# Inferring Discharge From River Geometry on Titan

C. Daudon, S. Rodriguez, E. Lajeunesse, A. Lucas, S. Jacquemoud

► To cite this version:

C. Daudon, S. Rodriguez, E. Lajeunesse, A. Lucas, S. Jacquemoud. Inferring Discharge From River Geometry on Titan. Geophysical Research Letters, 2025, 52 (8), 10.1029/2024GL111912. hal-05044729

HAL Id: hal-05044729

https://hal.science/hal-05044729v1

Submitted on 23 Apr 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2024GL111912

**Key Points:**

* Threshold theory is applied for the first time to an extraterrestrial body

* Threshold theory correctly predicts the geometry of alluvial and bedrock rivers on Earth

* The discharge of two rivers on Titan is estimated, with potential application to the rough evaluation of precipitations rates

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

C. Daudon,
caudon@caltech.edu

**Citation:**

Daudon, C., Rodriguez, S., Lajeunesse, E., Lucas, A., & Jacquemoud, S. (2025). Inferring discharge from river geometry on Titan. *Geophysical Research Letters*, *52*, e2024GL111912. https://doi.org/10.1029/2024GL111912

Received 26 AUG 2024
Accepted 30 JAN 2025

**Author Contributions:**

**Conceptualization:** C. Daudon,
S. Rodriguez, E. Lajeunesse, A. Lucas

**Formal analysis:** C. Daudon

**Investigation:** C. Daudon

**Methodology:** C. Daudon, S. Rodriguez,
E. Lajeunesse

**Supervision:** S. Rodriguez, A. Lucas,
S. Jacquemoud

**Validation:** C. Daudon

**Writing – original draft:** C. Daudon

**Writing – review & editing:**

S. Rodriguez, E. Lajeunesse, A. Lucas,
S. Jacquemoud

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution-NonCommercial-NoDerivs
License, which permits use and
distribution in any medium, provided the
original work is properly cited, the use is
non-commercial and no modifications or
adaptations are made.

<figure><img src="image_2.png" /></figure>

## Inferring Discharge From River Geometry on Titan

C. Daudon¹,², C. Rodriguez¹, E. Lajeunesse¹, A. Lucas¹, and S. Jacquemoud¹

¹Université Paris Cité, Institut de physique du globe de Paris, CNRS, Paris, France, ²Marine Science Institute, University of California Santa Barbara, Santa Barbara, CA, USA

**Abstract** Titan's dense atmosphere, composed mainly of methane and nitrogen, maintains a methane cycle that shapes its surface. Like water on Earth, methane precipitation erodes Titan's surface, carving river networks at all latitudes, as revealed by the Cassini-Huygens mission. On Earth, it is well known that laboratory and natural rivers exhibit a power-law relationship between their bankfull geometry and water discharge, as described by the threshold theory. Here, we investigate this hydraulic-geometric relationship on two rivers on Titan, one near the equator and the other at the south pole. We hypothesize that this relationship can be applied to any river, and test it for the first time on extraterrestrial rivers. Having shown that Titan's rivers are consistent with the threshold theory, we use this relationship to estimate river discharge from bankfull geometry. As a perspective, we then use these discharges to infer precipitation rates, which could help to better understand Titan's climate.

**Plain Language Summary** Titan, Saturn's largest moon, and Earth are the only bodies in the Solar System with active rivers. Their geometries are strikingly similar, although on Titan the rivers are filled with methane instead of water and are carved out of consolidated water ice. Our aim is to show that these rivers form in the same way as terrestrial rivers, and that their shape is governed by the same laws. We investigate two rivers on Titan, at the equator and at the south pole, and use a physics-based analytical model derived from terrestrial rivers to deduce their discharge.

## 1. Introduction

Rivers are found all over Titan's surface. They can be hundreds of kilometers long, such as those in the Xanadu region at the equator, which are over 450 km long and up to 5 km wide. They are found at all latitudes and take a variety of shapes. There are canyons and meandering rivers at the poles (Malaska et al., 2011; Poggiali et al., 2016), and braided rivers at the equator (Lucas, Rodriguez, et al., 2014). Their shapes are remarkably similar to those found on Earth, although the substrate and the fluid involved are different. This raises the question of whether the shape of Titan's rivers is governed by the same physical laws as terrestrial rivers. In particular, whether the discharge and bankfull geometry of the river follow a power-law type relationship. Since there are no in situ measurements of river discharge on Titan, this has to be inferred from transport models.

Few studies have yet attempted to estimate discharges on Titan. The most recent (Birch et al., 2023) used empirical relationships describing bankfull hydraulic geometry of bedload-dominated and suspended load-dominated rivers on Earth, established by Parker et al. (2007) and Wilkerson and Parker (2011) who qualified them as quasi-universal. Birch et al. (2023) used data from terrestrial rivers to calibrate these hydraulic geometry relationships but, although they show good prediction on Earth, it has never been demonstrated that these relationships can be applied to another body under different environmental conditions (gravity, sediment and fluid densities). Three other studies have also used empirical approaches to estimate discharge on Titan. The first estimated the unit discharge (discharge per unit area) required to transport the sediment (Burr et al., 2006). The authors combined several empirical equations assumed to apply to “any liquid of low viscosity” (Komar, 1979; Wilson et al., 2004). As no grain size or topographic data were available at the time, they fixed two median grain sizes (0.0625 and 256 mm) and varied the slope (0.001–0.003) and flow depth (0.001–100 m). Jaumann et al. (2008) used an empirical approach (Irwin et al., 2005) to calculate discharge as a function of width, flow depth, slope and gravity. As their method was calibrated for terrestrial rivers, they introduced several empirical conversion factors to estimate rough discharges and corresponding rainfall rates for various rivers on Titan.

Lorenz et al. (2007) used the empirical relationship of Carlston (1965), calibrated for meandering rivers on Earth, but never tested on other planetary bodies. They applied it to a river on Titan near the equator. Finally, in a more
detailed study, the precipitation rate of a river near the Huygens landing site (HLS) was estimated from images acquired by the Huygens probe (Perron et al., 2006). Assuming that the riverbed is at the threshold of movement, these authors used the Darcy-Weisbach equation to relate the river discharge $Q$ to its width $W$ and slope $S$, estimated using a digital terrain model (DTM) (Soderblom et al., 2007). They calculated the river discharge and the corresponding rainfall rate.

