A Solution to Small Sample Bias in Flood Estimation

Abstract

In order to design culverts and bridges, it is necessary to compute an estimate of the design flood. Regionalization of flows by regression analysis is currently the method advocated by the U.S. Geological Survey to provide an estimate of the culvert and bridge design floods. In the regression analysis a set of simultaneous equations is solved for the regression coefficients which will be used to compute a design flood prediction for a construction site. The dependent variables in the set of simultaneous equations are the historical estimates of the design flood computed from the historical records of gaged sites in a region. If a log normal distribution of the annual peak flows is assumed, then the historical estimate of the design flood for site i may be computed by the normal as log Q(d,i) = x(i) + k(d)s(i). However because of the relatively small samples of peak flows commonly used in this problem, this paper shows that the historical estimate should be computed by to log Q(d,i) = X(i) + t(d,n-1) √((n+1)/n) s(i) where t(d,n-1) is obtained from tables of the Student's t. This t-estimate when used as input to the regression analysis provides a more realistic prediction in light of the small sample size, than the estimate yielded by the normal.