This study analyzes north-south components of slope angles in Mars' global topography to determine if equatorward facing slopes in mid to high latitudes are steeper than poleward facing slopes, based on the hypothesis of sublimation exhuming an ice-rich crust. Past studies showed individual troughs in the polar layered deposits have steeper equatorward slopes. The current study finds empirical evidence that equatorward slopes are 0.1-0.3 degrees steeper than poleward slopes on a global scale, lending topographical support for an ice-rich shallow crust in mid to high latitudes on Mars. The study uses MOLA elevation data to calculate slope angles, aspects, north-south slope

1. North-south components of slopeNorth-south components of slope
in the global topography of Mars:in the global topography of Mars:
Evidence for an ice-rich shallowEvidence for an ice-rich shallow
crust?crust?
Jørn Atle JernslettenJørn Atle Jernsletten
joern@jernsletten.namejoern@jernsletten.name
http://water-on-Mars.info/http://water-on-Mars.info/
( Abstract #P31C-0219 )( Abstract #P31C-0219 )
Engineering Geophysics LaboratoryEngineering Geophysics Laboratory
Dept. of Civil & Environmental EngineeringDept. of Civil & Environmental Engineering
University of Nevada, Las VegasUniversity of Nevada, Las Vegas
2005 AGU Fall Meeting2005 AGU Fall Meeting
San Francisco, CA - Wednesday, December 7, 2005San Francisco, CA - Wednesday, December 7, 2005
Table 1 & Figure 1. Profiles of Trough inTable 1 & Figure 1. Profiles of Trough in
Northern Polar Layered Deposits.Northern Polar Layered Deposits.
[Adapted from[Adapted from Fenton and HerkenhoffFenton and Herkenhoff , 2000], 2000]

2. Figure 2. North-South Components of SlopeFigure 2. North-South Components of Slope
onon
Mars (Valles Marineris Region)Mars (Valles Marineris Region)
Key: Equatorward slope componentsKey: Equatorward slope components
are shown in dark red, poleward slopeare shown in dark red, poleward slope
components are shown in dark blue.components are shown in dark blue.
The way in which theseThe way in which these
slope componentsslope components
emphasizes reworkedemphasizes reworked
materials such as thosematerials such as those
in impact cratersin impact craters
(Figure 2) make them(Figure 2) make them
appropriate quantitiesappropriate quantities
from which to study thefrom which to study the
effects of sublimation ofeffects of sublimation of
ground ice expected toground ice expected to
be contained within thebe contained within the
shallow crust of Mars atshallow crust of Mars at
certain latitudes (>30º–certain latitudes (>30º–
40º).40º).

3. Figure 3. Global North-South Components ofFigure 3. Global North-South Components of
Slope on MarsSlope on Mars
To note in Figure 3 is the fact that given the large number of datapointsTo note in Figure 3 is the fact that given the large number of datapoints
(11520 each for equatorward and poleward slope components), equatorward(11520 each for equatorward and poleward slope components), equatorward
slope components exhibit a higher number of steeper slopes (the bulk ofslope components exhibit a higher number of steeper slopes (the bulk of
equatorward datapoints are hidden behind the poleward datapoints).equatorward datapoints are hidden behind the poleward datapoints).

4. Figure 4. Differences in Global North-SouthFigure 4. Differences in Global North-South
Components of Slope on MarsComponents of Slope on Mars
Figure 4 shows theFigure 4 shows the
differences betweendifferences between
equatorward andequatorward and
poleward slopepoleward slope
componentscomponents
(equatorward slope(equatorward slope
component minuscomponent minus
poleward slopepoleward slope
component at eachcomponent at each
increment in latitude).increment in latitude).
The steeperThe steeper
equatorward slopeequatorward slope
components arecomponents are
especially evident inespecially evident in
the mid latitudes (30º–the mid latitudes (30º–
60º, Figure 4).60º, Figure 4).

