Icarus 242 (2014) 105111Contents lists available at ScienceDirect

Icarus

journal homepage: www.elsevier .com/locate / icarusA toy climate model for Marshttp://dx.doi.org/10.1016/j.icarus.2014.07.0290019-1035/ 2014 Elsevier Inc. All rights reserved.

E-mail address: hannu.savijarvi@helsinki.fiHannu SavijrviDepartment of Physics, P.O. Box 48, 00014 University of Helsinki, Finlanda r t i c l e i n f o a b s t r a c tArticle history:Received 28 February 2014Revised 31 July 2014Accepted 31 July 2014Available online 10 August 2014

Keywords:Mars, atmosphereMars, climateMars, polar capsMars, surfaceRadiative transferA toy climate model TCM was constructed for Mars. It returns the midday surface and near-surface airtemperatures, given the orbital parameters, season (Ls), latitude, thermal inertia, albedo, surface pressureand dust visible optical depth (s). The TCM is based on the surface energy balance with radiation termscalibrated against line-by-line calculations and surface heat flux terms against 1D model simulations. TheTCM air temperatures match various lander observations reasonably well, e.g. the 3.4 martian years ofrecovered T1.6m from Viking Lander 1.The results demonstrate strong sensitivity of Ts and T1.6m to the dust load. All the VL1 years suggest

major dust storms around Ls 270300, while s appears only moderate in the simultaneous VL2 observa-tions. The TCM was further extended to increased surface pressures, using moist 1D simulations. Thegreenhouse warming remained modest and the diurnal range was small in a thick CO2 atmosphere. Asthe CO2 condensation temperature Tc increases rapidly with pressure, the range of afternoon tempera-tures at various latitudes remains quite narrow in a thick atmosphere. The TCM can also deal with orbitalparameter variations. A high-eccentricity, high-obliquity case was demonstrated for the present 7 mb (Tc150 K) and a 1 bar CO2 atmosphere (Tc 195 K). High obliquity of 45 led to quite wide winter polar icecaps, which extended down to the subtropics. In the 1 bar case even the equatorial Ts was close to Tcat aphelion; a major dust storm at that time led to a tropical CO2 ice cover.

2014 Elsevier Inc. All rights reserved.1. Introduction

The climate of Mars has undergone many variations and eventhe present climate is quite extreme in the sense that advancingand then retreating polar ice caps with temperatures around150 K extend to latitudes as low as 5060 every martian year,while in the equatorial regions the surface temperatures can soarwell above 273 K. Solar radiation is the only important heat sourcefor the surface and atmosphere of Mars, but the strongly varyingorbital parameters have made its distribution on the surface quitevariable in time. On Mars, the topography, the thermal inertia andthe surface albedo vary by large amounts. The present 95% CO2atmosphere is thin (69 mb) and dusty, with traces of H2O, but itmay have been a lot thicker in the past (Read and Lewis, 2004).

A good way to study the climate of Mars is to use general circu-lation models adjusted to the conditions of the study period. Thepresent climate is reproduced quite well by these models (e.g.Haberle et al., 1999; Richardson and Wilson, 2002; Madeleineet al., 2012) and they have hinted at findings, e.g. ancient tropicalmountain glaciers (Fastook et al., 2008), traces of which have beenobserved. A drawback of the GCMs is that they need huge com-puter resources, skill in the development and running, and skillalso in the interpretation of the results. Smaller models, e.g. thelocal column (1D) models, have also been relatively successful insimulating the present local temperatures on Mars as observedby the landers (e.g. Savijrvi, 1999, 2012a,b; Savijrvi andMttnen, 2010). Both model types indicate that the daytime sur-face temperature is strongly forced by the incoming net solar radi-ation and the outgoing near-blackbody surface thermal radiation(Petrosyan et al., 2011). These can be calculated rather exactly,whereas the less accurately known turbulent surface heat fluxesand the thermal radiation from the thin atmosphere are far smallerand might be parameterizable. Hence the surface temperaturecould perhaps be estimated knowing only the properties of theground and solar radiation at the surface. The practise and accu-racy of such a scheme motivated the present study.

