Sample Size Determination in Open-Channel Inverse Problems

Abstract

Open-channel flow simulations require values of friction parameters that are determined through formulating their inverse problems using a sample of historic events. However, there is a risk of the parameter values being biased toward the events used because of the sample size of historic events. Traditional sample-size determination approaches are known to suffer from a conflict between reliability and costs. In addition, there is no objective approach to determine a minimum size. These problems are solved through formulating the new “confidence calculation method,” which builds on the following: (1) the data points of a “parent sample” of friction parameters are resampled into “subsample populations,” where their “subsample means” contain latent information governed by the “central limit theorem”; (2) a rigorously derived formula makes it possible to calculate standard deviations of subsample populations, replacing direct resampling operations with mathematical ones; and (3) the method is parameterized for quantitatively trading off between sample sizes and reliability, minimizing the risk of the dependence of parameter values on their size. This paper illustrates the application of the method using synthetically generated samples of open-channel friction parameters.