Mars: atmosphere pressure (Pa)

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1 2 Mars: atmosphere Modelling the ma Stephen R Lewis shows how to model the climate of Mars, touching on the physics and dynamics of general circulation models, and the wealth of information that such models both need and produce useful to climatologists on Earth as well as engineers planning future Mars missions. Abstract Mars general circulation models, used to study the atmosphere of Mars, have developed almost in parallel with terrestrial weather and climate models. These models are now being confronted with a large amount of new spacecraft data, which is allowing the models to be validated more rigorously. This paper briefly reviews the current state of Mars models, highlighting areas of current development and particular challenges. The way in which models can be used to help to interpret observations, via data assimilation, and the way in which model results can be of help in planning for future missions are both discussed. Numerical modelling and simulation has led directly to much of our present knowledge of the martian atmosphere and its circulation, and has significantly enhanced the interpretation of spacecraft and telescopic observations. This process has mirrored developments in understanding of terrestrial weather and climate processes, making use of a hierarchy of models, from analytic work with simplified equations to large-scale numerical simulations. The most powerful tools for weather and climate prediction for the Earth are general circulation models (GCMs). These are attempts to model all the processes important to the large-scale atmosphere, from global scales down to the smallest horizontal scales that can be represented within computational constraints often km, depending on the problem in hand and the time scale of the simulation required. In no case is a GCM presently able to resolve down to the smallest, viscous scales of motion, which may still have a large net impact upon the large-scale synoptic weather systems. There is, therefore, the need to develop a complex set of parameterizations that attempt to predict the large-scale impact of small-scale processes, such as convective overturning and mixing. A significant part of the computational expense of a GCM lies in the representation and parameterization of physical processes, e.g. radiative : MGCM zonal-mean temperature (colour scale) and winds (contours at intervals of 2 m s, eastward positive, with negative values dashed) time-averaged over about 6 days following northern spring equinox, L S =. pressure (Pa) heating and cooling, cloud microphysics, interaction and coupling of the atmosphere with the solid surface, with the oceans and with smallscale, unresolved atmospheric waves. These parameterizations are often more timeconsuming than the explicit representation of the large-scale dynamical and thermodynamic equations in the GCM. An enormous number of ground-based, airborne and satellite observations are made of the Earth s atmosphere every day and are used to provide initial conditions for GCMs for weather forecasts, for example, as well as to validate the modelling techniques used. For many planets other than the Earth, the detailed physical modelling required for a comprehensive GCM might be difficult to justify at present, although much progress can be made with simplified models. There are relatively few observations of extraterrestrial planets with which such a model could be constrained, and they tend to be sparse in time coverage, rather than consisting of a continuous record. Mars is the most obvious exception, both because of its proximity to Earth, resulting in a relatively large set of observations being accumulated with time, and because it is in many ways the most Earth-like planet in our solar system. In addition to the intrinsic interest in understanding the Martian atmosphere, it also forms an almost ideal testbed for extending terrestrial GCMs to a new setting and for further validating the techniques used under other conditions. Mars general circulation models One of the first attempts at a comprehensive, Mars general circulation model (MGCM) was by Leovy and Mintz (969), who successfully adapted the then recently developed terrestrial GCM of the University of California, Los Angeles, to martian conditions. The model predicted atmospheric condensation of CO 2 and the presence of transient baroclinic waves in the winter mid-s, much like synoptic weather systems on Earth. Development of an MGCM has continued at NASA Ames Research Center since then, providing many insights into martian weather and climate (Pollack et al. 98, 99, Zurek et al. 992, Haberle et al. 99, Barnes et al. 99, 996, Murphy et al. 99, Hollingsworth and Barnes 996, Haberle et al. 2). By 99 other efforts were under way to model Mars, following the arrival of data from the highly successful Viking missions and in the build-up to the ill-fated Mars Observer mission, log-pressure height (km) Downloaded from by guest on 2 November August 2 Vol 44

2 . Mars: atmosphere rtian atmosphere 2: MGCM mean meridional circulation for the same period as figure. Positive streamfunction values mean anticlockwise circulation, arrows at Pa show flow in the upper levels. Contours are in units of 9 kg s (pseudologarithmic near zero). from which some of the instruments have since been re-flown successfully on Mars Global Surveyor (MGS) from 997. Work had begun on adapting the French Laboratoire de Météorologie Dynamique (LMD) terrestrial climate model to martian conditions (Hourdin 992). This model was the first from which a simulation of a full martian year, without any forcing other than insolation, was published (Hourdin et al. 99, 99). The LMD MGCM was able to reproduce in a realistic way the seasonal and transient pressure variations as observed by the Viking Landers (Hourdin et al. 99). A Mars GCM was also developed at Oxford in the early 99s, originally in the form of a simple dynamical model in collaboration