Utilizing Valley Network Junction Angle to Estimate the Duration of "Warm" Mars

Introduction: Although the widespread dendritic valley networks (VNs) on Mars strongly suggest erosion by overland flow of water from precipitation, the climate models of Mars failed to reproduce the “warm” Mars scenario due to the faint young Sun. Scientists are still debating whether episodic warm or non-precipitation dominated erosion can create the observed VNs. Despite the ongoing debate, the supporters of “Warm” Mars and “Cold” Mars seem to agree that abundant liquid water flowed on Mars in the Noachian period [1,2]. Previous research suggested that the means of stream junction angles on Earth varied with different climatic conditions [3]. The frequency distribution of junction angles, which includes more information than mean value alone and is less influenced by the resurfacing processes, can be accurately extracted from the existing stream datasets. Thus the frequency of VN junction angles offers a new way for understanding the early Mars climatic conditions. One comparison between the junction angles of terrestrial streams and those of Martian VNs concluded that the VNs on Mars were formed primarily by precipitation-sourced overland flow erosion and not in permafrost environment [4]. However, this research did not investigate the possibility of the “cold but episodic warm” Mars, because the “warm” scenario could exist but lasted very shortly. The key to addressing this problem is the formation timescale of VNs (or the duration of water flow in VNs). The longer the water flow duration, the higher the probability of a “warm” Mars. To further investigate the early climate of Mars, we first established the association between the frequency distribution of stream junction angles and the climatic conditions on Earth and applied that relationship to estimate the Noachian climatic condition on Mars based on VN junction angles, we then assessed the duration of “warm” Mars. Data and Method: The terrestrial stream junction angles were extracted based on NHDPlusV2 Dataset of the conterminous U.S. The climatic factors were represented by aridity index (AI) and Mean Annual Precipitation (MAP) provided by CGIAR-CSI [5]. (AI = MAP/MAE, where MAE is Mean Annual Potential Evapotranspiration [5].) We utilized the averaged AI and MAP by HUC-6 (Hydrologic Unit Code-6) watershed as the dependent variables, the frequencies of junction angles in bins of 10° as the independent variables, i.e., we have 18 independent variables for each averaged climatic variable within each watershed. Then, we ran multiple linear regression to establish the association between climate and junction angle. The RMSE of regression between Log10(AI) and frequencies of junction angles is 0.16, and the RMSE of regression between Log10(MAP) and frequencies of junction angles is 0.17. The Martian VN junction angles were extracted from the VN dataset by Luo and Stepinski [6]. The entire Mars surface were divided into small tiles or grids, each with size of 500 km by 500 km, which can be considered a climatically homogenous area. We selected the grids within denser junction angle belt for analysis. Before we apply and scale the association between junction angle and AI established on Earth to estimate the AI of Mars, we need to consider the different radiation each planet receives from the Sun. The Potential Evapotranspiration (PET) on Earth can be related to radiation by Hargreaves evapotranspiration equation [7] as follows: