The Topography
Phase 1 builds the shape of Mars in gray. The heights come from a laser altimeter that flew in the 1990s, reduced to 96 squares across and 2 km steps.
Stack height, in kilometers above or below the Martian datum. The colors are read off the published MOLA map's own color bar. Purple and blue mark the bottom of Hellas, green and yellow the middle of the planet, red and brown the Tharsis rise, and white the few places above 14 km.
The data
Where the heights come from
All of the elevation on this board comes from MOLA, the Mars Orbiter Laser Altimeter. It flew on Mars Global Surveyor and spent the late 1990s firing a laser at the ground about 10 times a second, timing the return, and building up the shape of the planet one point at a time. By the end it had measured Mars more accurately than we had measured large parts of Earth.
The version we started from is the global grid at 463 m per pixel.
Smith, D. E. et al. (2001) Mars Orbiter Laser Altimeter: experiment summary after the first year of global mapping of Mars. Journal of Geophysical Research 106(E10), 23689–23722.
The projection
Flattening a sphere
Any flat map of a planet distorts it in some way, and choosing a projection amounts to choosing which distortion to accept.
We chose the Hammer projection, which squeezes the globe into an ellipse and is equal-area. Each square on the board is the same 2x2 plate, so each one has to stand for the same amount of ground, or the brick counts stop meaning anything. Under a Mercator projection a plate near the pole would cover a tiny patch of Mars and a plate at the equator an enormous one.
The ellipse is why the board has bare corners. Of the 4,608 squares in the 96 x 48 grid, 980 fall outside the map and stay empty, showing the dark baseplate underneath.
The binning
From height to plates
Real Mars runs from about −7.2 km at the bottom of Hellas up to nearly +20 km on top of Olympus Mons. To turn that into something you can stack, we chop it into 2 km steps.
The bottom plate starts at −8 km, which puts 0 km, the height the rest of Mars is measured against, at exactly 5 plates up. The tallest stack on the board is 14 plates, or about 45 mm.
At 1 km per plate the tallest stack would be 27 plates and the model would need twice the bricks. At 5 km it would be 6 plates and Mars would go flat.
The colors
Why the grays cycle
Phase 1 uses 3 colors, repeating as the stack climbs. Dark Bluish Gray, Light Bluish Gray, White, then Dark Bluish Gray again, counting up from the baseplate.
Each cycle starts at the board, which fixes a given color at a given height everywhere on the map. The 4th plate is Dark Bluish Gray on Olympus Mons and in the middle of Hellas alike. From a few steps back the repeating bands form contour lines across the whole planet. We call them elevation bands, not grays, because one of the 3 is White.
The exceptions
Off the chart
The printed color bar runs out at 10 plates. 3 squares on the board go higher. R13 on baseplate VII (14 plates), S12 on baseplate VII (14 plates), b15 on baseplate VII (13 plates). All 3 sit on the Tharsis rise, and 2 of them are Olympus Mons.
We could have stretched the color scale to reach them, but that would have squashed the 10 bands that the rest of the board depends on. Instead those squares get named on their own card and built by hand.
The honest part
How much we threw away
MOLA measured the planet at 463 m per pixel and our squares are 222 km across, which makes a single 2x2 plate the average of a very large number of real measurements.
480 × 480 = about 230 thousand measurements to one plate
The same reduction happens vertically. Rounding each height into a 2 km step removes relief smaller than 2 km, so Valles Marineris survives at 4,000 km long and a 50 km crater does not.
The published map of Mars, and the same planet at the resolution of the board.
The poster is drawn in a Mercator projection and our board in a Hammer, so setting the two beside each other would introduce a difference of projection on top of the difference in resolution. The board has therefore been redrawn into the poster's projection using the poster's own color scale, so that resolution is the only remaining difference between the two pictures.
Tharsis, Valles Marineris, Hellas and the northern lowlands survive the reduction, together with the dichotomy running between them. What disappears goes roughly in order of size, beginning with the crater population, then the channel networks, then the surface texture that gives the upper picture its photographic quality.
The dark teeth along the left and right edges of the lower picture are the rim of the board. Our map is an ellipse with the 180 degree meridian running around its edge, and a square straddling that line falls half outside it, leaving nothing to build.
Are there better elevation maps?
Yes, and much sharper ones, though each of them trades coverage away for resolution.
HRSC about 50 m most of the planet
CTX about 20 m where two images overlap
HiRISE about 1 m small patches only
Those are all cameras. HRSC, the High Resolution Stereo Camera, flies on Europe's Mars Express. CTX, the Context Camera, and HiRISE, the High Resolution Imaging Science Experiment, both fly on NASA's Mars Reconnaissance Orbiter.
These cameras do not measure height directly the way MOLA does. They photograph the same ground twice from slightly different angles and work the height out from the difference, which is the trick your two eyes use. HiRISE sees the ground at about 25 cm per pixel, sharp enough to pick out a rover, but it has only ever photographed a tiny fraction of Mars.
The code
Doing it
Two commands do the reduction. The first reprojects the MOLA grid onto Mars and resamples it to 96 x 48 pixels, and the second converts meters to kilometers.
-ts 96 48 -r near mola.tif coarse.tif
gmt grdmath coarse.nc 0.001 MUL = mars_dem_km.nc
GDAL, the Geospatial Data Abstraction Library, is what nearly all mapping
software uses underneath to read, write and reproject map files. Its
gdalwarp command takes a grid in one projection and hands you the same
grid in another.
GMT, the Generic Mapping Tools, is a toolkit for making maps and doing
arithmetic on grids. Its grdmath is a calculator that works on a whole grid
at once. Here it multiplies each height by 0.001 to turn meters into kilometers.
-t_srs ESRI:104971 sets the target spatial reference system, meaning
the planet and projection the answer should come out in. ESRI is the company whose
catalog of these codes everyone borrows, and 104971 is their number for Mars measured
as a sphere.
-te -180 -90 180 90 is the target extent, covering all 360 degrees of
longitude and all 180 of latitude.
-ts 96 48 is the target size in pixels, and it is where 230 thousand
measurements become one plate.
-r near is the resampling rule. It takes the nearest value instead of
averaging, so each square holds a height that was really measured, not a blend of
many.