Dynamic rating method for computing discharge from time series stage data—Site datasets

Ratings are used for a variety of reasons in water-resources investigations. The simplest rating relates discharge to the stage of the river. From a pure hydrodynamics perspective, all rivers and streams have some form of hysteresis in the relation between stage and discharge because of unsteady flow as a flood wave passes. Simple ratings are unable to represent hysteresis in a stage/discharge relation. A dynamic rating method is capable of capturing hysteresis owing to the variable energy slope caused by unsteady momentum and pressure. Using some simplifying assumptions, Fread (1973) developed what was termed a “dynamic loop” rating method to compute discharge from a time series of stage at a single streamgage for channels with compact geometry (no flood plain). Dynamic loop has specific meaning as it refers to a rating method that accounts for the variable energy slope “associated with the dynamic inertia and pressure forces of the unsteady flood discharge “ (Fread, 1975) as opposed to rating loops imposed by alluvial bedform dynamics or scour and fill processes. A dynamic rating method developed to compute discharge from stage for compact channel geometry, referred to as DYNMOD, was previously developed through a simplification of the one-dimensional Saint-Venant equations. A dynamic rating method, which accommodates compound and compact channel geometry, referred to as DYNPOUND, has been developed through a similar simplification as a part of this study. The DYNMOD and DYNPOUND methods were implemented in the Python programming language. Discharge time series computed with the dynamic rating method implementations were then compared to simulated discharge time series and discrete discharge measurements made at U.S. Geological Survey streamgage sites. References: Fread, D.L., 1973, A dynamic model of stage-discharge relations affected by changing discharge, National Oceanic and Atmospheric Administration NWS Hydro-16, November 1973, Silver Spring, MD, 38 p.
Fread, D.L., 1975, Computation of stage-discharge relationships affected by unsteady flow, Water Resources Bulletin, American Water Resources Association, pp 213-228.