with Reading University (Collins and James 99). Independent studies included investigations of the dynamical regime of baroclinic waves (Collins et al. 996), the western boundary current nature of the low-level cross-equatorial branch of the Hadley circulation (Joshi et al. 994, 99) and atmospheric super-rotation under dusty conditions (Lewis and Read 2). By the mid-99s, the LMD and Oxford Mars GCMs shared a common package of representations of physical processes, since it is a daunting task to develop and test new physical schemes within a small modelling group, although both groups retain their different dynamical models (Forget et al. 999). One public manifestation of this collaboration has been the combination of results from both models in a freely available climate database (Lewis et al. 999), described below. The MGCMs have been further improved to include full, interactive dust lifting, transport and deposition schemes (Newman et al. 22a,b), to model water transport and ice clouds (Böttger 2, August 2 Vol 44 pressure (Pa) Montmessin and Forget 2) and to extend the top of the model above the thermopause (at about 2 km altitude) into the upper atmosphere (Angelats i Coll et al. 2). Another MGCM was constructed at the Geophysical Fluid Dynamics Laboratory (GFDL) and was used initially to study the role of thermal tides (Wilson and Hamilton 996) and polar warmings (Wilson 997). Recently, this model has been used in particular to investigate the martian water cycle (Richardson and Wilson 22, Richardson et al. 22). A range of other global Mars models have also been constructed (including Mass and Sagan 976, Moriyama and Iwashima 98, Nayvelt et al. 997, Segschneider et al. 2, Takahashi et al. 2), some of which include the full dynamics of the MGCMs above, but simplify aspects of the radiative forcing, for example. Such models play an extremely useful role in isolating individual processes in a less complex setting than a full GCM, and as a less computationally expensive tool for certain purposes. In addition to the global models, it is also worth noting that significant work has been done upon local, or mesoscale models for Mars (Savijärvi and Silli 99, Rafkin et al. 2,Toigo and Richardson 22, Toigo et al. 22, Michaels and Rafkin 2), which can be used to focus upon small-scale phenomena, such as dust lifting processes, slope winds or volatile transport in the planetary boundary layer. A further class of three-dimensional atmospheric model has been developed to model the martian upper atmosphere, above the thermopause (Bougher et al. 99, 999, 2). A thermosphere model introduces additional complications compared to the well-mixed, neutral lower atmosphere and must keep track log-pressure height (km) of different species and ion densities separately. A practical necessity, at present, is to couple the upper atmosphere model to output from an MGCM for the lower and middle atmosphere, usually via a boundary between km altitude, and the upper atmosphere model is often run for short periods of a few days rather than for full annual cycles. The possibility of extending a single model from the surface to the upper atmosphere is currently being investigated (Angelats i Coll et al. 2). The martian general circulation This section shows the overall zonal-mean martian circulation for two of the cardinal seasons, northern hemisphere spring equinox and winter solstice. These examples were produced by the Oxford MGCM, run with a prescribed dust field chosen to reproduce broadly lower atmosphere ( km) temperatures as observed in the first year of MGS operations. However, the details are not crucial beyond noting that dust amounts were moderate, with northern spring very clear and northern winter dustier, but not approaching global dust storm opacities. Figures and 2 show the zonal-mean atmospheric state at northern hemisphere spring equinox. It is worth noting that the equinoctial zonal-mean state is rather similar to the annualmean state, although the circulation is only in this pattern for a relatively short part of the martian year, during the transition from the winter solsticial state to the summer, or vice versa. The temperatures (figure ) are highest near the surface and close to the equator, with a pattern of westerly jets (eastward wind, or positive u) in the wind field in the mid-s of both hemispheres. The meridional circulation (figure 2) shows a pattern of rising motion near the equator with a Hadley Cell in each hemisphere and some evidence of smaller, counter-rotating cells at higher s. The Hadley Cells are of unequal strength, but this is sensitive to the averaging period chosen, and is also true on the Earth. Unlike the Earth, the Hadley circulation on Mars is not constrained by a strong tropopause and extends to above 6 km altitude, although the bulk of the mass flow is in the lowest one or two scale heights ( 2 km), as might be expected. The martian equinoctial circulation shown is not totally dissimilar from the global circulation of the Earth s atmosphere. Mars, however, becomes much more strongly asymmetric between the hemispheres for much of the year. Figures and 4 show a set of zonal-mean fields for northern hemisphere winter solstice. The 4.7 Downloaded from by guest on 2 November 28

