Seminar ~1.5 hour first version: 2007 most recent version: 2013

1. Dynamics of Ice Ages
on Mars
Norbert Schorghofer
University of Hawaii
July 2013

2. Planet Mars
• Polar caps, mostly made of H2O
• 5 mbar CO2 atmosphere, contains 1µbar water vapor
• Rotation period 24.6 hours, Length of year 687 earth days
• Axis tilt (obliquity) 25◦
• Effective temperature 210 K, range 145 K to 310 K

3. ice-free surface
Phoenix on Mars
May–November 2008
latitude: 68◦N
ice buried by ∼5cm

4. 1 “sol” = 1 solar day
never warm enough for melting

5. 140 160 180 200 220 240 260
0
0.1
0.2
0.3
Temperature (K)
ParitalPressureofH
2
O(Pa)
Mars average
Frostpoint
~198 K
sublimation
deposition
Triple point: 611 Pa, Sublimation environment;
Strongly nonlinear dependence of vapor pressure on temperature
p(T) ≥ p( T )

6. Subsurface Ice
Blue is water ice from neutron spectroscopy (Boynton et al. 2002).
White lines are prediction for subsurface/atmosphere equilibrium.
(The northern hemisphere ice is hidden by seasonal CO2 layer.)

7. Ground Ice in Equilibrium with
Atmospheric Water Vapor
Ground Ice
Soil
Atmosphere
Water Vapor
Ground ice can be stable (last indefinitely) in present-day climate
(Leighton & Murray 1966)
balance of annual mean vapor density ρatm = ρice table

8. Ice Emplacement Mechanisms
Precipitation Vapor Deposition
up to 100% ice at most pore space filling 40%
Neutron-inferred ice content is high (60% by weight, 70–85% by
volume) (Prettyman et al. 2004); Phoenix-inferred ice content
is low (pore ice, ∼40% by volume) (Mellon et al. 2009)

9. Phoenix Observation
of Pore Ice
Trench with ice-cemented soil (=
pore ice). Most of the exposed ice
is of this type (Mellon et al. 2009)

10. Timescale for Ice Retreat
190 200 210 220 230 240 250 260 270
10
−3
10
−2
10
−1
10
0
Marsequator
Mars,±55
°
latitude
dry
humid
dry
humid
Meteorological
station,
Beacon Valley,
Antarctica
D=10 cm
2 /s
D=0.06 cm
2 /s
Ice Temperature (K)
RetreatRate(m/ka)
−90°C −80°C −70°C −60°C −50°C −40°C −30°C −20°C −10°C
Loss rate of ice beneath a 0.5 m thick soil layer

11. Does the Atmospheric Humidity
Determine the Ground Ice Distribution?
Approach 1 Approach 2
Compare observed Determine diffusivity
ground ice distribution of soil simulants
with observed humidity
(planetary scale) (microscopic scale)
Answer: YES Answer: YES
Boynton et al. (2002)
Mellon et al. (2004)
Schorghofer & Aharonson (2005)
Diez et al. (2008)
Mellon et al. (2009)
Laboratory experiment:
Hudson et al. (2007)
Chevrier et al. (2007)
Sizemore & Mellon (2008)
Hudson & Aharonson (2008)
+ earlier theoretical work
Converging Lines of Evidence

12. Orbitally driven climate change

13. Orbital Elements
−6 −5 −4 −3 −2 −1 0
10
20
30
40
50
Obliquity(
°
)
−6 −5 −4 −3 −2 −1 0
0
0.05
0.1
Eccentricity
Time before present (Myrs)
after Laskar et al. (2004)
Milankovitch periods:
obliquity ∼120 ka, eccentricity ∼95 ka, precession ∼51 ka
Levrard et al. (2004): precipitation 3–5 Ma ago

14. Fourier Amplitudes of Milankovitch
Cycles for Earth & Mars
Inf 240 120 80 60 48 40 30 24 20
Obliquity
Inf 240 120 80 60 48 40 30 24 20
Eccentricity
Inf 240 120 80 60 48 40 30 24 20
e sinω
Frequency (ka−1
)

15. Vapor Exchange: Theory
Ground Ice
Soil
Atmosphere
Water Vapor
Ground ice can be stable (last indef-
initely) in present-day climate
J = −D
∂ρv
∂z
J ... vapor flux; D ... diffusion coefficient
z ... vertical coordinate; ρv ... H2O vapor density
J = − D
∂ρv
∂z
≈ − D
∂ρv
∂z
= − D
∂ ρv
∂z
≈ D
∆ ρv
∆z
... annual average; ∆ρv = ρv(surface) − ρv(ice table)
Condition for stability of ground ice:
J downward ⇒ ρv(surface) ≥ ρv(ice table)

