Numerical simulations of large-scale cataclysmic floodwater: A simple depth-averaged model and an illustrative application

A simple numerical simulation code is developed to quantitatively discuss the behaviors of past cataclysmic floods, whose rigorous hydraulic descriptions would be too complex to be supported by typically available field data. The code aims to keep the basic equations simple and the required computational costs low, which allows greater exploration of parameter space. Examination of both the qualitative meaning of turbulent equations and the relative importance of terms in the shallow water equation have resulted in the adoption of the depth-averaged diffusion wave approximation in two dimensions, as well as Manning's empirical equation for simplification. On the other hand, topography is included as a boundary condition, since topography plays an important role in selecting flood routes. The model provides important advantages over theoretical analyses or one-dimensional simulations, including: (1) the reproduction of complicated water flow paths such as bifurcations and reconvergences; (2) the reconstruction of hydrological relationships among the water paths; and (3) the direct comparison among the calculated extent of the flood inundation (including floodwater depths) and geological and geomorphological observations. Preliminary reconstructions of the Missoula floods demonstrate the advantages of this new approach. The method of coupling field-based flood information with two-dimensional analysis of an entire flow path provides a basis for estimating the peak discharges and flow durations of cataclysmic megafloods on Earth with direct bearing on the understanding of regional paleohydrological histories of Mars.