Using Methods of Dimension Reduction to Expand Data Integration and Reduce Uncertainty in Hydrological and Geophysical Parameters

Abstract:

The Method of Anchored Distributions (MAD), first demonstrated by Rubin et al. in 2010, has been particularly useful in hydrological and geophysical applications. MAD provides a new framework for successfully using diverse data for the characterization of heterogeneous subsurface quantities (eg. hydraulic conductivity). Through Bayesian inverse modeling, MAD is able to take a general, assumption-free approach, incorporating both local data, ie. data that pertains directly to the target quantity, as well as other indirectly related non-local data. The latter are used for the inversion and converted into local data, called ‘anchors’, therefore improving the overall characterization of the target variable. However, with the use of more and more data, problems arise with the inversion due to the high dimensionality of said data, eg. when using time series. As a result, MAD becomes increasingly difficult, if not impossible, to use for large data sets.

The objective of our study is therefore to investigate and demonstrate effective methods of dimension reduction that reduces large data sets to a small set of relevant parameters while still retaining a strong effect on the inversion procedure. The poster will explain the relevant methods and present examples of their effect on different data types, primarily looking at hydrological data (ie. concentration breakthrough curves, drawdown time series or vertical head profiles) then further theorizing its possible application to geophysical information. Ultimately, the broader goal of this study is to propose ways of applying dimension reduction to the realm of hydrogeophysics, which will not only expand the application of MAD, but also improve our ability to reduce uncertainty in the relevant parameters.