3 . 6 Mars: atmosphere temperature plot (figure ) shows that the warmest part of the planet moves to high southern s, where horizontal temperature gradients are small. There is a strong horizontal temperature gradient from the equator to the winter pole in the northern hemisphere. This pattern is reflected in the zonal wind which now has a single, strong westerly jet in the winter hemisphere and weaker easterly flow in the summer hemisphere. It is in this region of high horizontal temperature gradients and vertical wind shears that baroclinic instability leads to synoptic weather systems, as experienced in terrestrial mid-s. There is also evidence of a strong easterly mean flow in the equatorial upper atmosphere; the causes of this are complex, but thermal tides and planetary waves both contribute (Lewis and Read 2). The mean meridional circulation (figure 4) is now dominated by a single Hadley Cell, spanning more than 9 in, which rises in the summer hemisphere and descends in the winter. This circulation pattern, with descending motion in the winter hemisphere, and air subject to adiabatic compression, leads to the warming high above the winter pole around 8 km altitude, seen in figure. : Zonal-mean temperature and winds, shaded and contoured respectively, as in figure, but for a northern winter solstice period of about 4 days, L S = 27. 4: Mean meridional circulation plotted as in figure 2, but for northern winter solstice, as figure. pressure (Pa) Model structure GCMs can, somewhat arbitrarily, be thought of as dividing into two major parts, commonly called model dynamics and physics. The dynamics core of a GCM consists of the solution of the so-called primitive equations of meteorology. These are formed from the three-dimensional Navier Stokes equations, which express Newton s Second Law in a rotating frame of reference, and equations for mass conservation, the equation of state for a gas and a thermodynamic energy equation (Andrews 2, Holton 992). Often these equations are approximated by replacing the vertical component of the Navier Stokes equations by hydrostatic balance, assuming that the atmosphere is a thin (compared to the radius of the planet), spherical shell and neglecting some of the Coriolis force components associated with vertical motions. These approximations are reasonable for the large-scale atmosphere on both Earth and Mars and, made together, lead to consistent momentum and energy conservation properties, although it is possible to construct a GCM which uses the un-approximated equations (e.g. White 2). The dynamical core of the GCM solves the primitive equations in terms of variables (typically eastward and northward wind, atmospheric temperature and surface pressure) which have been discretized, usually employing a three-dimensional grid of points, although it is also possible to use a truncated series of spherical harmonics in the horizontal and a grid in the vertical only, as in the Oxford MGCM. A terrain-following vertical coordinate, with a grid stretched to resolve the planetary boundary layer is normally used, and is especially important with the large-scale martian topography. The dynamical core is largely the same whether a model represents Earth or Mars, except for the choice of parameters such as rotation rate, planetary radius and the specific gas constant. The detailed representation of other physical processes, often occuring on a smaller scale than can be represented explicitly by a global model, is known as the model physics. This requires careful consideration and is a large part of the work involved in any GCM, both in terms of development, validation and the computational resources required to run the full GCM. Some of the main physical parameterizations required for a successful MGCM are briefly outlined here, in particular where they are the subject of ongoing work and improvement. Radiative heating and cooling Radiative transfer in both the visible and infrared is a major forcing mechanism for the atmosphere and must be modelled as accurately as possible pressure (Pa) A radiative transfer scheme for a MGCM must calculate heating and cooling rates fast enough to be run on many thousands of individual profiles per day of simulation, so detailed spectral line-by-line calculation is far too slow. A radiative transfer scheme for the martian atmosphere must primarily consider the presence of CO 2 gas and mineral dust, and perhaps water vapour, water ice particles and CO 2 ice particles. These are generally treated by dividing the spectral region into a small number of bands, calibrated against more detailed off-line calculations. For example, in the thermal infrared, absorption and emission in the lower atmosphere is dominated by the strong CO 2 µm band (Hourdin 992). Around 7 km and above, departures from local thermodynamic equilibrium (LTE) become significant (Lopez- Valverde et al. 998). These are now incorporated in a simplified way in several MGCMs, e.g. the LMD Oxford MGCM schemes are now calibrated to be accurate to around 2 km altitude. Work is ongoing to extend and to improve the representation of non-lte effects further through the thermosphere log-pressure height (km) log-pressure height (km) Downloaded from by guest on 2 November August 2 Vol 44

4 Comparative planetology Some of the astronomical and atmospheric parameters that can be used to compare the Earth and Mars from an atmospheric modelling point of view are summarized in the table. Mars rotates with almost the same period as the Earth (one Martian solar day, or sol, is about 4 minutes longer than one Earth solar day), and has an atmosphere that is generally transparent to visible radiation, which can fall upon and heat the solid surface of the planet, or can heat the atmosphere internally through direct absorption, primarily by suspended dust. The axis of rotation of Mars is currently inclined at a similar angle to the plane of the ecliptic as that of the Earth, and a familiar pattern of seasons results, although the Martian year is almost twice as long. The time of year on Mars is measured in areocentric longitude, L S, with L S = being northern hemisphere spring equinox, but this angle does not change linearly with time owing to the significant eccentricity of the Martian orbit (see figure 8). Despite obvious differences in mean surface pressure and atmospheric composition, many of the essential dynamical processes that determine atmospheric circulation and transport heat and momentum between the equator and poles are similar on both planets. Both planets receive an excess of heating near the equator, mainly through visible radiation, and radiate to space in the thermal infrared, emitted from the surface and atmosphere. Atmospheric motions act to transport heat away from the equator