MATHEMATICAL-MODELING OF INVERSE PROBLEMS FOR OCEANS

This paper presents mathematical modelling of a theoretical "ocean" in which the fields of water velocity and turbulence and tracer concentrations are all known and together "perfectly" statisfy a steady-state advective-diffusive equation. The sensitivity to data errors is studied for box models representing portions of the ocean that are mathematically formulated as overdetermined systems. It is shown that very good results may be obtained from noisy data using naive inverse modelling techniques, provided that enough independent tracer data are available and the data are sufficiently noise-insensitive for the scales at which the model utilizes them. A formal statistical error estimate based on the Jacobian of the inverse transformation is introduced, which is useful if one has an a priori estimate of the noise level.