PICK A NUMBER MODELING SUBSURFACE PROCESSES This article also appears in the Oak Ridge National Laboratory Review (Vol. 26, No. 1), a quarterly research and development magazine. If you'd like more information about the research discussed in the article or about the Review, or if you have any helpful comments, drop us a line at: electronic mail, krausech@ornl.gov or pearcejw@ornl.gov; fax, 615/574-1001; phone, 615/574-7183 or 615/574-6774; or mail, ORNL Review, Oak Ridge National Laboratory, 4500-S 6144, Oak Ridge, TN 378312-6144. Thanks for reading the Review. Recently I spent a day in California looking at hydraulic fluid spills beneath old garages for servicing motor vehicles. Apparently hydraulic lifts leak small amounts of fluid. As a result, plumes of hydraulic fluid percolate through the ground and eventually may contaminate groundwater. At some time these sites must be cleaned up. However, to accomplish this task we must know where the contaminant is and where it will move as a result of cleanup activities. As with other subsurface problems, this question arises: Can soil samples at the contamination site provide an accurate picture of the location of specific contaminants? Unlike our more traditional areas of engineering, knowledge of subsurface flows is made difficult by the enormous uncertainty of the data collected. For example, a hapless engineer may insert a chemical-sensing probe at the very spot where a weary traveler spilled some unwanted soda pop the night before. In this case, the environment created for the sensor may be totally different from that of the rest of the site. This uncertainty is made more critical by the large cost of collecting soil data--possibly reaching several thousand dollars for a single sampling point. Thus, it is critical that methods be developed soon for economical sampling of possibly contaminated sites. Statisticians have developed sampling methods that seem almost miraculous. For example, within a few minutes after polls have closed, statistical methodology makes surprisingly precise election predictions. Their methodology is based on so-called "probability" models in which the parameters of interest are permitted to be random but are dictated by certain "probability distributions" indicating that random parameters are inclined to be nearer to certain values than others--much the same as heights of people or the way people vote in elections. These distributions have been found on the basis of exhaustive analysis of past elections and the determination of small but highly representative subsamples of the population. Peculiarities of certain subcollections of parameters (e.g., teenagers enjoying louder noises than do their parents) are taken into account for the sampling process. For subsurface processes, sources of such special behavior might include soil strata, hills, and the history of the site of interest. For many years mathematicians and engineers have developed deterministic (nonprobabilistic) models of flow in soil. These models, however, require precise knowledge of such features as contaminant distributions at some initial time and soil parameters at depth. Hence, they are not wholly suitable for the "real world" problem in which such knowledge is not really available. Recently, statisticians and mathematicians at ORNL have broken new ground by melding their respective perceptions of subsurface events. The mathematicians have models that are totally deterministic, whereas the statisticians have models that are wholly geared to data. By joining forces they have produced new tools that promise substantially improved sampling methods. They will be able to better answer questions of when and where to take samples and what kinds. Their approach is to "teach" the probability distributions to reflect the underlying behavior of processes when they are used to guide the sampling process. The teaching process uses a combination of tools drawn from partial differential equations on one hand and sampling theory on the other. Using these and similar approaches, eventually an environmental engineer can go to a site needing cleanup and determine from a dialogue with a computer where and when to sample the site to get the most nearly accurate view of underground contamination. Such a capability may even allow the engineer to say with certainty, "Someone spilled some soda here last night." Alan D. Solomon (keywords: sampling, environmental modeling) ------------------------------------------------------------------------ Please send inquiries or comments about this gopher to the mail address: gopher@gopher.ornl.gov Date Posted: 1/26/94 (ktb)