On the other hand, if only one variable were to characterize theclimate of a planet, the midday near-surface temperature at anysite and season is a good candidate. This is aimed for Mars here.Based on the above reasoning, a toy climate model (TCM) is con-structed with the help of line-by-line radiative transfer and 1Datmospheric model results (Sections 2 and 3). The TCM is validatedfor various lander sites in Section 4 and is shown to simulate theexisting lander-observed surface and near-surface air tempera-

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106 H. Savijrvi / Icarus 242 (2014) 105111tures reasonably well. The role of dust is here quite important: theViking 1 temperature data as interpreted with the TCM resultswould appear to indicate major regional dust storms every winter,whereas major storms have been less frequent in the recent yearsof intense observation (a change in climate?). In Section 5 the TCMis extended to higher surface pressures (up to 2 bar of CO2) with ademonstration for a high-pressure high-obliquity paleoclimatecase. The presented algorithms and parameterizations might beuseful for many other applications and the easily coded TCMmay also serve as a tool for education.

The TCM is in fact an energy balance model (EBM) in the tradi-tion of the invaluable BudykoSellers-type EBMs for the Earth (e.g.Sellers, 1969; North, 1975) and Mars (e.g. Hoffert et al., 1981;Kasting, 1991; Haberle et al., 1994). EBMs are usually aimed atthe zonal or global mean annual energy balance at the top of theatmosphere, whereas the TCM produces the instantaneous localmidday surface temperature incorporating all important effectssuch as those from dust, convection and conduction. Like the otherenergy balance models, it can be used to rapidly chart changes inclimate due to changes in the Sunatmosphereground systemfor a wide parameter space and so could for instance guide thetime-consuming GCM research.Fig. 1. Solar radiation onto a horizontal martian surface g as a function of the solarheight angle and dust visible optical depth s. Marks are from LBL calculations, linesare Eq. (3). The dotted line is the top-of-the-atmosphere flux S sin(h). S is here610.3 Wm2 and ps, 6 mb.2. Solar radiation

The solar radiation S at the distance r from the Sun is S = So/r2,where So is the observed Earth solar constant, about 1367Wm2

at the Earth mean distance of r = 1.0 AU (the fainter Sun of the dis-tant past could be taken into account by reducing So). The distanceof Mars from the Sun varies during the martian year of 668.6 solardays (sols, 88,775 s) due to the elliptic orbit. The four orbitalparameters with their present values are (1) the mean distance d,1.52366 AU, (2) the eccentricity of the orbit e, 0.09341, (3) the tiltangle (obliquity) ho, 25.19 and (4) the areocentric longitude Ls ofperihelion Lsp, 251 (Read and Lewis, 2004). Ls is the seasonalindex: 0 (180) during the northern hemisphere spring (autumn)equinox and 90 (270) in the northern summer (winter) solstice,one sol thus advancing Ls by 0.54 on the average. Presently Marsis closest to the Sun (Lsp = 251) prior to the southern summer sol-stice (Ls 270). Due to the relatively high eccentricity the southernhemisphere of Mars thus receives a lot of solar radiation duringsummer, and conversely, southern winters tend to be harsh (cf.Fig. 2). The orbital parameters have varied widely in the past, per-haps leading to huge climate changes.

The distance r and hence S(Ls) can be calculated for any combi-nation of d, e and Lsp from

r d 1 e2=1 e cosLs Lsp; S So=r2: 1

At a latitude u the solar height angle h at midday (12:00 localsolar time, LT) is determined via

sdecl sinho sinLs; cdecl ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 s2decl

q; sinh

sinu sdecl cosu cdecl; 2

where the current declination angle of the Sun is sin1(sdecl).The midday solar flux onto a horizontal plane at the top of the

atmosphere, S sin(h), can thus be calculated via (12), given thelatitude u, season Ls and the four orbital parameters d, e, ho andLsp. In the atmosphere the solar radiation is absorbed and scatteredby air molecules and by dust particles. The extinction effects of thelatter are characterized by the visible aerosol optical depth s. Dustamounts vary widely in Mars, the observed s being around 0.2 dur-ing relatively clear periods but rising to 12 during the hot south-ern summers, and even to 45 during the major dust storms thatmay then arise occasionally. The simultaneous absorption, emis-sion and scattering of the thermal longwave (LW) and solar short-wave (SW) radiation by the mixture of the CO2 molecules and dustparticles is a difficult, strongly wavelength-dependent problem,which needs quite sophisticated and computer-intensive multiplescattering spectral line-by-line (LBL) radiative transfer methodsfor good accuracy. Such reference LBL calculations were made inSavijrvi et al. (2005) for the present average conditions on Mars.The points in Fig. 1 display the LBL-produced total solar radiationat the surface (sum of direct and diffuse parts = global radiationg) as the function of s and h. Strong dependence on both s and hcan be seen. A simple fit S sin(h) 0.99exp(0.18s/sin(h)) pro-duces g within 17 Wm2 of the LBL results for s 01 but the val-ues are less accurate in dust storm conditions. A more accurate fit(Eq. (3); lines in Fig. 1) is obtained by handling the direct and dif-fuse solar radiation separately. This leads to

x 1 exp0:45s=sinh0:8;g S sinh 0:985 exps= sinh 1:89x 1:67x2;