However, this DTM proved to be unreliable for geomorphic measurements, mainly due to landscape leveling errors. A more reliable DTM has recently been produced by Daudon et al. (2020). Its spatial sampling is higher and the topography is more reliable. It can therefore be used to determine slope with greater confidence. In addition, earlier work by Perron et al. (2006) assumed that the river cross section was rectangular, so that slope and width were treated as two independent parameters. Another approach is to use the so-called threshold theory, which links the slope and width of a river. Lacey's law (Lacey, 1930) empirically relates the width of a river, or the inverse of its slope, to the square root of its discharge. This physical law was later formalized by assuming that rivers adjust their morphology (width and slope) so that the sediments in their bed are at the threshold of motion (Glover & Florey, 1951). The river is then said to be in equilibrium, as the forces that tend to mobilize sediment are counterbalanced by those that retain it. Under these conditions, the riverbed is naturally concave and its width and slope are set by the discharge of the river (Devauchelle et al., 2010; Métivier et al., 2017) (see full demonstration in Section S2 in Supporting Information S1):

$$W = \left(\frac{\pi}{I}\right) \left(\frac{c_f^2}{g\mu_f^3 L}\right)^{1/4} Q_w^{1/2}, \qquad (1)$$

$$S = I \left( \frac{g\mu_f^3}{c_f^2} \right)^{1/4} L^{5/4} Q_w^{-1/2}, \qquad (2)$$

with $Q_w$ the discharge (m³.s⁻¹), $I$ a constant equal to 1.32, $W$ the river width (m), $g$ gravity (m.s⁻²), $\mu_f$ the angle of repose, and $c_f$ the friction coefficient. The characteristic length $L$ depends only on the sediment and fluid properties:

$$L = \frac{\theta_t (\rho_s - \rho_f) d_s}{\mu_f \rho_f}, \qquad (3)$$

with $\rho_s$ the sediment density (kg.m⁻³), $\rho_f$ the fluid density (kg.m⁻³), $d_s$ the grain size (m), and $\theta_t$ the dimensionless critical Shields number. Thus, Equations 1 and 2 can be rewritten as:

$$Q_{wW} = \left(\frac{WI}{\pi}\right)^2 \left(\frac{g\mu_f^3}{c_f^2}\right)^{1/2} \left(\frac{\theta_t(\rho_s - \rho_f)d_s}{\mu_f\rho_f}\right)^{1/2}, \qquad (4)$$

$$Q_{w,S} = \left(\frac{I}{S}\right)^2 \left(\frac{g\mu_f^3}{c_f^2}\right)^{1/2} \left(\frac{\theta_t(\rho_s - \rho_f)d_s}{\mu_f\rho_f}\right)^{5/2}, \qquad (5)$$

This theory implies that $W$ and $S$ are inversely proportional:

$$W = \frac{\pi L}{S}, \qquad (6)$$

This formula, which is valid for a concave shape of the river bed, eliminates the need for one of the two morphological parameters of the river (slope or width) for calculating the discharge. Furthermore, since Equation 6 is independent of the discharge, it can be used to test the theory without flow measurements. The threshold theory has been validated on Earth for alluvial rivers (Métivier et al., 2017). Although it has rarely been applied to bedrock rivers, recent work (Baynes et al., 2020; Phillips & Jerolmack, 2016) suggests that bedrock channels also
self-organize so that their beds are close to the threshold of motion. Dimensionless discharge as a function of dimensionless width can be shown to follow a similar trend for both alluvial and bedrock rivers (Bagnold, 1980; Baynes et al., 2020; Birch et al., 2023; Métivier et al., 2017) (see Figure S1 in Supporting Information S1). This is a major asset for Titan, where the river type is unknown.

This approach has two advantages over the traditional empirical relationships used previously (Birch et al., 2023; Burr et al., 2006; Jaumann et al., 2008; Lorenz et al., 2007). First, it applies to any type of river. In addition, since all parameters are expressed, adapting the law to Titan conditions is straightforward, and there is no uncertainty in the empirical parameters. In the end, only gravity and the physical properties of sediments and fluids need to be adapted from one planetary object to another. In this study, we apply the threshold theory (Devauchelle et al., 2010; Seizilles et al., 2013) to Titan using DTMs (Aharonson et al., 2014; Daudon et al., 2020) where river networks are clearly visible and river geometry (width or slope) can be measured. After showing that the theory applies to Titan's rivers, we derive river discharges from Equation 4 at two sites, one at the equator and the other in the polar regions, where the climate and hence precipitation rates are assumed to be different (Mitchell & Lora, 2016). Finally, we propose a method for interpreting discharge estimates in terms of precipitation rates and compare them with climate model predictions.

## 2. Characterizing Titan's Rivers at Low and High Latitudes

The first site is a river network near the HLS, in the equatorial region (10.25°S, 192.5°W) (Figure 1). Optical images were taken by the DISR (Descent Imaging and Spectro-Radiometer) instrument on board the Huygens probe during its descent through Titan's atmosphere. These images (14–21 m/px) and the resulting DTM (18 m/px) are the most resolved of Titan's surface (Daudon et al., 2020). Dark areas in Figure 1 are interpreted as fluvial channels, where liquid methane has carved the bright highland region before draining material into the flat, dark lowlands (Perron et al., 2006; Tomasko et al., 2005). We focus on a branch of the main river, ~2 km long and gently sloping (~3°) from an elevation of ~200 m to ~100 m (Figure 1). The second site is near Titan's south pole (72°S, 245°W) where the climate is assumed to be wetter than at the equator (Mitchell & Lora, 2016). A DTM with a spatial resolution of 875 m (Figure S3 in Supporting Information S1) was extracted from radar images (Aharonson et al., 2014) acquired by the Cassini Synthetic Aperture Radar (ground sample distance 175 m). The selected portion of the river is ~100 km long: it extends from a mountainous area ~1,800 m high to a broad valley ~15 km wide (Figure 1).

All parameters of Equations 4 and 5 are calibrated to apply the threshold theory to both sites. The river slopes *S* are extracted directly from the two DTMs (Aharonson et al., 2014; Daudon et al., 2020). For the HLS, we used the mean and standard deviation (S = 0.05 ± 0.01) determined along the path of the main channel represented by the orange arrows in Figures 1a and 1c. Although less accurate, the south pole (SP) DTM shows a rather flat riverbed (S ∈ [10⁻⁴, 10⁻²]).

