Diffusive wave models for operational forecasting of channel routing at continental scale

Abstract

AbstractOperational forecast models require robust, computationally efficient, and reliable algorithms. We desire accurate forecasts within the limits of the uncertainties in channel geometry and roughness because the output from these algorithms leads to flood warnings and a variety of water management decisions. The current operational Water Model uses the Muskingum‐Cunge method, which does not account for key hydraulic conditions such as flow hysteresis and backwater effects, limiting its ability in situations with pronounced backwater effects. This situation most commonly occurs in low‐gradient rivers, near confluences and channel constrictions, coastal regions where the combined actions of tides, storm surges, and wind can cause adverse flow. These situations necessitate a more rigorous flow routing approach such as dynamic or diffusive wave approximation to simulate flow hydraulics accurately. Avoiding the dynamic wave routing due to its extreme computational cost, this work presents two diffusive wave approaches to simulate flow routing in a complex river network. This study reports a comparison of two different diffusive wave models that both use a finite difference solution solved using an implicit Crank–Nicolson (CN) scheme with second‐order accuracy in both time and space. The first model applies the CN scheme over three spatial nodes and is referred to as Crank–Nicolson over Space (CNS). The second model uses the CN scheme over three temporal nodes and is referred to as Crank–Nicolson over Time (CNT). Both models can properly account for complex cross‐section geometry and variable computational points spacing along the channel length. The models were tested in different watersheds representing a mixture of steep and flat topographies. Comparing model outputs against observations of discharges and water levels indicated that the models accurately predict the peak discharge, peak water level, and flooding duration. Both models are accurate and computationally stable over a broad range of hydraulic regimes. The CNS model is dependent on the Courant criteria, making it less computational efficient where short channel segments are present. The CNT model does not suffer from that constraint and is, thus, highly computationally efficient and could be more useful for operational forecast models.