towards the poles. At low s on both planets, heat transport is through a mean over-turning circulation, known as Hadley Cells on Earth. Warm air rises near the hottest, diverges at high levels and sinks at higher s with a low-level return flow. The vertical extent of this motion is limited to the troposphere (below about km altitude) by the strong tropopause on Earth, but on Mars may extend to much greater heights because of the lack of a clear transition to a stratosphere (which is maintained by ozone heating on Earth, absent on Mars). Planetary rotation acts to constrain the Hadley Cells to low s (unlike slowly rotating planets such as Venus). In mid-s, the Dust Dust is the major absorber of solar radiation in the lower martian atmosphere and, through feedbacks, the main source of interannual variability on Mars. Even in the absence of major dust storms, there always appears to be a significant background level of dust on Mars and its representation is vital to a successful MGCM. Forget et al. (999) describe how GCM heating rates are very sensitive to the dust properties, such as single-scattering albedo, and these properties are not known with certainty. Hence, there is some ambiguity in the combination of total dust optical depth which is appropriate to use within the MGCM broadband regions and in the dust properties for a given heating rate. Dust scattering must also be considered in the thermal infrared, at least outside the main CO 2 µm band (Forget et al. 998, 999). Infrared dust scattering is commonly ignored in terrestrial GCMs. The present LMD Oxford GCMs include a radiative transfer scheme that accounts for multiple scattering by dust particles and use a set of synthetic single scattering spectral properties derived in order to match the Mariner 9 observations of the 97 global dust storm in the infrared, without making detailed assumptions about the actual dust composition. The question of how dust is distributed in the atmosphere is of major importance in determining the thermal driving for an MGCM. An ideal would be to have an MGCM that can selfconsistently lift, transport and deposit dust, forming a realistic dust distribution as a function of location, height and time. Despite current progress with dust schemes, model uncertainties and sensitive feedbacks in dust processes mean that an MGCM which could itself produce a realistic dust climatology with interannual variability in a long multiannual run is still not possible, at least without some careful tuning of lifting scheme parameters (Newman et al. 22a,b). Historically, Mars GCMs have used simple, prescribed dust distributions, and these are of great value for performing controlled experiments that remain close to the present martian climate. Typically dust is taken to be well-mixed in the lower and middle atmosphere, below primary form of heat transport becomes an almost horizontal type of convection, baroclinic instability (e.g. Andrews 2), in the form of waves rather than a longitudinal-mean circulation. This instability gives rise to weather systems of cyclones and anticyclones. The similarities between Earth and Mars in rotation rate, stratification and vertical scale height, mean that the typical horizontal scale for mid weather systems on both planets, the radius of deformation, is comparable, at around km. There are also important differences between the planets that must be taken into account when developing a GCM for Mars. Some differences simplify the task for Mars compared to Earth, for example there are fewer important gaseous species (almost solely CO 2 ) that absorb infrared radiation in Martian atmosphere and there is no need to model complex atmosphere ocean interactions. Other processes are unique to Mars, for instance the formation of CO 2 ice, including the possibility of CO 2 -ice clouds and snow, near the winter pole. Table: Planetary and atmospheric parameters for Earth and Mars Earth Mars Orbital radius ( m) Orbital eccentricity.7.9 Planetary obliquity Rotation rate, Ω ( s ) Solar day, sol (s) Year length (sol) Equatorial radius ( 6 m) Surface gravity, g (m s 2 ) Surface pressure (Pa) 6 Atmospheric constituents (molar ratio) N 2 (.78) CO 2 (.9) O 2 (.2) N 2 (.) Ar (.) Ar (.2) Equilibrium temperature, T e (K) 26 2 Scale height, H = RT e / g (km) 7..8 Buoyancy frequency, N ( 2 s )..6 Deformation radius, L = NH / Ω (km) 92 around 6 km, and to decay above this to a clear upper atmosphere (following Conrath 97), with no variations in or longitude on a pressure surface. The total dust optical depth is then either set to a constant value, typically τ.. for non-dust storm conditions, (e.g. Pollack et al. 99, Hourdin et al. 99), or prescribed to vary as a function of time of year (e.g. Forget et al. 999, Lewis et al. 999). Southern hemisphere summer is typically warmer and dustier than northern hemisphere summer, even before major storms are taken into account. Making such simple assumptions can still produce a reasonable climatology from the MGCM (e.g. figures 4), except that dust storms cannot spontaneously be simulated, other than by arbitrarily increasing the optical depth, e.g. to τ 2, at appropriate times. Most MGCMs can also perform experiments with a full dust cycle incorporated explicitly, sometimes including transport of multiple dust particle sizes (Murphy et al. 99, Wilson and Hamilton 996, Newman et al. 22a,b). Earlier studies (Murphy et al. 99, Wilson and Hamilton 996, Wilson 997), have tried an Downloaded from by guest on 2 November 28 August 2 Vol

