Estimates of river paleodischarges have been used to constrain the former climate of Mars. Paleodischarge has been calculated using mechanistic approximations of the channel bed-shear stress at the threshold of particle motion or correlative width-discharge relations derived from empirical terrestrial hydraulic geometry data. We apply both these methods to a study set of gaged terrestrial rivers with field-measured bankfull properties to assess the reliability of discharge estimates given similar uncertainties as ancient martian rivers. We find that the threshold method yields conservative values, provided a reasonable grain size is used. However, we find that digital elevation models of a similar resolution to those constructed from Context Camera (CTX) data may not be of sufficient resolution to be useful for estimating paleohydrologic conditions. Results from our analysis demonstrate the inherent uncertainties when approximating paleodischarges on Mars and stress the need to consider realistic boundary conditions when determining such values. Plain Language Summary The amount of water, or discharge, that flowed through martian rivers can be used to understand the planet's former climate. Various methods have been used by researchers to estimate martian river discharge, including relating river width to discharge or calculating the water volume required to move sediment in the river, but it is uncertain which of these provide more accurate results. We applied these same methods to rivers on Earth that have field-assessed flow rates. We find that using grain size yields conservative discharge values, which is generally more desirable, but that there is significant uncertainty associated with both methods. Key Points Two methods of estimating martian paleoriver discharge are applied to terrestrial rivers with known bankfull discharges The threshold approach yields more conservative discharges when used with realistic grain sizes and high-resolution topographic data Uncertainties inherent in both methods emphasize the need to consider realistic boundary conditions when applied to Mars
