Resolution and uncertainty in hydrologic characterization

Abstract

Hydrologists have applied inverse techniques to obtain estimates of subsurface permeability and porosity variations and their associated uncertainties. Although inverse methods are now well established in hydrology, important aspects of inverse theory, the analysis of resolution, and the trade‐off between model parameter resolution and model parameter uncertainty have not been utilized. In this paper the concept of model parameter resolution is incorporated into the analysis of hydrological experiments. Model parameter resolution is a measure of the spatial averaging implicit in estimates of a distributed hydrological property such as permeability. There are two important uses of resolution and uncertainty estimates in hydrology. The first use is to plan a hydrologic testing program. Resolution matrices can be developed for proposed well tests in a variety of synthetic media. Then the effectiveness of the test design can be evaluated in terms of model parameter resolution and uncertainty. Secondly, when real data are available and used in an inversion determining the distribution of hydrologic parameters, estimates of model parameter resolution and uncertainty analysis can indicate the reliability of the solution. For synthetic tests in which the hydraulic conductivity varies and porosity does not, it is found that tracer data can provide better spatial resolution of subsurface hydraulic conductivity variations than transient pressure data. Pressure data are most sensitive to hydraulic conductivity variations immediately surrounding the well. Both pressure and tracer data better determine barriers to flow rather than channels to flow. The methodology is applied to a set of transient pressure data gathered at the Grimsel Rock Laboratory of the Swiss National Cooperative for the Storage of Radioactive Waste. In the fracture under study a low hydraulic conductivity region appears to partition the fracture plane into two distinct zones.