Applying microprocessor analysis methods to river network modelling

This paper describes the Simulation Program for River Networks (SPRINT) that is proposed as a tool for studying Continental River Dynamics (CRD), the solution of physics-based equations for large-scale river networks. Existing coupled hydrologic/hydraulic models have been unable to solve the full Saint-Venant equations for river networks larger than O(10) elements, but continental scales require 10 to 10 elements. The new model solves the full nonlinear Saint-Venant equations for one-dimensional (1D) unsteady flow and stage height in river channel networks with non-uniform bathymetry, and is demonstrated to compute networks of O(10) elements more than 330 times faster than real time on a desktop computer. The model incorporates ideas that were originally developed to address Very Large System Integration (VLSI) problems in microprocessor design, where solving large nonlinear computational problems is a common challenge. Computational speed is increased by applying Jacobian bypass techniques in a Newton-Raphson solution and smoothing the geometric depth-area and friction-area relationships where discontinuities otherwise slow convergence. Pre-processing of junction relationships is used to remove temporal nonlinearities where river tributaries meet. Model input/output are simplified and made readily accessible to other software through use of Application Programming Interface (API) standards and a “netlist” idea that was previously used to describe electric circuit topology. The model is tested on both simple and complex geometry through comparisons with the HEC-RAS model. A example simulation is conducted for 1.5× 10 river km of the Guadalupe and San Antonio river network during a 14 day rain event. NOTICE: This is the authors’ version of a work that has been accepted for publication in Environmental Modelling & Software. This Accepted Author Manuscript is being published online at the authors’ website in accordance with the journal’s policies at http://www.elsevier.com/about/ open-access/open-access-policies/article-posting-policy#accepted-author-manuscript. Note that changes resulting from the publishing process, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. ∗Corresponding author. Email addresses: [email protected] (Frank Liu), [email protected] (Ben R. Hodges) Preprint submitted to Environmental Modelling & Software (accepted, Sept. 19, 2013)September 20, 2013