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Histogram of elevation within the 179 HRSC DTM tiles used in Martian glaciers work

Dec 3, 2016

In my dissertation I used 179 High Resolution Stereo Camera digital terrain model tiles from the Mars Express spacecraft.

I have gone back to the code that generated the histograms below:

Elevation histogram consisting of the Souness glacier extent areas, glacier head areas, and the HRSC tiles as a whole, and multi-component Gaussian fits

Slope histogram consisting of the Souness glacier extent areas, glacier head areas, and the HRSC tiles as a whole, and multi-component Gaussian fits
The question I thought of recently, is how does the slope vary by elevation?

I will investigate this in two ways

  1.  average slope
  2.  percentage of terrain exceeding a threshold in slope.
This either in a whole tile or by elevation bin.

Summaries of whole tiles

Slope vs elevation, plotting the means of whole tiles. Error bars show the standard deviations of elevation and slope within each tile.

Percentage of the area in each tile exceeding slope thresholds of 5° and 10°.

Binning by elevation

Since there is often a wide variety of elevation within a tile, and the sometimes large north-south extent of each tile, they can encompass a wide variety of terrains, I developed the program to bin the data in each tile into elevation bins, and calculate the mean slope for each bin. I currently use a bin width of 200m in elevation.

There are 179 tiles, and several different ways of plotting them, which produces a large number of plots, so I thought I'd animate them.

The frames are ordered northern hemisphere first, then the southern, and within each hemisphere by longitude from -180 to 180 degrees.

The animated versions are linked to rather than shown since they are fairly large files.

I have taken the tile h1450 as an example in showing the plots.

The tile h1450 was discussed in an earlier post and on my neocities website. The hemispheric maps there can also help in putting the tiles in their context. It contains Lyot crater, the lowest elevation anywhere in the northern hemisphere of Mars , as well as part of the elevation dichotomy boundary and a number of Souness glaciers including this one, which has a 3D HiRISE anaglyph.

Animated elevation histograms and average slope by elevation bin


Link to animated version (6MB gif). The same data is plotted twice, firstly with an automatically scaled elevation axis, and secondly with fixed limits of -8000m, 10000m.

Link to animated version (8MB gif)  Mean slope in each elevation bin in each tile, and the % of terrain with slope >= 5° and 10° in each elevation bin. The density of shading depends on the area in each elevation bin, compared with the bin having the largest amount of area.

Link to animated version (5MB gif) Mean slope in each elevation bin, with fixed-limit axes both elevation, and slope.

Link to animated version (15MB gif). Placing the two subplots on the same frame - variable axes.

Link to animated version (8MB gif). Placing the two subplots on the same frame - fixed axes.

4 subplots version (on Youtube)

This version progresses slower through the tiles since there are 4 subplots to look at for each tile

Integrating all tiles - elevation histogram

Elevation histogram of all tiles, with area exceeding the slope thresholds overplotted as lines.

Integrating all tiles - average slope as a function of elevation

Mean slope as a function of elevation, and percent of terrain with slope >= threshold as a function of elevation.
The same as the last plot with the two subplots on the same frame.

Possibly some of the most obsfucated Python code I have ever written

Dec 3, 2016

I have recently been reviewing the Python code from my MSc dissertation which read in the Mars Express High Resolution Stereo Camera digital terrain model tiles, and produced histograms and statistics.

The code was not very well written, as much was edited hastily towards the end of the data analysis phase of my dissertation. However I have managed to do something even more silly since then.

The command gdalinfo allows some summary statistics of a GDAL compatible file to be output to the command line:

gdalinfo h0037_0000_da4.img
Driver: PDS/NASA Planetary Data System
Files: h0037_0000_da4.img
Size is 4391, 36200
Coordinate System is:
Origin = (-55150.000000000000000,2645890.000000000000000)
Pixel Size = (50.000000000000000,-50.000000000000000)
Corner Coordinates:
Upper Left  (  -55150.000, 2645890.000) (134d18'27.69"W, 44d38'24.94"N)
Lower Left  (  -55150.000,  835890.000) (133d57'33.77"W, 14d 6' 9.93"N)
Upper Right (  164400.000, 2645890.000) (129d 6' 6.55"W, 44d38'24.94"N)
Lower Right (  164400.000,  835890.000) (130d 8'24.44"W, 14d 6' 9.93"N)
Center      (   54625.000, 1740890.000) (131d56'32.83"W, 29d22'17.44"N)
Band 1 Block=4391x1 Type=Int16, ColorInterp=Undefined
  Min=-2721.000 Max=21234.000
  Minimum=-2721.000, Maximum=21234.000, Mean=2131.470, StdDev=6496.150
  NoData Value=-32768

The original purpose of using this in my Python was to find out which hemisphere we were in, for the processing of the aspect data, which was to separate the northern and southern hemisphere tiles.

So therefore I wrote this:

findHemisph_cmd = "gdalinfo *da4*img | grep 'Center' > CentreLoc.txt"

HemiSph = CentreLoc.split('"')[-1][0] # N or S hopefully

Recently, I though it useful to actually get the locations of the centres of each tile, so that output histograms for individual tiles can be labelled.