3

where the first term in g gives the direct radiation within0.8 Wm2 of the LBL results, the factor 0.985 taking into accountthe extinction by CO2. The x-terms fit the diffuse (scattered) partwithin 10 Wm2 of the LBL results for any s and h. The x2 termis physically due to the fact that with a lot of dust in the air the scat-tering of sunlight to the space increases (Mars looks blurred andwhiter during major dust storms), so that relatively less of the scat-tered light then makes it to the surface.

3. Thermal radiation and the heat fluxes at the surface

The LBL calculations provide a convenient reference for han-dling of the solar and thermal radiation in the martian atmosphere.Although the global radiation g is the dominant midday sourceterm in the heat budget of the surface, there are also other terms.The budget reads

g1 a Fd egrT4s Ho G 0; 4

neglecting the phase change effects (sublimation and freezing ofwater and CO2 ice), which are insignificant outside the polar areas.Here a is the surface albedo, g(1 a) the absorbed SW radiation, Fdthe downwelling longwave radiation from the atmosphere andegrTs4 = Fu the upwelling LW radiation from the surface (eg is thesurface emissivity 0.96, r the StefanBoltzmann constant and Tsthe ground surface temperature). Ho is the upward convective heatflux from the surface, and G the conduction of heat into the ground.

We make here the basic assumption that in the nearly cloudlessmidday conditions of Mars extra-polar latitudes both Ho and G areproportional to g(1 a): the more ground-absorbed solar radia-tion, the more energy there is available for convection and conduc-tion. Thus we set Ho G = gr g(1 a) where gr (ground) is a

H. Savijrvi / Icarus 242 (2014) 105111 107coefficient to be determined. The downwelling LW radiation Fddepends on the other hand on the current profiles of dust andtemperature in a rather complex fashion. A crude simplificationis to assume an effective emissivity e for the air column, usingthe surface temperature as a proxy for the associated dust andtemperature profiles that determine Fd. This is most useful duringthe midday hours, when the temperature profile is adiabatic upto several kilometres on Mars (Fig. 2) (except for a shallowsuperadiabatic surface layer) and the dust is well-mixedin this highly convective layer (Savijrvi and Mttnen, 2010).Hence we set Fd = erTs4. The benefit of these assumptions isthat one can now write the surface heat budget in the formg(1 a)(1 gr) rTs4(eg e) = 0 and solve for Ts, giving

Ts g1 a1 gr=reg e0:25; 5

which is the core of the TCM. The midday and afternoon air temper-atures as measured at 12 m heights by the various landers havebeen 9590% of Ts, so one can take e.g. T1m to be crudely c Ts withc 0.95. If Ts falls below the CO2 condensation temperature Tc (e.g.no sunshine in the polar winter), Ts and T1m are set to Tc to indicateCO2 ice, the condensation/sublimation of which keeps Ts at Tc. Forthe present surface pressures Tc 150 K; the expressionTc = 148.6 + 6.48 ln(0.135ps) + 0.39 ln2(0.41ps), a fit to p(Tc) valuesof Kasting (1991), gives Tc within 0.8 K for ps (in mb) up to 2 bar.

The crucial matter is now to determine the factors gr and e. Hereuse is made of the University of Helsinki column model (equationsin Savijrvi, 1999), which has quite successfully simulated theobserved 12 m temperatures of all the landers on Mars. This 1Dmodel resolves the atmosphere in 30 layers and the ground in fivelayers. It uses improved delta-discrete-ordinate SW and pressure-scaled emissivity LW radiation schemes (validated via the LBLresults), which take into account CO2, dust, water vapour, cloudsand fog. Turbulence is via the MoninObukhov theory in the lowestlayer with a mixing length theory aloft. The ground heat transferconsists of a numerically fairly accurate thermal diffusion forcedby conduction G, which is solved from the surface heat budget(4) at each model time step of about 10 s.

