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                   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. 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)
   
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   Date Posted:  1/26/94  (ktb)