5 : Isosurfaces of dust mixing ratio, showing the. kg/kg surface, plotted at four-day intervals (a d) during the development of a storm in the Chryse region in one year of an MGCM simulation. (a) height (km) ( N) longitude ( E) 2 (b) height (km) ( N) longitude ( E) 2 (c) height (km) ( N) intermediate approach in which the GCM is free to model dust transport and deposition, but the injection of dust into the atmosphere is prescribed. Recently some successes have been achieved in reproducing a full dust cycle, generally lifting dust through near-surface wind stresses and saltation processes and by smallscale dust devils, the lifting effects of which can be parameterized from the large-scale GCM atmospheric fields. Newman et al. (22b) find that, in an interactive model, near-surface wind stress lifting results in a positive feedback, since dust injected into the atmosphere will warm it locally and increase wind shears in turn. In contrast, dust devil lifting, which is most prevalent in the summer hemisphere, requires a thermal contrast between surface and atmosphere to drive the vortices and this will tend to be reduced as more dust is lifted, resulting in a negative feedback. It therefore seems likely that lifting by wind stress is of primary importance in forming runaway dust storms, whereas dust devils may contribute mainly to the lower background level of dust usually present in the martian atmosphere. Figure shows the three-dimensional growth of a spontaneously developing model dust storm in the Chryse region, similar to that described by Newman et al. (22b). In the early stages, some dust can be seen to accumulate low in the atmosphere, at high northern s, as a result of small storms around the edge of the north polar ice cap. Dust can then longitude ( E) 2 height (km) be seen to be drawn into the Chryse region, initializing more lifting, and then to be transported southwards across the equator in a low-level jet along the eastern edge of the Tharsis ridge (Joshi et al. 994, 99). Finally, the dust is swept high into the atmosphere, and back across the equator northwards, in the large Hadley circulation. This type of three-dimensional visualization of dust transport is currently only possible with models; observations of total optical depth over the whole atmosphere can be made (e.g. Smith et al. 2, 2, 22), but it is difficult to obtain much information about the vertical distribution of the dust, especially in the lower atmosphere and with good vertical resolution. CO 2 ice physics A unique feature of the martian atmosphere is that its major constituent may condense; around a third of the total martian atmospheric mass is exchanged with ice on the planet s surface over the course of the seasonal cycle. This process can be included in a martian GCM in a relatively straightforward way. If the atmospheric temperature falls below the CO 2 condensation temperature ( ln[.p] K, with p the pressure in Pa) atmospheric CO 2 is condensed into surface ice until the latent heat release brings the atmospheric temperature back to the condensation temperature. In more sophisticated schemes (Forget et al. 999), the CO 2 ice need not fall directly to the ground, but (d) ( N) might re-sublime on the way down. The emissivity of freshly fallen snow on the surface can also be lowered compared with that of older surface CO 2 ice. Finally, it is thought that CO 2 ice clouds could form, especially in polar winter regions. At present these are generally only simulated in the simplest way, by adjusting the albedo of the polar ice caps in the model. This is one area where the model microphysics could certainly be improved in future. Surface processes and the soil model The surface temperature is an extremely important driver for the martian atmosphere. Its evolution is determined by the balance between incoming solar radiation, incoming infrared radiation from the atmosphere, outgoing infrared radiation from the surface, turbulent atmospheric fluxes and thermal conduction in the soil below the surface. The martian soil is made up of mainly fine-grained particles with some coarser rock fragments, and can be modelled with a multilayer (around in the case of the LMD Oxford MGCMs) diffusive soil model (Hourdin et al. 99). The number of levels is chosen to allow the soil to reproduce temperature variations on timescales from minutes to several martian years. The surface thermal inertia and albedo are derived from spacecraft measurements and, although Mars does not have oceans, the surface properties show large-scale variations which can have the effect of thermal continents. 6 longitude ( E) Downloaded from by guest on 2 November August 2 Vol 44

6 Mars: atmosphere Convection, turbulence and the planetary boundary layer There are many scales of atmospheric motion which cannot be resolved explicitly in a GCM. Vertical convection, small-scale three-dimensional turbulence and the interaction of the atmosphere with the planetary surface in the boundary layer all require more detailed and careful treatment. Similar schemes for these processes are present in both terrestrial and most martian GCMs. Convective adjustment schemes rapidly mix heat and momentum in unstable atmospheric layers, until the atmosphere is brought to neutral stability. Turbulence and mixing within the planetary boundary layer is of particular importance in the martian desert-like climate. This region is treated with some care in most MGCMs, e.g. the LMD Oxford model has a highly stretched grid with many layers within a few kilometres of the surface and the lowest just 4 m above the surface (compared to a level spacing closer to km in the middle atmosphere). Turbulent kinetic energy is treated as an extra prognostic variable and turbulence closure equations (Mellor and Yamada 982) are solved to predict its evolution and effect upon the large-scale atmosphere (Forget et al. 999). Gravity waves and topographic drag Gravity waves are disturbances that are able to propogate in a stably-stratified atmosphere, with buoyancy providing the restoring force. Gravity waves can be excited by air flow over a rough topographic surface, among other means. Many of these waves would be on too small a scale (a few km) to be resolved adequately in a typical GCM, and would be of little consequence for the large-scale flow if it August 2 Vol Ls 6: Zonally averaged, column-integrated water-ice cloud abundance in precipitable microns as a function of over the course of one Mars year. The tenth year of an MGCM simulation is shown. were not