The river widths *W* are estimated directly from optical or radar images acquired at the two sites, because they have a better resolution than the DEMs. At the south pole, the riverbed is very bright and easily detectable in SAR images (Figure 1); therefore its width can be determined with more confidence than the HLS river. The width of the SP river is between 500 and 850 m in the selected area. The spatial resolution of the HLS images is too low to accurately determine the lateral extent of the river in the valley. As we do not know whether the river extends across the entire valley or not, the maximum width of the river (40 m) was determined by looking at the variation in albedo on the orthorectified image (Daudon et al., 2020) (Figure 1c), which represents the valley width. Ground images acquired by the Huygens probe after landing, 3 km from the mouth of the river, show rounded pebbles of various sizes (Figures 1a and 1b). Assuming that they are representative of sediment transported by the river, the size of the largest “downstream” sediment (20 cm) (Figure 1b) was used as an extremely conservative estimate of the lower bound of the river’s width. In other words, the lower bound of width is assumed to be one grain wide.

As there are no images of the riverbed itself, we also used these images to estimate the grain size *d*<sub>s</sub> at the HLS. It should be noted that the full grain size distribution of the transported sediments was measured from these images by Keller et al. (2008) (Figure 1b).

However, the resolution of the DISR images is not sufficient to distinguish grains smaller than 3 mm, so the median size *d*<sub>50</sub> could be biased. We therefore assumed that the sediment size *d*<sub>s</sub> was in the range 4 mm–13 cm, corresponding to the most frequent grain sizes in the images. We don't know if those grains have recently been
<figure><img src="image_3.png" /><figcaption>**Figure 1.** I. River network observed by the DISR camera at the Huygens landing site (10.25°S 192.5°W). (a) Mosaic showing the landing site (X) (E. Karkoschka, https://pds-atmospheres.nmsu.edu/PDS/data/hpdisr_0001/EXTRAS/MOSAICS/MOSIACS_PNG/). (b) Pebble bed photographed by the DISR camera shortly after the landing (courtesy of ESA/NASA/JPL/University of Arizona). (c) Orthorectified image superimposed on the DTM (Daudon et al., 2020). The vertical amplitude is 400 m (×1.5). Dark streams are interpreted as fluvial valleys and bright units as topographic features (Daudon et al., 2020; Perron et al., 2006). Orange arrows indicate the investigated river. Green dots (●) and blue dots (●) mark the upstream and downstream edges of the channel. II. River network at the south pole as observed by the Cassini Radar instrument. The image is the despeckled SAR image of the T55 radar swath (Lucas, Aharonson, et al., 2014). The rivers appear bright and meandering in the valley (Le Gall et al., 2010). The bright terrain around the valley is mountainous. The orange arrows indicate the river studied, the green dot (●) the upstream limit of the section studied, and the blue dot (●) the downstream limit.</figcaption></figure>
<table><caption>**Table 1**

Characteristic Parameters of River Channels Observed Near the Huygens Landing Site (HLS) and the South Pole (SP)</caption><thead><tr><th></th><th>ρ<sub>f</sub> (kg/m<sup>3</sup>)</th><th>ρ<sub>s</sub> (kg/m<sup>3</sup>)</th><th>c<sub>f</sub></th><th>θ<sub>t</sub></th><th>μ<sub>t</sub></th><th>d<sub>s</sub> (m)</th><th>S</th><th>W (m)</th></tr></thead><tbody><tr><td>HLS</td><td>500</td><td>990–1,500</td><td>0.02–0.1</td><td>0.03–0.04</td><td>0.5–0.7</td><td>4.10<sup>-3</sup>–0.13</td><td>0.05–0.06</td><td>0.2–40</td></tr><tr><td>SP</td><td></td><td></td><td></td><td></td><td></td><td>8.10<sup>-3</sup>–5.10<sup>-2</sup></td><td>5.10<sup>-4</sup>–0.01</td><td>500–850</td></tr></tbody></table>

Note. Parameters in italics are not used in the discharge calculation.

transported. But, some studies show that there is a good chance that this region experienced “recent” precipitation. The first one being thermal conductivity measurements that support the hypothesis of subsurface liquid evaporation (Lorenz et al., 2006), indicating that the surface was probably wet at the time of landing. Also, the surface showed signs of the presence of liquid methane, as a gradual 40% increase in methane abundance was measured by gas chromatograph and Huygens mass spectrometer (GCMS) just after landing (Niemann et al., 2005). Finally, two big storms have been observed at the equator (Turtle, Perry, et al., 2011). Their large extent (more than 500,000 km²) and the proximity of one of them to the Huygens landing site (about nearly 50° to the west) is an indication that recent rainfall may occur in this region.

For the south pole river, we used the radar images to extract information on grain size. The radar backscattering coefficient of the river bed is very high (up to ~1 dB) compared to that of the surrounding terrain (up to ~10 dB), for an angle of incidence of about 20°S (Figure S2 in Supporting Information S1). As this site is rich in water ice and flat, the most likely explanation for the backscatter enhancement at this angle of incidence is the presence of rounded icy pebbles in the riverbed, whose size is close to the wavelength of the Cassini radar imager (2.19 cm) (Le Gall et al., 2010). In fact, these pebbles are natural microwaves reflectors, which could explain the strong increase in brightness in the riverbed. The river would therefore be able to transport coarse grains in the centimeter range. We assume that the sediment is centimetric in size (from 0.8 to 5 cm). This value may not be the $d_{50}$, but grains of this size could certainly be transported by this river. An independent approach confirmed the consistency of the grain size values for both sites (Section S3 in Supporting Information S1).

So far, we have focused on the river geometry and on the grain size of the transported sediment. To estimate river discharge, we need to calibrate the other parameters of Equation 4 that are common to both rivers. The angle of repose $\mu_t$ depends mainly on the shape and arrangement of the grains. The typical value of $\mu_t$ = tan 30° used for granular media (Loiseleux et al., 2005) should apply to Titan sediments. As for the turbulent friction coefficient $c_f$, it depends on the intensity of the flow turbulence and the roughness of the river bed (Buffington & Montgomery, 1997). As this parameter is very difficult to calibrate on Earth, we use the same range of values on Titan as on Earth, that is, between 0.02 and 0.1 (Métivier et al., 2017). Although the nature of Titan's sediments remains unknown, water ice (density of 990 kg/m³) (Brossier et al., 2018; Soderblom et al., 2007; Tomasko et al., 2005) and complex solid hydrocarbons (density of 1,500 kg/m³) (Brossier et al., 2018; Le Mouélic et al., 2018) are the most likely. With a surface temperature of 93 K and an atmospheric pressure of 1.5 bar, methane is found in liquid form (density of 500 kg/m³) (Steckloff et al., 2020). It is the most abundant fluid on Titan and the main agent of fluvial incision (Burr et al., 2006; Perron et al., 2006; Tomasko et al., 2005). Finally, to estimate the critical Shields number, we use the viscous diameter (see Section S4 in Supporting Information S1), the grain size for which the effects of gravity and viscosity are of the same order of magnitude (Andreotti et al., 2013). The value we found for Titan is consistent with turbulent flow conditions (0.03–0.04). In the following, the threshold theory is applied to the two rivers with the parameters listed in Table 1 to estimate their discharge (Equation 4) and the associated precipitation rates.

