SUPPLEMENTAL MATERIAL
Materials and Methods
Model Description
In our 1D radiative-convective atmospheric model there are 55 wavelength bands in
which we use the correlated-k method to calculate the optical depths of the two gases
involved in this simulation, CO2 and H2O. The albedo ranges from 0.02 to 0.29 in the
infrared and from 0.001 to 0.26 in the visible. A 2-stream radiative transfer model
calculates the heating rate at each atmospheric level, while eddy diffusion handles the
vertical transport of static energy in the model. The static energy is then updated both
radiatively, from the heating rates, and via vertical transport and is used to update the
temperature and pressure at each atmospheric level. The surface pressure of CO2 is
assumed to be 150 mbar (13). We divide the atmosphere into 50 atmospheric layers
extending to 100 (200, 250) km for the 100 (200, 250) km object. The relative humidity
is calculated at each atmospheric level at every time step as the temperature evolves. The
time step ranges from 0.001 seconds to 8 hours, depending on model-determined
stability. When the humidity at a particular level exceeds 100%, the relative humidity is
decreased to 100%, new mixing ratios for the water are calculated, and the water rains
out to the “ground” where it is saved in an accumulating puddle. As the injected H2O
rains out we add a radiatively inert gas to the atmosphere to maintain hydrostatic
equilibrium. This is done for numerical convenience, though one could argue for
degassing of adsorbed CO2 and other materials from the warming regolith. In reality
clouds would form and the atmosphere would undergo horizontal transport to equalize
pressure gradients. A general circulation model is needed to more precisely model the
atmospheric evolution, to understand how CO2 might desorb, and where water might
preferentially rain out.
The atmospheric model is coupled to a time-marching, finite-differencing subsurface
model that calculates the temperature in 30 unequally spaced subsurface layers that
extend downward to 900 m. The subsurface model calculates the temperature change by
conduction in all layers. Conduction, radiation, and sensible heat to the atmosphere make
up the boundary condition at the surface layer. The subsurface model solves the diffusion
equation explicitly, using a thermal diffusion coefficient, k, of 2.4 W m-1 K-1, a density,
ρ, of 2500 kg/m3 and a specific heat, Cp, of 1400 m2 s-2 K-1 (6). We solve for subsurface
heating by dividing the subsurface into layers. In the top layer, the sensible heat is
calculated by C∆Τ, where C is a sensible heat constant, given by Cpsoil ρair vdep where we
have assumed a value of 1 cm/s for the deposition velocity, vdep. Radiation upward from
the top layer of the soil is simply given by εσT4 where emissivity, ε, is wavelength
dependent, and always ~ 1. When a layer's temperature exceeds the freezing point of
water, the amount of water melted is calculated and tabulated, until the layer is dry. The
water melted in each layer is summed to yield a total potential amount of water melted in
the ground (Fig. 2).
Fig. S1. From the crater record we can determine how many impacts of a given size
occurred in Martian history. Figure 1A shows impactor diameter as a function of transient
and final crater diameter (S1, S2). Figure 1B shows the cumulative number of impactors
larger than a given size (3). In 1A the craters listed at a single data point are craters which
are larger than the data point labeled below them, but not larger than the data point itself.
For example, Herschel and Deuteronilus B are both larger than Lowell but not larger than
the point 300 km. Each Martian landmark (except those indicated by +) is a multi-ring
impact basin so it is difficult to ascertain which ring corresponds to the final crater
diameter, unless the basin has only two rings. Thus we have plotted the second ring in all
instances, and if the second ring is also the outer ring, it is indicated by (o). Utopia’s
secondary, outer ring is larger than the scale of the plot at 4715 km.
1)Deuteronilus A
2)Liu Hsin (o), near Columbus (o), Ptolomaeus (o), Gale (o), Philips (o), Molesworth (o),
Lowell (o), Lyot (o)
3)Kaiser (o), Deuteronilus B (o), Kepler (o), Galle (o), Aram Chaos, Herschel (o)
4)Al Qahira, Nilosyrtis Mensae, Antoniadi (o), southeast of Ma’adim Vallis
5)Huygens (o), Ladon, Schiaparelli (o), Southeast of Hellas (o)
6)Al Qahira A, Cassini, Overlapped by Schiaparelli (o), Mangala (o), Holden (o),
Arcadia A (o)
7)Cassini A, Overlapped by South Crater
8)Sirenum, Amazonis+, overlapped by Newcomb (o)
9)West Tempe+, South Polar+
10)southeast of Hephaestus Fossae (o)
11)Argyre
12)South Hesparia (o)
13)Arcadia B, Acidalia
14)Chryse, Elysium
15)Isidis (o), Memnonia (o)
16)Hellas, North Tharsis
17)Daedalia B, Scopulus (o)
+Have only one ring
SOM References
S1. H.J. Melosh, Impact Cratering A Geologic Process (Oxford University Press, New
York, 1989), p. 121. We used Equation 7.8.4 modified to include an incidence angle to
compute the transient crater diameter as a function of impactor diameter in Figure 1:
D = 1.8 ρp0.11 ρt-1/3 g –0.22 L 0.12 W 0.22 cos θ 0.33 where
ρp is the density of the impactor, ρt is the density of target material, g is gravity, L is the
impactor diameter, W is the kinetic energy of the impact and θ is the impacting angle.
For this discussion, we have chosen an asteroid (ρp =3 g/cm3) , traveling at 9 km/s
(average for Mars), at an angle of 45 degrees, impacting a target material density of ρt = 3
g/cm3.
S2. W.B. McKinnon et. al. Cratering on Venus, in Venus II, S.W. Bougher, D.M. Hunten,
R.J. Philips, Eds. (University of Arizona Press, Tucson, 1997), p. 977. Equation 8 gives
the final crater diameter expected for a given transient crater size:
D ~ 1.17 Dtr 1.13 / Dc 0.13
We assume Dc, the transition diameter from simple to complex craters, is 6 km for Mars.
This final crater, a result of gravitational slumping, would be what we observe today on
the Martian surface.