Measuring wave celerity in the West Branch of the Susquehanna River using cross-correlation of stage data for adjacent stream gages

Authors: Martin Roberge*, Towson University
Topics: Water Resources and Hydrology, Geomorphology
Keywords: rivers, floods, flood routing, celerity, Python
Session Type: Guided Poster
Day: 4/5/2019
Start / End Time: 5:00 PM / 6:40 PM
Room: Roosevelt 3.5, Marriott, Exhibition Level
Presentation File: Download


Celerity expresses the speed of a wave crossing a water surface. In rivers, waves typically travel faster than the velocity of the water. In this study, I adapted cross-correlation techniques from coastal wave research and applied them to flood waves in the West Branch of the Susquehanna River using the HydroFunctions Python package. Four years of 15-minute river stage and discharge data captured flood waves as they passed a series of US Geological Survey stream gages. Shorter, eleven-day slices of this data were lagged successively; the lag with the highest correlation to the downstream record was considered a match and used to calculate wave celerity. Unfortunately, flood waves are more irregular in shape, amplitude, and period than coastal waves and require pre-processing to improve the matching efficiency. A second-order, forward-backward, one-day high-pass Butterworth filter produced better results than the use of either raw values or differenced values in the cross-correlation analysis. The use of stage data produced matches as efficiently as the use of discharge data. Ten randomly-selected waves were also tracked manually to serve as a validation data set. Results indicate the expected positive, linear relationship between stage and celerity when considering a single reach, but surprisingly, an inverse relationship appears when multiple reaches are considered together longitudinally. Celerity and discharge typically increase in downstream reaches, while stage decreases. The ability to quickly produce empirical measurements of wave celerity allows the calibration of flood routing models and aid in model selection.

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