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

North-south components of slope in the global topography of Mars: Evidence for an ice-rich shallow crust? Jørn Atle Jernsletten Jørn Atle Jernsletten [email protected]

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North-south components of slopeNorth-south components of slopein the global topography of Mars:in the global topography of Mars:Evidence for an ice-rich shallow Evidence for an ice-rich shallow

crust?crust?

Jørn Atle JernslettenJørn Atle Jernsletten

[email protected] [email protected]

http://water-on-Mars.info/http://water-on-Mars.info/

( Abstract #P31C-( Abstract #P31C-0219 )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 MeetingSan 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]

Figure 2. North-South Components of Figure 2. North-South Components of Slope onSlope on

Mars (Valles Marineris Region)Mars (Valles Marineris Region)

Key: Equatorward slope components Key: Equatorward slope components are shown in dark red, poleward slope are shown in dark red, poleward slope components are shown in dark blue.components are shown in dark blue.

The way in which The way in which these slope these slope components components emphasizes reworked emphasizes reworked materials such as materials such as those in impact those in impact craters (Figure 2) craters (Figure 2) make them make them appropriate quantities appropriate quantities from which to study from which to study the effects of the effects of sublimation of ground sublimation of ground ice expected to be ice expected to be contained within the contained within the shallow crust of Mars shallow crust of Mars at certain latitudes at certain latitudes (>30º–40º).(>30º–40º).

Figure 3. Global North-South Figure 3. Global North-South Components of Slope on MarsComponents of Slope on Mars

To note in Figure 3 is the fact that given the large number of datapoints To 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 of slope 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).

Figure 4. Differences in Global North-Figure 4. Differences in Global North-South Components of Slope on MarsSouth Components of Slope on Mars

Figure 4 shows the Figure 4 shows the differences between differences between equatorward and equatorward and poleward slope poleward slope components components (equatorward slope (equatorward slope component minus component minus poleward slope poleward slope component at each component at each increment in increment in latitude). The steeper latitude). The steeper equatorward slope equatorward slope components are components are especially evident in especially evident in the mid latitudes the mid latitudes (30º–60º, Figure 4). (30º–60º, Figure 4).

Table 2. Paired-Samples T-Test Table 2. Paired-Samples T-Test Differences in North-South Components of Differences in North-South Components of

Slope (> 5º)Slope (> 5º)

The The ± 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, except All differences statistically significant at the 99% (0.01) level or above, except Global (Both Hemispheres) Global (Both Hemispheres) vs.vs. High Latitudes High 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.

Table 3. Spearman Rank Correlations of Table 3. Spearman Rank Correlations of North-South Slope Components and North-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, except All correlations 2-tailed significant at the 99% (0.01) level or above, except Northern HemisphereNorthern Hemisphere Equatorward vs. Latitude Equatorward 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. Incidence Southern Hemisphere Difference vs. Incidence at 0°- 90° Latitudesat 0°- 90° Latitudes and and vs. Latitude vs. 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.

Figure 5. Counts of Global North-South Figure 5. Counts of Global North-South Components of Slope on MarsComponents of Slope on Mars (> 5º) (> 5º)

Figure 5 shows counts Figure 5 shows counts of slope components of slope components >5º, equatorward and >5º, equatorward and poleward respectively. poleward respectively. Note that sample sizes Note that sample sizes (counts) are (counts) are statistically significant statistically significant at all latitude bands, at all latitude bands, although just barely so although just barely so at the 60º to 80º at the 60º to 80º latitudes in the latitudes in the northern hemisphere, northern hemisphere, yielding high yielding high uncertainties in the uncertainties in the differences at these differences at these latitudes (ref. Table 2).latitudes (ref. Table 2).

Figure 6. Paired-Samples T-Tests OverFigure 6. Paired-Samples T-Tests Over19 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 slope Note in Figure 6 that equatorward slope components are significantly steeper in components are significantly steeper in the mid latitudes, particularly in the the mid latitudes, particularly in the southern hemisphere. southern hemisphere.

SummarySummary

From an analysis of north-From an analysis of north-south components of slope angle south components of slope angle in the global topography of Mars, in the global topography of Mars, this study asks the question: Are this study asks the question: Are equatorward facing slopes in the equatorward facing slopes in the mid to high latitudes are steeper mid to high latitudes are steeper than poleward facing slopes?, than poleward facing slopes?, based in the hypothesis of based in the hypothesis of sublimation exhumation of very sublimation exhumation of very ice-rich materials.ice-rich materials.

Past studies [Past studies [Fenton and Fenton and HerkenhoffHerkenhoff, 2000 – , 2000 – IcarusIcarus, , 147147, , 433 – 443 ] have shown that 433 – 443 ] have shown that equatorward (warmer) slopes are equatorward (warmer) slopes are steeper than the poleward slopes steeper than the poleward slopes as measured in individual troughs as measured in individual troughs in the polar layered deposits.in the polar layered deposits.

Empirical results from Empirical results from this study show that this study show that equatorward facing slopes equatorward facing slopes range from 0.1º to 0.3º range from 0.1º to 0.3º steeper than poleward facing steeper than poleward facing slopes, thus lending slopes, thus lending topographical evidence for an topographical evidence for an ice-rich shallow crust on Mars ice-rich shallow crust on Mars in the mid to high latitudes.in the mid to high latitudes.

This study is based on This study is based on MOLA 1/64º gridded elevation MOLA 1/64º gridded elevation data, from which slope angles, data, from which slope angles, slope aspects, north-south slope aspects, north-south components of slope angles, components of slope angles, and other derivative data are and other derivative data are calculated.calculated.