Reliability of linear regression for estimation of mean annual low flow: a Monte Carlo approach

To estimate the mean annual low flow, or other statistics on more extreme low flows, a commonly used technique is ordinary leastsquares linear regression using small samples of concurrent flows, between a flow recorder and secondary sites with occasional gaugings. The reliability of this technique is seldom tested or even discussed. Furthermore, the inadvisability of using ordinary least-squares when both variables in the regression are subject to natural variability and measurement errors is seldom recognised. Monte Carlo simulation using daily mean flow pairs from recorder sites has been used to assess the uncertainty of such regression procedures. Trials were done with a range of sample sizes typically used in practice. The sampling scheme is described, including sample size, temporal separation, recession length and flow filtering. For each of many samples, two linear regression methods were applied: ordinary least-squares and geometric mean regression. There are sound statistical arguments for the use of geometric mean regression when there are errors in both variables. The predicted value of the mean annual low flow from both regression methods was compared with the "known" value from analysis of annual low flows. For the site pairs sampled, the standard error of prediction of the mean annual low flow is ± 40% (95% confidence).