Kinematic routing using finite elements on a triangular irregular network

Automated extraction of geometry for hydraulic routing from digital elevation models (DEM) is a procedure that must be easily accomplished for widespread application of distributed hydraulically based rainfall excess-runoff models. One-dimensional kinematic routing on a regular grid DEM is difficult due to flow division and convergence. Two-dimensional kinematic routing on a triangular irregular network (TIN) surmounts many of these difficulties. Because TIN DEMs typically require far fewer points to represent topography than regular grid DEMs, substantial computational economy is also realized. One-dimensional routing using vector contour data overcomes the grid-based routing disadvantages but often requires several orders of magnitude more storage points than a TIN. The methodology presented in this paper represents a compromise between slightly increased computational complexity and the economy of TIN topographic representation. We take the unique approach of subdividing each topographic triangle (TIN facet) into a set of coplanar triangular finite elements, performing routing on a single facet and then routing the resulting excess hydrograph to downstream facets and channels via upstream boundary conditions. Results indicate that shock conditions are readily handled, computed depths match analytic results to within +/- 3% and volume balances are typically within 1%. This modeling system illustrates the viability of kinematic routing over a TIN DEM derived directly from digital mapping data