16. Accumulation of Subsurface Ice
170 180 190 200 210
0
0.5
1
1.5
2
2.5
3
3.5
4
temperature (K)
Depthz(m)
0 0.05 0.1 0.15
0
0.5
1
1.5
2
2.5
3
3.5
4
pressure (Pa)
0 1 2
0
0.5
1
1.5
2
2.5
3
3.5
4
ice filling fraction (ppm)
Movie of Ice Growth [online] [local]

17. Two Modes of Ice Growth
0 20 40 60 80 100 120
0
0.2
0.4
0.6
0.8
1
equilibrium
Ice fraction (%)
Depthbelowsurface
Jdry
Jicy
Volumetric Growth
0 20 40 60 80 100 120
0
0.1
0.2
0.3
0.4
0.5
equilibrium
Ice fraction (%)
Depthbelowsurface
Jdry
Vertical Growth
Illustration of a) the “volumetric” and b) the “vertical” mode of
ice deposition. The gray area shows incremental ice growth. Ice
fraction is relative to pore volume.

18. Ice Age Model
• 1-dimensional thermal model of subsurface an atmosphere
• Realistic Soil Diffusivity 4cm2/s (Hudson et al. 2007)
1 Initial ice sheet formed by precipitation (Levrard et al. 2004)
2 Retreat of ice sheet; ice contains dust or soil ⇒ Sublimation
lag
• integrate history using time varying orbital elements (Laskar 2004)
(time-averaged and asynchronous model)
3 Growth and retreat of pore-ice
• North polar cap is source of atmospheric humidity

19. Near-surface Humidity
15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
Obliquity (deg)
Humidity(Pa)
supply−limited
GCM based
no variation
present−day
LMD-GCM, as in Levrard et al. 2004; Forget et al. 2006

20. Accelerated Numerical Method
for Subsurface Ice Dynamics
Vapor diffusion and deposition calculations are nonlinear, be-
cause of phase transitions, and require explicit numerical meth-
ods with a time step requirement of ∆t < ∆z2/(2D) ≈ 0.1 seconds.
Diurnal temperature cycle is resolved with ∆t ≈ 1000 seconds. ⇒
solve time-averaged transport equations (Schorghofer, 2007,
2010); swap derivative with integral
Vapor flux J = −D
∂ρsv
∂z
= −D
∂ ρsv
∂z
∆ρ
Time fast oscillations are averaged out

21. Comparison between
Fast and Slow Method
0 2 4 6 8
x 10
−3
0
1
2
3
4
Depth(m)
Ice density (kg/m
3
)
seasonal ice
perennial ice
slow method
fast method
Speedup is about 104-fold! About the same speed as a thermal
model.
Fast method does not resolve diurnal and seasonal cycle.

22. a) Initial condition, 4.5Ma ago
−80 −60 −40 −20 0 20 40 60 80
0
1
2
3
Latitude
Depth(m)
b) Present-day
−75 −60 −45 −30 −15 0 15 30 45 60 75
0
0.5
1
1.5
Latitude
Depth(m)
ice sheet
pore ice
dry soil
equilibrium
retreating ice sheet leaves sublimation lag; triangle = PLS [M]

23. Schematic Structure of Subsurface Ice
consistent with: MONS geographic boundary, MONS burial depths,
MONS ice content (!), pore-ice at Phoenix Landing Site

24. Mean Annual Insolation
−5 −4 −3 −2 −1 0
0
50
100
150
200
Time before present (Ma)
MeanAnnualInsolation(W/m
2
)
−80
°
−60
°
−50
°
−40
°
0
°
for several latitudes
obliquity effect on equator and at pole has opposite phase

25. Mean Annual Temperature
−5 −4 −3 −2 −1 0
140
160
180
200
220
Time before present (Ma)
MeanAnnualTemperature(K)
−80°
−60°
−50°
−40°
0°
Mean temperature barely changes at 60◦ latitude, and has a
different periodicity (precession cycle).

