North - South Slope Asymmetries on Mars: Statistical Analysis of Mola Data

Introduction: Mars Orbiter Laser Altimeter (MOLA) onboard Mars Global Surveyor (MGS) spacecraft produced a large homogeneous data set of precise elevation measurements along MGS tracks [1]. We have used this data set to map and study statistical characteristics of kilometerand subkilometer-scale topography [e.g., 2, 3]. In the present work we use MOLA data set to map and study slope asymmetry on Mars. Slope asymmetry is an important parameter in processes related to insolation and water mobility. Data processing: The direction of all MOLA tracks is close to meridianal except the high-latitude regions. The deflection from the meridian is about 5° in a wide equatorial zone. Poleward from 60° latitude, the deflection slowly, then more quickly increases, and reaches 17° at 80° latitude. Thus, sampling of Mars surface with MOLA is strongly anisotropic, and the data set does not allow complete study of slope anisotropy at subkilometer scale. The data can be used, however, to study the north south asymmetry of the slopes. The data processing technique we used was similar to that applied in [2] and [3]. For each pair of consecutive MOLA shots, we calculated the differential slope, keeping slope direction information (positive/negative sign was used for the south-/north-facing slopes). The differential slope was defined as the slope at 0.3 km baseline (the shot-to-shot distance) minus the slope at 0.9 km. The use of the differential slope instead of ordinary slope was necessary to eliminate the influence of regional topography on slope statistics. All calculated slopes were binned into map cells in a simple cylindrical projection; for each cell we calculated the median slope and the quartiles of the slope frequency distribution. The difference between the quartiles characterizes the width of the slope-frequency distribution, and serves as a measure of roughness. It is very close to doubled median absolute value of the differential slope used in [2]. Fig. 1 shows the roughness map obtained in this way; brighter shades denote rougher surface. Major geomorphic features are clearly distinguishable in the map; the latitudinal trend of roughness (smoother terrains at high latitudes) is pronounced even more clearly than in [2, Fig. 12], because the baseline here is twice shorter. The median signed slope can be used to quantify the deviation of the slope-frequency distribution from symmetric. The mean slope is always equal to zero. Nonzero median slope means a different balance of steep and gentle slopes for northand south-facing surfaces. To eliminate roughness and characterize solely the distribution shape we divided the median by the quartile difference. The map of this parameter is shown in Fig. 2; brighter shades denote positive median slope. The positive median slope means that the area covered by south-facing slopes is greater than the area covered by north-facing slopes. Since the mean slope is zero, this means, that the north-facing slopes are generally steeper than south-facing slopes.