Discharge-Stage Relationship on Urban Streams Evaluated at USGS Gauging Stations, St. Louis, Missouri

Extensive USGS data tables and detailed, 1 m² LiDAR surveys are used to determine the optimal power n that relates discharge (Q) to stage (h*) above channel bottom (h_o) at 39 gauging stations on small streams in the St. Louis, Missouri area, all of which have catchments of 0.6 to 220 km². Four different methodologies are employed to determine both n and h_o:(1) optimizing linearity in a plot of Q^1/n vs. local stage (h_L) using USGS field measurements at each site; (2) optimizing linearity in a plot of Q^1/n vs. h_L using USGS rating tables at each site; (3) a mathematical inverse method applied to the same USGS rating tables; (4) use of LiDAR data on channel geometry to determine the power dependences of channel area A and hydraulic radius H on h*, combined with the Manning and rational equations to predict n. Of these methods, only methods 2 and 3 compare favorably, and these values compare poorly with Method 1 based on field data, and with method 4 based on theoretical and empirical relationships. Because Method 4 is predictive, it provides a useful alternative to methods 1-3 that are based on USGS field measurements, which are heavily weighted toward low discharges. We conclude that the apparent values of n in the USGS rating tables are systematically too low for small streams.