH₃C₂H or C₃H₄) and diacetylene (C₄H₂) have been discovered in Spitzer 10-20 μm spectra of Uranus, with 0.1-mbar volume mixing ratios of (1.0±0.1)×¹⁰⁻⁸, (2.5±0.3)×¹⁰⁻¹⁰, and (1.6±0.2)×¹⁰⁻¹⁰, respectively. These hydrocarbons complement previously detected methane (CH₄) and acetylene (C₂H₂). Carbon dioxide (CO₂) was also detected at the 7-σ level with a 0.1-mbar volume mixing ratio of (4±0.5)×¹⁰⁻¹¹. Although the reactions producing hydrocarbons in the atmospheres of giant planets start from radicals, the methyl radical (CH₃) was not found in the spectra, implying much lower abundances than in the atmospheres of Saturn or Neptune where it has been detected. This finding underlines the fact that Uranus' atmosphere occupies a special position among the giant planets, and our results shed light on the chemical reactions happening in the absence of a substantial internal energy source.     

Ice clathrate as a possible source of the atmospheres of the terrestrial planets

The presence and compositions of atmospheres on the terrestrial planets do not follow directly from condensation models which would have Earth accreting near 500°K. No single mechanism yet proposed adequately accounts for the abundances of noble gases and carbon and nitrogen in the atmospheres. We show that the composition of clathrates forming at low temperatures in cold regions of the nebula can be predicted. Addition of about 1 ppm clathrate material to the Earth can explain observed abundances of Ar, Kr, and Xe. Condensation and adsorption processes occuring at 400–500°K are necessary to explain the observed abundances of Ne, H₂O, C, and N. Possible sources of clathrates could be cometary bodies formed in the outer solar system.     

Water and related chemistry in the solar system. A guaranteed time key programme for Herschel

“Water and related chemistry in the Solar System” is a Herschel Space Observatory Guaranteed-Time Key Programme. This project, approved by the European Space Agency, aims at determining the distribution, the evolution and the origin of water in Mars, the outer planets, Titan, Enceladus and the comets. It addresses the broad topic of water and its isotopologues in planetary and cometary atmospheres. The nature of cometary activity and the thermodynamics of cometary comae will be investigated by studying water excitation in a sample of comets. The D/H ratio, the key parameter for constraining the origin and evolution of Solar System species, will be measured for the first time in a Jupiter-family comet. A comparison with existing and new measurements of D/H in Oort-cloud comets will constrain the composition of pre-solar cometary grains and possibly the dynamics of the protosolar nebula. New measurements of D/H in giant planets, similarly constraining the composition of proto-planetary ices, will be obtained. The D/H and other isotopic ratios, diagnostic of Mars’ atmosphere evolution, will be accurately measured in H₂O and CO. The role of water vapor in Mars’ atmospheric chemistry will be studied by monitoring vertical profiles of H₂O and HDO and by searching for several other species (and CO and H₂O isotopes). A detailed study of the source of water in the upper atmosphere of the Giant Planets and Titan will be performed. By monitoring the water abundance, vertical profile, and input fluxes in the various objects, and when possible with the help of mapping observations, we will discriminate between the possible sources of water in the outer planets (interplanetary dust particles, cometary impacts, and local sources). In addition to these inter-connected objectives, serendipitous searches will enhance our knowledge of the composition of planetary and cometary atmospheres.     

A methodology to construct a reduced chemical scheme for 2D-3D photochemical models: Application to Saturn

We present a methodology to build a reduced chemical scheme adapted to the study of hydrocarbons in the atmospheres of giant planets and Titan. As an example, we have built a reduced chemical scheme, containing only 25 compounds and 46 reactions (including photolysis), which is well adapted to compute the abundance of the main hydrocarbons observed so far in the atmosphere of Saturn (CH₃, CH₄, C₂H₂, C₂H₄, C₂H₆, CH₃C₂H, C₃H₈ and C₄H₂). This scheme gives similar results, within the error bars of the model, as a 1D photochemical model using an initial chemical scheme containing 90 compounds and more than 600 reactions. As a consequence, such a methodology can be used to build a reduced scheme well adapted to future 2D (or 3D) photochemical models and GCMs.     