### 3. Threshold Theory Applied to Titan

The threshold theory has only been applied to terrestrial rivers, so the first step is to see if Equation 6, which only involves slope and width, applies to Titan's rivers. Figure 2 shows the relationship between width and slope for a large number of terrestrial rivers, as well as for the two Titan rivers. The terrestrial rivers form two groups that differ in their median grain size, and hence, in critical Shields number. The threshold theory seems to predict a lower limit for the aspect ratio (Equation 6), which means that this ratio is generally underestimated. The small difference between the river aspect ratio estimated by the theory and the observations can be explained by the fact that sediment transport is not taken into account in the threshold theory (Abramian et al., 2020; Parker, 1978;
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Measured slope *S* as a function of dimensionless width *W/L*, with *W* the measured width and *L* the characteristic length (see Equation 3) for natural terrestrial (Métivier et al., 2017; Seizilles et al., 2013) and two Titan rivers. The vertical colorbar corresponds to the logarithm of the dimensionless Archimedes number. The black lines correspond to the threshold theory calculated for two extreme values of the critical Shields number found on Earth ($\theta_t = 0.02$ for a gravel-bed river and $\theta_t = 0.4$ for a sand-bed river). Error bars for Titan rivers are due to parameter variability (S, W and L), summarized in Table 1.</figcaption></figure>

Popović et al., 2021). In addition, as noted by Dunne and Jerolmack (2020) and Phillips et al. (2022), the deviation of the threshold theory from the field measurements could be due to the lack of characterization of its bank materials, as the threshold stress of cohesive bank-toe material is suggested to be a key factor in the cross-sectional geometry of rivers. Overall, however, the threshold theory correctly predicts the general geometric behavior of both types of terrestrial river.

The correlation between grain size and slope, represented by two groups of different colors on Figure 2, is well documented for terrestrial rivers. It corresponds to the transition between gravel-bed and sand-bed rivers (Parker, 2008; Sambrook Smith & Ferguson, 1995). At the grain scale, this transition is observed when the flow around the grain changes from turbulent to laminar. To quantify this transition, we introduce the Archimedes number *Ar*, the ratio of sinking forces (i.e., the difference between weight and buoyancy) to viscous forces:

$$Ar = \frac{gd_s^3 \rho_f (\rho_s - \rho_f)}{\eta}, \qquad (7)$$

with $\eta$ the dynamic viscosity of the fluid (Pa.s). Small values of *Ar* (typically <1) correspond to laminar flow, while large values (>1000) indicate turbulent flow at the grain scale. On Earth, rivers vary mostly with grain size, so do the Archimedes and Shields parameters. But here we are comparing Earth data with Titan data, where the fluid and the grains have different compositions and densities, so the Archimedes number is useful for normalization and comparison purposes. From a river dynamics perspective, the clustering of terrestrial river types (gravel-bed and sand-bed rivers) is clearly visible in Figure 2. If we add the two Titan rivers to this graph, we see that the HLS river follows the trend of the gravel-bed rivers (large Archimedes number, $Ar \approx 5.5 \cdot 10^9$). In addition, the dimensionless width *W/L* of the HLS river is comparable to that of terrestrial gravel-bed rivers. The south pole (SP) river lies between the gravel-bed and sand-bed river groups, in the transition zone. Its Archimedes number of about $8.5 \cdot 10^7$ is slightly higher than the surrounding river points ($2 \cdot 10^3 - 10^6$), probably because its grain size is slightly overestimated (Table 1). The relationship between width and slope for the HLS and SP rivers is consistent with the threshold theory, as it follows the predicted trend when $\theta_t = 0.4$ (Figure 2).
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Log-log plot of dimensionless discharge $Q^* = \frac{Q_{f}^{1/2}}{\sqrt{gds}}$ of terrestrial and Titan rivers as a function of dimensionless width $W^* = \frac{W}{ds} (\frac{\rho_f - \rho_t}{\rho_f})^{1/4}$. Dots correspond to alluvial rivers (~2,600) and squares to bedrock rivers (~35). Orange dots correspond to laboratory data (Baynes et al., 2020; Métivier et al., 2017) while green dots correspond to natural rivers (Birch et al., 2023; Métivier et al., 2017; Phillips et al., 2022). The thick gray line indicates the threshold theory (Equation 4) calculated with the parameters in Table 1, while the two thin gray lines represent the uncertainty in the calculation of the river width at the threshold. This uncertainty is due to the intrinsic variability of the two dimensionless coefficients ($c_f$ and $\mu_f$) and the critical Shields number $\theta_f$. The blue areas represent the estimated discharge at two Titan sites with their uncertainties (resulting from uncertainties in drainage areas, river widths and transported grain sizes) for the HLS and the south pole. The shaded bands represent the discharge estimates calculated from GCM precipitation rates for the two study sites (Barth & Rafkin, 2010; Hueso & Sánchez-Lavega, 2006; Lora et al., 2015; Mitchell et al., 2011; Rafkin et al., 2022; Schneider et al., 2012) (see also Section S7 in Supporting Information S1). Uncertainties in these discharge estimates arise from both variability between model predictions and drainage area estimates.</figcaption></figure>

## 4. Results and Discussion

We have shown that the geometry (width and slope) of Titan's two rivers fits well with the threshold theory, allowing us to use Equation 4 to estimate their discharge. Figure 3 shows a comparison of these discharge values with those measured on Earth (Métivier et al., 2017; Seizilles et al., 2013). Notably, the threshold theory does not require both river width and slope to calculate discharge, allowing us to use the most accurately known variable for each site. For the SP river, we calculated discharge based on the width extracted from the images, while for the HLS river, we relied on the slope obtained from the digital terrain model (DTM), which is considered reliable in this region (Daudon et al., 2020). The width of the HLS river was not clearly visible in the images. In addition, to represent the discharge of the HLS river in Figure 3, we calculated the corresponding width using Equation 6.

