The Topography

The data

Where the heights come from

The elevation data on this board comes from MOLA, the Mars Orbiter Laser Altimeter. It flew on Mars Global Surveyor and returned altimetry from 1997 to 2001. It fired a laser at the ground 10 times a second and timed how long each reflection took to come back (see below). By the end it had measured Mars more accurately than we had measured large parts of Earth.

That timing gives the range R from the spacecraft down to the ground. The spacecraft's own height H above the areoid, the Martian equivalent of sea level, comes from tracking its orbit. The difference between the two is the elevation of the ground below.

Each pass measures a single line of points across the surface. The global grid is assembled from hundreds of millions of them, collected along successive orbits over several years. We started from that grid at 463 m per pixel at the equator.

Toward the poles the grid narrows. MOLA's near-polar orbit also crowded its ground tracks together there, leaving the poles measured more densely than the equator.

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. As a result, 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. Every square on the board is the same 2x2 plate and an equal-area projection gives each one the same amount of ground to stand for.

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 published MOLA map further down this page is a Mercator, where the ground near the top and bottom is drawn far larger than the same amount of ground at the equator.

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

In Phase 1 we use 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 fall 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 resolution

The power of the little plate

One square on the board covers 222 km of ground and one MOLA pixel covers 463 m, which puts about 480 MOLA pixels across a single plate in each direction.

The height that gets built is one of those pixels, the one nearest the center of the square. The rest are dropped. Height is then rounded to a whole number of 2 km steps, which removes relief smaller than 2 km.

The canyon of Valles Marineris is 4,000 km long, which is 18 plates, and under 200 km wide, which is less than one square. It appears on the board as a broken line of squares 3 or 4 plates lower than the plateau around them, in the places where the sampled pixel happened to fall inside the canyon.

The poster is drawn in a Mercator projection and our board in a Hammer. Setting the two beside each other would add 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. The two pictures now differ in resolution alone.

Tharsis, 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. The 180 degree meridian runs around the edge of the Hammer ellipse, where a square that straddles it lies half outside the map and stays empty.

Are there better elevation maps?

Yes! Several cameras have mapped parts of Mars far more finely than MOLA. However, none of them cover the whole planet.

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 calculate the height from the difference, in the same way your two eyes judge distance. The method is called stereophotogrammetry. 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.

A laser altimeter like MOLA (see above) supplies the light it measures, which makes it active remote sensing. A camera is passive and records sunlight or heat that was already there.

The code

Doing it

There are two important commands we use to achieve this. The first reprojects the MOLA grid onto Mars and resamples it to 96 x 48 pixels. The second converts meters to kilometers.

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 360 degrees of longitude and 180 of latitude.

-ts 96 48 is the target size in pixels, where 230 thousand MOLA pixels become one plate.

-r near is the resampling rule. It takes the nearest value instead of averaging, leaving each square with a height that was really measured.