Unmixing of lead, 137Cs, and PAH records in lake sediments using curve fitting with first- and second-order corrections

Two methods to unmix pollutant records obtained from sediment core data are investigated. A first-order method is expanded to include polynomial curve fitting to the original data. In addition, a new second-order method is developed; this method is based on the advection—diffusion equation for a tracer with constant mixing in a layer of thickness zm and no mixing below. The original data are fitted with a polynomial. The first-order method effectively unmixes lead and 137Cs profiles in a core from northern Lake Michigan that was collected in 1984. Without unmixing, a 1969 maximum in the lead record would have been missed, and the 1963 137Cs maximum would have been underestimated, and incorrectly dated as 1956. Unmixing profiles of polycyclic aromatic hydrocarbons (PAHs) in two cores collected from central and northern Lake Michigan in 1988 produces more equivocal results, probably because of smaller zm values in these latter cores. The second-order method gives profiles of similar shapes as the first-order method, but the time scales are only identical for zm < 0.5–1.0 cm. For larger zm, the first-order method gives extrema at more recent and correct times. Equivalent mixing parameters in the two methods are obtained by maintaining the Peclet number constant for conservative tracers. Errors in the reconstructed profiles are smaller for the first than for the second-order method. Accurate error estimates may be obtained by a Monte-Carlo method that takes into account the correlation between adjacent data points.