A transfer function modelling approach to understanding the turbidity of a lake

Abstract

Transfer function modelling, which is a statistical technique used to relate a dependent or output variable to one or more independent or input variables when there may be time lags between inputs and output, is used in this study to examine the dynamic relationships between the turbidity of the surface water of Lake Eppalock with the inflows from its tributary streams and rainfall. The formulation of transfer function models is considered first, then single-input and finally double-input models are given. Single-input models are identified using the sample cross-correlation function. The problems caused by correlated input series are overcome by identifying the double-input models with a biased regression technique. Akaike's Information Criterion is used to choose between competing models. The results indicate that the turbidity of the lake is mostly explained by the inflow from the Coliban River and the rainfall in the vicinity of the dam. We conclude that the catchment of the Coliban River and the foreshore of the lake are the most important regions affecting the turbidity of its surface waters.