# Mars km-scale roughness maps

The maps are calculated in a way described in [Kreslavsky and Head 2000] (pdf) with minor modifications.

These papers should be referenced when using the data.

The map scale is 8 pixels per degree.

E8R.TIF Roughness map of the whole planet in simple cylindrical projection

N8R.TIF Roughness map of the Northern hemisphere in Lambert azimuthal polar equal-area projection

S8R.TIF Roughness map of the Southern hemisphere in Lambert azimuthal polar equal-area projection

The maps are presented as RGB composite images stored in TIFF format.

The Blue, Green and Red channels contain roughness at 0.6 km, 2.4 km, and 9.2 km baselines.

Brighter shades denote rougher surface. Thus, general brightness denotes general roughness, and color hue denotes the nature of the scale dependence of roughness. See [Kreslavsky and Head 2000] (pdf) for further details.

DN values in channels are stretched for the best visual presentation of the whole maps. This stretch is the same for all map projections.

Roughness data files

 Projection 0.6 km baseline 2.4 km baseline 9.2 km baseline Simple cylindrical projection E8R0.RAW E8R1.RAW E8R2.RAW Lambert azimuthal polar equal-area projection - North N8R0.RAW N8R1.RAW N8R2.RAW Lambert azimuthal polar equal-area projection - South S8R0.RAW S8R1.RAW S8R2.RAW

Projections.

Simple cylindrical projection.

2880 x 1440 pixels.

If the uppermost leftmost pixel has coordinates x = 1, y = 1, then

north latitude (deg) = (720.5 - x) / 8

east longitude (deg) = (y + 0.5) / 8

Lambert azimuthal polar equal-area projection for the Northern hemisphere

1440 x 1440 pixels.

If the uppermost leftmost pixel has coordinates x = 1, y = 1, then

r2 = (x - 720.5)2+ (y - 720.5)2

north latitude (deg) = -2 asin( p r / 2880) + 90, where asin should be taken in degrees

east longitude (deg) = atan2(x - 720.5, y - 720.5), where atan2 should be taken in degrees

Lambert azimuthal polar equal-area projection for the Southern hemisphere

1440 x 1440 pixels.

If the uppermost leftmost pixel has coordinates x = 1, y = 1, then

r2 = (x - 720.5)2+ (y - 720.5)2

south latitude (deg) = -2 asin( p r / 2880) + 90, where asin should be taken in degrees

east longitude (deg) = atan2(x - 720.5, 720.5 - y), where atan2 should be taken in degrees

Technical information

Roughness was calculated with the following procedure.

Good MOLA shots from nadir-looking orbits were selected.

For each given MOLA shot, profile curvature was calculated as:

c = ( h+ + h- - 2h) / (4l2),

where h, h+, and h- are MOLA-measured surface elevations from the given shot, a shot half-a-baseline ahead and a shot half-a-baseline behind along the orbit; l is the baseline length.
The baselines used correspond to 2, 8, and 32 shot-to-shot distances.

All calculated curvature values were binned in the map cells.

The interquatrile width C of the curvature-frequency distribution was used as a measure of roughness for each map cell.

Data files are simple data arrays without any labels and headers, one byte per pixel, arranged line by line from the top to the bottom of the map. Roughness C is called to the pixel value DN by the following logarithmic equation:

DN = 80 log10(C l) + 511

Further technical questions should be addressed to

M. Kreslavsky misha@mare.geo.brown.edu