The 1D model has reproduced the daily and annual cycles ofthe mini-TESobserved boundary layer temperatures at therover Spirit (Savijrvi and Kauhanen, 2008). Hence weestimate the factors gr and e via 1D simulations at Spirit(a = 0.20, I = 285 J m2 s0.5 K1) during the low-dust season(Ls = 57, ps = 7 mb, s = 0.2) where the results were particularlyaccurate (Savijrvi, 2012a,b). The 1D model is run varying I ands, with gr and e determined from the models midday surfacefluxes. The midday surface winds are 45 ms1 and the precipita-ble water content is around 2 lm in the experiments, as observedby the mini-TES (Smith et al., 2006). The simulations (examplesgiven in Tables 1 and 2) suggest that the expressionsFig. 2. Spirit mini-TES-retrieved air temperature T at 1, 100 and 1000 m heights at16LT (from Smith et al., 2006), and the TCM T1m with and without dust.gr 0:41 0:185 lnI=285 0:03s;e 0:10 0:11sI=2850:1; 6

describe the midday gr and e reasonably well as functions of theground thermal inertia I and atmospheric dustiness s. The logarith-mic dependence of gr on I reflects the strong diurnal surface tem-perature variations at low I. The effective emissivity of 0.10without dust (i.e. for CO2 only) is less than the values 0.150.16 sug-gested by Leovy (1982) and Savijrvi et al. (2005), the reason beingthat e here refers, instead of the usual near-surface air tempera-tures, to Ts, which during the midday hours is 1525 K higher thanthe air temperature at 12 m (cf. Tables 1 and 2). With that takeninto account (6) also agrees with the reference LBL results for mid-day conditions.

The TCM thus consists of Eqs. (1)(3), (6) and (5), applied in thatorder. It is formally a zero-dimensional energy balance model,returning the midday surface temperature Ts. The near-surfaceair temperature is then approximated from Ts for comparison withthe measured lander mission values. The no-dust case is obtainedfor comparisons by setting s = 0.

4. Results

The TCM is now applied at the southern hemisphere Spirit site(Gusev Crater, 14.6S) using the present orbital parameters (Sec-tion 2). The mini-TES-derived local s varied mainly between 0.3and 1.3 during the first Spirit year (Smith et al., 2006). There wereweak dust storms at Ls 150 and 230 with s temporarily up to2, but no temperature retrievals for T1m exist for those times. Asimple sine function s = 0.80.5 sin(Ls) is hence used in the TCMin order to describe schematically the annual dust cycle asobserved at Spirit.

Fig. 2 displays the mini-TES-retrieved 15:4516:15LT air tem-peratures at 1 m, 100 m and 1000 m heights at Spirit from Smithet al. (2006), and the TCM T1m curve with c = 0.95. The no-dustTCM T1m is shown for comparison. The differences of about 4 Kbetween the observed T100m and T1000m obey the adiabatic lapserate (4.5 K/km on Mars), while the larger differences between T1mand T100m reveal the strongly superadiabatic surface layer dis-cussed above and in Savijrvi (2012b). The TCM T1m is withinthe cloud of the observed T1m, whereas the no-dust T1m tendsto the high side. The TCM curves of Ts for Spirit and Opportunity(not shown) similarly fit quite well the samples of the mini-TES-retrieved afternoon Ts from Spanovich et al. (2006). Dust appearsto act as a thermostat for the southern hemisphere: increased dustamounts during the hot perihelion/summer season (Ls 251270)tend to keep the surface temperatures lower than withoutdust in Fig. 2, while during the cold aphelion/winter season(Ls 7190) the dust load is minimal.

Fig. 3 shows the 12LT Viking Lander 2 T1.6m (PDS observa-tions) and T1.6m from the TCM for this site (48N, a = 0.24,I = 360 J m2 s0.5 K1, c = 0.91). The Spirit sinusoidal s is used,which roughly matches also the VL2 observations of s. It appearsadequate for the second VL2 year but the first year would needslightly more dust during the summer and some dust decay ataround sol 290 (Ls 290) for a better match with the observedT1.6m. The VL2 winter midday temperatures drop to near 160 Kat Ls 270. The moderate dust load of s 1.3 has here a large rolebecause of the low wintertime solar height angles at 48N; theno-dust comparison is 192 K. A major dust storm at around Ls270 might hence extend the northern polar ice cap to the VL2latitude of 48N.