Early Mars serpentinization‐derived CH4 reservoirs,H2‐induced warming and paleopressure evolution

CH₄ has been observed on Mars both by remote sensing and in situ during the past 15 yr. It could have been produced by early Mars serpentinization processes that could also explain the observed Martian remanent magnetic field. Assuming a cold early Mars, a cryosphere could trap such CH₄ as clathrates in stable form at depth. The maximum storage capacity of such a clathrate cryosphere has been recently estimated to be 2 × 10¹⁹ to 2 × 10²⁰ moles of methane. We estimate how large amounts of serpentinization‐derived CH₄ stored in the cryosphere have been released into the atmosphere during the Noachian and the early Hesperian. Due to rapid clathrate dissociation and photochemical conversion of CH₄ to H₂, these episodes of massive CH₄ release may have resulted in transient H₂‐rich atmospheres, at typical levels of 10–20% in a background 1–2 bar CO₂ atmosphere. The collision‐induced heating effect of H₂ present in such an atmosphere has been shown to raise the surface temperature above the water freezing point. We show how local and rapid destabilization of the cryosphere can be induced by large events (such as the Hellas Basin or Tharsis bulge formation) and lead to such releases. Our results show that the early Mars cryosphere had a sufficient CH₄ storage capacity to have maintained H₂‐rich transient atmospheres during a total time period up to several million years or tens of million years, having potentially contributed to the formation of valley networks during the Noachian/early Hesperian.     

Ionospheric models of Saturn,Uranus, and Neptune

Model ionospheres are calculated for Saturn, Uranus, and Neptune. Protons are the major ions above 150 km altitude measured from a reference level where the hydrogen density is 1 × 10¹⁶ molecules cm^?3, while below 150 km quick conversion of protons to H₃⁺ ions by a three-body association mechanism leads to a rapid removal of ionization in dissociative recombination of H₃⁺. Electron density maxima are found at about 260 km for Saturn and Uranus and 200 km for Neptune. Present knowledge of the physical and chemical processes in the atmospheres of these planets suggests that their ionospheres probably will not be Jupiter-like.     

The binary collision-induced second overtone band of gaseous hydrogen: modelling and laboratory measurements

Collision-induced absorption (CIA) is the major source of the infrared opacity of dense planetary atmospheres which are composed of nonpolar molecules. Knowledge of CIA absorption spectra of H₂–H₂ pairs is important for modelling the atmospheres of planets and cold stars that are mainly composed of hydrogen. The spectra of hydrogen in the region of the second overtone at 0.8 μm have been recorded at temperatures of 298 and 77.5 K for gas densities ranging from 100 to 800 amagats. By extrapolation to zero density of the absorption coefficient measured every 10 cm⁻¹ in the spectral range from 11,100 to 13,800 cm⁻¹, we have determined the binary absorption coefficient. These extrapolated measurements are compared with calculations based on a model that was obtained by using simple computer codes and lineshape profiles. In view of the very weak absorption of the second overtone band, we find the agreement between results of the model and experiment to be reasonable.     

Planetesimal dissolution in the envelopes of the forming,giant planets

We have assessed the ability of planetesimals to penetrate through the envelopes of growing giant planets that form by a “core-instability” mechanism. According to this mechanism, a core grows by the accretion of solid bodies in the solar nebula and the growing core becomes progressively more effective in gravitationally concentrating gas from the surrounding solar nebula in an envelope until a “runaway” accretion of gas occurs. In performing this assessment, we have considered the ability of gas drag to slow down a planetesimal; the effectiveness of gas dynamical pressure in fracturing and ultimately finely fragmenting it; the ability of its strength and self-gravity to resist such fracturing; and the degree to which it is evaporated due to heating by the surrounding envelope, including shock heating that develops during the supersonic portion of its trajectory. We also consider what happens if the planetesimal is able to reach the core at free-fall velocity and the ability of the envelope to convectively mix dissolved materials to different radial distances. These calculations were performed for various epochs in the growth of a giant planet with the model envelopes derived by Bodenheimer and Pollack (1986,67, 391–408). As might have been anticipated, our results vary significantly with the size of the planetesimal, its composition, and the stage of growth of the giant planet and hence the mass of its envelope. Over much of the growth phase of the core, prior to its reaching its critical mass for runaway gas accretion, icy planetesimals less than about 1 m in size dissolve in the outer region of the envelope, ones larger than about 1 m and smaller than about 1 km dissolve in the middle region of the envelope, ones larger than 1 km either reach the core interface or dissolve in the deeper regions of the envelope. Similarly rocky planetesimals smaller than about a kilometer dissolve in the middle portion of the envelope, while larger ones can penetrate more deeply. Furthermore, the convection zones of the envelopes during this stage are confined to localized regions and hence dissolved materials experience little radial mixing then. Thus, if much of the accreted mass is contained in planetesimals larger than about a kilometer, the critical core mass for runaway accretion is not expected to change significantly when planetesimal dissolution is taken into account. After accretion is terminated and the planet contracts toward its present size, the convection zone grows until it encompasses the entire envelope. Therefore, dissolved material should eventually become well mixed through the envelope. We proposed that the envelopes of the giant planets should contain significant enhancements above solar proportions in the abundances of virtually all elements relative to that of hydrogen, with the magnitude of the enhancement increasing approximately linearly with the ratio of the high Z mass to the (H, He) mass for the bulk of the planet. This prediction is in accord both qualitatively and quantitatively with the systematic increase in the atmospheric C/H ratio from Jupiter to Saturn to Uranus and Neptune and semiquantitatively with the results of recent interior models of the giant planets. It is not clear whether it is consistent with the abundances of H₂O and NH₃ in the atmospheres of some of the outer planets. Finally, the complete reduction of some dissolved materials, especially C containing compounds, is expected to consume some of the H₂ in the envelopes. Consequently, the He/H₂ ratios in the atmospheres of Uranus and Neptune may be slightly enhanced over the solar ratio. We estimate that the He/H₂ ratios for Uranus' and Neptune's atmospheres should be about 6 and 15% larger, respectively, than the solar ratio.     

