Abstract

A contaminated surface patch has diffused in time within an aqueous volume when it is discovered. Emergency workers, with limited access and time, collect surface samples and those at one other nearby elevation. Only sparse space-time data is available and clever detective work is needed. Where, when and how did the pollution originate? What was its size and shape? Can this information be extrapolated, knowing only the diffusion coefficient, from this sparse set of data? An intuitively motivated inverse procedure, assisted by an accurate Alternating Direction Implicit solver operable in reverse time, shows that this is possible, and detailed three-dimensional diffusion equation validations are provided. This capability is useful to remedial correction, policy development, liability assignment and other issues pertinent governance, as well as to other related technical applications.

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