We present the first three-dimensional model simulations of ozone on Mars. The model couples a state-of-the-art gas-phase photochemical package to the general circulation model developed at Laboratoire de Météorologie Dynamique (LMD). The results do not contradict the classical picture of a global anticorrelation between the ozone (O3) and water vapor columns. However, the quantitative approach shows significant departures from this relationship, related to substantial orbital variations in the O3 vertical distribution. Over the period Ls = 180°–330°, low-latitude to midlatitude O3 is essentially confined below 20 km, has a weak diurnal cycle, and is largely modulated by topography. During the rest of the year (Ls = 330°–180°) the model predicts the formation of an O3 layer at 25–70 km altitude, characterized by nighttime densities about one order of magnitude larger than during the day. Throughout the year, high-latitude O3 peaks near the surface and reaches maximum integrated amounts (∼40 μm-atm) in the winter polar vortex, with considerable (30 to 50%) dynamically induced day-to-day variations. The most stringent comparison to date with O3 observational data reveals contrasted results. A good quantitative agreement is found in the postperihelion period (Ls = 290°–10°), but the model fails to reproduce O3 columns as large as those measured near aphelion (Ls = 61°–67°). Current uncertainties in absorption cross sections and gas-phase kinetics data do not seem to provide credible explanations to explain this discrepancy, which may suggest the existence of heterogeneous processes.
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 Ozone (O3) was first observed on Mars by the Mariner 7 and 9 ultraviolet (UV) spectrometers in 1969 and 1971–1972 [Barth and Hord, 1971; Barth et al., 1973]. Direct measurements of ozone have then been performed from the Mars 5 and Phobos 2 Russian spacecraft [Krasnopolsky and Parshev, 1979; Blamont and Chassefière, 1993], from Earth [Espenak et al., 1991], or from the Hubble Space Telescope (HST) [Clancy et al., 1996, 1999]. Since the first modeling studies carried out in the early 1970s [Parkinson and Hunten, 1972; McElroy and Donahue, 1972], it has been known that the local amount of ozone on Mars is controlled by the abundance in odd hydrogen species (H, OH, HO2 − HOx family) produced by the photolysis of water vapor and its reaction with O(1D). HOx compounds have also been recognized to be responsible for the apparent stability of the Mars CO2 atmosphere, by a process that involves the OH-catalyzed recycling of CO into CO2. Although the more stable hydrogen species H2O2 has recently been detected on Mars [Clancy et al., 2004; Encrenaz et al., 2004], HOx radicals have never been directly measured. Their abundance must be calculated from the amount of water vapor, which has been shown to vary considerably with latitude and season [Jakosky and Farmer, 1982; Smith, 2002]. This large variability might explain the difficulties encountered by globally averaged chemical models to reach a proper balance between the CO2 production and loss rates [see, e.g., Atreya and Gu, 1994].
 Another option is to use ozone, the most active species measured in the Martian atmosphere, as a chemical tracer of the odd hydrogen photochemistry. The abundance of O3 being so tightly linked to those of HOx species, the comparison between O3 measurements and model simulations provides extremely valuable information on our quantitative understanding of the Martian photochemistry. This approach has been used in a number of one-dimensional (1-D) modeling studies [e.g., Krasnopolsky, 1993, 2003b; Nair et al., 1994], which showed that a simultaneous agreement between the calculated and observed values of O3, CO, and O2 was difficult to achieve when using the standard gas-phase reaction rates. As underlined in these studies, however, one-dimensional models have their own limitations. Although these models are very useful to estimate the globally averaged distribution of chemical species as a function of height, they cannot represent the dramatic latitudinal variations in the distribution of trace species caused by the usually strong pole-to-pole gradient of atmospheric temperature and water vapor. The redistribution of chemical species by horizontal transport is ignored, and a highly uncertain eddy diffusion coefficient has to be used to represent the vertical transport and mixing. The only two-dimensional (2-D) simulation, published by Moreau et al. , provided a better description of the interactions between dynamics, radiation, and chemistry, although the model did not include a consistent representation of the water cycle nor a treatment of the dynamics near the surface, where the topographical effects are important. Furthermore, by nature a detailed treatment of the diurnal cycle of chemical species cannot be properly achieved by a 2-D zonally averaged model.
 We present here the first general circulation model simulations of the Martian photochemistry. Three-dimensional (3-D) models have a number of advantages over 1-D and 2-D models to represent the chemistry. First, atmospheric transport is fundamentally three-dimensional, and only 3-D models can properly calculate its effects on the distribution of chemical species. Another crucial point is that general circulation models (GCM) are now able to provide a realistic description of the variations in water vapor at all spatial scales and timescales [Richardson and Wilson, 2002; F. Montmessin et al., The origin and role of water ice clouds in the Martian water cycle as inferred from a general circulation model, submitted to Journal of Geophysical Research, 2004 (hereinafter referred to as Montmessin et al., submitted manuscript, 2004)]. Clancy and Nair  illustrated the necessity of a realistic description of the seasonal water cycle to fully understand the variations in the composition of the Martian atmosphere. Diurnal cycles of temperature and insolation can also be accurately described by GCMs, as well as the effects of topography. All of these factors allow us to make much more stringent comparisons between 3-D model results and coincident measurements.
 The aim of this paper is to provide a three-dimensional view of our current understanding of the ozone chemistry on Mars using a state-of-the-art chemical model. We will also compare our results to available O3 measurements in order to reevaluate our level of quantitative understanding of the Martian photochemistry. Note that we chose to initialize the long-lived species CO, O2, and H2 to their observed values and to focus only on the fast photochemistry, after a relatively short (two Martian years) simulation. Therefore the classical problem of the stability of the Mars atmosphere will not be addressed here and will be the subject of a forthcoming study.
2. Model Description
 The new chemical model employed in this work is an adaptation of the chemical package used in the Reprobus model developed earlier for the terrestrial stratosphere [Lefèvre et al., 1994, 1998]. It provides a comprehensive description of the oxygen, hydrogen, and CO chemistries on Mars and is implemented as a chemical subroutine into the GCM that has been in development since the early 1990s at Laboratoire de Météorologie Dynamique (LMD). The main characteristics of the chemical routine, the LMD GCM, and the coupling method are described below.
2.1. Absorption Cross Sections and Photolysis
 For each photolyzed species we employed the most recent absorption cross sections or the data recommended by Sander et al.  commonly used in the modeling of the Earth atmospheric chemistry (Table 1).
Table 1. Photolitic and Chemical Reactions With Their Rate Coefficients and References Used in the Modela
Units are s−1 for photolysis reactions, cm3 s−1 for two-body reactions, and cm6 s−1 for three-body reactions. Photolysis rate coefficients are given at 10 km for the following conditions: solar zenith angle of 60°, sun distance of 1.52 AU, pground = 6 hPa, midlatitude temperature profile, O3 column of 1 μm-atm, τdust = 0.2. Three-body reaction rates have been multiplied by 2.5 to account for the higher efficiency when the third body is CO2. k0 and k∞ are the low- and high-pressure rate coefficients, respectively, for three-body reactions.
 For CO2, shortward of 167 nm, where O(1D) atoms are produced, cross sections are taken from Yoshino et al. [1996a]. At longer wavelengths we used the recent measurements performed at high resolution by Parkinson et al. . The measurements were made at 295 K and 195 K and are available at a wavelength interval of 0.001 nm. At 295 K, data are available up to 200 nm, where a flattening of the measured cross section is noticed. This may indicate the growing relative influence of Rayleigh scattering in this wavelength region, as mentioned by Shemansky . To obtain the CO2 absorption cross section in this wavelength domain, we subtracted the Rayleigh scattering cross section from the measured cross sections using the expression given by Atreya and Gu . At 195 K, Parkinson et al.  data are available only up to 192.5 nm. Beyond this wavelength we extrapolated the cross sections up to 200 nm from the values at 295 K by assuming the same temperature dependence as measured by Lewis and Carver  in the 192–197 nm interval. Finally, beyond 200 nm the obtained CO2 cross sections at 295 K and 195 K were extrapolated by linear decrease with the logarithm of the cross section up to 210 nm. At this wavelength our cross-section value at 195 K (3 × 10−26 cm2) is identical to the value calculated by Atreya and Gu .
 Photochemical models of the Mars atmosphere are very sensitive to the values of the absorption cross sections of H2O, in particular beyond 180 nm, where radiation can penetrate low enough to photolyze the larger water vapor amounts located in the first 30 km above the surface. We use the new laboratory measurements of the H2O ultraviolet cross sections performed by Cheng et al.  over the 140–196 nm spectral range. Data are in relatively good agreement with the cross sections by Thompson et al.  generally used in previous studies of the Mars photochemistry but have a largely improved spectral resolution (0.2 nm). H2O cross sections shortward of 140 nm are from Yoshino et al. [1996b].
 Using the absorption cross sections described above, photolysis rate coefficients (J values) are calculated by the Tropospheric Ultraviolet and Visible (TUV) model [Madronich and Flocke, 1998], initially developed to compute the spectral irradiance, actinic flux, and photodissociation in the terrestrial atmosphere. We have adapted TUV to the Martian atmosphere by defining CO2, O2, H2O, and O3 as the main absorbers of the incident radiation. Solar flux at 1 AU is taken from the high-resolution (0.15 nm) data obtained by the SUSIM instrument [VanHoosier et al., 1988] from 120 to 400 nm and given by Neckel and Labs  from 400 to 850 nm. Scattering and absorption through the atmosphere are treated in spherical geometry by the multistream discrete ordinate method of Stamnes et al. . We have adapted the wavelength resolution to describe accurately all of the spectral features in the solar flux or the absorption cross sections: 5 nm in the Chappuis band of O3, 0.5 nm in the CO2 band shortward of 175 nm and the Hartley band of O3, 0.1 nm in the Lyman α region, and 0.01 nm in the CO2 band longward of 175 nm and in the Schumann-Runge bands of O2. Temperature dependence of the absorption cross sections is taken into account, as is Rayleigh scattering.
 Our calculations also include the absorption and scattering of radiation by dust in the atmosphere. We assumed the vertical optical depth of dust in the UV to be approximately τdust = 0.2 on a reference pressure level of 6 hPa. Values of up to τdust = 0.3 are reached in regions of low surface elevation. This is typical of minimum dust-loading conditions, as measured, for instance, by Phobos 2 [Chassefière et al., 1995]. We set the dust UV single-scattering albedo to ω = 0.6 [Pang and Ajello, 1977] and set the scattering asymmetry parameter to g = 0.7, as in the work of Krasnopolsky . A wavelength-independent value of 0.015 is adopted for the Martian surface albedo, as suggested by the UV observations of Clancy et al. .
 In order to save computational resources, the photolysis rates are calculated off-line and are stored in a four-dimensional lookup table as a function of the overhead CO2 column, the overhead O3 column, the solar zenith angle, and the temperature. The vertical resolution of the table is about 1 km and extends down to a CO2 column of 3.7 × 1023 cm−2 (10 hPa), in order to cover the large surface pressures of the northern hemisphere summer. Different O3 columns ranging from 0.1 to 50 μm-atm are accounted for in the calculations. Solar zenith angle (SZA) is tabulated from 0 to 95°, with a resolution of 1° beyond 90° to describe the rapidly varying photolysis rates at sunrise and sunset. The temperature dependence of the absorption cross sections is taken into account by using different climatological temperature profiles from the GCM as an input for the photolysis model. Their surface value ranges from 190 K (corresponding to sunlit high latitudes in winter) to 260 K (southern hemisphere summer, noon). The photolysis rates are calculated by TUV and are stored in the table for each of these temperature profiles.
2.2. Gas-Phase Chemistry
 In this first study the chemical model computes the three-dimensional distribution of 12 constituents (O(1D), O, O2, O3, H, OH, HO2, H2, H2O, H2O2, CO, and CO2) using the 42 photolytic or chemical reactions listed in Table 1. Most of the rates and branching ratios that we have adopted are those recommended by the Jet Propulsion Laboratory 2003 compilation [Sander et al., 2003]. For reaction c08, we use the rate measured by Christensen et al. , which leads to a much better agreement between observed and simulated profiles of H2O2 in the terrestrial stratosphere than with the previous recommendations. The rate for the loss mechanism of CO by reaction with OH is from McCabe et al. . As in all of the previous chemical models of the Mars atmosphere, we also increased the rates of the reactions tabulated with N2, O3, or Ar as a third body. We chose a factor of 2.5 to account for the greater efficiency of CO2, identical to the value used by Nair et al. .
 For long-lived species (O2, H2, H2O, CO) the rate of chemical change is solved using the implicit method described by Shimazaki , which we include in an iterative procedure to ensure mass conservation. This technique is also applied to H2O2, which has a long lifetime in darkness, and to the chemical families Ox and HOx, which we define as Ox = O + O3 and HOx = H + OH + HO2.
 During the day the Ox family has a short lifetime in the lower atmosphere (less than half an hour at the hygropause level), and we use a chemical time step of 10 min. Within the Ox and HOx families, only the members O3, OH, and HO2 are assumed to be in photochemical equilibrium. The species O and H, which have a long lifetime at high altitudes, are derived from the concentration of the family and the calculated ratios , , and . O(1D) is assumed to be in photochemical equilibrium at all heights. At night, photolysis processes vanish, and the hypothesis of photochemical equilibrium does not hold for O3. In these conditions, O and O3 are integrated separately, but a short time step of 10 min is conserved to describe properly the fast conversion of O into O3 at sunset, especially in the lower atmosphere. We also use a simplified treatment of the nitrogen chemistry in order to account for the reaction d03 breaking the O-O bond via NO. As pointed out by Krasnopolsky , this reaction is an indirect source of Ox and increases the ratio in the lowermost atmosphere. The NOx = NO + NO2 mixing ratio is set to 0.6 ppbv, as obtained below 30 km by Nair et al.  with their comprehensive model of the nitrogen chemistry. NO and NO2 are then derived from the justified hypothesis of photochemical equilibrium within the NOx family.
 We consider the results presented in this paper as a baseline case which only takes into account chemical processes that are well identified and supported by reasonably accurate kinetics data. The effects of more speculative processes, such as heterogeneous reactions involving HOx species on airborne particles or chemical interactions between the atmosphere and the regolith, are, for the present time, ignored in these first simulations.
2.3. Coupling to the LMD General Circulation Model
 A recent description of the LMD general circulation model is given by Forget et al. . In the updated version used here, the Martian topography is based on the elevations measured by the Mars Orbiter Laser Altimeter (MOLA) [Smith et al., 1999], and the model is vertically extended up to 120 km altitude using non-LTE radiative transfer calculations [Angelats-i-Coll et al., 2004; F. Forget et al., manuscript in preparation, 2004]. The amount of airborne dust used in the GCM is prescribed and varies with latitude, altitude, and solar longitude. This “dust scenario” was designed by Forget et al.  in order to match most of the thermal profiles observed by the Radioscience instrument [Hinson et al., 1999] and the Thermal Emission Spectrometer (TES) [Smith et al., 2001] on board Mars Global Surveyor. For the moment, the evolving dust loading used in the GCM differs from the constant dust amount considered in the photochemical module, but both data sets will be unified in the next version of the coupled model. Note that the effect of a varying dust opacity on photolysis rates and ozone is later examined in the present work.
