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.

A new sweep-search algorithm (SSA) is developed and tested to identify the channel geometry transitions responsible for numerical convergence failure in a Saint-Venant equation (SVE) simulation of a large-scale open-channel network. Numerical instabilities are known to occur at “sharp” transitions in discrete geometry, but the identification of problem locations has been a matter of modeler’s art and a roadblock to implementing large-scale SVE simulations. The new method implements techniques from graph theory applied to a steady-state 1D shallow-water equation solver to recursively examine the numerical stability of each flowpath through the channel network. The SSA is validated with a short river reach and tested by the simulation of ten complete river systems of the Texas–Gulf Coast region by using the extreme hydrological conditions recorded during hurricane Harvey. The SSA successfully identified the problematic channel sections in all tested river systems. Subsequent modification of the problem sections allowed stable solution by an unsteady SVE numerical solver. The new SSA approach permits automated and consistent identification of problem channel geometry in large open-channel network data sets, which is necessary to effectively apply the fully dynamic Saint-Venant equations to large-scale river networks or for city-wide stormwater networks.

The conventional approach to generating synthetic rating curves (SRC) using the Height‐Above‐the‐Nearest‐Drainage (HAND) method typically relies on the assumption of uniform flow, such as Manning's equation, to establish stage‐discharge ratings. The zero‐physics application of the uniform flow equation is insufficient for capturing detailed hydraulic features (e.g., backwater effect) and neglects the hydraulic effects from adjacent channels. This lack of hydrodynamic computation can impact the accuracy and effectiveness of riverine flood risk estimation and management. To reduce this foreseeable error, we introduce the HAND‐hd workflow, which integrates sophisticated hydrodynamic computations in the production of HAND‐based SRC with hydrodynamic features (SRC_hd). The results indicate that SRC_hd demonstrates consistent agreement with both gauge observations and benchmark solutions. Additionally, the comparative analysis suggests that SRC_hd provides notable improvements in stage‐discharge ratings over conventional HAND‐based SRCs, particularly in channels with mild bed gradients, where it reduces water stage prediction errors and percent biases. In steeper channel segments, SRC_hd maintains comparable accuracy to conventional methods. The comprehensive evaluation in this study emphasizes the potential discrepancies and inaccuracies associated with the adoption of the uniform flow assumption in the conventional HAND‐SRCs and addresses the necessity of including hydrodynamic physics in the application of HAND‐based SRC (e.g., inundation map) in channels with mild gradients.

This study introduces a novel workflow, HAND-RAS, designed for the generation of synthetic rating curves (SRCs) utilizing the Height-Above-the-Nearest-Drainage (HAND) method. The HAND-RAS workflow proposed in this study advances tra- ditional methods for generating SRCs by incorporating the application of the sophisticated hydrodynamic computation from the HEC-RAS model to capture detailed hydraulic fea- tures, thereby enhancing the accuracy of the stage-discharge relationship. The performance of the HAND-RAS workflow is tested in a regional-scale river basin located in central Tai- wan. The analysis results indicate that the generated HAND- based SRCs exhibit strong agreement with gauge observa- tions, with r 2 > 0 . 8 5 and RMSE<0.509m . The performance of HAND-RAS is also validated with the physically simulated H-Q ratings from field topographic surveys. The comparison between HAND-SRCs generated using both conventional meth- ods (Manning’s equation) and the proposed HAND-RAS work- flow is also conducted in this study. The comparison results show that HAND-RAS can produce comparable results in steep channels dominated by gravitational force and demonstrates better capability in capturing hydraulic behaviors in chan- nels characterized by milder slopes, where pressure gradi- ent plays a significant role. The workflow proposed in this study offers a modified method for generating reach-scale representative synthetic rating curves with hydraulic prop- erties derived from the HAND method, thereby enhancing accuracy and avoiding erroneous calibration processes.