Summary: • Modern mathematical methods are available for a wide variety of applications.        These methods allow the simultaneous use of many different data types.        Irregular spatial or temporal data coverage is not a problem. • New and useful results can be obtained for marine productivity, particle fluxes,        remineralization rates, air-sea gas exchange rates and other parameters. • More inverse studies of biogeochemical systems should be undertaken to        make use of high-quality, global datasets available now or in the near future.