So I took the "Centre" line from the output of gdalinfo, and converted the degrees and minutes to decimal degrees accurate to one decimal place:

centrelocation = CentreLoc.split("(")[-1].strip()
centrelocation = centrelocation[:-1]
centrelocation = DMSstr2dec(centrelocation)

An example of the histograms, showing total area within elevation bins of width 200m, and amount of that area that has slope exceeding 5° and 10°.

The next thing I wanted to do, was to make the tiles appear in a specific order, namely northern hemisphere first, going from -180° to 180° longitude, then the same for the southern hemisphere:

The filename of the histogram above is prefixed by frame0048000606h0037_0000 which since it is at 132°W, this is converted to  48°, which produces the first part of the string as "00480". The latitude is 29.4°N, which is 60.6° counting from the north pole down which converts to "00606".

I recently discovered that gdalinfo has a -json switch so that it produces output in JSON format, which produces this:

  "driverLongName":"NASA Planetary Data System",
    "wkt":"PROJCS[\"SINUSOIDAL MARS\",\n    GEOGCS[\"GCS_MARS\",\n        DATUM[\"D_MARS\",\n            SPHEROID[\"MARS\",3396000,0]],\n        PRIMEM[\"Reference_Meridian\",0],\n        UNIT[\"degree\",0.0174532925199433]],\n    PROJECTION[\"Sinusoidal\"],\n    PARAMETER[\"longitude_of_center\",227],\n    PARAMETER[\"false_easting\",0],\n    PARAMETER[\"false_northing\",0]]"

This would of course have been much easier to process, with the standard Python JSON library.

I will write another post on the histograms themselves later.

Elevation and slope statistics for the Mars Express HRSC DTM tiles used in Martian glacier work

Dec 1, 2016

In the last post I noted the distribution of glacier-like forms according to elevation relative to Mars datum, and slope, as measured by the Mars Express HRSC DTM data.

One issue is whether the distribution according to elevation is a primary function of elevation, or the fact that the distribution of slope varies according to elevation in the area of study.

The distribution of slope and elevation was considered previously:

What will be needed however is the histogram of slope as a function of elevation. Below is a table of 179 HRSC DTM tiles that contain coverage of Souness objects, detailing mean, minimum and maximum elevation and slope, etc. A more comprehensive statistical assessment would use all HRSC DTM tiles that exist in the latitude range 25° - 70° that Souness studied.

Here are a couple of plots, showing the mean slope as a function of mean elevation, with errorbars, and the area of the plotting symbol proportional to the area of each tile, and a plot showing the proportion of each tile having slope exceeding 5° and 10° respectively.

