A Quantitative Model of the Dispersal of Detrital Inputs and Minor Compositional Components in Lake Michigan Sediments

Abstract

This study involves the development and application of mathematical models which are used to ascertain the sources, distribution, and fate of sedimentary material entering Lake Michigan. Major compositional end-members are identified by a modified Q-mode factor analysis procedure, and estimates of the relative amount of each end-member in each sample are obtained by linear programming. Four factors account for 93.8% of the total variance. These are interpreted as representing the inputs of fine-grained (Factor 1), and coarse-grained (Factor 2) detrital minerals, manganous carbonate (Factor 3) and non-manganous carbonate (Factor 4) to the lake sediment. Significant linear correlations between the relative amount of each compositional end-member and the grain-size distribution for each sample support these interpretations. Contour plots of end-member distributions suggest that the sediment chemistry of Lake Michigan is primarily influenced by regional-scale physical processes. In a revised version of the model, the distribution of minor sediment components (ferromanganese oxyhydroxides and siliceous plankton tests) are examined. Each model accounts for approximately 90% of the measured elemental concentrations in lake sediment. We conclude that this modeling approach is a viable method for determining the distribution of sedimentary inputs in large lacustrine basins, and may also be useful in monitoring the dispersal pathways of coastal erosion products or chemical pollutants.