An integrated approach to flood hazard assessment on alluvial fans using numerical modeling, field mapping,

and remote sensing

“In addition to providing better hazard information to the public, revising the floodplain maps could have a major economic impact on the rapidly growing Southwest.” – ScienceDaily, Oct. 1, 2005

2 dimensional continuity equation for unsteady flow

However, their model uses steady flow b/c, 1) direct constraints on flood duration are unavailable, 2) no specified hydrograph shape

Time dependent variable removed, continuity equation for steady flow

This simplifies the analysis b/c now 1) only peak flood stage needs to be specified, 2) each flood stage has unique inundation.

Mannings Equation

Continuity equation combined with flow equation that relates discharge to flow depth in each pixel

Assuming uniform roughness cancels n out of Eq. 3, and using square pixels cancels out delta x and delta y

Equations 2 and 3 are solved for the whole grid simultaneously using Newton’s Method

Eq. 2 rearranged to find the residual vector, which goes to zero when the exact solution is found

Eq 5 is solved implicitly using the Alternating-Direction-Implicit (ADI) technique – which converges to the exact solution (h) from any starting point.

Iteratively estimates the vectors of flow depth for the entire grid