Table of HRSC tiles

For comparison, the area of the UK is 243600km2. Several individual tiles are larger than this, the largest being h0533. The average area of each tile is 87055km2. Total area, ignoring overlap is 15.6 million km2, and taking account of overlap, it is 13.4 million km2. To find more about an individual tile, click on the link in the first column to the tile's page on Arizona State University's Mars Image Explorer or using HRSCview.
FieldDimensionsDTM ResolutionCentre locationAreaMean elevMin elevMax elevAverage slopePercentage exceeding 10°
h0022_0000(12781, 1173) px100m100.9°E, 29.4°S98445km2314.1-235643995.4°16.9%
h0037_0000(36203, 4729) px50m131.9°W, 29.4°N217870km21762.4-2722212345.5°16.3%
h0248_0000(6562, 1216) px50m102.6°E, 37.2°S18548km2110.1-81633584.1°9.8%
h0266_0000(6715, 1463) px50m94.7°W, 43.3°S18355km23653.4200284273.5°6.0%
h0280_0000(8361, 1039) px75m153.6°E, 39.9°S34376km2754.2-5218422.8°3.8%
h0365_0000(10801, 1685) px75m90.7°E, 45.5°S56958km2-4177.5-5841-4593.3°4.3%
h0368_0000(12191, 1663) px75m118.3°E, 41.9°S67909km2783.8-72828083.1°5.5%
h0376_0000(13048, 2782) px50m29.1°W, 48.7°S46781km2-346.6-339237305.6°17.2%
h0383_0000(1601, 1068) px75m37.9°W, 43.1°S8767km2-1715.5-430510256.4°21.4%
h0394_0000(7360, 1523) px75m52.0°W, 42.4°S42870km2561.4-184737417.9°29.9%
h0397_0000(22832, 2260) px75m13.0°E, 37.1°S146656km21612.3-14329813.7°5.4%
h0416_0000(8537, 1457) px100m55.2°W, 46.6°S73480km2236.5-251336085.9°17.7%
h0424_0000(10549, 2394) px50m121.4°W, 44.3°S45403km22071.658835262.9°3.4%
h0427_0000(8101, 2100) px75m57.1°W, 44.0°S53877km21200.5-123037354.8°12.0%
h0451_0000(6222, 2598) px100m103.2°E, 38.8°S70761km2-87.0-255746924.5°11.3%
h0453_0000(10385, 1838) px75m92.0°W, 41.2°S79320km24257.265089784.0°6.9%
h0466_0000(6081, 1339) px150m69.7°E, 20.8°S145309km2-327.9-446936384.9°10.7%
h0469_0000(7227, 2011) px75m135.0°E, 40.5°S63422km21630.0-58127863.0°5.1%
h0478_0000(18069, 2865) px125m30.2°W, 23.6°S410550km2-1037.0-466121675.6°15.8%
h0479_0000(3458, 1348) px100m128.1°W, 42.7°S40474km22102.051548373.2°5.6%
h0497_0000(10101, 1885) px100m97.0°W, 37.0°S135551km24503.0182873793.4°4.5%
h0506_0000(11762, 1920) px125m98.3°E, 33.1°S221775km2-367.1-317554583.5°8.1%
h0508_0000(12599, 2646) px75m98.8°W, 34.0°S138944km25258.3242991554.1°7.3%
h0528_0000(11402, 2553) px100m93.1°E, 29.6°S208685km2-599.9-523036963.6°6.8%
h0533_0000(13073, 2294) px150m38.2°W, 22.0°S456221km2-409.1-543026405.6°15.0%
h0544_0000(2790, 1207) px150m37.9°W, 40.6°S66060km2-985.3-428822205.3°15.2%
h0550_0000(4445, 1789) px125m92.3°E, 32.5°S111078km2-2117.2-539012213.0°5.8%
h0558_0000(6320, 2251) px125m25.5°E, 32.1°S174245km21948.4-16135622.9°5.5%
h0988_0000(14122, 1433) px75m77.2°E, 22.5°N83411km2-1307.1-352315056.2°18.5%
h1201_0000(5202, 1373) px75m24.6°E, 43.5°N28478km2-3224.1-3909-17324.7°12.1%
h1210_0000(2491, 931) px75m138.1°W, 39.0°N12230km2-1629.8-31681794.9°11.2%
h1232_0000(3912, 1097) px75m140.3°W, 37.4°N17785km2-1977.9-3581-54.6°10.2%
h1241_0000(4672, 1362) px75m54.2°E, 44.6°N24804km2-2578.1-3295-1835.3°13.8%
h1258_0000(5101, 1072) px75m177.6°W, 32.5°N22915km2-3837.0-4161-26103.5°9.3%
h1312_0000(7271, 1337) px75m84.7°W, 35.8°N36762km2926.3-100127004.6°9.7%
h1316_0000(5401, 1233) px100m119.7°W, 31.7°N40045km21893.066328212.1°0.9%
h1317_0000(4001, 886) px100m144.6°E, 31.7°N28788km2-1767.1-468116802.8°3.1%
h1351_0000(8402, 1977) px75m41.0°E, 47.4°N48721km2-2762.2-46599783.8°7.6%
h1391_0000(12890, 1476) px100m68.3°E, 37.3°N120274km2-1699.3-508015734.9°12.9%
