Reconstructing river flows remotely on Earth, Titan, and Mars

Abstract

Alluvial rivers are conveyor belts of fluid and sediment that provide a record of upstream climate and erosion on Earth, Titan, and Mars. However, many of Earth's rivers remain unsurveyed, Titan's rivers are not well resolved by current spacecraft data, and Mars' rivers are no longer active, hindering reconstructions of planetary surface conditions. To overcome these problems, we use dimensionless hydraulic geometry relations-scaling laws that relate river channel dimensions to flow and sediment transport rates-to calculate in-channel conditions using only remote sensing measurements of channel width and slope. On Earth, this offers a way to predict flow and sediment flux in rivers that lack field measurements and shows that the distinct dynamics of bedload-dominated, suspended load-dominated, and bedrock rivers give rise to distinct channel characteristics. On Mars, this approach not only predicts grain sizes at Gale Crater and Jezero Crater that overlap with those measured by the Curiosity and Perseverance rovers, it enables reconstructions of past flow conditions that are consistent with proposed long-lived hydrologic activity at both craters. On Titan, our predicted sediment fluxes to the coast of Ontario Lacus could build the lake's river delta in as little as ~1,000 y, and our scaling relationships suggest that Titan's rivers may be wider, slope more gently, and transport sediment at lower flows than rivers on Earth or Mars. Our approach provides a template for predicting channel properties remotely for alluvial rivers across Earth, along with interpreting spacecraft observations of rivers on Titan and Mars.

Keywords: Mars; Titan; hydrology; planetary landscapes; rivers.

Fig. 1.

Alluvial rivers on Earth, Mars, and Titan. (A) The Yellowstone River, with gravel bed and banks (photo: J. Peaco); Images of gravel on both Mars (B) and Titan (C) from the Curiosity rover and Huygens lander. The larger grains in the Huygens image are ~10 cm in diameter; (D) Peace Vallis fan, an alluvial fan within Gale Crater on Mars; (E) The western delta within Jezero Crater on Mars, the target of exploration for the Perseverance Rover; (F) Saraswati Flumen on Titan, terminating in two delta-like lobes along the western shoreline of Ontario Lacus; (G) Vid Flumina on Titan, a large tributary network that terminates at Ligeia Mare. Yellow regions indicate locations where channel widths and slopes were measured.

Fig. 2.

Dimensionless width $(\stackrel{\sim }{B}$ ), depth ( $\stackrel{\sim }{H}$ ), and slope ( $S$ ), as functions of the dimensionless discharge ( $\widehat{Q}$ ) for 491 suspended load-dominated (red) and bedload-dominated (blue) rivers on Earth. Rivers with floodplains are plotted with solid colors; semitransparent points indicate rivers with widths potentially constrained by topography or with some bedrock on their beds or banks. For suspended load-dominated rivers, we plot the fits according to Eq. 1 assuming a constant Re_p, adopting the median grain size of our suspended load-dominated river dataset and 1-sigma of the D₅₀ distribution as shaded lines. Suspended load-dominated rivers are in red (Right), with bedload-dominated rivers in blue (Left).

Fig. 3.

Comparing the predictions of dimensionless hydraulic geometry with measurements. In all plots, the 1:1 line is in black, with the gray shaded regions representing 1:3 and 3:1 bounds (A–C) and 1:10 and 10:1 bounds (D). Colors are as in Fig. 2. In panels A/B/D, the orange and green triangles represent calculations for the Rhine River and rivers in the Amazon Basin, respectively. All Rhine and Amazon rivers are suspended load-dominated, but we do not have measurements of D₅₀ for either, or H for those in the Amazon. For these select rivers, all Q_s measurements are lower bounds, as only the suspended sediment loads are reported. Error bars represent 16th and 84th percentiles and derive from uncertainties in the measurements and hydraulic geometry fits. To compare our predicted volumetric sediment fluxes to the measured mass fluxes, we assume sediment with a density of 2.65 g/cm³.

Fig. 4.

Relative bed grain size, width, depth, and slope of planetary and terrestrial rivers. Bedload-dominated river ratios are shown with solid colors, while suspended load-dominated rivers are shown with a striped pattern. Assuming equivalent flow discharge and sediment flux, bedload-dominated and suspended load-dominated rivers on Titan may be both wider and more gently sloping than comparable rivers on Earth, while depth and bed grain size are less affected. Values for Titan are more extreme if even more buoyant sediment is assumed (arrows). Both river types on Mars are only marginally different from those on Earth, as gravity only weakly affects relative geometries.