5. Table 2. Paired-Samples T-Test DifferencesTable 2. Paired-Samples T-Test Differences
in North-South Components of Slope (> 5º)in North-South Components of Slope (> 5º)
TheThe ± ranges are the statistical 95% confidence intervals of the differences.± ranges are the statistical 95% confidence intervals of the differences.
Negative differences are shaded.Negative differences are shaded.
Equatorward north-south slope components steeper than poleward north-south slopeEquatorward north-south slope components steeper than poleward north-south slope
components in all casescomponents in all cases , except Southern Hemisphere vs. High Latitudes (*,, except Southern Hemisphere vs. High Latitudes (*, ‑0.072º ± 0.048º‑0.072º ± 0.048º ).).
All differences statistically significant at the 99% (0.01) level or above, exceptAll differences statistically significant at the 99% (0.01) level or above, except Global (Both Hemispheres) vs.Global (Both Hemispheres) vs.
High LatitudesHigh Latitudes at 60°- 80° Latitudesat 60°- 80° Latitudes (**), which is significant at the 95% (0.05) level or above.(**), which is significant at the 95% (0.05) level or above.
N (Global, 0°- 90° Latitudes) = 11520, N (N or S Hemisphere, 0°- 90° Latitudes) = 5760,N (Global, 0°- 90° Latitudes) = 11520, N (N or S Hemisphere, 0°- 90° Latitudes) = 5760,
N (Global, 30°- 60° Latitudes) = 3840, N (N or S Hemisphere, 30°- 60° Latitudes) = 1920,N (Global, 30°- 60° Latitudes) = 3840, N (N or S Hemisphere, 30°- 60° Latitudes) = 1920,
N (Global, 60°- 80° Latitudes) = 2560, N (N or S Hemisphere, 60°- 80° Latitudes) = 1280.N (Global, 60°- 80° Latitudes) = 2560, N (N or S Hemisphere, 60°- 80° Latitudes) = 1280.

6. Table 3. Spearman Rank Correlations ofTable 3. Spearman Rank Correlations of
North-South Slope Components andNorth-South Slope Components and
DifferencesDifferences
Positive correlations are shaded.Positive correlations are shaded.
All correlations 2-tailed significant at the 99% (0.01) level or above, exceptAll correlations 2-tailed significant at the 99% (0.01) level or above, except Northern HemisphereNorthern Hemisphere
Equatorward vs. LatitudeEquatorward vs. Latitude at 60°- 80° Latitudesat 60°- 80° Latitudes (*), which is significant at the 95% (0.05)(*), which is significant at the 95% (0.05)
level or abovelevel or above ; and; and Southern Hemisphere Difference vs. IncidenceSouthern Hemisphere Difference vs. Incidence at 0°- 90° Latitudesat 0°- 90° Latitudes andand
vs. Latitudevs. Latitude at 60°- 80° Latitudesat 60°- 80° Latitudes (**), which are not statistically significant.(**), which are not statistically significant.
N (Global, 0°- 90° Latitudes) = 11520, N (N or S Hemisphere, 0°- 90° Latitudes) = 5760,N (Global, 0°- 90° Latitudes) = 11520, N (N or S Hemisphere, 0°- 90° Latitudes) = 5760,
N (Global, 30°- 60° Latitudes) = 3840, N (N or S Hemisphere, 30°- 60° Latitudes) = 1920,N (Global, 30°- 60° Latitudes) = 3840, N (N or S Hemisphere, 30°- 60° Latitudes) = 1920,
N (Global, 60°- 80° Latitudes) = 2560, N (N or S Hemisphere, 60°- 80° Latitudes) = 1280.N (Global, 60°- 80° Latitudes) = 2560, N (N or S Hemisphere, 60°- 80° Latitudes) = 1280.

7. Figure 5. Counts of Global North-SouthFigure 5. Counts of Global North-South
Components of Slope on MarsComponents of Slope on Mars (> 5º)(> 5º)
Figure 5 shows countsFigure 5 shows counts
of slope componentsof slope components
>5º, equatorward and>5º, equatorward and
poleward respectively.poleward respectively.
Note that sample sizesNote that sample sizes
(counts) are statistically(counts) are statistically
significant at all latitudesignificant at all latitude
bands, although justbands, although just
barely so at the 60º tobarely so at the 60º to
80º latitudes in the80º latitudes in the
northern hemisphere,northern hemisphere,
yielding highyielding high
uncertainties in theuncertainties in the
differences at thesedifferences at these
latitudes (ref. Table 2).latitudes (ref. Table 2).