h1395_0000(5203, 1512) px100m34.7°E, 43.5°N44511km2-2828.2-4259-6984.4°10.1%
h1412_0000(11403, 1941) px100m165.0°E, 41.4°N113313km2-3078.8-41784874.0°9.3%
h1423_0000(15994, 2143) px75m163.3°E, 39.5°N127585km2-3021.1-40722833.5°6.7%
h1428_0000(13002, 3085) px75m30.3°E, 42.3°N102455km2-2734.8-71531654.7°11.0%
h1429_0000(20803, 3289) px75m67.5°W, 39.2°N171804km2-966.9-376513264.8°11.5%
h1446_0000(11318, 2014) px100m60.8°E, 38.4°N133749km2-1916.4-37977675.7°16.9%
h1450_0000(18203, 4148) px75m27.8°E, 41.8°N163141km2-2807.8-7127-1694.9°11.8%
h1461_0000(16986, 4749) px75m25.4°E, 43.9°N154244km2-2924.2-6588-4923.6°6.3%
h1468_0000(19462, 3367) px75m58.6°E, 47.6°N169273km2-3114.9-5556-383.0°5.7%
h1483_0000(11102, 3084) px100m23.5°E, 42.8°N143811km2-3036.0-4265-6713.5°6.6%
h1498_0000(7603, 2119) px100m11.6°W, 34.3°N110710km2-3640.2-5207-21654.3°8.1%
h1523_0000(10543, 3418) px75m49.8°E, 43.1°N116809km2-1814.8-36369144.3°10.5%
h1526_0000(5503, 2821) px75m115.0°E, 40.1°N63553km2-4952.7-6556-43012.1°1.7%
h1528_0000(16803, 3537) px75m80.5°W, 40.3°N196042km2480.7-296527914.1°7.9%
h1545_0000(9373, 3847) px75m46.5°E, 44.1°N113871km2-2069.4-42126645.1°14.8%
h1550_0000(16403, 3782) px75m83.5°W, 41.0°N208952km2419.0-257332224.1°8.6%
h1578_0000(8602, 3013) px100m43.0°E, 44.1°N160965km2-2107.2-448310323.8°7.9%
h1600_0000(7501, 2721) px125m38.6°E, 39.7°N199966km2-1366.3-39009723.7°6.5%
h1607_0000(5002, 2045) px175m71.4°E, 38.0°N226517km2-2320.6-41328894.3°11.3%
h1628_0000(5002, 3727) px100m165.4°E, 40.9°N138771km2-3025.3-46704553.6°7.5%
h1629_0000(5302, 2471) px150m63.3°E, 38.9°N215818km2-2235.9-4490124.6°12.3%
h1644_0000(1952, 1607) px175m33.7°E, 40.4°N86440km2-1930.3-37625413.7°6.7%
h1887_0000(2502, 1418) px250m108.5°E, 41.6°S171008km2675.1-92044294.4°10.0%
h1932_0000(4227, 1298) px225m6.4°E, 40.5°S206200km21318.3-160727203.1°3.5%
h1937_0000(9003, 1817) px100m125.1°W, 30.9°S125929km22777.4111541732.6°2.8%
h2159_0000(4012, 1367) px75m19.6°E, 45.6°S26129km21506.139430483.3°3.6%
h2181_0000(4804, 1207) px100m17.4°E, 48.3°S43588km21551.670228412.5°2.9%
h2195_0000(3952, 993) px100m82.8°E, 45.1°S31518km2-6126.6-7179-53862.8°2.1%
h2197_0000(2011, 1302) px100m114.0°W, 52.0°S19989km21505.8-35434285.1°11.9%
h2210_0000(1502, 1067) px100m47.2°E, 48.3°S12625km2-2184.6-454210645.7°18.5%
h2220_0000(5682, 2373) px75m144.4°E, 48.1°S34383km21560.7-11532083.7°6.0%
h2224_0000(6432, 1196) px75m112.9°E, 41.3°S27821km2632.7-148437164.5°10.4%
h2247_0000(8833, 2025) px75m12.3°E, 53.5°S58270km21553.7-13527802.9°2.9%
h2279_0000(8393, 1550) px50m108.5°E, 41.5°S24411km2670.6-34443196.0°18.2%
h2287_0000(11802, 3213) px75m41.7°E, 55.2°S77249km2267.2-111320022.1°1.7%
h2312_0000(6001, 1723) px75m106.7°E, 43.4°S27029km2286.2-39923423.6°5.6%
h2345_0000(2401, 1116) px75m104.5°E, 45.1°S11286km2-130.5-125646193.5°6.3%
h2356_0000(2802, 974) px75m103.6°E, 40.5°S13506km2-34.6-168547015.3°16.6%
h2359_0000(2832, 1177) px75m169.2°E, 45.8°S13662km21732.517332114.6°10.9%
h2386_0000(13002, 2303) px75m36.8°E, 50.3°S71588km2564.7-100515302.7°3.5%
h2387_0000(10002, 1899) px75m61.0°W, 48.0°S54648km21497.9-65632444.9°11.6%
h2400_0000(2613, 1613) px50m102.2°E, 40.5°S9657km2-699.9-248140634.1°9.6%
h2403_0000(8652, 1648) px75m167.8°E, 50.0°S50246km22010.549531593.3°4.8%
h2430_0000(6606, 1747) px75m35.6°E, 52.1°S40109km2739.1-73515822.4°2.3%
h2438_0000(10043, 1416) px100m30.2°W, 45.4°S85303km2-494.9-338133585.0°13.2%
h2441_0000(13702, 2759) px75m33.8°E, 50.5°S87345km2890.6-128422104.0°7.3%