Fig. 4 (top panel) shows the TCM T1.6m at every 30 of Ls on theViking Lander 1 site (22.3N, a = 0.22, I = 283 J m2 s0.5 K1,c = 0.91), together with 2245 sols (3.4 martian years) of repro-cessed VL1 T1.6m observations at 12LT (mean of 11:3012:30)

Table 1Ts, T1m, the surface fluxes and e = Fd/(rTs4), gr = (G + Ho)/(g(1 a)) at 12LT from Spirit site 1D model simulations at Ls = 57 as the function of ground thermal inertia I(J m2 s0.5 K1). The absorbed solar radiation g(1 a) is 311.2 Wm2. Fu = egrTs4, eg = 0.96. No dust; s = 0.

I Ts, K T1m, K Fd, W m2 Fu, W m2 G, W m2 Ho, W m2 e gr

485 236.0 223.1 18.6 168.8 151.6 9.5 0.11 0.52385 241.1 226.2 19.3 183.8 136.2 10.6 0.10 0.47285 247.4 229.6 20.3 204.0 114.3 13.2 0.10 0.41185 256.0 234.9 21.8 233.9 84.1 15.1 0.09 0.3285 266.5 241.4 24.0 274.7 42.7 17.9 0.08 0.19

Table 2As Table 1 but for I = 285 J m2 s0.5 K1 with variable dustiness s.

s Ts, K T1m, K g(1 a), W m2 Fd, W m2 Fu, W m2 G, W m2 Ho, W m2 e gr

0 247.4 229.6 311.2 20.3 204.0 114.3 13.2 0.10 0.410.5 242.7 226.6 279.7 29.1 189.0 108.3 11.7 0.15 0.431.0 238.3 223.8 248.3 37.5 175.5 99.9 10.5 0.20 0.442.0 230.2 219.3 190.6 51.8 152.9 81.8 7.8 0.33 0.475.0 214.3 210.3 78.0 78.8 114.4 40.0 2.4 0.66 0.54

Fig. 3. The 12LT mean temperatures at 1.6 m from Viking Lander 2 (+) with the TCMT1.6m (solid line) and the TCM no-dust T1.6m (dashed line). Ls at 90 intervals isindicated by the vertical lines, Ls 270 being the solid line.

Fig. 4. Top panel: The 12LT mean temperatures at 1.6 m from Viking Lander 1 (+;Kemppinen et al., 2013) with the TCM T1.6m (solid), TCM no-dust T1.6m (longdashed) and TCM T1.6m with the VL2 dust scenario (short dashed) at 30 intervalsof Ls. Mid panel: The dust scenarios. Bottom panel: The 12LT TCM solar fluxes; g1 isfor VL1 dust, g2 for VL2 dust.

108 H. Savijrvi / Icarus 242 (2014) 105111from Kemppinen et al. (2013). The VL1 dust scenario (mid panel) isbased on the first year of observations; note the big dual duststorms at Ls 210 (s 2.5) and at 270300, with s up to 4 at Ls300. The VL2/Spirit scenario is also shown for comparison (shortdashed lines). The dust scenarios are repeated for the other years(in lack of observations). This makes the TCM curves identical forall the years. The TCM T1.6m with the VL1 dust nevertheless fitsthe VL1 T1.6m observations reasonably well for the first and thirdyear, whereas those with the VL2 dust tend to stay too warm inwinter and in spring. Unfortunately the VL1 data is missing for sols8001000 due to a missing data tape.

The effects of the dust storms are striking: the observed winter-time 1.6 m temperatures fall below 200 K at Ls 270300 duringthe first and also during the third VL1 year while the no-dustTCM then displays 240 K. All the first three Viking years appearto indicate major dust storm conditions (low T1.6m) during Ls300320 at the VL1 site and low temperatures at around sol2200 (Ls 210) on the fourth year in the end of the period ofobservations.

The moderate VL2 dust scenario produces winters clearly toowarm at the VL1 site by the TCM (Fig. 4, top panel). Therefore itappears that major regional dust storms did arise at the VL1 siteevery winter (except perhaps the second), but they did not growglobal, as the simultaneous VL2 observations and the TCM T1.6mresults (Fig. 3) indicate much less dust at the VL2 site. This is inter-esting and warrants further studies, since the recent years ofintense observations have not resulted in major regional duststorms being observed every winter on Mars.

