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

Extensive USGS data tables and detailed, 1 m2 Li DAR surveys are used to determine the optimal power n that relates discharge(Q) to stage(h*) above channel bottom(ho) 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 ho:(1) optimizing linearity in a plot of Q1/n vs. local stage(hL) using USGS field measurements at each site;(2) optimizing linearity in a plot of Q1/n vs. hL using USGS rating tables at each site;(3) a mathematical inverse method applied to the same USGS rating tables;(4) use of Li DAR 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.