Deciphering Early Mars Climate Conditions from Valley Network Erosion

Introduction: The Martian surface hosts an extensive geologic record indicative of widespread surface water during the 'valley network-forming era' (~3.7–3.5 Ga [1]). However, the climatic conditions required to incise the eponymous valley networks (VNs) remain poorly constrained. Proposed end-member solutions range from a long-lived 'warm and wet' climate with regular rainfall [2,3] to a 'cold and dry' climate with episodic snowmelt events [4,5]. The primary reason for this uncertainty is the wide range of unconstrained model parameters, exacerbated by a lack of quantitative ground-truth observations for model validation. In an attempt to compare VN erosion and climate conditions, previous studies have performed simple comparisons between model precipitation maps and the location of VNs [6,7]. However, these approaches have thus far led to poor spatial correlations. 

On Earth, the relationship between erosion and precipitation is well documented [8,9], albeit complex. However, quantitative precipitation-discharge-erosion models have seen limited application in deciphering the climate history of Mars. Here, we bridge the gap between climate simulations and geomorphic observations by integrating a mechanistic understanding of precipitation, runoff, and erosion. 

Methods: We use the hydrological toolbox WhiteboxTools [10] to run flow accumulation analysis: a simulation of the flow at each elevation grid cell to its steepest downslope neighbor. We use the digital elevation model (DEM) from the Mars Orbiter Laser Altimeter (MOLA; ~463 m/pixel [11]) to simulate flow directions. In the resultant flow accumulation map, each pixel represents the number of cells (or area) upstream of that point. Standard flow accumulation methods assume that precipitation is spatially constant. We refine this by using global precipitation maps from existing Mars climate model outputs [6,7,12,13] as weights (Fig. 1a-d). In the resulting 'precipitation-weighted' flow accumulation map (Fig. 1e), each pixel represents the cumulative precipitation rates of the upstream pixels, i.e., the discharge, Q, at each point, assuming no losses in conversion between precipitation and discharge. 

The relationship between erosion and precipitation on Earth is generally quantified through the stream power law [14], which states that the erosion rate is nonlinearly proportional to channel slope, S, and precipitation-sourced discharge Q, given a constant rock erodibility. Applying this to the Martian context, we compare our modeled global discharge maps to observed erosion, assuming steady erosion rates. We first measure channel slope, S, as the mean channel gradient between the second point upstream and second point downstream of each pixel, based on the MOLA DEM. Using a global map of eroded depths of VNs [15], we generate a planetwide, pixel-wise comparison of model discharge and channel slope, Q × S, to measured VN depth, d, along mapped stream lines (e.g., Fig. 2). Using this framework, we test the question: which climate models yield a good fit to the geomorphic record, as evidenced by positive correlations between observed eroded depths and a model's flow map (i.e., large valley depths, d, occur in areas of high model discharge, Q)? Through this intercomparison, we determine which climate scenarios within the explored parameter space (n = 91) yield the best fit. 

Results and Discussion: We find that the best-performing climate scenario [13] uses a pre-Tharsis paleotopography [16] and a global water inventory of 500 m global equivalent layer (GEL), achieving a Spearman’s rank correlation of ρ = 0.325 (Fig. 2). In climate model outputs, the Tharsis plateau typically causes westerly surface winds to be orographically lifted, leading to a 'rain shadow' east of Tharsis. Previous studies have speculated that poor agreement between precipitation from climate models and the surface record could be a result of Tharsis' rain shadow [6,13].  The growth of Tharsis likely induced a reorientation of Mars with respect to its spin axis, known as TPW. However, the timing of Tharsis' emplacement [17] and associated TPW (e.g., [18,19]) remains under debate. We find that 9 of the top 10 best-performing climate scenarios use a putative pre-Tharsis paleotopography. Our results thus suggest that the erosional record is most compatible with global VN incision prior to, or contemporaneous with, Tharsis' emplacement and associated TPW. 

References: [1] Fassett, C. I. et al. (2008) Icarus 195, 61–89. [2] Craddock, R. A. et al. (2002) JGR: Planets 107, 21-1-21–36. [3] Pollack, J. B., et al. (1987) Icarus 71, 203–224. [4] Wordsworth, R. et al. (2013) Icarus 222, 1–19. [5] Squyres, S. W. et al. (1994) Science 265, 744–749. [6] Wordsworth, R. D., et al. (2015) JGR: Planets 120, 1201–1219. [7] Steakley, K., et al. (2019) Icarus 330, 169–188. [8] Ferrier, K. L., et al. (2013) Nature 496, 206–209. [9] Marder, E. et al. (2023) Geology 51, 424–427. [10] Lindsay, J. B. (2016) Comp. & Geosci. 95, 75–84. [11] Smith, D. E. et al. (2001) JGR: Planets 106, 23689–23722. [12] Kamada, A. et al. (2020) Icarus 338, 113567. [13] Guzewich, S. D. et al. JGR: Planets 126, e2021JE006825. [14] Leonard, J. S. et al. (2021) JGR: Earth Surface 126, e2021JF006183. [15] Goudge, T. A., et al. (2021) Nature 597, 645–649. [16] Bouley, S. et al. (2016) Nature 531, 344–347. [17] Anderson, R. C. et al. (2001) JGR: Planets 106, 20563–20585. [18] Roberts, J. H. et al. (2007) Icarus 190, 24–31. [19] Matsuyama, I. et al. (2010) JGR: Planets 115, 2156-2202. 

Fig. 1(a)-(d) Global precipitation maps showing representative examples from [6,7,12,13]. (e) Modeled discharge map for a single Martian basin given the climate scenario in (d), overlaid on MOLA DEM. Blue outline shows a closed-basin lake which the VNs drain into. 

Fig. 2: Global comparison of observed valley erosion depth, d, against modeled discharge, Q, and channel slope, S, for the best-performing climate scenario [13]. Dashed line indicates line of best fit.