 The GCM incorporates a comprehensive physical modeling of the Martian water cycle using a microphysical scheme to describe the sublimation and condensation processes as well as the sedimentation of water ice particles in the atmosphere. This new version of the GCM water cycle is described in detail by Montmessin et al. (submitted manuscript, 2004). Water ice particles are transported by the model winds, as is water vapor and all of the chemical species. Transport of tracers is calculated using a second-order finite volume scheme with slope limitation [Van Leer, 1977; Hourdin and Armengaud, 1999]. Turbulent mixing of chemical species at the subgrid-scale is also taken into account from the turbulent kinetic energy diagnosed by the model in each grid box (see Forget et al. [1999, and references therein] for a complete description of the scheme). In addition, a standard energy-conserving convective adjustment scheme rapidly mixes heat, momentum, and tracers in convectively unstable layers.
 At each model time step the CO2, H2O, and other chemical fields are exchanged between the GCM and the chemical routine to achieve a fully interactive coupling between dynamics, radiation, water cycle, and chemistry: every 10 min the photochemical routine is called to calculate the atmospheric chemical composition in all GCM grid cells. Chemical reaction rates are calculated using the GCM temperature and pressure profiles. For the photodissociation rates, the CO2 and O3 vertical columns are first computed for all the grid points located in sunlight. The actual J values used in the chemistry are then interpolated in CO2, O3, and SZA within the lookup table. Finally, the photolysis rates obtained at 1.52 AU are scaled to their appropriate value according to the exact Sun-Mars distance calculated by the GCM. The ∼40% variation in solar flux during the Martian year, which results from the large eccentricity of the Mars orbit, is therefore taken into account in our simulations.
 The condensation of hydrogen peroxide (H2O2) is also taken into account by means of a simplified scheme that compares the H2O2 pressure to its vapor pressure at saturation [Lindner, 1988] and transfers the excess quantity to the level below. If saturation occurs near the ground, H2O2 is deposited on the surface as H2O2 ice. For the moment, sublimation of this surface deposit is not implemented in the model.
 The coupled model was run on 32 vertical levels with a horizontal resolution of 64 longitudes by 48 latitudes (5.625° × 3.75°). The initial state includes a water cycle fully established after appropriate spin-up time and uniform mixing ratios for the well-mixed species O2 (1.3 × 10−3 [Owen et al., 1997]), CO (8 × 10−4 [Lellouch et al., 1991; Krasnopolsky, 2003a]), and H2 (1.5 × 10−5 [Krasnopolsky and Feldman, 2001]). The results presented here were obtained after two Martian years of simulation.
3.1. Ozone Total Column
 Ozone is produced by the photolysis of CO2 and O2, followed by the recombination of the product O with O2. It is destroyed by odd hydrogen catalytic cycles that effectively control the local amount of ozone on Mars. An anticorrelation between the abundances of water vapor, which is the source of HOx, and ozone is therefore expected in the Martian atmosphere.
 The overall behavior of the ozone seasonal evolution calculated by the model may be examined in Figure 1, showing the zonally averaged ozone column as a function of latitude and solar longitude (Ls). Note that the values are here averaged over 24 hours and are therefore a mean of daytime and nighttime abundances. Compared to Earth, the extremely strong spatial and temporal variations in ozone are a striking feature of the Martian atmosphere: there is a factor of about 100 between the largest ozone columns, calculated at high latitudes in winter, and the smallest amounts, obtained in the southern hemisphere around perihelion and summer solstice. The O3 column evolution can be related to the water vapor abundance calculated by the model, also shown in Figure 1. A detailed discussion of the results regarding the water cycle in the LMD GCM is given by Montmessin et al. (submitted manuscript, 2004), who note a good quantitative agreement with the measurements of the water vapor column performed by TES on board Mars Global Surveyor [Smith, 2002]. At first glance the anticorrelation between the ozone and water vapor columns seems clearly visible. At high latitudes of both hemispheres the ozone column is maximum in winter, when condensation on polar caps suppresses most of the atmospheric water vapor. Polar ozone is minimum in summer, indicating an efficient O3 destruction by the HOx radicals released from the large amounts of water vapor and sunlight. However, the O3 polar minimum also presents a strong north/south asymmetry: the ozone abundance at high latitudes in southern summer is smaller than that in northern summer by a factor of 4 (∼0.5 μm-atm and ∼2 μm-atm, respectively), despite a smaller water vapor abundance in southern summer. This departure from the O3-H2O anticorrelation is related to differences in the H2O vertical distribution. The same reason explains the O3 column orbital cycle in the equatorial region, where there is about three times more ozone shortly before aphelion (∼3 μm-atm at Ls = 60°) than at perihelion (∼1 μm-atm at Ls = 250°), although the water column amount is similar in both cases (15 pr-μm).
 Thus it appears that the picture of a global O3-H2O anticorrelation is strictly verified only for a given solar longitude. When considering a single latitude band over the Martian year, the O3 column may show little correlation with the H2O column, especially at low latitudes. The sign of the correlation may even reverse and become positive if one compares the O3 and H2O columns for the same season of different hemispheres (i.e., the northern and southern polar winters). These differences in the O3-H2O relationship are related to variations with Ls in the altitude of water vapor saturation, which will be discussed in the next sections. They must be kept in mind when analyzing measurements of the vertically integrated amounts of O3 and H2O taken at different times (Ls) of the Martian year.
3.2. Ozone Vertical Distribution
 The photochemical theory predicts substantial changes in the vertical distribution of low-latitude to midlatitude ozone on Mars. Using a one-dimensional model forced by a simple stepwise annual cycle of the water vapor profile, Clancy and Nair  showed that the ozone variations above 10 km were essentially driven by the annual cycle of the hygropause altitude. This process is confirmed by our three-dimensional simulation, which predicts a smoothly varying evolution of the water vapor vertical distribution during the Martian year. Figure 2 shows the annual cycles of the diurnally averaged H2O and O3 profiles calculated by the model at the equator as a function of solar longitude. Above 20 km the H2O vertical distribution is clearly determined by the variations in temperature, in response to the evolution of dust and solar flux along the Mars orbit. Around aphelion (Ls = 60°–120°) the cold and dust-free atmosphere leads to a low saturation altitude for water vapor (10–15 km), with rapidly decreasing mixing ratios above the hygropause. Immediately after aphelion the water saturation altitude shows a steady increase until Ls = 250° at perihelion. In the warmer and dustier conditions of this time of the year, water vapor saturation occurs in the model above 40 km altitude. We note that the seasonal evolution of the water condensation level calculated by the model at the equator is in excellent agreement with the TES observations [Smith, 2002]. The ∼30 km rise of the hygropause that occurs from perihelion to aphelion causes very large annual variations of the water content above 20 km, with a difference of two to three orders of magnitude at the equator between the two extreme points of the orbit. In the sunlit conditions of low latitudes to midlatitudes this substantial change has strong implications on the amount of odd hydrogen produced by the photolysis of H2O. HO2 is an indirect product of the H2O photolysis. As shown in Figure 2, the HO2 vertical distribution is closely correlated to H2O in the lower atmosphere. The largest HO2 abundance (several ppbv) calculated by the model occurs around perihelion in an altitude layer between 20 and 50 km. This is where the product of the water vapor concentration and its photolysis rate J, related to the intensity of the UV flux, reaches its maximum value. There is also some indication of cross-hygropause transport of HO2 at Ls = 270°–320°. The photochemical lifetime of the HOx family is indeed of the order of a few days at 40–50 km. In the case of ascending motions near the hygropause level the upward transport of increased HOx coming from the lower atmosphere may affect the photochemistry at levels located above the H2O saturation altitude.
