Consistent initial conditions for the Saint-Venant equations in river network modeling

Abstract

Abstract. Initial conditions for flows and depths (crosssectional areas) throughout a river network are required for any time-marching (unsteady) solution of the onedimensional (1-D) hydrodynamic Saint-Venant equations. For a river network modeled with several Strahler orders of tributaries, comprehensive and consistent synoptic data are typically lacking and synthetic starting conditions are needed. Because of underlying nonlinearity, poorly defined or inconsistent initial conditions can lead to convergence problems and long spin-up times in an unsteady solver. Two new approaches are defined and demonstrated herein for computing flows and cross-sectional areas (or depths). These methods can produce an initial condition data set that is consistent with modeled landscape runoff and river geometry boundary conditions at the initial time. These new methods are (1) the pseudo time-marching method (PTM) that iterates toward a steady-state initial condition using an unsteady Saint-Venant solver and (2) the steady-solution method (SSM) that makes use of graph theory for initial flow rates and solution of a steady-state 1-D momentum equation for the channel cross-sectional areas. The PTM is shown to be adequate for short river reaches but is significantly slower and has occasional non-convergent behavior for large river networks. The SSM approach is shown to provide a rapid solution of consistent initial conditions for both small and large networks, albeit with the requirement that additional code must be written rather than applying an existing unsteady Saint-Venant solver.

The Next Frontier: Making Research More Reproducible

“…Adopt the practices of six articles that Stagge et al (2019) awarded badges to for full and partial reproducible results. For example, these papers • Provided all model and code in a Github (Buscombe 2017;Neuwirth 2017;Xu et al 2017), institutional (Yu et al 2017), or HydroShare (Horsburgh et al 2017) repository. • Had an easy-to-find README file that explained the contents and gave directions to setup and run code (Buscombe 2017;Horsburgh et al 2017;Neuwirth 2017;Xu et al 2017).…”

Using Steady‐State Backwater Analysis to Predict Inundated Area from National Water Model Streamflow Simulations

“…Steady‐state SPRNT solves the steady‐state continuity and momentum equations for flow and is therefore expected to simulate backwater effects more accurately than NWM. Herein, we follow Yu et al () in using the steady‐state version of the SVE as the governing equation of the steady‐state SPRNT model:where A is cross‐sectional area, Q is flow rate, S 0 is the local channel bottom, q 1 is local lateral net inflow, and S f is friction slope.…”

“…Steady-state SPRNT solves the steady-state continuity and momentum equations for flow and is therefore expected to simulate backwater effects more accurately than NWM. Herein, we follow Yu et al (2017) in using the steady-state version of the SVE as the governing equation of the steady-state SPRNT model:…”

A new form of the Saint–Venant equations for variable topography

“…SPRNT is an open-source, 1-D hydrodynamic solver using the fully-implicit Preissmann numerical scheme (Preissmann, 1961) with Newton-Raphson iteration and computational acceleration techniques developed from Very Large Scale Integration (VLSI) semiconductor design. Details on the baseline SPRNT model and its application to large river networks are provided 165 in Liu and Hodges (2014) and Yu et al (2017).…”