Application of the log-normal and normal distributions to stormwater quality parameters

Concentrations of water quality constituents in urban stormwater are often expressed in probabilistic terms—using statistics such as the mean and standard deviation and selected quantiles. In many studies, the log-normal distribution has been assumed to apply. In this 3-year study, the distributions of concentrations of 14 constituents in five sources of run-off were studied—parking-lot run-off discharging into an on-stream pond, baseflow and event flow in a small suburban creek feeding the same on-stream pond, and the pond outflow under both baseflow and event flow conditions. Two probability distributions, log-normal and normal, were fitted and the goodness-of-fit was assessed using probability plots and the Cramer-von Mises test. Of the two, the log-normal was the better distribution in most of the cases tested. It was more suitable for parking-lot run-off and creek baseflow, and somewhat less suitable for creek event flow and pond baseflow. With a few exceptions, the log-normal distribution did not apply for soluble constituents (total dissolved solids, chlorides, sulphate, COD) and/or event outflow from the pond. In these cases the normal distribution was preferred. The composition of outflow from the pond was controlled by intense mixing of the incoming event run-off with the water stored in the pond. The assumption of an inappropriate probability distribution can result in substantial errors when estimating the mean concentration for censored data. This in turn can affect calculation of pollutant loads and extrapolation to estimate quantiles.