GROUND TRUTH IN PROVENANCE ANALYSIS: A NEW STATISTICAL APPROACH FOR DETRITAL ZIRCON ANALYSIS

Analysis of modern river systems is central to understanding active surface processes and provides ground truth for evaluating our ability to reconstruct past depositional systems. The Kolmogorov-Smirnov (K-S) statistic is widely used to test the null hypothesis (i.e., are two distributions drawn from the same population?). In detrital zircon provenance analysis of river systems, it is useful to have an equivalent statistical measure for comparisons involving composite samples that collectively represent the contributions of tributaries to regionally extensive river systems. We present a generalized K-S statistic that depends on the proportional contribution and sample size of individual distributions as well as the correlation between the respective individual populations. Our generalized K-S statistic can be calculated from either error weighted age distributions (i.e., cumulative probability density functions) or raw data series (i.e., cumulative distribution functions). Analytical expressions are provided for end member cases in which the individual populations are either completely independent or identical. Although intermediate cases must still be tested by numerical analysis, the bounding end member solutions permit conservative evaluation of the null hypothesis. This is demonstrated with an example from the modern Marsyandi River (central Nepal Himalaya) river system. Our results from the Marsyandi River also clarify the manner in which detrital zircon age distributions from tectonically active areas may be used to constrain key parameters such as erosion rates.