In the absence of direct measurements of precipitation rate and intensity on Titan, alternative approaches based on river morphology provide valuable insights (Perron et al., 2006). Climate and regional meteorology on Titan are primarily studied using general circulation models (GCMs), which provide estimates of seasonal and latitudinal methane precipitation rates (Faulk et al., 2020; Lora et al., 2015; Mitchell et al., 2011; Rannou et al., 2006; Schneider et al., 2012; Tokano, 2019). Mesoscale cloud-resolving models further simulate methane cloud formation and predict localized instantaneous precipitation rates (Barth & Rafkin, 2010; Hueso & Sánchez-Lavega, 2006). However, both modeling approaches are limited by several key unconstrained variables in Titan's atmosphere and surface, such as temperature, humidity, and methane evaporation rates. While the Huygens probe has provided valuable in-situ atmospheric data, including humidity and altitude profiles of constituents (Niemann et al., 2005), its measurements remain limited to a single location.

There are limited direct observations of clouds (Rodriguez et al., 2009, 2011; Turtle, Del Genio, et al., 2011; Turtle et al., 2009, 2018) and rainfalls (Barnes et al., 2013; Dhingra et al., 2020; Turtle, Perry, et al., 2011) on Titan, mainly at the south pole (Turtle et al., 2009) and north pole (Dhingra et al., 2020), as well as at the equator (Turtle, Perry, et al., 2011). Most of the condensable methane (equivalent to 5 m thickness at the surface) is in the atmosphere (Müller-Wodarg et al., 2014). This could generate storms that produce most

of the total precipitation. By dividing the discharge by the drainage area measured from DTMs or imagery (Section S6 in Supporting Information S1), a precipitation rate can be calculated using equation:

$$Q_w = cAP, \qquad (8)$$

with A the drainage area (m²), P the precipitation rate (m².s⁻¹) and c a coefficient between 0 and 1 that depends on the infiltration and evaporation. In this study, we assume that c is equal to 1 (no infiltration nor evaporation) in order to estimate a minimum precipitation rate required to initiate sediment transport (the same condition was used by Perron et al. (2006). Equation 8, known as the rational method, was first introduced by Kuichling (2019) and is used in hydrology to predict peak runoff in a watershed (Chin, 2019; Perron et al., 2006). In this study, we want to see how the prediction from this method compares with the prediction from climate models.

Very low discharge values (0.001–1 m³/s) are observed at the HLS, reminiscent of the hydrological regime of arid regions on Earth. These estimates are compared with estimates from previous work in Section S7 in Supporting Information S1. From these discharges, we inferred instantaneous precipitation rates at the equator (0.01–2 mm/hr) that would be considered “weak” on Earth, rather than torrential as expected in thunderstorms (rainfall is considered “strong” above 7 mm/hr). This suggests that equatorial rivers could form from episodic, low-intensity rainfall. This is consistent with the fact that it is easier to transport sediments on Titan than on Earth (Burr
<caption>**Table 2**</caption>

Table of Precipitation Rate Extracted From Climate Models (Barth & Rafkin, 2010; Hueso & Sánchez-Lavega, 2006; Mitchell, 2008; Rafkin et al., 2022; Schneider et al., 2012) and Their Corresponding Discharges for Each Site

<table><thead><tr><th rowspan="2"></th><th colspan="2">HLS</th><th colspan="2">SP</th></tr><tr><th>P (m/s)</th><th>Q (m³/s)</th><th>P (m/s)</th><th>Q (m³/s)</th></tr></thead><tbody><tr><td>Schneider et al. (2012)</td><td>3e<sup>-8</sup>-6e<sup>-8</sup></td><td>0.09-0.07</td><td>1e<sup>-8</sup>-8e<sup>-8</sup></td><td>35-850</td></tr><tr><td>Mitchell (2008)</td><td>1e<sup>-8</sup></td><td>0.01-0.03</td><td>1e<sup>-8</sup>-5e<sup>-8</sup></td><td>44-132</td></tr><tr><td>Hueso and Sánchez-Lavega (2006)</td><td>2e<sup>-6</sup>-4.5e<sup>-5</sup></td><td>2-122</td><td></td><td></td></tr><tr><td>Barth and Rafkin (2010)</td><td>2e<sup>-6</sup>-8e<sup>-6</sup></td><td>2-22</td><td></td><td></td></tr><tr><td>Rafkin et al. (2022)</td><td></td><td></td><td>7e<sup>-7</sup>-3e<sup>-6</sup></td><td>2,000-40,000</td></tr><tr><td>This work</td><td>3e<sup>-8</sup>-5e<sup>-7</sup></td><td>0.001-1</td><td>1.5e<sup>-6</sup>-1.5e<sup>-4</sup></td><td>10,000-400000</td></tr></tbody></table>

*Note.* The bottom line of the table displays the results from our study, using the threshold theory and the rational method. If the study does not provide instantaneous precipitation rates for the HLS or SP, the corresponding cell is grayed out in the table.

et al., 2006; Perron et al., 2006), as they are more buoyant, leading to lower discharge for an equivalent sediment flux (Amy & Dorrell, 2021; Burr et al., 2006). Thus, the formation of a river of similar geometry on Titan would require less liquid and therefore less precipitation than on Earth.

At the south pole (SP), we obtain much higher discharge values (10,000–400,000 m³/s), comparable to those of the largest rivers on Earth, such as the Mississippi River (~16,500 m³/s), which has a similar average width (~1 km). It is worth noting here that the SP river is much larger than the HLS river, that is, the size of a creek (1–2 orders of magnitude smaller, see Table 2), as well as its drainage area (1.2–2.6 km² for HLS and 3,000–9,000 km² for SP). Since the discharge is proportional to the drainage area and to the square of the width, this explains why the two rivers have very different discharges. Calculated instantaneous precipitation rates (5–500 mm/hr) are significantly higher at the south pole than at the equator. These estimates may be overestimated due to the potentially biased grain size estimated from remote sensing (see Section 2). However, these results are consistent with the most recent mesoscale cloud-resolving model (Rafkin et al., 2022). Titan's poles show greater cloud activity (Rodriguez et al., 2009, 2011; Turtle et al., 2018) than the equator, indicating a wetter atmosphere, and increased and more frequent precipitation (Turtle et al., 2009). The presence of seas and lakes at the north pole, most of them filled with liquid hydrocarbons, confirms this observation (Mastrogiuseppe et al., 2019).

The instantaneous precipitation rates predicted by global and mesoscale climate models (Barth & Rafkin, 2010; Hueso & Sánchez-Lavega, 2006; Rafkin et al., 2022) were converted to discharge using Equation 8 and the estimated drainage areas (1.2–2.6 km² for HLS and 3,000–9,000 km² for SP). The range of discharge estimates derived from these climate models is plotted in Figure 3 and compared to our estimates in Table 2.

Climate model predictions of current Titan precipitation rates (Mitchell, 2008; Rafkin et al., 2022; Schneider et al., 2012) are consistent with discharge estimates derived from the threshold theory and the rational method. This suggests that this workflow could be used in future studies to infer precipitation rates, provided certain parameters (grain size and river slope or width) are better constrained.

