Hack’s law of Mars Valley Networks

Abstract:

Valley networks (VNs), as the fingerprints of climatic and geologic processes of the early Mars, are widely distributed on the Martian Noachian upland. Their presence is evidence that liquid water flowed on the surface of early Mars and that the temperature of Mars’ surface was above-freezing. The formation of VNs could be explained under two contrasting hydroclimatic scenarios: (1) a warm climate with highly active hydrologic cycle, the water for doing the erosion was mainly supplied by rainfall, or (2) a cold climate with episodic warming events, the surface runoff was primarily fed by snowmelt and the rate of the hydrologic cycle would be much slower than the first scenario.

The Hack’s law, which is the power law relationship between the upstream contributing area and the length of the mainstream channel, is controlled by the scale of watershed and forming conditions. To test which scenario is closer to the environment conditions of Martian VN formation, we compared the exponents of Hack’s law of streams/VNs extracted from Earth and Mars DEM data and streams created by Optimal Channel Networks (OCN) algorithm, which minimizes gravitational energy loss when generating the networks.

Our results based on the contiguous U.S. streams and the Martian global VNs dataset show that most of the exponents of Hacks’ law on Earth and Mars are within the reasonable range of 0.5-0.6, which is also consistent with the exponents range from the VNs created by the OCN algorithm. These results suggest that the optimizing process played a role in landscape evolution on Mars and in forming VNs. The similar range of exponents of Hacks’ law on Earth and Mars suggest that that the Martian VNs and some Earth streams were formed under the same or similar conditions.