for the fact that they grow in amplitude exponentially as they propagate upwards, eventually leading to instability and wave breaking (e.g. Andrews 2, Holton 992). When gravity waves break, their momentum is mixed turbulently. In the case of topographically generated waves, locked to surface features, this momentum mixing tends to drag the large-scale wind towards rest. Several studies have attempted to model gravity wave effects in idealized Mars atmospheric models, ranging from two-dimensional studies to GCMs (Barnes 99, Théodore et al. 99, Joshi et al. 99, 996, Collins et al. 997) and conclude that gravity wave drag might be a large effect on Mars above 4 km altitude. The LMD Oxford MGCMs have a detailed gravity wave and low-level topographic drag formulation (Collins et al. 997, Forget et al. 999), based on the terrestrial scheme of Lott and Miller (997) and Palmer et al. (986). This scheme treats both gravity wave breaking, mainly in the middle and upper atmosphere, and drag from small-scale, unresolved topography, in the lower atmosphere. Properties of the topography on scales smaller than the GCM can resolve are now known accurately for Mars thanks to the MOLA laser altimeter aboard MGS (Smith et al. 999). The accurate calibration and testing of a gravity wave drag scheme remains an outstanding problem, although measurements of temperatures above 6 km altitude and possibly even direct wind observations should help in future. Water Partly owing to the search for possible evidence of past life on Mars, modelling the present-day water cycle and inferring water reservoirs has become of increasing significance. Unlike the Earth, the thermodynamic effect of water in the martian atmosphere is negligible because the amounts are so small; often the entire atmospheric column holds the amount of water equivalent to a few microns of precipitation, much drier than the driest conditions in Antartica. Clouds of water ice can form at certain regions and times of day and year, and reach significant opacities. Particular examples are water-ice clouds in the equatorial belt, which are prominent around the time of aphelion in northern hemisphere summer, and ice clouds around the polar winter ice caps. Owing to the lower pressure on Mars, water generally sublimes directly from ice to vapour, although there are some regions and times of year where the surface pressure and temperatures are high enough for liquid water to be stable near the surface, especially when there are dissolved salts. It is only recently that clouds and microphysical schemes have been introduced to MGCMs, although there is now active work incorporating CO 2 and water-ice clouds into all the major Mars models (Colaprete and Toon 22, Richardson et al. 22, Böttger et al. 2, Montmessin and Forget 2). MGCMs have had some success in modelling the basic annual cycle of water vapour seen by the Viking MAWD instrument and, more recently, by the MGS Thermal Emission Spectrometer (TES) (Smith 22), although there are still questions about whether they can reach a suitable equilibrium level in longer experiments, should such an equilibrium indeed exist. Water vapour and ice particles can be transported by a GCM in the same way as dust particles and other tracers are transported, with a test being made to see if the water becomes saturated and condenses. Water in three forms, as vapour, ice and as an adsorbate on regolith grains, can also be tracked within each level of the martian regolith, where it is modelled using a diffusion equation similar to that employed for soil temperature. Water exchange between the atmosphere and regolith must also be considered. Figure 6 shows the total water-ice cloud abundance over the course of a martian year from the Oxford MGCM. In this simulation the model was initialized with a water-ice cap at the north pole, which is able to sublime if temperatures are high enough and if it is not covered with CO 2 ice, and with water in the regolith at high s, poleward of 6 N and 6 S. The main features are a cloud belt in low s during northern summer (near aphelion; the atmosphere is warmer near perihelion in southern summer and clouds do not form), caused by moist air being lifted by the Hadley circulation, and water-ice clouds close to the CO 2 -ice cap edges in both hemispheres. Such features are familiar from the observational record, both from telescopes and spacecraft. 4. Downloaded from by guest on 2 November 28

7 Data assimilation for Mars Data assimilation (e.g. Daley 99) is a technique in which information from both present and past observations are combined with a numerical model to produce a best guess for an atmospheric state. Data assimilation for the Earth has largely developed from the operational need for an initial state for a weather forecast model, based on a variety of recent observations. In the context of Mars, assimilation is of use for a post-analysis of observations, e.g. when an evolving map of synoptic-scale features is required from data taken asynchronously. A simple analysis of observations from a single, polar-orbiting satellite might lead to ambiguities in interpretation of features that change significantly over the course of a day. Further benefits of assimilation are its ability to combine information from different observations and to produce a full, physically consistent global analysis of all atmospheric fields, including those not directly observed. The examination of misfits between model forecasts and observations is also useful in helping systematically to identify potential model deficiencies. Until recently, data assimilation was not feasible for planets other than the Earth, but with the advent of new, larger atmospheric data sets from orbital missions such as MGS and developments in MGCMs, data assimilation for Mars is possible (Banfield et al. 99, Lewis and Read 99, Lewis et al. 996, 997) and has begun to be applied to the MGS TES (Conrath et al. 2, Smith et al. 2) temperature retrievals (Houben 999, Zhang et al. 2) and to both TES