The bottom panel of Fig. 4 displays the TCMmidday solar fluxesat the VL1 site. The dashed line S (Eq. (1)) demonstrates the effectof the eccentric orbit, while S sin(h) (thin line, Eqs. (1) and (2))smooths the eccentricity effects seasonally at the subtropical VL1latitude of 22N. The solar radiation at the surface g (thick line,Eqs. (1)(3)) is strongly damped every VL1 winter, when the dustamounts are high. The SW transmissivity of the atmosphere thengets as low as 0.3 at Ls 300 with the VL1 dust scenario, which cor-responds to a relatively thick low cloud on the Earth.

Fig. 6. Top panel: The afternoon T1m at some key latitudes from the TCM for typicalpresent-day Mars conditions. Bottom panel: As the top panel but for an extremeorbital case with eccentricity of 0.12, obliquity of 45 and perihelion at Ls 270.

H. Savijrvi / Icarus 242 (2014) 105111 109Fig. 5 (top panel) presents the TCM midday T1m at the polarPhoenix site (68N, a = 0.18, I = 150 J m2 s0.5 K1, c = 0.93) withthe same schematic s as for Spirit and VL2. The summer tempera-tures reach 242 K at Ls 90 and 239 K at Ls 122 (as observed atPhoenix, Savijrvi and Mttnen, 2010) but then start to sink rap-idly with CO2 ice indicated at the surface during Ls 210330. Thesolar fluxes (lower panel) reveal that the low midday solar heightangles combined with the increased dust loads toward the north-ern winter force the TCM temperatures to Tc well before the polarnight actually begins at Ls 240. Likewise, the springtime melting ofthe polar ice cap takes place only from about Ls 330 onward; about60 sols after the first sunrise.

Fig. 6 illustrates schematically the martian climate, displayingthe annual TCM 1 m noon temperatures at latitudes 75N, 45N,equator, 45S and 75S for the sinusoidal Spirit s(Ls), ps of 7 mb,no clouds, ground thermal inertia of 300 J m2 s0.5 K1 and albedoof 0.20 at all latitudes. The top panel is for the present orbitalparameters (Section 2). The polar latitudes are ice-covered in win-ter but warm up during the summer. The lower panel applies thesame typical present-day atmospheric and ground parameters,but for an extreme orbital case with high eccentricity of 0.12, highobliquity of 45 and perihelion at Ls 270 (such values may haveoccurred individually in the martian past, Read and Lewis, 2004).One may note that the warmest temperatures occur at 45S duringthe southern summer, despite the dust amounts of s 1.3, whilethe equatorial latitudes display a simultaneous notch and thehigher latitudes indicate winter polar ice caps, which extend downto the subtropics on both hemispheres. Thus mountain glaciersmay well have grown in such conditions, perhaps developing lay-ering of dusty ice, which partially melts in the intense summersunshine and freezes again in the coldness of winter. If in suchorbit change simulations the longitude of perihelion Lsp is otherthan 251270, the dust cycle maximum should perhaps beadjusted to follow it, e.g. by defining s = 0.8 + 0.5 cos(Lsp Ls).

Fig. 6 is just a demonstration of the potential of the TCM in sim-ulating the present, past and future climates of Mars. Further addi-tions could include the faint young Sun paradox (by simplydecreasing So by 2530%), and variations in the surface pressure(atmospheric density), which is parameterized into the TCM inthe next section.Fig. 5. Top panel: The midday TCM T1m for the Phoenix site (68N) with the no-dust comparison. Bottom panel: The 12LT solar fluxes from the TCM.5. Pressure effects greenhouse Mars?

The topographic and other surface pressure variations were notyet included in the TCM. The topography is quite variable on Marswith high mountains and low valleys, and the local surface pres-sures may also vary temporally as much as 30% during the yeardue to the freezing and sublimation of CO2 at the poles. Further-more, the surface pressures may have been a lot higher on ancientMars. To include the pressure effects, the 1D Spirit model for Ls 57with s = 0 was run as before but with increased surface pressures,after checking that its radiation results did agree with those of anarrow band RT model (Savijrvi, 2006, 2012b), in which the pres-sure and temperature effects on the spectral lines of CO2 and H2Oare properly included. The initial precipitable water content is keptat 2 lm as in the previous experiments. The results are in Table 3,which displays Ts and T1m at 06LT and 12LT, T at 10 km height (asan indication whether the free atmosphere is warming or coolingin these greenhouse gas experiments) and the surface fluxes at12LT.

