Dynamic rating method for computing discharge and stage from time-series data

Ratings are used for several reasons in water-resources investigations. The simplest rating relates discharge to the stage of a river (the stage-discharge relation). From a pure hydrodynamics perspective, all rivers and streams have some form of hysteresis in the relation between stage and discharge because flow becomes unsteady as a flood wave passes. The stage-discharge relation is unable to represent hysteresis. However, a dynamic rating method can capture hysteresis, which is driven by the variable energy slope of a flood wave.

A dynamic rating method called DYNPOUND, which accommodates compact and compound channel geometry, was developed by simplifying the one-dimensional Saint-Venant equations. The DYNPOUND method was developed in the Python programming language and computes discharge from stage and stage from discharge. Stage and discharge time series computed with this dynamic rating method were compared to the U.S. Geological Survey (USGS) published stage and discharge time series. The results from the DYNPOUND method were also compared to in-person field measurements of stage and discharge made at 10 USGS streamgages.

DYNPOUND was calibrated for 10 USGS streamgages using published discharge time-series data computed with a simple rating method. The calibration objective was to minimize the mean squared logarithmic error (MSLE) of the DYNPOUND-computed discharge with respect to the discharge time series computed by a simple rating method. For each site, the calibration process also included comparing all field measurements within a selected water year to the corresponding DYNPOUND-computed discharge data points. The MSLE of the DYNPOUND-computed discharge time series for the 10 sites ranged from 8.51×10⁻⁴ to 1.36×10⁻¹. For each site, an event-based period was selected to compare the discharge time series computed with the dynamic rating method to discharge field measurements made at the streamgages; the range of MSLE for the 10 DYNPOUND-computed discharge sites was from 4.79×10⁻⁴ to 2.30×10⁻².