 In Figure 2 the ozone profile at the equator responds quickly to the annual variations in HOx. From Ls = 0° to Ls = 180° the 24 hour averaged ozone mixing ratio shows a layer of a few tenths of ppmv between 40 km and 80 km, well anticorrelated with the H2O abundance calculated during this cold and dry period. Starting at Ls = 150° and as Mars approaches its perihelion, more water vapor is allowed to reach high altitudes. A gradual decrease in ozone is clearly visible and propagates upward until Ls = 250°, when the hygropause reaches its highest level. During this period the massive release of odd hydrogen species leads to a dramatic ozone loss between 30 and 80 km altitude. The ozone layer that was present in this altitude range almost entirely disappears and is replaced by an absolute O3 minimum, with mixing ratios lower by three orders of magnitude compared to the aphelion season. Results plotted in terms of number density reveal, in daily average, two distinct altitude regions:
 1. Below 20 km the O3 “surface layer” shows a weak annual cycle that slowly evolves as a function of the available water vapor and the heliocentric distance. The maximum thickness of this layer is computed shortly before aphelion (Ls = 60°) and at perihelion (Ls = 250°). Near the equator this is when the product of the low atmosphere H2O density and the solar flux intensity is minimum. Interestingly, the stronger solar flux at perihelion is compensated by a decreased near-surface H2O, resulting in similar O3 amounts for both periods.
 2. Above 20 km the O3 “aphelion layer” extends up to ∼70 km but exists for only about half of the Martian orbit (Ls = 330°–180°), centered on aphelion. This layer disappears almost entirely for the rest of the year. The orbital variability of the layer, where the peak densities are comparable to those calculated in the first 10 km above the surface, is clearly responsible for the factor of ∼3 increase in the O3 column that is simulated at low latitudes from the perihelion to the aphelion season (Figure 1).
 This process also explains the differences between our results and those calculated by the two-dimensional chemical model of Moreau et al. , who found almost no variability with Ls in the low-latitude O3 column. In their simulation, Moreau et al.  used prescribed water vapor fields designed to reproduce the Viking measurements [Jakosky and Farmer, 1982], assuming a H2O vertical decrease with a fixed scale height over the Martian year. Clearly, this assumption does not hold during the whole annual cycle, and it is likely that the amplitude of the variation in the H2O saturation altitude was underestimated. This emphasizes the advantage of the interactive coupling between the chemistry and a physically based water cycle for more accurate simulations of ozone on Mars, under the necessary condition that the H2O amounts calculated by the model are in good quantitative agreement with the observations.
 The ozone annual cycle obtained in both layers defined above compares favorably with the ozone profiles calculated at Ls = 60° and Ls = 240° by Clancy and Nair . As seen in Figure 2d, the peak O3 density computed in the middle atmosphere layer near aphelion is about 0.4 × 1010 cm−3, which is in rather good agreement with their 1-D study. The altitude of the peak is higher by about 20 km in our simulation. This results from the higher hygropause and weaker H2O vertical gradient above the saturation altitude in the 3-D model. In terms of the O3 vertical column the factor of ∼3 increase that we obtain at low latitudes from perihelion to aphelion is in excellent agreement with Clancy and Nair .
3.3. Ozone Diurnal Cycle
 Previous one-dimensional modeling studies have shown that ozone may be highly variable during the Martian day [Krastitsky, 1978; Shimazaki, 1981; Nair et al., 1994]. In our model the O3 column is on average larger during nighttime than during the day. However, the amplitude of this diurnal cycle varies largely with latitude and solar longitude. To illustrate this, Figure 3 displays the instantaneous total O3 field calculated by the model in four Martian seasons, with local noon at longitude 0. At northern spring equinox (Ls = 0°), no O3 diurnal cycle is apparent at high latitudes, whereas the sunlit part of the 40°N–40°S latitude band is characterized by significantly lower O3 values. In this region the O3 columns calculated in daylight are about four times smaller (∼0.5 μm-atm versus ∼2 μm-atm) than those obtained at night. The O3 column distribution also shows a substantial modulation by topography: large O3 columns are calculated in sunlight from the Chryse Planitia low plain to Valles Marineris, whereas strong O3 reductions are associated with elevated regions such as the Tharsis Ridge and Alba Patera. This indicates a major contribution to the column of the O3 surface layer. Although there is some indication of a late morning secondary maximum of photochemical origin at 30°S, the variations in the O3 sunlit distribution are dominated, at this season, by the topography. During the night, no significant O3 variation with local time is apparent. The synoptic map for northern summer (Ls = 90°) shows globally larger ozone columns, with a factor of about two between the nighttime values (∼4 μm-atm) and the more apparent late morning maximum (∼2μm-atm). Slightly smaller O3 columns are calculated at sunrise and in the late afternoon. The topographic structures are also less visible in the O3 field. Only Alba Patera appears at sunrise as a ∼50% decrease in the O3 column, as well as the Hellas basin, where the extreme surface pressure favors the accumulation of O3 near the ground. Maximum O3 amounts fill the entire polar night region. The northern fall equinox (Ls = 180°) O3 distribution is similar to what is obtained for spring. Again, the daytime O3 column is far from being uniformly distributed owing to variations in surface elevation. Finally, the results for northern winter (Ls = 270°) show much less ozone than for all other seasons at all latitudes southward of 40°N. No diurnal cycle is seen, and the O3 column distribution reflects entirely the variations in topography, suggesting a maximum contribution of the O3 surface layer to the total column. As in southern winter, the largest O3 amounts are computed in the polar night region, with a rather homogeneous distribution.
 An example of the diurnal variation of ozone along the vertical is given in Figure 4, showing the variation with local time of the O3 profile at the equator, for four different seasons. As already seen in Figure 2, during the first two seasons (Ls = 0°–30° and Ls = 60°–90°) the ozone density profile is characterized by a double-layer structure, peaking near the ground for the surface layer below 20 km and located between 25 and 70 km at night in the middle atmosphere layer. The middle atmosphere O3 layer is maximum in the aphelion season, is vanishing at the northern fall equinox, and has totally disappeared by the perihelion season. In terms of diurnal variation the surface and altitude O3 layers exhibit very different behavior:
 1. Below 20 km the available amount of O is small, and the nighttime conversion of O to O3 does not lead to a large variation with local time. In the model the largest daytime O3 variation is actually found in the first ∼3 km above the Martian surface. At these levels a considerable increase in temperature (+60 K) may occur between sunrise and afternoon. At sunrise the low atmospheric temperatures favor reaction d03, converting NO into NO2. Subsequent photolysis of NO2 produces O atoms and an early morning O3 peak. Then, the rapid warming of the atmosphere slows down the reaction a01, producing ozone, and may even inhibit the formation of the noon O3 maximum that is calculated at higher levels in the model. The combination of both effects leads to a daytime maximum occurring at about 1000 LT, when the O3 column is vertically integrated. At night, O3 is affected only by the slow reaction c15 and can be considered as a quasi-passive tracer in the whole 0–20 km layer.
 2. Above 20 km the amount of O rapidly increases with altitude. The fast conversion between O and O3 induces a significant diurnal cycle in the O3 layer that forms in the middle atmosphere between Ls = 0° and Ls = 180°. During this period the nighttime O3 number density is comparable to what is obtained near the surface but is about one order of magnitude smaller during the day (∼0.1 × 1010 cm−3 versus ∼1 × 1010 cm−3). Most of the diurnal variation observed in the total O3 column can therefore be attributed to the O3 diurnal variation in the middle atmosphere, since the thickness of the O3 surface layer does not undergo much change during the Martian day. As seen earlier, the O3 layer at 25–70 km also shows considerable variations with Ls, and this is the main cause for the seasonal change in the O3 column diurnal cycle: at the equinoxes the amplitude of the diurnal cycle in the middle atmosphere is maximum, leading to a substantial difference between the daytime and nighttime O3 columns (Figures 3a and 3c). In contrast the absence of any apparent diurnal cycle in the total O3 field calculated near perihelion (Figure 3d) is a direct consequence of the disappearance of the O3 middle atmosphere layer.