## 5. Conclusion

Despite uncertainties due to the lack of direct field measurements, we have shown for the first time that threshold theory can be successfully applied to an extraterrestrial body. By combining observations with a conservative approach, we have estimated river discharges on Titan at both low and high latitudes. This study underscores the critical need for high-resolution Digital Terrain Models (DTMs) to accurately measure river slopes and high-resolution imagery to determine channel widths. Currently, most of Titan's DTMs lack the resolution required for accurate slope measurements. However, this approach can be extended to other regions where bright channels are visible in SAR images. The upcoming Dragonfly mission, scheduled to arrive on Titan in the mid-2030s, will greatly improve our understanding (Barnes et al., 2021). It will provide in-situ measurements of key sediment properties, such as grain size, density, and river width, allowing for a more detailed characterization of Titan's river dynamics and methane precipitation rates.
Acknowledgments

The authors thank Sam Birch, Edwin Baynes and François Métivier for sharing their data and Olivier Devauchelle and the reviewers for their valuable comments. Authors acknowledge financial support by LabEx UnivEarthS (ANR-10-LABX-0023 and ANR-18-IDEX-0001). They also thank the Centre National d'Etudes Spatiales for its financial support.

Data Availability Statement

HLS DTM and orthoimage from Daudon et al. (2020) are available on PSA via European Space Agency (2020). SP image is available on Zenodo via Lucas (2017).

References

Abramian, A., Devauchelle, O., & Lajeunesse, E. (2020). Laboratory Rivers adjust their shape to sediment transport. *Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, 102(5), 053101. https://doi.org/10.1103/physreve.102.053101

Aharonson, O., Hayes, A. G., Lopes, R., Lucas, A., Hayne, P., & Perron, J. T. (2014). Titan: Surface, atmosphere and magnetosphere. In *Chap. Titan's surface geology* (pp. 43–75). Cambridge University Press.

Amy, L., & Dorrell, R. (2021). Equilibrium sediment transport, grade and discharge for suspended-load-dominated flows on Earth, Mars and titan. *Icarus*, 360, 114243. https://doi.org/10.1016/j.icarus.2020.114243

Andreotti, B., Forterre, Y., & Pouliquen, O. (2013). *Granular media: Between fluid and solid*. Cambridge University Press.

Bagnold, R. A. (1980). An empirical correlation of bedload transport rates in flumes and natural rivers. *Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences*, 372(1751), 453–473.

Barnes, J. W., Buratti, B. J., Turtle, E. P., Bow, J., Dalba, P. A., Perry, J., et al. (2013). Precipitation-induced surface brightenings seen on titan by Cassini vims and ISS. *Planetary Science*, 2(1), 1. https://doi.org/10.1186/2191-2521-2-1

Barnes, J. W., Turtle, E. P., Trainer, M. G., Lorenz, R. D., MacKenzie, S. M., Brinckerhoff, W. B., et al. (2021). Science goals and objectives for the dragonfly titan rotorcraft relocatable lander. *The Planetary Science Journal*, 2(4), 130. https://doi.org/10.3847/psj/abfdcf

Barth, E. L., & Rafkin, S. C. (2010). Convective cloud heights as a diagnostic for methane environment on Titan. *Icarus*, 206(2), 467–484. https://doi.org/10.1016/j.icarus.2009.01.032

Baynes, E. R. C., Lague, D., Steer, P., Bonnet, S., & Illien, L. (2020). Sediment flux-driven channel geometry adjustment of bedrock and mixed gravel-bedrock rivers. *Earth Surface Processes and Landforms*, 45(14), 3714–3731. https://doi.org/10.1002/esp.4996

Birch, S., Parker, G., Corlies, P., Soderblom, J. M., Miller, J. W., Palermo, R. V., et al. (2023). Reconstructing river flows remotely on Earth, Titan, and Mars. *Proceedings of the National Academy of Sciences of the United States of America*, 120(29), 2206837120. https://doi.org/10.1073/pnas.2206837120

Brossier, J. F., Rodriguez, S., Cornet, T., Lucas, A., Radebaugh, J., Malttagliati, L., et al. (2018). Geological evolution of Titan's equatorial regions: Possible nature and origin of the dune material. *Journal of Geophysical Research: Planets*, 123(5), 1089–1112. https://doi.org/10.1029/2017je005399

Buffington, J. M., & Montgomery, D. R. (1997). A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers. *Water Resources Research*, 33(8), 1993–2029. https://doi.org/10.1029/96wr03190

Burr, D. M., Emery, J. P., Lorenz, R. D., Collins, G. C., & Carling, P. A. (2006). Sediment transport by liquid surficial flow: Application to Titan. *Icarus*, 181(1), 235–242. https://doi.org/10.1016/j.icarus.2005.11.012

Carlston, C. W. (1965). The relation of free meander geometry to stream discharge and its geomorphic implications. *American Journal of Science*, 263(10), 864–885. https://doi.org/10.2475/ajs.263.10.864

Chin, D. A. (2019). Estimating peak runoff rates using the rational method. *Journal of Irrigation and Drainage Engineering*, 145(6), 04019006. https://doi.org/10.1061/(asce)ir.1943-4774.0001387

Daudon, C., Lucas, A., Rodriguez, S., Jacquemoud, S., Escalante López, A., Grieger, B., et al. (2020). A new digital terrain model of the Huygens landing site on Saturn's largest Moon, Titan. *Earth and Space Science*, 7(12), e2020EA001127. https://doi.org/10.1029/2020ea001127

Devauchelle, O., Petroff, A. P., Lobkovsky, A. E., & Rothman, D. H. (2010). Longitudinal profile of channels cut by springs. *Journal of Fluid Mechanics*, 667, 38–47. https://doi.org/10.1017/s0022112010005264

Dhingra, R. D., Barnes, J. W., Heslar, M. F., Brown, R. H., Buratti, B. J., Sotin, C., et al. (2020). Spatio-temporal variation of bright ephemeral features on Titan's North Pole. *The Planetary Science Journal*, 1(2), 31. https://doi.org/10.3847/psj/ab9c2b

Dunne, K. B. J., & Jerolmack, D. J. (2020). What sets river width? *Science Advances*, 6(41). https://doi.org/10.1126/sciadv.abc1505

European Space Agency. (2020). IPGP DTM Huygens. PSA. https://doi.org/10.5270/esa-3uja374

Faulk, S. P., Lora, J. M., Mitchell, J. L., & Milly, P. C. D. (2020). Titan's climate patterns and surface methane distribution due to the coupling of land hydrology and atmosphere. *Nature Astronomy*, 4, 390–398. https://doi.org/10.1038/s41550-019-0963-0

Glover, R. E., & Florey, Q. L. (1951). *Stable channel profiles* (*Tech. Rep.). Bureau of Reclamation.

