Modelling Non-Linear Spatial Dependence with Applications to MADE Hydraulic Conductivity Data

Abstract:

Advances in field data collection have been made in recent years. However, methods that are capable of describing multivariate spatial dependence based on measurements and soft information are uncommon.

This talk will demonstrate the flexibility of multidimensional models, the associated parameter estimation schemes based on field measurements, the possibilities to include secondary information (e.g., landuse) and censored measurements (“measurements below detection limit” or beyond some threshold). Even more, this talk will demonstrate the effects of non-Gaussian type of spatial dependence on solute transport.

The objective of the presented work is to use multidimensional non-linear spatial copulas to describe and model the spatial dependence of the spatial structure of K at the heterogeneous MADE site, and evaluate the effects of this multidimensional description on solute transport. This approach relies neither on assumptions of marginal ("log-normal histogram") nor on multivariate normal dependence. Uncertainty in the data due to particularly large and particularly small K values and the related pressure responses is accounted for.

At the MADE site, hydraulic conductivity (K) has been measured in exceptional detail. Two independently collected data-sets were used for this study: (1) ~2600 flowmeter based K measurements, and (2) ~31,000 direct-push based K measurements. These datasets exhibit a very heterogeneous spatially distributed K field. A copula analysis reveals that the pure spatial dependence structure without the influence of the marginal of the flowmeter and direct-push datasets are essentially the same, despite the fact that the vertical resolution of the direct-push dataset is ten times finer than that of the flowmeter dataset.