temperature and dust data (Lewis et al. 2). An illustration of output from a continuous assimilation of TES thermal and dust opacity observations into the Oxford MGCM is shown in figure 7. This shows snapshots of transient surface pressure (that at the current moment in time, minus the mean in a 2-day running window centred on the current time in order to remove topographic signals) at 2 points during the two martian years of MGS data currently available. It should be noted that there is no surface-pressure data being introduced, but the model surface-pressure field is one that is physically consistent with the atmospheric state which produces the best fit to the thermal and dust observations, as far as the data assimilation scheme can achieve this. The diagram shows anomalous high and low pressure systems, analogous to cyclones and anticyclones on Earth and at a similar horizontal scale, although the apparent wavenumber about the pole is smaller because Mars has a smaller radius; typically wavenumbers one to four dominate, versus roughly five to eight on Earth. It can be seen that waves are strongest in autumn, winter and spring (L S = 8 6 in the northern hemisphere) and are virtually absent in the summer. Ls =, first year Ls =, first year Ls = 6, first year Ls = 2, second year Ls =, second year Ls = 8, second year Ls = 2, second year Ls = 24, second year Ls = 27, second year 7: Transient surface pressure in the northern hemisphere at different aerocentric longitudes during the first and second year of the MGS mission, taken from an MGCM experiment with data assimilation. Each frame is a polar stereographic projection of the northern hemisphere, with the north pole in the centre out to N around the edge, with the prime meridian pointing upward. Each plot is made at 4 UT, i.e. local solar time 4 at longitude. The remaining signal that can be seen throughout the year is the signature of the atmospheric thermal tides. Results broadly of this type would be expected from independent model experiments, but the details of the particular highs and lows, their strengths, locations and wavenumber, the times of wavenumber transitions etc, in the assimilation should reflect that particular year on Mars. The plot at L S =2 in the second MGS year of observations shows a striking transient high over the pole; this is a result of the beginning of the 2 global dust storm and transient changes in the atmosphere as a result of the sudden warming leading to a rise in pressure as more CO 2 ice sublimes. A climate database for Mars The results of MGCM simulations are potentially of great use for a variety of applications other than direct atmospheric investigations. One example is in spacecraft mission planning, e.g. providing upper atmosphere density profiles for satellite aerobraking or aerocapture, estimating entry profiles for landers and assessing the near-surface atmospheric conditions, both in terms of the mean and a likely range of variability. Another might be in providing trial profiles for retrievals of remotely sounded atmospheric observations. One immediate problem with such studies is that they often require many MGCM experiments, sampled at a particular location or time, or run under particular assumptions. This is a time-consuming undertaking, and very costly in computation time. It is also impractical to supply an MGCM to the likely users of such data and support their efforts to run the model and interpret the output, even if sufficient resources are available. The European Mars Climate Database (MCD) (Lewis et al. 999 describes the earliest version; see www-mars.lmd.jussieu.fr) was formulated by the LMD and Oxford groups, supported partly by ESA and CNES, with the aim of making MGCM data more easily and widely available in the community for use both as an engineering resource and for scientific studies. A particular strength of using an MGCM to compile a climate database is that it provides a physically consistent estimate of the environmental conditions on Mars for seasons, dust loadings and locations that are not covered by past observations. A previous set of environmental statistics for Mars were collected in the Mars Global Reference Atmosphere Model (MarsGRAM) (Justus et al. 996). MarsGRAM originally used a blend of observational data and simple physical models. Since 2 more recent versions of MarsGRAM have included data from Ames MGCM experiments. Seasonal variations are taken into account by Downloaded from by guest on 2 November August 2 Vol 44

8 8: A schematic diagram showing the orbit of Mars about the Sun. The orbital eccentricity (actually.9) has been exaggerated for clarity. The positions of aphelion and perihelion (at L S = 2 ) are shown by the dashed line. The 2 months used for the Mars climate database are numbered around the orbit, dividing the Martian year into equal segments of areocentric longitude. Northern hemisphere spring equinox (L S = ) is directly below the Sun as drawn, summer solstice (L S = 9 ) to the right, autumn equinox (L S = 8 ) above and winter solstice (L S = 27 ) to the right. The arrow indicates the rotation axis of the planet, at 2.9 obliquity. The colour shading shows the surface temperature on Mars, taken from the MCD at an approriate time of day for the position of the Sun in each case, with the colour scale varying from deep purple at 4 K to bright red at K, the highest temperatures are only reached close to perihelion. The position of the polar CO 2 ice caps can be seen as a region of cold surface temperatures. 