Data assimilation with implicit ocean models

The ocean is an important part of the climate system, controlling the climate variability on many time-scales. Climate change, for example, has been linked to changes in the thermohaline circulation. This thesis is motivated by theoretical results on the stability of this circulation, especially the Atlantic Meridional Overturning circulation (AMOC). These results indentify a scalar whose sign is an indicator for the stability of the AMOC. This indicator measures the net advective freshwater transport in the Atlantic. The central problem adressed in this thesis is the determination of a time-mean value for this indicator from observational records. Since the observational records is sparse and short, one needs a data assimilation methods in combination with a models of the AMOC. The main focus is: (i) to determine best values of the freshwater transports of the present ocean circulation in the Atlantic basin rom available observations; (ii) to determine values for the indicator; and (iii) to assess which processes contribute to the uncertain values for this indicator. The approach suggested here is: (i) develop fully implicit ocean models with which it is possible to calculate equillibrium solutions efficiently because large time-steps can be taken; (ii) adapt a variational data-assimilation method for use in these implicit models; and (iii) develop a data-handling technique such that the effect of temporal variability on the time-mean state can be computed relatively efficient. This approach requires the development of several pieces of new numerical methodology. In this thesis these pieces are developed systematically and tested with idealized models. The foces therefore is on the developement and testing of the new methodology and not on the application in realistic situations with realistic observations. For a wide range of test problems the new methodology performed well and better than traditional data-assimilation schemes using explicit ocean models.