Gradients on the floors of the Martian outflow channels that are derived from radar-elevation profiles across Lunae Planum and the Chryse Basin have much lower values than those obtained from the U. S. Geological Survey's topographic map. To arrive at this conclusion, 26 radar-elevation profiles clustered at four latitudinal channel crossings were analyzed and approximate longitudinal gradients of the channel floors were constructed. Whereas the gradients of Maja and Ares Valles are similar to those of the catastrophic flood channels in the Scablands of Washington State and water or ice could have moved through them without difficulty, the gradients of Simud and Tiu Valles are essentially level, and the movement of fluids to the north poses problems. It is proposed that ponding from local runoff occurred before channel formation along the course of Simud and Tiu Valles. The ponding may have formed lakes in depressions associated with the Valles Marineris grabens, ancient craters in the chaotic terrain area, and possibly even the regional low where most chaotic terrains occur. It is envisioned that lakes eventually overflowed, drainages became integrated, and headward erosion breached interfluves, thus forming the present channel configurations. When dams broke, floods, mudflows, or mixtures of water, sediment, and ice were released catastrophically, with a final gigantic flood from the Valles Marineris system of troughs. This flood would have had sufficient head to move fluids across nearly level gradients through the Simud and Tiu channels. The ponding and flooding probably occurred during a time when the climate was different from that at present, permitting surface runoff of fluids and standing bodies of water.