Parameter optimisation techniques and the problem of underdetermination in marine biogeochemical models

Ward, Ben A., Friedrichs, Marjorie A.M., Anderson, Thomas R. and Oschlies, Andreas (2010) Parameter optimisation techniques and the problem of underdetermination in marine biogeochemical models. Journal of Marine Systems, 81 (1-2), 34-43. (doi:10.1016/j.jmarsys.2009.12.005).

Abstract

Parameter values in marine biogeochemical models can strongly affect model performance, but can be hard to define accurately and precisely. When making quantitative comparisons between models it is helpful to objectively assign optimal parameter values, so it is the best model performance rather than the degree (or lack) of tuning which is assessed. The efficacy of two optimisation techniques, a variational adjoint (VA) and a micro genetic algorithm (?GA), was studied with respect to the calibration of two simple one-dimensional models for Arabian Sea data. Optimisations were randomly initialised a number of times, and given the level of uncertainty in the data, the two techniques performed equally well in terms of reducing model-data misfits.

When ten parameters were optimised for either model, the Arabian Sea data were insufficient to constrain unique solutions; several parameters could be set anywhere across a wide range of values while providing a similarly good fit to the data. The significance of this underdetermination was assessed by evaluating model solutions against unassimilated equatorial Pacific data. When no prior information was used to assist the optimisation, the underdetermined solutions led to highly variable and often poor performance at the equatorial Pacific. Prior information was used to gain a more reliable solution in two ways: (1) by fixing all poorly-constrained parameters to their default prior values, optimising only parameters that were well-constrained by the data; or (2) by placing broad limits on the search to exclude unrealistic parameter values. Using the first approach the optimisation routines could constrain unique solutions and model performance in the equatorial Pacific was very consistent. The precise results were however sensitive to the uncertain a priori values of the fixed parameters. The second approach was less prescriptive, and consequently led to a more variable performance in the equatorial Pacific. It is argued that the first approach is unrealistically precise as it ignores any uncertainty in the unconstrained parameters, while solutions from the second approach may be unnecessarily broad. In conclusion, unconstrained parameter optimisation procedures should be assisted by stating all that is known a priori about the parameters, but no more.

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