Spectra of simulated lightning on Venus,Jupiter, and Titan

Laser-induced plasmas in various gas mixtures were used to simulate lightning in other planetary atmospheres. This method of simulation has the advantage of producing short-duration, high-temperature plasmas free from electrode contamination. The laser-induced plasma discharges in air are shown to accurately simulate terrestrial lightning and can be expected to simulate lightning spectra in other planetary atmospheres. Spectra from 240 to 880 nm are presented for simulated lightning in the atmospheres of Venus, Earth, Jupiter, and Titan. The spectra of lightning on the other giant planets are expected to be similar to that of Jupiter because the atmospheres of these planets are composed mainly of hydrogen and helium. The spectra of Venus and Titan show substantial amounts of radiation due to the presence of carbon atoms and ions and show CN Violet radiation. Although small amounts of CH₄ and NH₃ are present in the Jovian atmosphere, only emission from hydrogen and helium is observed. Most differences in the spectra can be understood in terms of the elemental ratios of the gas mixtures. Consequently, observations of the spectra of lightning on other planets should provide in situ estimates of the atmospheric and aerosol composition in the cloud layers in which lightning is occuring. In particular, the detection of inert gases such as helium should be possible and the relative abundance of these gases compared to major constituents might be determined.     

Modelling the atmospheric CO2 10-μm non-thermal emission in Mars and Venus at high spectral resolution

A study of the CO₂ atmospheric emissions at 10-μm in the upper atmospheres of Mars and Venus is performed in order to explain a number of ground-based measurements of these emissions recently taken at very high spectral resolution in both planets. The measurements are normally used to derive atmospheric temperatures and winds, but uncertainties on the actual emission layers were so far a serious drawback for their correct interpretation. The non-LTE models used for Mars and Venus in the present analysis are entirely similar in order to perform consistent comparisons between the two planets. In particular, the same scheme of CO₂ states and ro-vibrational bands are used, with similar assumptions on collisional routes and rate coef?cients, and also the same radiative transfer approximations. The emissions at 10-μm are produced in both atmospheres by the same excitation mechanism: radiative pumping of the CO₂(00⁰1) vibrational state by direct solar absorption(at 4.3 μm) and indirect absorption (at 2.7 μm, followed by collisional quenching). The computed radiances are specially strong in the upper mesosphere and lower thermosphere of the two planets during maximum solar illumination, producing a population inversion in such conditions with the lower states of the bands, the CO₂ (10⁰0) and CO₂(02⁰0). We obtained that other population inversions are also possible, involving higher energy CO₂ states. The larger solar ?ux available on Venus is found to produce larger vibrational populations and stronger emissions than equivalent atmospheric layers on Mars, in agreement with the observations. A number of perturbation studies were used to determine the exact emission altitudes, or weighting function peaks, for usual nadir sounding. The sensitivity of the emission to non-LTE model uncertainties and to atmospheric variations in temperature and CO₂ density is also presented. The dependence with the solar zenith angle and with the emission angle, as obtained with this model, could also be useful for guiding future observations.