The ability of the adjoint technique to recover decadal variability of the North Atlantic circulation

In order to provide error bounds for current assimilation products, prescribed artificial errors for a priori control parameter, synthetic observations and initial conditions are introduced systematically to our setup. We find that errors with reasonable magnitude in synthetic observations as well as a priori information of the surface heat fluxes lead to a reconstructed decadal-scale MOC variability with tolerable errors of less than a few percent. Errors in initial conditions lead to a “cold start” problem and can degrade the quality of the MOC reconstruction, but can be damped by sufficient a priori information about the surface forcing in the subsequent integration, even without including the initial conditions as a control parameter. The impact of a model error is analyzed by assimilating synthetic observations from different model configurations, which resembles most likely an underestimation of the “real” model error. Even with this optimistic estimate, the reconstruction is very sensitive to the model error and leads to a large error in the reconstructed MOC variability. Taking all possible errors together, the error of decadal MOC reconstruction in current data assimilation products appears to be larger than 60% (about 1 Sv) with a correlation with the “real” MOC variability by less than 0.5.