Hueso, R., & Sánchez-Lavega, A. (2006). Methane storms on Saturn's moon titan. *Nature*, 442(7101), 428–431. https://doi.org/10.1038/nature04933

Irwin, R. P. R., Craddock, R. A., & Howard, A. D. (2005). Interior channels in Martian valley networks: Discharge and runoff production. *Geology*, 33(6), 489–492. https://doi.org/10.1130/g21333.1

Jaumann, R., Brown, R. H., Stephan, K., Barnes, J. W., Soderblom, L. A., Sotin, C., et al. (2008). Fluvial erosion and post-erosional processes on Titan. *Icarus*, 197(2), 526–538. https://doi.org/10.1016/j.icarus.2008.06.002

Keller, H., Grieger, B., Küppers, M., Schröder, S., Skorov, Y., & Tomasko, M. (2008). The properties of titan's surface at the Huygens landing site from DISR observations. *Planetary and Space Science*, 56(5), 728–752. (Titan as seen from Huygens - Part 2). https://doi.org/10.1016/j.pss.2007.11.020

Komar, P. D. (1979). Comparisons of the hydraulics of water flows in Martian outflow channels with flows of similar scale on Earth. *Icarus*, 37(1), 156–181. https://doi.org/10.1016/0019-1035(79)90123-4

Kuichling, E. (2019). *The relation between the rainfall and the discharge of sewers in populous districts* (pp. 1–56). Transactions of the American Society of Civil Engineers.

Lacey, G. (1930). Stable channels in alluvium. In *Minutes of the proceedings of the institution of civil engineers* (Vol. 229, pp. 259–292).

Le Gall, A., Janssen, M., Paillou, P., Lorenz, R., Wall, S., & the Cassini Radar Team. (2010). Radar-bright channels on titan. *Icarus*, 207(2), 948–958. https://doi.org/10.1016/j.icarus.2009.12.027

Le Mouélic, S., Rodriguez, S., Robidel, R., Rousseau, B., Seignovert, B., Sotin, C., et al. (2018). Mapping polar atmospheric features on titan with vims: From the dissipation of the northern cloud to the onset of a southern polar vortex. *Icarus*, 311, 371–383. https://doi.org/10.1016/j.icarus.2018.04.028

Loiseleux, T., Gondret, P., Rabaud, M., & Doppler, D. (2005). Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow. *Physics of Fluids*, 17(10), 103304. https://doi.org/10.1063/1.2109747
Lora, J. M., Lunine, J. I., & Russell, J. L. (2015). GCM simulations of titan's middle and lower atmosphere and comparison to observations. *Icarus*, 250, 516-528. https://doi.org/10.1016/j.icarus.2014.12.030

Lorenz, R. D., Wall, S., Radebaugh, J., Boubin, G., Reffet, E., Janssen, M., et al. (2006). The sand seas of Titan: Cassini radar observations of longitudinal dunes. *Science*, 312(5774), 724-727. https://doi.org/10.1126/science.1123257

Lorenz, R. D., Wood, C. A., Lunine, J. I., Wall, S. D., Lopes, R. M., Mitchell, K. L., et al. (2007). Titan's young surface: Initial impact crater survey by Cassini radar and model comparison. *Geophysical Research Letters*, 34(7), L07204. https://doi.org/10.1029/2006gl028971

Lucas, A. (2017). NLDSAR - Cassini non-local denoised SAR dataset. *Journal of Geophysical Research*. https://doi.org/10.5281/zenodo.528545

Lucas, A., Aharonson, O., Deledalle, C., Hayes, A. G., Kirk, R., & Howington-Kraus, E. (2014). Insights into titan's geology and hydrology based on enhanced image processing of Cassini radar data. *Journal of Geophysical Research: Planets*, 119(10), 2149-2166. https://doi.org/10.1002/2013je004584

Lucas, A., Rodriguez, S., Narteau, C., Charnay, B., Courrech Du Pont, S., Tokano, T., et al. (2014). Growth mechanisms and dune orientation on Titan. *Geophysical Research Letters*, 41(17), 6093-6100. https://doi.org/10.1002/2014gl060971

Malaska, M., Radebaugh, J., Le Gall, A., Mitchell, K., Lopes, R., & Wall, S. (2011). High-volume meandering channels in titan's south polar region. *LPI(1608)*.1562.

Mastrogiuseppe, M., Poggiali, V., Hayes, A., Lunine, J., Seu, R., Mitri, G., & Lorenz, R. (2019). Deep and methane-rich lakes on titan. *Nature Astronomy*, 3(6), 535-542. https://doi.org/10.1038/s41550-019-0714-2

Métivier, F., Lajeunesse, E., & Devauchelle, O. (2017). Laboratory rivers: Lacey's law, threshold theory, and channel stability. *Earth Surface Dynamics*, 5(1), 187-198. https://doi.org/10.5194/esurf-5-187-2017

Mitchell, J. L. (2008). The drying of titan's dunes: Titan's methane hydrology and its impact on atmospheric circulation. *Journal of Geophysical Research*, 113(E8), E08015. https://doi.org/10.1029/2007je003017

Mitchell, J. L., Ádámkovics, M., Caballero, R., & Turtle, E. P. (2011). Locally enhanced precipitation organized by planetary-scale waves on titan. *Nature Geoscience*, 4(9), 589-592. https://doi.org/10.1038/ngeo1219

Mitchell, J. L., & Lora, J. M. (2016). The climate of titan. *Annual Review of Earth and Planetary Sciences*, 44(1), 353-380. https://doi.org/10.1146/annurev-earth-060115-012428

Müller-Wodarg, I., Griffith, C. A., Lellouch, E., & Cravens, T. E. (2014). *Titan: Interior, surface, atmosphere, and space environment, chap 6* (Vol. 14). Cambridge University Press.

Niemann, H. B., Atreya, S. K., Bauer, S. J., Carignan, G. R., Demick, J. E., Frost, R. L., et al. (2005). The abundances of constituents of Titan's atmosphere from the GCMS instrument on the Huygens probe. *Nature*, 438(7069), 1476-1487. https://doi.org/10.1038/nature04122

Parker, G. (1978). Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river. *Journal of Fluid Mechanics*, 89(1), 127-146. https://doi.org/10.1017/s0022112078002505

Parker, G. (2008). Transport of gravel and sediment mixtures. In *Sedimentation engineering* (pp. 165-251). American Society of Civil Engineers.

