Estimating Point Concentrations of Total Organic Carbon in Water Sediments by Geostatistical Downscaling

Attribute data such as contaminant concentrations in water sediments are typically obtained in core sections of varying lengths, and only the average concentration of each section is measured. Estimating the attribute distribution at a uniform support (i.e. spatial resolution) is often needed to characterize the site and for the design of appropriate risk-based remediation alternatives. Because attributes exhibit spatial autocorrelation, geostatistical methods have become an essential tool for estimating the spatial distribution of attributes based on limited sampling. The purpose of this work is to infer fine resolution concentrations from average concentrations using downscaling, formulated as a geostatistical inverse problem. Taking sediment total organic carbon (TOC) concentration observations as an example, we compare inverse modeling to the more traditional ordinary kriging. Traditional kriging methods are not able to estimate the point concentration using the average concentrations accurately, because these approaches are designed for data with uniform support. Geostatistical inverse modeling, on the other hand, can resolve this problem by accounting for the relationship between the known average concentrations and the unknown point concentrations to be estimated. The Restricted Maximum Likelihood (RML) approach is used to estimate the spatial covariance of the concentration distribution at finer resolutions. Results from both pseudodata and field data show that, in general, inverse modeling is better able to estimate the concentration distribution for data with variable support. Pseudodata examples confirm that the estimates of both covariance parameters and point concentrations from inverse modeling are closer to the true situation, relative to estimates obtained from ordinary kriging. Field data from a ten-kilometer stretch of the Passaic River were also used to validate the proposed approach. Consistent with our initial hypothesis, inverse modeling is better able to represent small scale variability, while honoring the average concentrations measured at larger scales.