26. I1/4 Milankovitch Theory
Inf 120 60 40 30
Annual mean temperature at 60N
Inf 120 60 40 30
Annual mean insolation at 60N
Inf 120 60 40 30
Annual mean of
4th root of insolation at 60N
Frequency (ka
−1
)
Fourier amplitudes from the last 3 Ma;
obliquity ∼120ka, precession ∼51ka

27. Phoenix
Landing Site
a) Depth to pore ice
and depth to ice sheet.
Present-day thickness of
the pore ice layer is only
9mm. Its filling frac-
tion is always 100% (ver-
tical growth mode). b)
Mean surface tempera-
ture and frostpoint tem-
perature; partial cancella-
tion

28. Modified Climate Scenario:
Recent massive ice sheet;
not yet in equilibrium

29. Recent Impacts into Pure Ice
(Byrne et al. 2009) Latitude 46.3◦N

30. Possible Explanations
1. Very recent climate fluctuation, such that the present-day
atmospheric humidity is not representative of the recent past.
2. Severe lack of near-surface mixing. The column-integrated
water abundance might not be representative of the near-
surface humidity.
3. Seasonal snow that enhances the humidity on the surface
4. Hydrothermal convection of brines
5. The initial snow/ice cover has not yet retreated to equi-
librium.

31. Present-day ice distribution
Scenario: Ice sheet emplaced 863 ka ago
−75 −60 −45 −30 −15 0 15 30 45 60 75
0
0.5
1
1.5
Latitude
Depth(m)
consistent with: MONS geographic boundary, MONS burial depths,
MONS ice content, pore ice at PLS, mid-latitude icy impact sites
(!)

32. Present-day Water Vapor Output
−60 −30 0 30 60
0
2
4
6
8
10
12
14
Latitude
H2
Ooutput(µm/year)
1Ma
5Ma
Example of zonally averaged H2O vapor output from the re-
treating subsurface ice for two climate scenarios. Observable in
atmospheric water vapor abundance? Deposition onto NPLD.

33. Three Ice Age Scenarios

34. North Polar Layered Deposits
The layering is most likely related
to orbital cycles

35. Ice Reservoirs on Mars
Tropical
Mountain Glacier
exchange
Polar Cap + Polar Layered Deposits
Ice−Rich Permafrost
white line is the margin of the ice-rich permafrost (∼ 55◦)

36. Areal Coverage of Ice on Mars
Area
(106 km2)
North polar cap 0.837 (Kieffer et al. 1992)
South polar cap 0.088 (Kieffer et al. 1992)
Polar layered terrain (N+S) 1.8 (Kieffer et al. 1992)
Subsurface ice (N+S) 21
Tropical glaciers, Tharsis 0.3 (Shean et al. 2005)
1◦ movement of ice layer margin in latitude corresponds to 0.6 ×
106 km2, comparable to the size of the north polar cap.
Depth of ice at margin of today’s ice layer: ∼10 meters (annual
thermal skin depth of ice-filled soil)
Variations in subsurface content are important for global H2O
budget.

37. Subsurface Ice → NPLD stratigraphy
−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0
x 10
6
−1
0
1
2
3
4
5
x 10
16
Time (yrs)
∆SubsurfaceIceMass
(kg)
north
south
total
0
5
10
15
20
25
30
35
40
45
50
66ka369ka
487ka
618ka
843ka
974ka
3100ka
3235ka 3354ka
3842ka
3964ka
4098ka
4211ka
4323ka
4435ka
4545ka
4651ka
4793ka
4903ka
5389ka
5502ka
5736ka
7961ka
8072ka
Depthbelowpresent−daysurface(m)

38. Ice Age Cycle on Mars
1. Precipitation 3–5 Ma ago
2. Ice retreats during dry low-obliquity periods.
3. Ice forms in soil pores by diffusion of atmospheric vapor; 3-
layered distribution at high latitudes, including the Phoenix
Lander site
4. Pore-ice retreats and reforms many times (∼40 major obliq-
uity cycles in the past 5 Ma)

39. Conclusions
1. Water vapor in the atmosphere controls the geographic ex-
tent and burial depth of ice.
2. Three layers are expected at high latitudes: dry, pore-ice,
almost pure ice
3. Pore-ice layer at the Phoenix Landing Site may be very thin,
and its growth is dominated by precession cycles (as explained
by I1/4 Milankovitch Theory) and formed by “vertical” (and
not by volumetric) growth mode.
4. There is a transition between completely ice filled pores and
partially ice-filled pores.
5. Mid-latitude icy impacts can be explained with recently em-
placed ice sheet; the mid-latitude subsurface ice has not yet
equilibriated with the atmosphere; it still retreats and is a
source of water vapor.

40. History of Terrestrial Ice Ages
19th century
Jean de Charpentier (1786–1855) and others:
glaciers extended over larger areas
James Croll (1821–1890): theory of cli-
mate change based on Earth’s orbit
20th century
Milutin Milankovic (1879–1958): detailed
calculations of insolation changes
(Milankovic cycles)
∼1975: Milankovitc cycles found in ocean
sediment record
Insolation changes are much larger for Mars than for Earth.