Age and the time lag method

The time lag method is one of the most straightforward methods used to estimate transit times from experimental data and is therefore widely used. The transit time between two points is estimated from the analysis of time series taken at these two points that suggest the propagation of a signal from one point to the other. To account for the distortion of the signal during its propagation between the two points an optimum time lag can be estimated by the analysis of the cross-correlation of the two time series. This study clarifies the relation between the transit time estimated by the time lag method and the well-defined concept of the age of a water mass. It is shown, through simplified process models, that the time lag method systematically underestimates the true mean age. The error can be quantified by means of a dimensionless parameter which is the inverse of a Peclet number based on a characteristic length given by the ratio of the velocity of the flow to the frequency of the signal. (c) 2008 Elsevier Ltd. All rights reserved.