h2460_0000(7274, 1464) px100m31.8°W, 47.6°S66541km2-952.4-328524475.5°16.7%
h2466_0000(3562, 1519) px100m98.9°E, 41.5°S35078km2-1243.3-278326174.0°9.4%
h2475_0000(5903, 1822) px75m65.2°W, 46.1°S43430km21863.8-42336723.9°5.8%
h2493_0000(9635, 2247) px75m33.6°W, 49.3°S75915km2-950.4-268261135.9°18.6%
h2494_0000(15301, 2927) px75m131.8°W, 49.7°S121366km22181.430344513.7°5.4%
h2501_0000(3501, 1770) px75m99.7°W, 47.8°S28233km22931.554938783.1°4.5%
h2508_0000(15095, 3569) px100m67.7°W, 54.1°S171382km21469.5-86835453.2°3.0%
h2510_0000(4885, 1230) px125m96.6°E, 40.5°S75220km2-2179.3-543630174.4°9.6%
h2515_0000(16219, 6793) px75m36.8°W, 62.6°S149827km2783.7-271861433.4°7.5%
h2526_0000(6887, 1443) px125m35.4°W, 39.0°S116216km2-717.2-322428885.1°14.0%
h2527_0000(5006, 1956) px75m133.8°W, 43.0°S47661km22001.1-9433773.4°4.6%
h2529_0000(10450, 2096) px100m29.8°E, 48.0°S131221km21640.6-2633633.1°4.9%
h2530_0000(9003, 1937) px125m68.6°W, 33.4°S188667km23159.135659173.9°5.6%
h2538_0000(5029, 1263) px150m134.4°W, 34.7°S113579km21867.03632682.8°3.8%
h2540_0000(4782, 1518) px150m28.9°E, 32.8°S128114km21751.6-6631673.8°6.3%
h2541_0000(13269, 3723) px100m70.0°W, 55.8°S174235km21531.7-56237883.2°4.3%
h2550_0000(5801, 2127) px100m126.0°E, 43.3°S85395km21425.5-61135384.1°7.2%
h2595_0000(7500, 1778) px150m24.5°E, 41.9°S202177km22128.610338012.6°2.8%
h2596_0000(7469, 2162) px125m74.3°W, 34.8°S188443km23766.4183171053.4°4.0%
h2607_0000(9723, 3249) px100m75.3°W, 49.5°S174840km22141.2-9339693.1°2.9%
h2609_0000(4484, 1891) px125m88.5°E, 39.6°S110090km2-4757.3-6323-27383.0°3.8%
h2612_0000(8101, 3567) px100m152.9°E, 50.5°S146882km21264.3-63430763.2°3.6%
h2613_0000(1552, 1243) px200m55.2°E, 32.0°S71030km2-4570.5-75236545.1°10.3%
h2625_0000(2802, 1977) px150m44.2°W, 39.0°S104012km2-396.2-307931605.5°16.5%
h2631_0000(4801, 1724) px175m86.0°E, 36.2°S196628km2-3991.4-644642903.4°6.1%
h2638_0000(5134, 2061) px150m118.0°E, 37.1°S184526km2764.2-79228492.4°3.6%
h2639_0000(5502, 1922) px150m19.9°E, 39.9°S182385km21856.0-34237572.8°3.2%
h2640_0000(7401, 2142) px150m78.2°W, 42.1°S242593km23239.4-114970852.9°3.6%
h2644_0000(3752, 2019) px150m111.4°W, 45.0°S123347km22524.645243603.1°4.3%
h2660_0000(3838, 1899) px175m115.6°E, 38.0°S166908km2746.1-138133262.5°4.0%
h2665_0000(4323, 2316) px125m15.4°W, 42.1°S131624km2946.2-158723303.5°4.9%
h2669_0000(2373, 1508) px200m48.7°W, 38.2°S122633km2758.1-171439465.5°17.5%
h2681_0000(2652, 1704) px175m148.1°W, 44.8°S118773km22258.49645553.0°4.5%
h2689_0000(4201, 2187) px150m145.4°E, 39.2°S173432km21473.9-119931412.7°4.1%
h2694_0000(2861, 1379) px250m13.7°E, 38.8°S199978km21633.5-46430072.5°3.1%
h2864_0000(2206, 1891) px175m58.0°E, 35.2°N92242km2-1283.3-32853464.9°13.4%
h2878_0000(1682, 1190) px250m121.8°E, 37.3°N104112km2-4714.1-6381-39591.4°1.0%
h2908_0000(5594, 2184) px150m53.4°E, 41.4°N214663km2-1762.7-34746313.8°7.8%
h2913_0000(4962, 1513) px175m78.0°W, 35.1°N178236km2675.9-77120783.5°4.5%
h2996_0000(2801, 806) px150m44.9°E, 28.9°N45651km2-996.3-25113153.4°3.5%
h3249_0000(8001, 1690) px75m21.4°E, 44.4°N47924km2-3560.4-5099-12043.4°6.6%
h3253_0000(7142, 1678) px50m9.6°W, 40.5°N24933km2-4278.1-4996-31774.3°10.8%
h3272_0000(1912, 1284) px75m77.5°W, 47.0°N11410km255.9-302818894.1°7.5%
h3283_0000(5353, 1318) px75m78.7°W, 45.3°N29879km2815.1-266026783.4°4.7%
h3289_0000(4141, 1061) px100m51.1°E, 45.9°N31014km2-2653.7-3596-6465.1°12.4%
h3316_0000(2772, 1447) px75m83.0°W, 46.5°N15598km2614.1-110527926.7°19.3%
h4087_0000(10465, 1175) px100m80.2°W, 31.1°S91348km23431.6189354463.1°3.6%