8. Figure 6. Paired-Samples T-Tests OverFigure 6. Paired-Samples T-Tests Over
19 Latitude Ranges19 Latitude Ranges
10º latitude bands centered at every 10º of10º latitude bands centered at every 10º of
latitude from 85º north to 85º, plus equator.latitude from 85º north to 85º, plus equator.
All differences statistically significant at the 95%All differences statistically significant at the 95%
(0.05) level or above, except those labeled(0.05) level or above, except those labeled
(65º and 55º north, and 65 south), which(65º and 55º north, and 65 south), which
are not significant.are not significant.
Note in Figure 6 that equatorward slopeNote in Figure 6 that equatorward slope
components are significantly steeper in thecomponents are significantly steeper in the
mid latitudes, particularly in the southernmid latitudes, particularly in the southern
hemisphere.hemisphere.

9. SummarySummary
From an analysis of north-From an analysis of north-
south components of slope anglesouth components of slope angle
in the global topography of Mars,in the global topography of Mars,
this study asks the question: Arethis study asks the question: Are
equatorward facing slopes in theequatorward facing slopes in the
mid to high latitudes are steepermid to high latitudes are steeper
than poleward facing slopes?,than poleward facing slopes?,
based in the hypothesis ofbased in the hypothesis of
sublimation exhumation of verysublimation exhumation of very
ice-rich materials.ice-rich materials.
Past studies [Past studies [ Fenton andFenton and
HerkenhoffHerkenhoff, 2000 –, 2000 – IcarusIcarus,, 147147,,
433 – 443 ] have shown that433 – 443 ] have shown that
equatorward (warmer) slopes areequatorward (warmer) slopes are
steeper than the poleward slopessteeper than the poleward slopes
as measured in individual troughsas measured in individual troughs
in the polar layered deposits.in the polar layered deposits.
Empirical results fromEmpirical results from
this study show that equatorwardthis study show that equatorward
facing slopes range from 0.1º tofacing slopes range from 0.1º to
0.3º steeper than poleward facing0.3º steeper than poleward facing
slopes, thus lendingslopes, thus lending
topographical evidence for antopographical evidence for an
ice-rich shallow crust on Mars inice-rich shallow crust on Mars in
the mid to high latitudes.the mid to high latitudes.
This study is based onThis study is based on
MOLA 1/64º gridded elevationMOLA 1/64º gridded elevation
data, from which slope angles,data, from which slope angles,
slope aspects, north-southslope aspects, north-south
components of slope angles, andcomponents of slope angles, and
other derivative data areother derivative data are
calculated.calculated.

10. SummarySummary
From an analysis of north-From an analysis of north-
south components of slope anglesouth components of slope angle
in the global topography of Mars,in the global topography of Mars,
this study asks the question: Arethis study asks the question: Are
equatorward facing slopes in theequatorward facing slopes in the
mid to high latitudes are steepermid to high latitudes are steeper
than poleward facing slopes?,than poleward facing slopes?,
based in the hypothesis ofbased in the hypothesis of
sublimation exhumation of verysublimation exhumation of very
ice-rich materials.ice-rich materials.
Past studies [Past studies [ Fenton andFenton and
HerkenhoffHerkenhoff, 2000 –, 2000 – IcarusIcarus,, 147147,,
433 – 443 ] have shown that433 – 443 ] have shown that
equatorward (warmer) slopes areequatorward (warmer) slopes are
steeper than the poleward slopessteeper than the poleward slopes
as measured in individual troughsas measured in individual troughs
in the polar layered deposits.in the polar layered deposits.
Empirical results fromEmpirical results from
this study show that equatorwardthis study show that equatorward
facing slopes range from 0.1º tofacing slopes range from 0.1º to
0.3º steeper than poleward facing0.3º steeper than poleward facing
slopes, thus lendingslopes, thus lending
topographical evidence for antopographical evidence for an
ice-rich shallow crust on Mars inice-rich shallow crust on Mars in
the mid to high latitudes.the mid to high latitudes.
This study is based onThis study is based on
MOLA 1/64º gridded elevationMOLA 1/64º gridded elevation
data, from which slope angles,data, from which slope angles,
slope aspects, north-southslope aspects, north-south
components of slope angles, andcomponents of slope angles, and
other derivative data areother derivative data are
calculated.calculated.