Limits on inference of Mars small‐scale topography from MOLA data

Abstract

The surface roughness of Mars at scales from ∼1–200 m is of interest for lander hazard and radar‐sounder clutter analysis, but MOLA data are the only current source of global topographic information. We use synthetic fractal profiles to determine the uncertainties associated with deriving self‐affine statistics from detrended segments of MOLA tracks. The mean Hurst exponent derived from such segments is an underestimate of the true value, H, for H > 0.5, and an overestimate for H < 0.5. Values of H from independent samples along a profile are distributed about this biased mean value. The magnitudes of the bias and variance in H increase for shorter segments. Terrestrial topography data show that extrapolation of roughness statistics to smaller scales based on self‐affine relationships is uncertain. Roughness at the 1–15 m scales may be poorly correlated with topography at >100‐m scales. We suggest that any extrapolation be regarded as a lower bound on the true terrain statistics.