h4180_0000(4501, 971) px100m141.2°E, 38.8°S34336km21633.812332624.0°7.7%
h4234_0000(3601, 1185) px75m125.5°W, 40.2°S17789km22382.7115647444.5°8.5%
h4293_0000(2501, 1002) px75m163.4°W, 43.0°S11825km21362.858734174.8°10.7%
h4330_0000(6901, 1022) px75m160.5°E, 36.9°S30127km21012.0-96923644.2°7.5%
h4365_0000(5002, 1218) px75m39.6°W, 35.4°S23863km2121.8-276518775.0°12.7%
h4376_0000(4453, 1027) px100m40.7°W, 36.0°S29258km297.7-178221125.5°15.7%
h5081_0000(11371, 2145) px75m92.4°W, 36.0°N104607km2777.6-70329961.9°2.8%
h5173_0000(14685, 1201) px75m63.0°E, 27.1°N72584km2-309.5-262822635.6°15.4%
h5195_0000(5743, 1104) px75m22.4°E, 32.3°N30026km2-1848.9-4014-2084.9°9.9%
h5213_0000(9533, 1474) px75m20.6°E, 34.8°N52161km2-2087.6-3904-2044.9°11.1%
h5249_0000(9682, 1367) px75m18.3°E, 35.9°N50841km2-2323.2-3695-13114.2°8.2%
h5263_0000(1901, 1982) px125m57.6°E, 28.8°S39685km2-2299.6-61548074.8°11.2%
h5267_0000(9301, 1314) px75m17.0°E, 36.4°N47984km2-2356.2-4417-8874.4°9.6%
h5281_0000(5252, 1315) px75m56.6°E, 38.3°N27428km2-2083.0-3202987.1°24.7%
h5285_0000(9503, 1447) px75m15.8°E, 36.6°N48208km2-2342.2-4333-9074.2°8.8%
h5286_0000(12437, 2499) px50m84.3°W, 44.7°N51054km2352.5-212431924.1°8.9%
h5288_0000(7205, 989) px75m76.5°E, 26.4°N32079km2-820.7-297214997.9°27.4%
h5299_0000(7368, 1569) px75m55.2°E, 38.8°N38310km2-1278.4-30933546.0°18.1%
h5303_0000(8752, 1349) px75m14.7°E, 36.9°N44190km2-2389.0-4249-10844.3°8.9%
h5304_0000(5767, 2267) px50m85.4°W, 41.9°N21127km21403.9-23231594.5°9.8%
h5306_0000(10740, 1140) px75m74.8°E, 24.6°N49345km2-439.1-345418637.0°22.9%
h5314_0000(6601, 879) px100m5.5°W, 37.9°N45091km2-3626.2-5167-21132.6°2.9%
h5317_0000(5703, 1415) px100m52.6°E, 44.2°N44583km2-2354.1-3417-2294.5°9.9%
h5321_0000(4153, 974) px100m13.9°E, 38.8°N28588km2-2641.5-3894-15343.4°5.8%
h5322_0000(11803, 1319) px75m86.2°W, 37.1°N59678km2899.2-66831424.8°11.9%
h5324_0000(3577, 1087) px75m73.6°E, 30.2°N16795km2-1439.1-3462172410.1°38.4%
h5328_0000(4952, 1353) px100m32.7°E, 43.5°N37536km2-2845.0-37736163.2°5.1%
h5335_0000(6852, 1311) px100m52.1°E, 46.0°N54418km2-2721.0-3605594.2°9.8%
h5339_0000(11202, 1377) px75m12.6°E, 40.0°N60184km2-2815.6-4172-9133.6°6.4%
h5340_0000(12402, 1321) px75m87.4°W, 38.1°N64076km2588.7-106423173.4°6.2%
h5342_0000(12303, 1124) px75m72.7°E, 25.0°N61556km2-85.3-317617305.8°16.5%
h5360_0000(7976, 1248) px75m71.4°E, 28.8°N40686km2-1.4-282717397.9°27.5%
h5376_0000(12049, 1437) px75m89.7°W, 38.1°N64857km2674.9-92424582.9°4.9%
h5378_0000(6071, 977) px100m70.2°E, 29.0°N44808km2137.2-230615146.5°20.9%
h5380_0000(2689, 1598) px75m131.0°W, 44.5°N15263km2-1551.1-2293-10551.8°0.9%
h5383_0000(3176, 1592) px75m71.0°W, 49.0°N19640km2-2274.4-36122374.4°10.8%
h5401_0000(1385, 1211) px100m72.6°W, 48.1°N11121km2-1689.0-3416-3724.9°12.2%
h5405_0000(9603, 2538) px50m111.9°W, 46.6°N38658km21488.0-140553482.3°1.7%
h6395_0000(3753, 762) px100m16.7°W, 30.9°S23456km2464.7-123014644.5°9.3%
h6408_0000(13202, 1385) px75m121.4°E, 35.1°S63518km2891.4-21323863.1°3.7%
h6409_0000(9796, 949) px100m20.4°E, 29.5°S65961km21730.5-81130143.6°6.0%
h6419_0000(3202, 1267) px75m99.5°E, 38.4°S15688km2-921.4-280526446.3°19.8%
h6437_0000(1282, 885) px100m97.2°E, 37.5°S8733km2-1262.9-332530357.3°25.3%
h6465_0000(9817, 1324) px75m169.5°E, 33.4°S57385km21096.9-53530904.5°8.6%
h6486_0000(8681, 1737) px75m143.0°W, 43.7°S50290km22302.547638883.2°5.2%
h6544_0000(2801, 1598) px100m127.9°E, 40.7°S27010km21561.651425753.4°4.8%
h6552_0000(2002, 1306) px125m42.4°E, 45.7°S24423km2294.7-189018554.0°8.2%