Table 3 shows that as the surface pressure increases, the down-welling solar radiation g decreases (due to increased absorptionand Rayleigh scattering by the thicker CO2 atmosphere) but thedownwelling thermal radiation Fd increases relatively more. Thesensible heat flux increases dramatically, whereas conduction tothe ground decreases. The 06LT surface and near-surface tempera-tures increase, the 12LT temperatures decrease, and all the 1 mtemperatures tend closer to the surface temperatures. In the7 mb atmosphere the 12/06LT mean of T1m is 206 K and the differ-ence is 47 K, whereas in the 1000 mb CO2 atmosphere the mean is213 K but the difference only 13 K. Thus the mean temperaturedoes increase, but only about 7 K near the surface; a similar 7 Kupward trend is seen at 10 km. The increase of ps from 7 to2000 mb therefore does not seem to lead to a strong greenhousewarming on Mars without other warming effects, a result in agree-ment with some recent GCM experiments (Forget et al., 2013). TheCO2 15 lm band is simply so narrow that the LW broadband effec-tive emissivity e does not grow to values large enough for a strongsurface temperature increase, even with the help of some watervapour in the cold air. Other gaseous or aerosol LW absorbers, suchas volcanic sulphur/ash products, thick clouds (CO2, H2O) or heavy

Table 3As Table 1 but for increased surface pressures, I = 285 J m2 s0.5 K1, s = 0. The 06LT Ts, T1m and 12LT T at 10 km height are also shown.

ps, h Pa 06LT, Ts 06LT, T1m 12LT, Ts 12LT, T1m 12LT, T10km g(1 a), W m2 Fd, W m2 G, W m2 Ho, W m2 e gr

7 179.9 182.3 247.4 229.6 192.5 311.2 20.3 114.3 13.2 0.10 0.4120 181.9 184.9 246.5 231.6 196.8 310.0 28.5 108.7 29.1 0.14 0.4450 184.1 187.3 243.4 231.4 198.6 308.7 35.3 94.5 58.5 0.18 0.50

100 186.3 189.4 239.0 229.4 199.2 307.5 39.3 77.3 92.1 0.21 0.55200 189.9 192.7 233.4 226.5 199.6 305.9 43.3 60.1 127.7 0.26 0.61500 197.5 199.6 225.8 222.1 199.8 302.1 47.5 44.0 164.1 0.32 0.69

1000 204.9 206.3 221.3 219.2 199.9 296.7 49.9 33.5 182.5 0.37 0.732000 211.0 211.8 218.9 217.7 200.0 286.5 53.4 26.9 188.1 0.41 0.75

110 H. Savijrvi / Icarus 242 (2014) 105111dust might change the situation but these were not assumed in ourexperiments. In particular opaque water ice clouds might providethe extra emissivity for the warmer surface temperatures (Urataand Toon, 2013). The TCM could be used to chart what kind ofincrease of e together with the possible associated decrease in gwould be needed to produce a given paleo-Ts, in order to pin downcandidates for the extra absorbers.

The pressure effects can now be parameterized to the TCM withthe help of Table 3. It appears that the increased SW extinction ofthe thicker CO2 atmosphere can be taken into account by replacingthe factor 0.985 in (3) by exp{0.011 (ps/7 mb/sin(h))0.34}. Thesurface pressure effects appear nearly logarithmic in e and gr,and can be included by adding new terms: +0.054 ln(ps/7 mb) toe and +0.062 ln(ps/7 mb) to gr of (6). These can also be used to dem-onstrate the present topographic effects by setting the surfacepressure ps(z) = po exp(z/H) for any grid point or site s, where pois 7 mb as used in the Spirit experiments of Tables 1 and 2, z isthe height of s relative to the Spirit site altitude (1.9 km MOLA),and H is the scale height, 11 km in Mars.

