A systematic over-estimation of flows

For medium-sized runoff plots to small watersheds, it is a common practice to record water levels in a flume or upstream of a weir and to convert the data on water level into flow hydrographs via a rating curve. The flow hydrograph can be integrated using the trapezoidal rule to determine the runoff amount for storm events. It can be shown that such an approach to runoff calculation involves a systematic error, always resulting in an over-estimation of the runoff amount. The relative error lies in the range from 0 to (b−1)/2, where b is the exponent of the power function describing the rating curve. A case study using the data for 34 storm events with runoff amount varying from 2.7 to 186 mm showed that the average relative error was 8.6% and the maximum relative error can be as high as 23%. Formulas with essentially no additional computational cost are recommended to calculate the runoff amount exactly.