Global Spatial Distribution of Hack's Law Exponent on Mars Consistent With Early Arid Climate

Widespread valley networks (VNs) on Mars and other evidence point to an early warm and wet climate. However, ongoing debates still exist about VN's formation processes and associated climatic conditions. The power law relationship between basin length and area (Hack's Law) can be diagnostic of different fluvial processes related to climatic conditions. Past studies of Hack's Law on Mars at local sites have produced inconclusive results. Here we used a parameter-free method to delineate watersheds globally on Mars based on mapped VNs and extracted their Hack's Law exponent (h). The majority of h values on Mars are similar to those in arid areas on Earth, suggesting similar runoff processes and arid conditions for VN formation on early Mars. Statistical analyses show that the spatial distribution of h on Mars is not random, but with a few clustered high and low values, likely controlled by local conditions (e.g., regional topographic slope).

Automated summary

Widespread valley networks and other evidence suggest an early warm and wet climate on Mars. However, the formation processes and associated climatic conditions of these valley networks are still debated. This study used a parameter-free method to delineate watersheds globally on Mars based on mapped valley networks and analyzed their Hack's Law exponent. The majority of Hack's Law exponents on Mars are similar to those in arid areas on Earth, indicating similar runoff processes and arid conditions for valley network formation on early Mars. Statistical analyses show a non-random spatial distribution of Hack's Law exponent on Mars, with clustered high and low values likely controlled by local conditions such as regional topographic slope.