9: (a) Mean entry profiles over 2 km altitude, taken from the MCD, for 2 different local times of day at twohourly intervals, at a tropical location, 4 E, N, for northern winter solstice, L S = 27. (b) The lowest 2 km of the altitude range on an expanded scale, showing the development of strong nocturnal inversions. altitude above surface (km) 2 dividing the martian year into 2 seasons, or months, each of areocentric longitude, as shown in figure 8. Within each month, the diurnal cycle is also represented by storing mean values of all atmospheric and surface fields from the model at 2 different times of day, illustrated by the generation of some sample mean entry profiles in figure 9. A simple measure of variability in the model is provided by also storing the variance of these fields over the month at fixed local time of day. It is often desirable to provide a large set of profiles as if sampled from the full GCM under identical conditions and time of day, but from many different Mars years, in order to gain some understanding of day-to-day variability. This variability is called large-scale variability in the database, because it derives from atmospheric processes that are modelled explicitly rather than very local variations. Simple measures of variance are not enough, since variability in one model field at any point is generally correlated with variability at other locations and in other fields. For example, a perihelion synoptic-scale weather system has both horizontal and vertical correlations between pressure, temperature and winds. It is desirable to be able to reconstruct this variability in some way that is much more efficient than re-running the MGCM many times. Large-scale variability in the database is modelled using an approach based on empirical orthogonal function (EOF) analysis (North 984, Mo and Ghil 987). A data set is formed by storing MGCM output at frequent intervals throughout a multiannual integration. A large covariance matrix is formed, based on this record, including covariances between variables at each location in the model atmosphere and between each atmospheric field recorded. The eigenvectors of the covariance matrix, or EOFs, form a linear basis such that those with the largest eigenvalues account for the most total variance. This means that it is possible to reconstruct the main characteristics of the original data from a limited set of EOFs, by ordering them according to their eigenvalues. Retaining just the largest 72 EOFs over the course of the : 2: 4: 6: 8: : 2: 4: 6: - 8: 2: 22: 8 altitude above surface (km) : 2: 4: 6: 8: : 2: 4: 6: - 8: 2: 22: 2 martian year from each MGCM experiment allows more than 9% of the total variance to be reconstructed, with realistic patterns of correlations in height, longitude and between different variables. The generation of the three-dimensional, multivariate EOF patterns and their amplitudes throughout the martian year is a time-consuming computational process. The advantage of a climate database is that the computation only need be done once, at the time of creation of the database. In use, the database software can rapidly reconstruct variability by adding proportions of the stored EOFs on to mean data. An illustration of the way in which EOFs can be used rapidly to build an ensemble of realistic profiles is given in figure a. The profiles shown here were generated by the EOF technique, but are similar in form and statistical properties to a real ensemble generated from a long run of the Mars GCM. Individual profiles that are anomalously warm at one height in the lower atmosphere tend to be similarly warm compared to the mean at other heights, as might 4 aphelion Downloaded from by guest on 2 November 28 August 2 Vol 44 4.

9 : (a) An ensemble of entry profiles all generated for 4 LT at 4 E, N, L S = 27. The mean profile is shown in black. Variability was generated using the large-scale EOF model from the MCD. (b) The same ensemble with variability added from the small-scale gravity wave model. altitude above surface (km) altitude above surface (km) be expected, although more complicated effects are seen higher, e.g. profiles that tend to be warm at 7 km are often relatively cool at km and above, in this case. Some account can also be taken of possible variability which is not modelled explicitly by the GCM, generally because of limits in resolution. The gravity wave drag parameterization for the Mars GCM has already been mentioned, and it is possible to add a set of small-scale waves of this type back on to simulated profiles, modelling the vertical propagation, breaking and saturation of the waves on each profile. A further illustration of a simple ensemble of profiles, this time with a gravity wave perturbation of vertical wavelength 6 km and random phase added, is shown in figure b. Summary Mars modelling is now at a relatively advanced state, compared to that for any other planet except for the Earth. Several different Mars GCMs exist and can produce apparently realistic simulations of martian weather and climate. This brief review has indicated some of the major areas of activity in model development, which include raising the model top above the natural break at the thermopause (around 2 km) and realistic simulation of the present-day dust and water cycles. There are still many improvements that can be made to the models treatments of subgrid-scale effects, such as gravity wave drag and the convective boundary layer, and the models will further improve with increasing computational power, allowing experiments at finer resolution. All are areas in which more and different new observations will be required to constrain and test the models. An area that has not been discussed is the simulation of possible past climate and climate change on Mars, perhaps associated with changes in obliquity and orbital eccentricity, but there is now some significant activity on these problems using different MGCMs. Two particular applications were discussed: the use of MGCMs to introduce knowledge of physical processes into a consistent systematic analysis as part of the data assimilation procedure and the means by which MGCM output may be made more easily accessible to the wider community in the form of a climate database. Both are becoming of increasing importance with the current level of interest in Mars. Stephen R Lewis, Atmospheric, Oceanic and Planetary Physics, Department of Physics, Oxford University, Oxford OX PU. 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