3.4. Ozone at Polar Latitudes
 The maximum abundances of O3 are observed at polar latitudes, where O3 also exhibits the greatest seasonal variability. The O3 behavior predicted by our model in these regions is discussed here more specifically.
Figure 5 displays the calculated seasonal cycle of the ozone column zonally averaged at 70°N and 70°S. The overall seasonal evolution is similar in the two hemispheres. It can be described by a O3 minimum in summer, a rapid buildup after fall equinox, maximum values in winter, and a decline in spring. In the southern hemisphere the O3 column at 70°S is greatest at winter solstice (Ls = 90°) and reaches a maximum value of 27 μm-atm. In the northern hemisphere, O3 continues to increase after solstice to reach maximum values approaching 40 μm-atm at Ls = 320°. This mean behavior is accompanied by variations at short timescales that are particularly apparent during the northern hemisphere winter and spring. According to the model, the late winter O3 at 70°N can easily vary by ±10 μm-atm (i.e., 30 to 50%) in a 24 hour interval. Figure 6 illustrates the origin of this variability. The synoptic maps of the O3 column plotted at 12 hour intervals from Ls = 350° to Ls = 353° exhibit a strong O3 maximum confined inside the polar vortex, with maximum values of about 40 μm-atm. At this time of the year the ozone column has already started to decrease at 70°N (Figure 5) but shows a maximum variability. A striking feature of the O3 geographical distribution is the considerable day-to-day changes associated with the dynamical disturbances of the polar vortex. Baroclinic waves have a maximum activity in late winter and spring. This results in rapidly evolving distortions of the polar vortex edge that are easily identifiable by the steep O3 gradients. Note that although solar light has almost reached the pole at this time of the year, there is no apparent diurnal cycle in the O3 column field. Wintertime polar O3 is indeed essentially confined near the surface (Figure 7), where the concentration of O atoms is low and does not induce O3 variations at sunrise and sunset. Furthermore, at Ls ≃ 350° the HOx production at 70°N is virtually zero: as shown in Figures 1 and 7a, the cold polar vortex remains isolated from the midlatitude air and is still extremely dry. Less than 1 pr-μm total H2O is computed by the model, with only ∼1 ppmv at the surface. Note that the short duration of the day and the large SZAs do not allow significant H2O photolysis anyway. In these conditions, HOx may be produced in the model by reaction b03:
However, O(1D) is produced by O3 photodissociation, which is itself attenuated by the significant O3 opacity. In accordance with Lindner , dust also contributes to reduce largely the O3 photolysis at large SZA, even in the relatively clean conditions assumed in the model (τdust = 0.2). Thus O3 can be considered as a quasi-passive tracer inside the polar vortex at least until spring equinox. Its variations over short timescales at latitudes close to the vortex edge may be entirely attributed to variations in the shape of the polar vortex.
 Although similar in character, the behavior of polar ozone also shows some asymmetry between the northern and southern hemispheres. In winter the day-to-day variability is much less at 70°S than at 70°N. This can be attributed to the weaker wave activity of the southern high latitudes. Ozone is a good tracer of dynamics at this time of the year, and from Figure 1 it is evident that the vortex edge has a smooth evolution in latitude and is little perturbed until Ls ≃ 150°. In summer, polar ozone is close to zero in the southern hemisphere, whereas amounts of 1.5 μm-atm are computed in the northern hemisphere. This difference is again linked to the vertical distribution of water vapor and is clearly illustrated in Figure 7. At 70°N the low atmospheric temperatures that prevail near aphelion prevent H2O from reaching high altitudes: even at solstice (Ls = 90°) the H2O mixing ratio decreases rapidly with height, and the 100 ppmv contour remains confined below 30 km. In stark contrast, the H2O vertical distribution at southern hemisphere solstice (Ls = 270°) shows a dramatic vertical expansion, bringing the 100 ppmv contour up to 90 km altitude. To this large increase in the H2O amount must be added the effect of the ∼40% faster photolysis at perihelion compared to aphelion. The consequence on low-atmosphere O3 is a mixing ratio about one order of magnitude smaller in southern summer than in northern summer. Thus the north-south asymmetry in summertime O3 at high latitudes is essentially of photochemical origin, the differences in topography playing only a marginal role at this season.
 The diurnal cycle of the ozone vertical profile at 70°N (Figure 8) does not show, in general, a double-layer structure comparable to what is found at the equator. The main cause for this difference is the much drier environment that characterizes the northern polar region for most of the year. Large SZAs also contribute to slowing down the production of HOx from H2O photolysis. In these conditions the maximum Ox loss that usually occurs in the 10 km layer below the hygropause is largely inhibited, and O3 decreases monotonically with height up to 40 km. It is only in the aphelion season (Ls = 60°–90°) at 70°N that an O3 minimum is apparent at 20–30 km. H2O abundance is maximum at this time of the year, resulting in an O3 chemistry comparable to that of low latitudes to midlatitudes. In other seasons the polar chemistry is much less active, as shown by the reduced O3 diurnal variation at the equinoxes compared to what is computed at the equator. Another outstanding feature is the large ozone concentration that we obtain throughout the year at the surface level. This is particularly true in the polar night (Ls = 270°–300°), with a O3 density close to 10 × 1010 cm−3 but also in summer (Ls = 60°–90°), though H2O near the ground is more abundant at 70°N than at the equator. The difference lies in the lower surface elevation of the northern polar region compared to the tropics: in the low plains the stronger UV optical thickness and dust opacity reduce the H2O and O3 photolysis rates, whereas the large surface pressure favors the three-body reaction producing O3.
3.5. Comparison to Observations
 The model results are now compared to published observations of the latitudinal distribution of the ozone column on Mars. Unfortunately, these are available only for a limited range of solar longitudes. In the following, NH and SH are used for northern hemisphere and southern hemisphere, respectively.
3.5.1. NH Winter/SH Summer (Ls = 270°–360°)
 The first systematic measurements of ozone on Mars were made by the Mariner 9 ultraviolet spectrometer [Barth et al., 1973]. At Ls = 292°–300° the O3 content above the south polar cap was below the detection limit of the instrument, 3 μm-atm. In January 2002, Novak et al.  measured the O2(a1Δg) dayglow emission to retrieve the ozone column above ∼20 km at about the same season (Ls = 306°). They did not find any ozone in the 30°N–90°S latitude band above the noise level of 0.1 μm-atm. The model results are consistent with these observations. In Figure 1 the modeled O3 total column is lower than 0.5 μm-atm over a wide latitude band in SH summer and is indeed well below the detection limit of Mariner 9. In Figure 4d the complete absence of ozone above 20 km in our model also explains the absence of O2(a1Δg) emission noted by Novak et al. . At the end of SH summer the maximum O3 amounts measured by Mariner 9 in the 50°S–75°S latitude band passed above the detection limit at Ls = 330° and reached an amount greater than 10 μm-atm at Ls = 360°. This rapid increase occurs later and is not strong enough in the model. However, measurements of the O2(a1Δg) dayglow emission made in January 2004 at Ls = 333° showed no ozone above ∼20 km (R. Novak, personal communication, 2004), suggesting a possible interannual variability in the onset of the late summer O3 increase in the southern hemisphere.
