Abstract
Abstract. Initial conditions for flows and depths (cross-sectional areas) throughout a river network are required for any time-marching (unsteady) solution of the one-dimensional (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.
Highlights
1.1 MotivationSetting initial conditions for unsteady simulations of the Saint-Venant equations (SVEs) across large river networks can be challenging
It is demonstrated that inconsistencies between initial conditions and boundary conditions for a large river network solver of the Saint-Venant equations can lead to long spin-up times or solution divergence
We note that synthetic initial conditions are preferred over observed synoptic initial conditions due to the ability of the former to provide smooth and consistent spin-up
Summary
1.1 MotivationSetting initial conditions for unsteady simulations of the Saint-Venant equations (SVEs) across large river networks can be challenging. Every element of the river network must be given initial values of flow and depth, and these values should be consistent with the inflow boundary conditions (e.g., from a land surface model) at the starting time to prevent instabilities. This issue has not been previously addressed in the literature, arguably because (i) adequate initial conditions are fairly trivial for small SVE reaches, (ii) hydrological models with large river networks often do not use the full SVE (e.g., Beighley et al, 2009) or use it over a smaller set of reaches (e.g., Paiva et al, 2012), and (iii) timemarching models only consider results after spin-up time is complete (i.e., after the effects of the initial conditions have been washed out of the system solution), which implies the initial conditions are entirely irrelevant in analyzing the model results. Note that the need for consistency in an SVE model initialization is due to the coupling of nonlinearity and the water surface slope in the momentum equation, so common reduced-physics models
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