Transient tracers as a problem in control theory

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Abstract
The problem of interpreting transient tracer surveys in the ocean is formally identified as corresponding to placing a “terminal constraint” on a “distributed system boundary control problem.” The mathematics available in control theory can then be brought to bear on the tracer data. Some of control theory is reviewed in the context of a simple tracer example to isolate the major issues. To use a transient tracer to invert for flow and mixing rates involves a two‐step process: start with an initial model, found independently, and determine if acceptable boundary conditions drive the model to reproduce the interior transient tracer at the observation times. If the model succeeds in that reproduction, one stops; the model is adequate and need not be changed. Only if this test fails does one obtain constraints on the fluid flow and mixing, which can be invoked in parameter estimation techniques of control theory. Terminal constraint observations can also be used to estimate the tracer concentrations at earlier times using a smoothing filter.