 In the northern hemisphere the wintertime (Ls = 330°–360°) measurements by Mariner 9 revealed the largest O3 amounts ever observed on Mars. Values up to 60 μm-atm were detected in the 50°N–75°N latitude band [Wherbein et al., 1979] but also showed wide variations from day to day. From the Mariner 9 individual observations presented by Traub et al.  it appears that the O3 amounts at 70°N may fall anywhere in the range 5–40 μm-atm from one orbit to the other. In the face of this variability the model results at 70°N (Figure 5) can be considered to be in good quantitative agreement with the observations: model O3 values are in the range 10–35 μm-atm in the Ls = 330°–360° period. Barth  attributed the large O3 variability to rapid variations in the H2O content. As discussed previously, we argue that the day-to-day variability observed by Mariner 9 was essentially of dynamical origin. Our results show that dynamical disturbances of the polar vortex may lead to large excursions in latitude of the polar vortex edge, characterized by strong O3 gradients. Three-dimensional model simulations run at higher horizontal resolution would resolve better small-scale structures in the O3 field at this time of the year. This would certainly increase further the O3 variability that we find at 70°N (±10 μm-atm in 24 hours) and would be in even better agreement with the Mariner 9 data. Equatorward of 40°N, Mariner 9 did not observe ozone at any time at Ls = 330°–360°. This is consistent with our simulation, which shows that the detection limit contour (3 μm-atm) lies at about 40°N in zonal average (Figure 1). Previous 2-D model results by Moreau et al.  indicated O3 amounts of about 8 μm-atm at 40°N and 5 μm-atm at 20°N (Ls = 351°), which seem to be too large relative to the observations.
3.5.2. NH Spring/SH Fall (Ls = 0°–90°)
Clancy et al.  employed the Faint Object Spectrograph (FOS) on the HST to measure the latitudinal distribution of ozone in NH spring at Ls = 10° (September 1996) and Ls = 61° (January 1997). The model results are compared to these observations in Figure 9. For both periods the O3 column daytime value was extracted from the model at the same Ls for five different longitudes spanning the quadrant of the Martian globe where the measurements were performed. At Ls = 10°, shortly after northern spring equinox, the model ozone columns are in excellent agreement with the observed values. As already shown in Figure 3, the effects of topography are important at this season. The five curves in Figure 9 are taken at longitudes with different surface elevation and explain much of the variability of the measurements, as already speculated by Clancy et al. . The strong latitudinal gradient of high-latitude O3 is also well reproduced by the model, both in intensity and in geographical position.
 Mariner 9 data are available in NH midspring at Ls ≃ 45°. Only the maximum O3 amounts detected in the 50°N–75°N latitude band were shown by Barth et al. , with values in the 5–17 μm-atm range. Considering the O3 latitudinal gradient and longitudinal variability that exist in this season, these observations do not seem to contradict the model results (Figure 1). In the absence of more accurate information about the exact location of the measurements it is difficult, however, to go further in the analysis.
 Later in the NH spring season, at Ls = 61°, the comparison of our results with the FOS data does not show an agreement as good as at Ls = 10° (Figure 9b). Although the calculated seasonal decrease in the high-latitude O3 seems consistent with the observations, there is about 50% less ozone at low latitudes to midlatitudes than measured by Clancy et al. . At latitudes south of 20°N, note that the model does produce increased O3 columns compared to what is obtained at Ls = 10°. However, the amplitude of this seasonal variation is largely underestimated. Let us reiterate that the H2O total column does not show a marked trend during this period. According to our model, the increase in O3 column is essentially driven by the growth of the “aphelion layer” above 25 km, which results from the decrease in the hygropause altitude. Considering the good agreement obtained at Ls = 10°, when the surface O3 layer is the dominant contributor to the total column, the underestimation of O3 at Ls = 61° might indicate that the increase in the O3 middle atmosphere layer is not strong enough.
Novak et al.  (Figure 9c) retrieved the ozone column above ∼20 km from the O2(a1Δg) dayglow emission at the same season (Ls = 67°, January 1997) as Clancy et al. . When integrated over the same altitude range, the model O3 columns at low latitudes to midlatitudes are smaller than the observational data. If we exclude the measured O3 minimum around 25°N, which may be related to the presence of clouds reducing the signal [Novak et al., 2002], we note that the O3 underestimation by the model is quantitatively similar to what is obtained at Ls = 61° with Clancy et al.  data. The fact that the measurements of the O2(a1Δg) dayglow emission are sensitive only to the O3 located above ∼20 km might indicate that most of the discrepancy between the model and the data lies in the O3 middle atmosphere layer rather than in the O3 surface layer. However, the middle atmosphere O3 abundance is rather poorly defined by the O2(a1Δg) dayglow emission alone. The relationship between both quantities depends on relatively uncertain rate coefficients and also requires the shape of the O3 vertical profile, which is unknown at the time of the measurement. Using different parameters, Krasnopolsky [2003c] suggested that the O3 columns calculated by Novak et al.  should be reduced by a factor of 1.95. This reduction factor would bring their observations in much better agreement with our model calculations. Thus comparisons of O3 columns derived from O2(a1Δg) dayglow emission with model results must be considered with caution. The conversion of the ozone vertical profiles calculated in the model to dayglow intensities should provide less uncertain comparisons. They will be the subject of a forthcoming dedicated paper.
 The water vapor columns derived by Novak et al.  at Ls = 67° are not subject to the same uncertainty as their derived O3 columns. The comparison with the model H2O columns shows good agreement (Figure 9d), in terms of both absolute amounts and latitudinal gradient. Therefore an overestimation of the total H2O by the model cannot be invoked to explain the too low O3 amounts at this time of the year. This does not exclude, however, an excess in the H2O mixing ratio at elevated altitude levels. Above the hygropause level the H2O number density is small and decreases very rapidly with altitude: a possible wet bias in the model would not be detectable when examining only the total H2O column.
3.5.3. NH Summer/SH Winter (Ls = 90°–180°)
 The only published observational data of O3 in NH summer are those collected at the end of the Mariner 9 mission near Ls = 102°. Ozone was searched above the north polar cap and was found to be below the 3 μm-atm detection limit of the instrument. The model indicates O3 columns of the order of 1 μm-atm at these latitudes (Figures 1 and 3b) and is therefore consistent with this observation.
3.5.4. NH Fall/SH Spring (Ls = 180°–270°)
 Using infrared spectroscopy, Espenak et al.  measured O3 from 80°S to 20°N in SH spring at Ls = 208°. The retrieved O3 columns were less than 2.2 μm-atm at all latitudes sampled (Figure 9e). When taking into account the day-to-day variability, the model results are consistent with the observations made at 20°N and 60°S. The only previous ozone measurement at this season (Ls ≃ 204°) was made above the south polar cap by Mariner 7 and revealed an O3 abundance of about 10 μm-atm [Barth and Hord, 1971]. To explain the much smaller abundance retrieved at SH high latitudes, Espenak et al.  invoked the possible role of heterogeneous chemistry in controlling ozone variability. The good agreement that we obtain at 60°S with a pure gas-phase scheme suggests that heterogeneous processes may not be necessary to explain this particular observation. At 80°S the upper limit of 0.5 μm-atm given by Espenak et al.  shows an even greater difference with the Mariner 7 observations. The model results are in the range 1–2 μm-atm but evolve rapidly with time: the limit of 0.5 μm-atm at 80°S is reached shortly after the measurement at Ls = 220°. Near the pole, O3 is rapidly decreasing at this season as a result of the release of water vapor from the receding south polar cap (Figure 1). Because the timing of this O3 decline is rather sensitive to details of the GCM water and dust cycles, as well as horizontal resolution, we think that the discrepancy noted at 80°S must not be overinterpreted. More problematic is the underestimation of O3 between 40°S and the equator. Compared to what is found near aphelion, the difference with the observations is, however, reduced (∼1 μm), which might be related to the lesser role the O3 middle atmosphere layer is expected to play at this season. Thus the underestimation of O3 by the model noticed at Ls = 61° and Ls = 208° could have the same origin, but measurements of the O3 vertical profile will be needed to clarify this issue. For both seasons we emphasize that the calculated H2O column amounts are in rather good agreement with the observational data (see Figure 9d at Ls = 67° and Smith  for Ls = 208°). We reject overestimation of the low-atmosphere H2O as a cause of the low O3 bias in the model.
