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/nvs. local stage (h_L) using USGS field measurements at each site; (2) optimizing linearity in a plot of Q^1/nvs. h_Lusing 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.

广泛的USGS数据表和详细的1 m ² LiDAR调查用于确定最佳功率n，该最佳功率n将流量（Q）与通道底部（h _o）的级（h *）关联到St.的39个小站上的通道底部（h _o）。密苏里州路易斯地区，所有这些地区的流域面积均为0.6至220 km ²。四种不同的方法用于确定n和h _o：（1 ）使用每个站点的USGS现场测量，在Q ^{1 / n}与局部阶段（h _L）的关系图中优化线性度；（2）在使用每个站点的USGS评级表，Q ^{1 / n}与h _L的关系；（3）应用于相同USGS评级表的数学逆方法；（4）利用LiDAR数据对通道几何形状的确定来确定通道面积A和水力半径H对h *的功率依赖性，并结合曼宁方程和有理方程来预测n。在这些方法中，只有方法2和3比较好，并且这些值与基于字段数据的方法1和基于理论和经验关系的方法4的比较差。由于方法4是预测性的，因此它可以替代基于USGS现场测量的方法1-3（有用的替代方法），该方法的重点是低排放量。我们得出的结论是，对于小流，USGS评级表中的n的表观值系统地太小。