Scaling relations for large Martian valleys

The dendritic morphology of Martian valley networks, particularly in the Noachian highlands, has long been argued to imply a warmer, wetter early Martian climate, but the character and extent of this period remains controversial. We analyzed scaling relations for the 10 large valley systems incised in terrain of various ages, resolvable using the Mars Orbiter Laser Altimeter (MOLA) and the Thermal Emission Imaging System (THEMIS). Four of the valleys originate in point sources with negligible contributions from tributaries, three are very poorly dissected with a few large tributaries separated by long uninterrupted trunks, and three exhibit the dendritic, branching morphology typical of terrestrial channel networks. We generated width‐area and slope‐area relationships for each because these relations are identified as either theoretically predicted or robust terrestrial empiricisms for graded precipitation‐fed, perennial channels. We also generated distance‐area relationships (Hack's law) because they similarly represent robust characteristics of terrestrial channels (whether perennial or ephemeral). We find that the studied Martian valleys, even the dendritic ones, do not satisfy those empiricisms. On Mars, the width‐area scaling exponent b of −0.7–4.7 contrasts with values of 0.3–0.6 typical of terrestrial channels; the slope‐area scaling exponent θ ranges from −25.6–5.5, whereas values of 0.3–0.5 are typical on Earth; the length‐area, or Hack's exponent n ranges from 0.47 to 19.2, while values of 0.5–0.6 are found on Earth. None of the valleys analyzed satisfy all three relations typical of terrestrial perennial channels. As such, our analysis supports the hypotheses that ephemeral and/or immature channel morphologies provide the closest terrestrial analogs to the dendritic networks on Mars, and point source discharges provide terrestrial analogs best suited to describe the other large Martian valleys.