 The model reproduces successfully many features of the available measurements of ozone on Mars. In particular, the results obtained in the period corresponding to the northern hemisphere winter and early spring appear to be in good quantitative agreement with the observational data. An outstanding problem is the underestimation of O3 that is computed in late spring, near aphelion. A possible cause might be the substantial uncertainty that is associated with some important photochemical and kinetics parameters of Martian interest. We now examine the model sensitivity to the choice of these parameters. The crude assumption of a constant dust loading in the photochemical routine is also checked.
3.6.1. CO2 Absorption Cross Sections
 The CO2 absorption cross sections have a critical impact on the Martian photochemistry. When photolyzed, CO2 is the primary source of odd oxygen at all altitudes. It is also the main ultraviolet absorber of the atmosphere of Mars: the CO2 absorption spectrum controls the transmitivity of the atmosphere and therefore also affects the photolysis rate of other species involved in the ozone chemistry, such as H2O or O2.
 Since the measurements of DeMore and Patapoff , followed by those of Lewis and Carver  and Parkinson et al. , it has been known that the CO2 absorption spectrum shows a significant sensitivity to temperature as well as large variations over small wavelength intervals. In the CO2 absorption region our photolysis rate calculations are made at a spectral resolution that is a factor of 10 (from 124 to 175 nm) to 500 (from 175 to 205 nm) larger than the resolution of 5 nm already considered to be adequate by Anbar et al. [1993a]. Therefore the possible problems associated with data averaging over large intervals can be excluded. The situation with the low-temperature data is less satisfactory. In particular, a potentially important problem concerns the value of the CO2 absorption cross sections at temperatures lower than those at which laboratory data are available. In the reference experiment described in this paper, we assumed that the cross sections below 200 K were identical to the values measured at 200 K. However, as shown by Anbar et al. [1993a], the computed photodissociation rates are quite sensitive to the manner of estimating the temperature dependence below 200 K. In a second 3-D model experiment (hereafter called case A) we extrapolated the temperature dependence of the CO2 cross sections measured between 300 K and 200 K to the temperatures below 200 K. This assumption leads to significantly lower CO2 absorption and UV opacity, in particular in the middle atmosphere, where temperatures are typically in the 140–160 K range. Subsequently, between 30 and 50 km the case A values for are about 100% larger than those obtained in the reference experiment. This result, obtained at a 60° SZA, is in good agreement with Anbar et al. [1993a]. Less sensitivity is found at lower altitudes, where the temperatures approach or are above 200 K: compared to the reference case, in case A shows a 30% increase at 20 km and only a 10% increase at the ground level. In contrast, the case A values for are lower than the reference values by about 30% above 50 km. At these altitudes the effect of the decreased CO2 cross sections dominates the effect of the reduced atmospheric opacity. The opposite effect is found in the lower atmosphere (0–20 km), where slightly increases (+5 to +15%) in case A. The O3 latitudinal distribution obtained with case A at Ls = 61° is compared to the reference experiment and the measurements by Clancy et al.  in Figure 10. At all latitudes the O3 columns of case A are smaller than those of the reference experiment. This was expected from the larger , which causes up to a doubling of the HOx abundance at the hygropause level. As a result, the O3 mixing ratio is reduced by half around 30 km altitude. Thus extrapolating the temperature dependence of the CO2 cross sections below 200 K does not reduce the discrepancy between the model and the observational data. On the contrary, even smaller O3 columns are computed with this assumption, which suggests that the solution to increase O3 near aphelion must be found elsewhere.
3.6.2. H2O Absorption Cross Sections
 The production of ozone-destroying HOx radicals occurs through the photolysis of water vapor in the ultraviolet. H2O absorption cross sections are now available to good accuracy up to 196 nm [Cheng et al., 1999]. However, measurements were performed at room temperature (295 K), and there is no information regarding a possible temperature dependence in the long-wavelength tail, similar to that of the CO2 absorption cross section. Krasnopolsky  and Atreya and Gu  reduced the H2O absorption cross sections by a factor of 2 to investigate the effect of their possible temperature dependence and found a better agreement between the production and loss of CO2. The reduction in the HOx production that resulted from the smaller H2O cross sections also led to an increase in the calculated O3, found to be of the order of 15% by Krasnopolsky . On the other hand, Nair et al.  noted that the extrapolation of the H2O cross sections from 196 nm out to 210 nm, assuming a linear decrease with the logarithm of the cross section, leads to an opposite effect, with a 25% decrease in ozone. Model results are therefore relatively sensitive to the assumed H2O absorption at temperatures and wavelengths for which laboratory data are not available. On the basis of the numbers mentioned above, it seems unlikely, however, that a better knowledge of the H2O cross sections could lead to the doubling of the O3 column that is needed to match the observations made near aphelion.
3.6.3. HOx Reaction Rates
 In addition to the H2O photolysis, the other main process controlling the abundance of HOx radicals in the Martian atmosphere is the loss mechanism c07:
The rate of this reaction is still subject to a large uncertainty, which might directly affect the amount of calculated ozone in the model. In our reference simulation we used for c07 the value recommended by Sander et al. , who estimate the uncertainty to be about 50% at 200 K. In order to reproduce better the observed abundances of CO, O2, and O3, Nair et al.  proposed to increase the rate of c07 by 81%, a change also adopted by Clancy and Nair . However, this modification is inconsistent with the observations performed in the terrestrial stratosphere by Jucks et al. , who provided the only set of simultaneous vertical profiles of OH and HO2. According to their study, the measured OH and HO2 are modeled best by calculations that use, on the contrary, a 25% decrease in the c07 rate, together with a 25% decrease in the reaction rate of c01:
We have tested the impact of these kinetics changes in a third simulation of the coupled model (hereafter called case B). The ozone column meridional distribution obtained with case B at Ls = 61° is compared to the reference simulation and case A in Figure 10. At low latitudes to midlatitudes, a moderate (+5 to +25%) increase is found relative to the reference experiment, but the obtained values are still significantly smaller than the observations. Interestingly, the increased ozone column found in case B is obtained in an atmosphere that is richer in HOx. This is explained by the reduced rate of reaction c01, which is the main loss mechanism of odd oxygen in the lower atmosphere. This change outweighs the effect of the increase in HOx that results from the reduced efficiency of reaction c07. However, the overall effect on the O3 column remains limited. The kinetics parameters required to explain the observations of OH and HO2 on Earth do not appear to be the solution to reaching a satisfying quantitative agreement between the model and the measurements in the Mars aphelion season.
