Using transient tracers: the regularization problem

Abstract

The generic problem of deducing fluid properties, velocity, mixing, and boundary conditionsfrom realistic tracer observations is formulated and attacked. The focus is on oceanic transienttracers, but the same problem elements appear in many other fields including meteorology,medicine and chemical engineering. It becomes clear that use of tracers, transient orotherwise, requires at some stage the solution of the advection/diffusion equation eitherupstream, or backwards in time, or both, a situation notorious for its instability becausediffusive processes progressively destroy information in the “forward” direction. We consideran example in simple finite difference form for one space dimension and time. The problem isrun “backwards” but regularized by solving it through linear programming. Linear programmingis shown also to have several potential advantages for stable and unstable forwardproblems, and the inverse problem: knowledge of the form of the answer is easily used; datauncertainty is accommodated; the positivity constraints on concentrations are implicit; sparsesystem software is available; questions of best observational strategy are addressed by the dualsolution ; and the strong instabilities of the inverse and backwards problems are suppressed.