Mathematics – Probability
Scientific paper
Dec 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufm.h42c1090h&link_type=abstract
American Geophysical Union, Fall Meeting 2003, abstract #H42C-1090
Mathematics
Probability
1815 Erosion And Sedimentation, 1824 Geomorphology (1625), 5415 Erosion And Weathering, 6225 Mars
Scientific paper
Knowledge of the planet Mars largely derives from remote sensing. Although these data are of increasing resolution and spectral coverage, including global topography at about 1 km2 resolution, interpretations vary widely about past processes and environments. Most uncertain is the environment of early Mars, during the Noachian Period (4.5 to about 3.5 b.y.). Interpretations range from a relatively warm wet climate with lakes and precipitation runoff, to a cold, dry Mars with valley networks originating solely from hydrothermally-driven seepage. Geomorphic analysis has generally been based upon image interpretation and terrestrial analogs. Increasingly, however, quantitative process and landform modeling is being brought to bear, including simulation modeling of landform evolution. A simulation model incorporates geomorphic processes relevant to Mars. Impact cratering is simulated geometrically by randomly-located impacts drawn from a size-frequency distribution. Scaling of crater dimensions is based upon fresh martian crater morphology, and heuristic rules govern inheritance from the pre-existing topography. Simulated cratered landscapes serve as initial conditions for simulated eolian erosion and deposition, inundation by lava flows,and fluvial denudation.
The heuristic eolian model assumes that the long-term rate of eolian deposition and erosion is a function of an "exposure index", which is based upon the relative height of a location, such that valleys and crater floors are rapidly filled, level plains either receive no deposition or are slightly eroded, and crater rims and hill summits are eroded. Deposition on Mars is assumed to occur from saltation, deposition of dust from dust storms, and long-distance transport of crater ejecta and volcanic ash. The eolian model predicts that craters should infill at a nearly constant rate. Simulation of lava flow emplacement is also heuristic, based upon flow events of variable duration from specified source vents. The probability of a lava flow extending in a given direction is assumed greatest at the margins of recently active portions of the flow and is proportional to the local topographic gradient. Inundation of a cratered landscape is highly stochastic, with some craters surviving unscathed while neighbors are filled. Sumulation of fluvial erosion largely follows the landform evolution model of Howard [1994], with: 1) weathering rates a function of regolith thickness; 2) mass wasting involving both linear diffusional creep and accelerated motion as slopes approach a limiting angle; 3) detachment-limited fluvial erosion based upon shear stress, unit stream power, or bedload abrasion; and 4) sediment transport and deposition/erosion in alluvial channels, fans, deltas, and pediments. Fluvial erosion of cratered landscapes under assumed desert climate results in short valley systems with enclosed drainages in and between craters that resemble landscapes of the terrestrial Mojave and Basin and Range provinces. Drainage integration increases with time, but continued impact cratering disrupts fluvial networks. Model validation is limited by low resolution of images and topography, lack of stratigraphic information, absence of dating methods, and strong post-Noachian modification of landscapes by wind, mass-wasting, and "gardening" by small impacts. Nevertheless, the profiles of streams and fans are consistent with the gentle sections being sand or fine gravel, and steeper bedrock or boulder-floored sections. Simulated landscapes also compare favorably with the visual appearance of degraded Noachian cratered landscapes and with hypsometry and slope geometry statistics.
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