Parker, G., Wilcock, P. R., Paola, C., Dietrich, W. E., & Pitlick, J. (2007). Physical basis for quasi-universal relations describing bankfull hydraulic geometry of single-thread gravel Bed Rivers. *Journal of Geophysical Research*, 112(F4), F04005. https://doi.org/10.1029/2006jf000549

Perron, J. T., Lamb, M. P., Koven, C. D., Fung, I. Y., Yager, E., & Ádámkovics, M. (2006). Valley formation and methane precipitation rates on Titan. *Journal of Geophysical Research*, 111(E11), E11001. https://doi.org/10.1029/2005je002602

Phillips, C. B., & Jerolmack, D. J. (2016). Self-organization of river channels as a critical filter on climate signals. *Science*, 352(6286), 694-697. https://doi.org/10.1126/science.aad3348

Phillips, C. B., Masteller, C. C., Slater, L. J., Dunne, K. B. J., Francalanci, S., Lanzoni, S., et al. (2022). Threshold constraints on the size, shape and stability of alluvial rivers. *Nature Reviews Earth and Environment*, 3(6), 406-419. https://doi.org/10.1038/s43017-022-00282-z

Poggiali, V., Mastrogiuseppe, M., Hayes, A., Seu, R., Birch, S., Lorenz, R., et al. (2016). Liquid-filled canyons on titan. *Geophysical Research Letters*, 43(15), 7887-7894. https://doi.org/10.1002/2016gl069679

Popović, P., Devauchelle, O., Abramian, A., & Lajeunesse, E. (2021). Sediment load determines the shape of rivers. *Proceedings of the National Academy of Sciences of the United States of America*, 118(49), https://doi.org/10.1073/pnas.2211215118

Rafkin, S. C., Lora, J. M., Soto, A., & Battalio, J. M. (2022). The interaction of deep convection with the general circulation in titan's atmosphere. Part 1: Cloud resolving simulations. *Icarus*, 373, 114755. https://doi.org/10.1016/j.icarus.2021.114755

Rannou, P., Montmessin, F., Hourdin, F., & Lebonnois, S. (2006). The latitudinal distribution of clouds on titan. *Science*, 311(5758), 201-205. https://doi.org/10.1126/science.1118424

Rodriguez, S., Le Mouélic, S., Rannou, P., Sotin, C., Brown, R., Barnes, J., et al. (2011). Titan's cloud seasonal activity from winter to spring with Cassini/VIMS. *Icarus*, 216(1), 89-110. https://doi.org/10.1016/j.icarus.2011.07.031

Rodriguez, S., Le Mouélic, S., Rannou, P., Tobie, G., Baines, K. H., Barnes, J. W., et al. (2009). Global circulation as the main source of cloud activity on titan. *Nature*, 459(7247), 678-682. https://doi.org/10.1038/nature08014

Sambrook Smith, G. H., & Ferguson, R. I. (1995). The gravel-sand transition along river channels. *Journal of Sedimentary Research*, 65(2a), 423-430.

Schneider, T., Graves, S., Schaller, E., & Brown, M. (2012). Polar methane accumulation and rainstorms on titan from simulations of the methane cycle. *Nature*, 481(7379), 58-61. https://doi.org/10.1038/nature10666

Seizilles, G., Devauchelle, O., Lajeunesse, E., & Métivier, F. (2013). Width of laminar laboratory rivers. *Physical Review E*, 87(5), 052204. https://doi.org/10.1103/physreve.87.052204

Soderblom, L. A., Kirk, R. L., Lunine, J. I., Anderson, J. A., Baines, K. H., Barnes, J., et al. (2007). Correlations between Cassini VIMS spectra and RADAR SAR images: Implications for Titan's surface composition and the character of the Huygens probe landing site. *Planetary and Space Science*, 55(13), 2025-2036. https://doi.org/10.1016/j.pss.2007.04.014

Steckloff, J., Soderblom, J., Farnsworth, K., Chevrier, V., Hanley, J., Soto, A., et al. (2020). Stratification dynamics of titan's lakes via methane evaporation. *The Planetary Science Journal*, 1, 2. https://doi.org/10.3847/psj/ab974e

Tokano, T. (2019). Orbitally and geographically caused seasonal asymmetry in titan's tropospheric climate and its implication for the lake distribution. *Icarus*, 317, 337-353. https://doi.org/10.1016/j.icarus.2018.07.025

Tomasko, M. G., Archinal, B., Becker, T., Bézard, B., Bushroe, M., Combes, M., et al. (2005). Rain, winds and haze during the Huygens probe's descent to Titan's surface. *Nature*, 438(7069), 765-778. https://doi.org/10.1038/nature04126

Turtle, E., Del Genio, A., Barbara, J., Perry, J., Schaller, E., McEwen, A. S., et al. (2011). Seasonal changes in titan's meteorology. *Geophysical Research Letters*, 38(3), L03203. https://doi.org/10.1029/2010gl046266

Turtle, E., Perry, J., Barbara, J., Del Genio, A., Rodriguez, S., Le Mouélic, S., et al. (2018). Titan's meteorology over the Cassini mission: Evidence for extensive subsurface methane reservoirs. *Geophysical Research Letters*, 45(11), 5320-5328. https://doi.org/10.1029/2018gl078170
Turtle, E., Perry, J., Hayes, A., Lorenz, R., Barnes, J., McEwen, A., et al. (2011). Rapid and extensive surface changes near Titan's equator: Evidence of April showers. *Science*, **331**(6023), 1414–1417. https://doi.org/10.1126/science.1201063

Turtle, E., Perry, J., McEwen, A. S., DelGenio, A., Barbara, J., West, R., et al. (2009). Cassini imaging of titan's high-latitude lakes, clouds, and south-polar surface changes. *Geophysical Research Letters*, **36**(2), L02204. https://doi.org/10.1029/2008gl036186

Wilkerson, G. V., & Parker, G. (2011). Physical basis for quasi-universal relationships describing bankfull hydraulic geometry of sand-bed rivers. *Journal of Hydraulic Engineering*, **137**(7), 739–753. https://doi.org/10.1061/(asce)hy.1943-7900.0000352

Wilson, L., Ghatan, G. J., Head, I. J. W., & Mitchell, K. L. (2004). Mars outflow channels: A reappraisal of the estimation of water flow velocities from water depths, regional slopes, and channel floor properties. *Journal of Geophysical Research*, **109**(E9), E09003. https://doi.org/10.1029/2004je002281