The Souness Martian glacier-like forms - looking at the lowest and highest elevation objects

Nov 30, 2016

Colin Souness, in his 2012 paper listed a total of 1309 'glacier-like forms' on the surface of Mars, in the mid-latitudes centred around 40° latitude, found from Mars Reconnaisance Orbiter context camera images.

In my dissertation (version for tablets) I studied descriptive statistics of them, including the distribution by elevation.

Since then, I have produced a web index to the objects, including a Top Trumps page for each object. I below show a table of links to the 30 Souness objects at the lowest and highest elevations. The Mars Express High Resolution Stereo Camera digital terrain model tile is shown where there is coverage, and it is also indicated where there are HiRISE images, or 3d anaglyphs that intersect with the outline of the object. These are linked to from the Top Trump page.

The elevation distribution looks as follows:
Elevation histograms for Souness object extents and head areas, compared with the overall elevation distribution in the coverage of the HRSC DTM tiles used

Slope histograms for Souness object extents and head areas, compared with the overall slope distribution in the coverage of the HRSC DTM tiles used
Showing the ratio of the GLF distribution as a function of elevation and slope / elevation and slope distribution in the HRSC tiles for extents.
The GLF distribution as a function of elevation  / elevation distribution in the HRSC tiles for the head areas.

The GLF distribution as a function of slope  / slope distribution in the HRSC tiles for the head areas.
I noted in the dissertation that that the numbers of glaciers appeared to be depleted below elevations of -3000m relative to Mars datum. There are two types of explanation for this, firstly that they were not formed, or secondly that they were more rapidly ablated. Fewer may have formed in the range -5000 to -3000 due to slope effects, with a large proportion of the these elevations being made up of the flat plains in the northern hemisphere, and the Martian glaciers are preferentially found on slopes. Alternatively in the higher-obliquity epoch, ablation may have been favoured at low elevations, due to higher temperatures, and possibly wind-stripping of debris cover allowing sublimation.

The outliers at the extreme ends of the elevation distribution may be of interest, since they may show something about what limited the distribution of Souness objects on Mars.

There is a secondary peak in the distribution at very low elevations. These could have formed at a later epoch at a lower obliquity in a cooler climate where glacier accumulation was only significant at the lowest elevations.
It is also an interesting question whether the objects at very high elevations formed at the same epoch as the main distribution, or whether these come from an older, more extreme obliquity epoch.

Lowest and highest 30 Souness glacier-like forms

Based on mean elevation of 5km circular radius buffer (from Souness et al. 2012 paper)

Lowest elevation 30 GLFs (buffer mean from Souness catalog):

Catalog numberElevation (m)RegionHRSC DTM tileCentre LatitudeCentre LongitudeArea (sq. km)N HiRISE footprints intersectingN anaglyphs intersecting
1130-6664West of HellasH2613_0000-32.5156.615.6300
1123-6603East of Hellasnone-35.6275.610.8000
1126-6540West of Hellasnone-30.8264.500.7100
1119-6534East of HellasH2195_0000-44.2983.562.8500
1122-6533East of Hellasnone-35.5675.580.7900
1120-6466East of HellasH2195_0000-44.3083.572.9200
1118-6001East of HellasH2631_0001-42.7185.991.3500
1301-5507East of HellasH2631_0001-39.8286.160.7500
1302-5456East of HellasH2631_0001-39.8286.140.8410
193-5431Utopia Planitia and Phlegra Montesnone38.59137.201.0310
1117-5334East of HellasH2631_0001-39.8286.160.7000
1114-5283East of HellasH2609_0000-38.2288.122.2400
1300-5227East of HellasH2631_0001-39.8286.1718.4700
198-5137Utopia Planitia and Phlegra MontesH1526_000038.93116.361.9931
200-5108Utopia Planitia and Phlegra MontesH1526_000039.08116.073.6210
1112-5097East of HellasH0365_0000-40.9790.172.0510
1113-5077East of HellasH0365_0000-40.9990.160.6110
194-5025Utopia Planitia and Phlegra MontesH2878_000040.12120.161.9610
199-5019Utopia Planitia and Phlegra MontesH1526_000039.05116.050.5910
195-5008Utopia Planitia and Phlegra MontesH2878_000040.11120.232.6410
1115-4981East of HellasH2609_0000-38.2188.064.7400
196-4958Utopia Planitia and Phlegra MontesH2878_000040.58120.398.7800
1111-4886East of HellasH0365_0000-40.6290.283.0700
197-4881Utopia Planitia and Phlegra MontesH2878_000040.52120.536.1100
1116-4860East of HellasH2609_0000-38.6287.948.0100
1131-4842West of Hellasnone-35.2051.268.6400
1103-4588East of HellasH0528_0000-38.5494.372.0021
1134-4193West of Hellasnone-35.6148.982.1400
1110-4187East of HellasH0550_0000-36.5190.170.8400
3-4161Deuteronilus MensaeH3253_000038.33-9.762.4100

Highest elevation 30 GLFs (buffer mean from Souness catalog):