Fig. 7 demonstrates the TCM-predicted midday T1m as in theextreme orbital case of Fig. 6 but for a thick 1000 mb CO2 atmo-sphere, without dust (upper panel) and in a global dust storm,s = 2.5 (lower panel), using the above parameterizations. Herethe CO2 condensation temperature Tc is 194.6 K and c = T1m/Ts = 0.99 because of the thick atmosphere (cf. Table 3). Two thingsbecome clear from Fig. 7. Firstly, even if the diurnal mean temper-atures have increased due to the greenhouse warming by the thickFig. 7. As Fig. 6, lower panel (the extreme orbital case), but for a 1000 mb CO2atmosphere without dust (s = 0, upper panel) and in a global dust storm condition(s = 2.5, lower panel).CO2 atmosphere, the midday 1 m temperatures are neverthelesslower at all latitudes than in Fig. 6, because the diurnal range isnow small (cf. Table 3). Secondly, the vastly increased Tc makesthe ice-covered winter polar caps very wide; even the equator isclose to freezing in the dust-free case during the aphelion season.Thus the temperature zone available for the afternoon near-surfaceair temperatures is quite narrow in a thick-atmosphere Mars, espe-cially if there is dust in the air.

A major dust storm at around aphelion leads to a temporarytropical CO2 ice cover (Fig. 7, lower panel) according to the TCM.Although thick dust might be unlikely in a thick atmosphere, thisexercise nevertheless demonstrates the capacity of the TCM to rap-idly chart given scenarios of p and s for the past and present.6. Concluding remarks

A simple and extremely rapid toy climate model TCM wasconstructed for Mars. It returns the midday surface temperatureTs and an estimate for air temperature at 12 m height, given theorbital parameters, the season (Ls), the site latitude, thermal inertiaand albedo, and the current atmospheric surface pressure and dustvisible optical depth (s). The model is based on the surface energybalance, in which the radiation terms have been parameterizedusing line-by-line and narrow band model RT results, and the sur-face heat flux terms using results from realistic 1D model simula-tions with dust and water vapour.

The TCM air temperature results appear to match all the avail-able lander observations in the latitude range 15S68N during allseasons on Mars. In particular the long preliminary data set for 3.4martian years of the reprocessed and recalibrated T1.6m observa-tions from Viking Lander 1 (Kemppinen et al., 2013) is reasonablywell simulated. These validation results demonstrate strong sensi-tivity of Ts and T1m to the current dust load. All the three first VL1years, for instance, appear to display big dust storms at the VL1 site(22N) around Ls 270300, and one is starting at around Ls 210 onthe fourth year, while the dust loads were apparently much moremoderate at the VL2 site (48N) in the simultaneous VL2 T1.6mobservations of 1.5 martian years.

The TCM was extended via 1D moist model simulations toinclude the effects of increased surface pressure with the resultthat in a thick CO2 atmosphere the diurnal range was small andthe greenhouse warming remained modest. Hence the afternoontemperatures were in fact about 10 K lower in a 1 bar atmospherethan in the present 7 mb atmosphere, despite the 7 K increase inthe diurnal mean temperatures. Furthermore, since the CO2 con-densation temperature Tc increases rapidly with pressure (from150 K at 7 mb to 195 K at 1 bar), the range of afternoon tempera-tures at various latitudes is quite narrow in a thick martian CO2atmosphere.

The TCM can also deal with orbit parameter variations. Thehigh-eccentricity (0.12) high-obliquity (45) case was demon-strated for the present 7 mb and for a 1 bar CO2-sphere. High obliq-uity led to quite wide winter polar caps, which extended down to

H. Savijrvi / Icarus 242 (2014) 105111 111the subtropics in both cases. In the 1 bar case even the equatoriallatitudes were dangerously close to Tc, to the extent that a duststorm at aphelion triggered a tropical CO2 ice cover.

The TCM in its present form needs the surface pressure anddustiness as external parameters, which limits its usefulness tosome extent. However, it could be coupled into mass budget mod-els (e.g. Haberle et al., 1994; Greve et al., 2010), providing rela-tively accurate surface temperatures for them, while the massmodels would provide the surface pressures and perhaps dustinessfor the TCM.

Acknowledgments

The preliminary Viking Lander 1 dataset was kindly provided byDr. Ari-Matti Harri and his Finnish Meteorological Institute team.The data is presently at the validation phase. This work was sup-ported by the Finnish Academy Grants 132825 and 131723. Thetwo reviewers provided thoughtful comments that improved thearticle.

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A toy climate model for Mars1 Introduction2 Solar radiation3 Thermal radiation and the heat fluxes at the surface4 Results5 Pressure effects greenhouse Mars?6 Concluding remarksAcknowledgmentsReferences