3.6.4. Dust and Clouds
 Another possibility is that the assumed dust loading in the model differs significantly from the actual dust levels on Mars when the O3 observations were made in January 1997. In his comprehensive modeling study of the effect of airborne particles on ozone on Mars, Lindner  showed that O3 increases when dust opacity increases. This arises because the absorption of solar radiation by dust reduces more effectively the O3 loss mechanisms (H2O photolysis and odd hydrogen catalytic cycles) than the O3 production mechanism (CO2 photolysis and reaction a01). Too low O3 amounts could then result from the underestimation of dust opacity in the model. This hypothesis is not supported by the observations. On the contrary, Clancy et al.  reported minimal dust loading in January 1997 (τdust ≤ 0.2), meaning that our assumed dust optical depth (τdust = 0.2) is actually an upper limit. Thus we rule out the underestimation of dust as a possible explanation for the too low O3 amounts computed near aphelion. This conclusion is reinforced by the sensitivity experiment (case C) carried out with an extreme level of dust (τdust = 2.0) similar to those reported during global dust storms [Zurek, 1982]. Even with this unrealistically large dust loading for 1997, it can be seen in Figure 10 that the modeled O3 increase at low latitudes to midlatitudes (+15 to +40%) is still largely insufficient to match the observations.
 Unlike dust, the effect of water ice clouds on photolysis rates is not implemented in the model. However, as shown by Lindner , scattering of the incoming solar radiation by clouds does little to change the O3 abundance. Using a cloud opacity of τcloud = 0.5 at 57°N, Lindner  found slightly less ozone than in a cloudless case, with a maximum reduction of only ∼5% at 40 km. Note that water ice cloud opacities reported in the aphelion equatorial belt are more generally in the range τcloud = 0.2–0.3 [James et al., 1994; Wolff et al., 1999] and were as low as 0.02–0.08 in 1997 [Clancy et al., 1999]. Furthermore, because of smaller SZAs, photolysis rates are expected to be less affected by clouds at low latitudes to midlatitudes than at 57°N. For both reasons the impact of the aphelion cloud belt on photolysis rates and O3 should be even weaker than in the case discussed by Lindner  and hence may be safely neglected.
 In addition to the absorption and scattering of the incoming solar radiation, airborne particles can also provide appropriate adsorption sites for heterogeneous chemical reactions to occur. This issue has often been a matter of debate in past 1-D modeling studies. Anbar et al. [1993b] demonstrated that heterogeneous chemistry could be important in lowering the abundance of HOx in the Martian atmosphere but also emphasized the clear need for laboratory data to constrain better the rate of HOx adsorption on surfaces and at temperatures more representative of Mars. The large uncertainties that affect critical parameters such as the HOx reaction probabilities on dust and ice, or the altitude distribution of aerosols, are perhaps at the origin of the contradictory results found in the literature. Several studies noted a better agreement with the observations when a heterogeneous sink of HOx is taken into account [Krasnopolsky, 1993, 2003b; Atreya and Gu, 1994], while others concluded that there was no need to invoke such processes to reconcile models and observations [Nair et al., 1994; Clancy et al., 2004]. It must also be realized that the inclusion of heterogeneous chemistry in 1-D models can only provide first-order results, which represent globally and seasonally averaged conditions. The fact that a 3-D homogeneous gas-phase model is unable to reproduce O3 amounts observed at specific times and locations is a much stronger indication that some heterogeneous process may be needed. This argument is reinforced by the manipulations of gas-phase data previously discussed, of which none seems to be a viable option to solve the model difficulties. Thus, because the adsorption of HOx is expected to increase the O3 amount, heterogeneous chemistry is a particularly attractive candidate in the aphelion season. However, if it is the only important missing process, it must not degrade in the same time the satisfactory results obtained with the gas-phase homogeneous scheme in the postperihelion period. In terms of aerosols this may suggest that heterogeneous processes must be especially effective on water ice clouds, which are known to dominate at the largest Sun-Mars distances, rather than on dust, which is much more abundant in the perihelion period [Clancy et al., 2003]. This first-order indication will have to be confirmed by a dedicated study that will be the subject of another paper.
 The model simulations presented here establish an updated picture of our understanding of the ozone chemistry and transport on Mars. The results do not contradict the fundamental aspects of the ozone behavior that were previously predicted by 1-D and 2-D modeling studies. However, the coupling between the photochemistry, a consistent representation of the Martian water cycle, and three-dimensional transport make it possible to go further in the analysis of the O3 variability on various scales of time and space.
 We find that the classical anticorrelation expected between the O3 and H2O columns is spatially verified only at a given solar longitude. Over the Martian year the low-latitude O3 column shows, for instance, little anticorrelation with the H2O column. At high latitudes, O3 may even look correlated with H2O if one compares the columns of each hemisphere in summer.
 Departures from the expected anticorrelation between the O3 and H2O columns are almost entirely due to orbital (Ls) variations in the H2O vertical distribution. Our results confirm the effectiveness of a mechanism first hypothesized by Clancy and Nair : over the period Ls = 180°–330° centered on perihelion, water vapor saturation occurs in the model at high altitude (>40 km at Ls = 250°), leading to considerable HOx production and Ox loss in the middle atmosphere. As a result, O3 is essentially confined in a “surface layer” below 20 km. During the rest of the year (Ls = 330°–180°), the altitude of water vapor saturation is lower (∼10 km at Ls = 90°), which reduces the HOx production and allows the formation of an additional O3 layer at 25–70 km. The maximum O3 densities in this layer are reached around aphelion.
 In general, less ozone is computed during the day than during the night. The daytime low-latitude to midlatitude O3 column is maximum in midmorning, whereas little change is observed over the night. The amplitude of this diurnal cycle is linked to the presence of the O3 middle atmosphere layer, which is characterized by daytime densities about one order of magnitude smaller than during the night. Near perihelion, the absence of this layer leads to the complete disappearance of the day-night contrast in the total ozone field.
 Other aspects of the ozone variability on Mars are more specifically three-dimensional and are represented for the first time. Topography is the main factor modulating the O3 column in the perihelion season and explains the variability of the measurements made at this time of the year. At high latitudes, dynamics and horizontal transport play an important role when the O3 photochemical lifetime becomes long in winter and early spring. The model reproduces rather well the wide day-to-day O3 variations observed by Mariner 9, which are shown to be related to dynamical disturbances of the polar vortex.
 The stringent comparison of the modeled Mars O3 abundance with observational data reveals contrasted results. A good quantitative agreement is found in the postperihelion period (Ls = 290°–10°), but the model fails to reproduce O3 columns as large as those measured near aphelion (Ls = 61°–67°). Current uncertainties in absorption cross sections and gas-phase kinetics data do not seem to provide credible explanations to explain this discrepancy. This supports the possible existence of heterogeneous processes removing odd hydrogen radicals, as suggested by previous 1-D model studies [Krasnopolsky, 1993, 2003b; Atreya and Gu, 1994]. However, the probabilities of these reactions on the surfaces of Martian interest are still poorly documented by laboratory data, especially at low temperatures. Their potential impact on the ozone abundance in our model will require a dedicated study.
 Although the total water vapor columns computed by the model generally agree with the observations, we do not exclude a possible overestimation of the high-altitude H2O mixing ratio as a possible cause for the too low O3 amounts in the aphelion season. Clearly, systematic measurements of the ozone and water vapor vertical profiles would be highly desirable to clarify this issue. Recently arrived at Mars, the SPICAM UV and infrared spectrometer [Bertaux et al., 2000] on board Mars Express should provide an unprecedented wealth of simultaneous observations of ozone and water vapor. These new data sets will improve significantly our knowledge of the three-dimensional distribution of ozone on Mars and provide the chemical models with the strongest observational constraints to date. As they do for the terrestrial atmosphere, it is likely that three-dimensional chemical models will play a major role in their interpretation and will be invaluable tools to make further progress toward a quantitative understanding of the Martian photochemistry.
 We are grateful to Vladimir Krasnopolsky and Robert Novak for their manuscript reviews. S.L. acknowledges support from the postdoctoral fellowship program of Centre National d'Etudes Spatiales (CNES). F.M. is supported by a National Research Council Research Associateship Award at NASA Ames Research Center.