Catalog numberElevation (m)RegionHRSC DTM tileCentre LatitudeCentre LongitudeArea (sq. km)N HiRISE footprints intersectingN anaglyphs intersecting
825894Olympus Mons and surrounding areanone41.69-110.671.1600
814139Olympus Mons and surrounding areaH5405_000044.92-111.193.2900
793927Olympus Mons and surrounding areanone38.33-103.580.6710
10343533East of HellasH2356_0002-40.83103.0220.4921
12873444East of HellasH2279_0001-42.76108.159.7100
10433155East of HellasH0451_0000-37.89103.3817.2921
9983134East of HellasH1887_0000-42.03109.5938.6200

Based on mean HRSC DTM elevation of immediate head area (100m radius)

Lowest elevation 30 GLFs (head):

Note that a terminus elevation of 0 is due to the terminus falling in a no data area.
Catalog numberHead elevation (m)Termimus elevation (m)RegionHRSC DTM tileHead LatitudeHead LongitudeArea (sq. km)N HiRISE footprints intersectingN anaglyphs intersecting
1130-6858-7173West of HellasH2613_0000-32.5056.655.6300
1119-6667-6943East of HellasH2195_0000-44.2783.582.8500
1120-6639-6918East of HellasH2195_0000-44.3083.602.9200
1118-5779-6047East of HellasH2631_0001-42.7085.991.3500
1117-5550-5647East of HellasH2631_0001-39.8386.170.7000
1301-5550-5663East of HellasH2631_0001-39.8386.160.7500
1302-5430-5659East of HellasH2631_0001-39.8486.130.8410
198-5251-5718Utopia Planitia and Phlegra MontesH1526_000038.90116.381.9931
1300-5180-5595East of HellasH2631_0001-39.2186.1818.4700
1113-50500East of HellasH0365_0000-40.9990.170.6110
200-4996-5782Utopia Planitia and Phlegra MontesH1526_000039.08116.043.6210
1115-4937-5051East of HellasH2609_0000-38.1988.074.7400
1112-49340East of HellasH0365_0000-40.9790.192.0510
199-4927-5397Utopia Planitia and Phlegra MontesH1526_000039.05116.040.5910
1114-4912-5228East of HellasH2609_0000-38.2288.102.2400
1116-4861-5262East of HellasH2609_0000-38.6587.988.0100
1111-4775-5282East of HellasH0365_0000-40.6190.253.0700
1103-4691-5009East of HellasH0528_0000-38.5594.342.0021
1-4222-4534Deuteronilus MensaeH5314_000037.89-5.9310.9531
2-4149-4530Deuteronilus MensaeH5314_000037.99-5.9618.9531
1110-4037-4049East of HellasH0550_0000-36.5090.180.8400
6-3805-4014Deuteronilus MensaeH1498_000030.59-11.342.7910
192-3772-4407Utopia Planitia and Phlegra MontesH1317_000034.24144.324.3920
3-3746-4196Deuteronilus MensaeH3253_000038.32-9.782.4100
120-3691-3845Olympus Mons and surrounding areaH1258_000134.22-177.334.7100
121-3684-4010Olympus Mons and surrounding areaH1258_000134.22-177.336.5800
4-3677-3914Deuteronilus MensaeH3253_000038.27-9.311.3500
5-3604-4058Deuteronilus MensaeH3253_000040.04-10.362.5000
299-3447-3681Nilosyrtis MensaeH1629_000042.4762.491.4000
1299-3393-4112East of HellasH0550_0000-35.3091.181.6571

Highest elevation 30 GLFs (head):

Catalog numberHead elevation (m)Termimus elevation (m)RegionHRSC DTM tileHead LatitudeHead LongitudeArea (sq. km)N HiRISE footprints intersectingN anaglyphs intersecting
8139143587Olympus Mons and surrounding areaH5405_000044.91-111.213.2900
128736341951East of HellasH2279_0001-42.82108.199.7100
10433367752East of HellasH0451_0000-37.81103.3917.2921
10343225-175East of HellasH2356_0002-40.70103.0120.4921
129030131087East of HellasH2356_0002-41.71104.1221.9810
104228251510East of HellasH0451_0000-37.83103.324.6321
10152800569East of HellasH2345_0000-44.83104.7515.2620

Gul Dukat wins 2374 Galactic Presidential election with Brunt as VP

Nov 12, 2016

Campaign poster showing Gul Dukat and Brunt. Background from APOD by Rogelio Bernal Andreo.
The shock victory of Gul Dukat and Liquidator Brunt in the galactic presidential election has left the Federation wondering if Earth will reconsider plans to leave the Federation following the referendum in which the population narrowly voted to do so.
Although it is now eight Earth years since the Earth voted by 52% to 48% to leave the Federation, the President of Earth has not invoked Article 50 of the planet's membership treaty and is in battle over whether she can do so without a vote in the Planetary Assembly. The Earth orbital and lunar colonies strongly voted remain. The First Minister of Luna is advocating an independence referendum and several asteroid colonies are exploring transferring to Martian jurisdiction which has its own Federation membership.

Losing access to the Federation single market would make Earth more vulnerable to economic exploitation by the Ferengi.

The Leave campaign is now widely regarded as overestimating the amount of dilithium contributed to the Federation budget by Earth.

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