Simulating Fluvial and Mass-Wasting Erosion and Deposition

One possible class of erosional processes on early Mars may have been erosion and deposition resulting from precipitation as snow or rain which produces weathering, mass-wasting, and fluvial erosion and deposition.  The type of modification that such precipitation-induced denudation may have produced on Mars is explored by the use of a modified version of a drainage basin simulation model (Howard, A.D., 1994, A detachment-limited model of drainage basin evolution, Water Resources Research, 30, 2261-2285).  The starting point for the simulations are the cratered landscape simulations discussed elsewhere  and shown at right.

This cratered landscape is scaled to represent an area of 100 by 100 km, and as discussed above, the boundaries are repeated so that the landscape repeats like a wallpaper pattern (an area of about 160 by 160 kilometers is shown, so that some repetition occurs at the boundaries).  Craters vary in size from 50 to 1 km and the surface is initially saturated with craters.

In the first simulation shown below all surface materials are assumed to be equally erodible and weatherable.  The surface materials are assumed to be either loose (e.g. crater-produced regolith) or are weatherable at a rate that keeps pace with erosion.   Mass wasting is a combination of a negligible amount of linear creep plus an accelerated mass wasting that approaches a nearly instantaneous rate as slope gradients approach 30 degrees.  Fluvial erosion is detachment-limited and proportional to shear stress, such that the erosion rate depends upon the 0.3 power of contributing drainage area and the 0.7 power of local gradient.  Any surface depression is assumed to undrained and all sediment eroded from upslope is deposited as a fan-like form.  The assumed surface conditions are assumed to be like a desert with no external drainage, similar to the situation in the Great Basin of the western US. Inner crater rims suffer the greatest amount of erosion, and locally become gullied.  Craters therefore enlarge with time, with the greatest relative enlargement for the smallest craters.  As a result, the crater walls of small craters generally enlarge until they intersect each other, producing a network of intersecting ridges on the uplands between large craters.  Relatively few large channels develop because of the restrictive assumption that no depression is drained.  Crater floors fill in with low-gradient alluvial fans, obscuring small craters on the floors of larger ones.  Individual craters serve as local base levels, so that the sediments that accumulate in the crater bottoms are at different levels in each crater.  In some cases rims between adjacent craters become breached, and a former depositional basin in the higher-floored crater becomes eroded and the sediment transported to the lower crater.  The sediment deposition model has a "feature" such that some low areas escape deposition for a period of time, resulting in local depressions on the otherwise smooth fan surfaces.  These "holes" are more prevalent where deposition rates are most rapid.  The fluvially-sculpted crater walls and the nearly flat, featureless crater floors correspond most closely to cratered landscapes of Mars.  On the other hand, the rough texture of the intercrater uplands and the lack of appreciable channels on the upland do not compare favorably with most Martian cratered landscapes.

  The rough upland is somewhat less obvious if the initial cratered surface is deficient in small craters (in the cratered landscape at left craters less than 10 km are less frequent than the power law dependency for larger craters).

When the above cratered landscape is eroded, the uplands are relatively smoother with broad, shallow depositional basins in the remains of old, muted crater basins.  Locally the remnants of the walls of old crater basins are sculpted into dissected ridges of low relief.  The intercrater uplands still lack appreciable fluvial channels.
If this landscape is then subjected to a moderate amount of eolian deposition, very smooth intecrater plains result, with only dissected crater rims as the indicators of former extensive fluvial erosion.

Cratered surfaces are often superimposed upon regional slopes.  These may have been created by tectonic deformation, intrusions below the surface, or as the degraded inner or outer rims of large impact basins.  Prior large-scale relief is simulated by creating a fractal surface (also with repeating top and bottom and left-right boundaries) and then subjecting the surface to subsequent impact erosion, as is shown to the right.
When this rolling cratered surface is eroded, considerable channeling occurs on the steep portions of the intercrater surfaces.  At this advanced stage of erosion, appreciable dissected uplands and crater rims are eroded, creating primitive drainage basins.  Long channel systems are still a rarity due to the lack of drainage of enclosed depressions.  Note again that some of the rapidly filling alluvial basins have "holes" in them due to problems in the sediment routing procedure. 
It is interesting to see how a modest amount of eolian deposition modifies the surface. Most of the fine channels are obliterated, particularly in low-relief areas, whereas a few dissected ridges protrude through the eolian blanketing as the sole indicator of former fluvial erosion and deposition.
Another possible way to create fairly smooth intercrater uplands is to start from a cratered surface that has been subject to considerable eolian deposition.  This surface is then the starting point for the erosion simulation below:
Note the smoothness of the intercrater uplands that results from this simulations starting from a dust-mantled surface.  Because of the smoothness of the original surface, the resulting drainage pattern has a parallel and trellis pattern due to the restriction that flow can occur only in one of eight directions.  This directional bias is not noticeable when the original starting surface is rougher.
These are just exploratory simulations.  An effort is underway to explore in a systematic way the effect of varying initial conditions, combinations of processes, and different rate laws for mass wasting, fluvial erosion, and sediment deposition.  In addition, a systematic comparison of simulated landscapes with images of Martian cratered terrain will be made to judge the ability of the simulations to reproduce the observed landscape.  Stay tuned for further results!!