CYCLOCIM: A 4-D variational assimilation system for the climatological mean seasonal cycle of the ocean circulation

Abstract

We describe a new 4-D variational assimilation system, called CYCLOCIM, to estimate the climatological seasonal cycle of the residual mean ocean circulation. CYCLOCIM assimilates monthly mean potential temperature and salinity data from the World Ocean Atlas, and CFC-11, CFC-12 and natural radiocarbon measurements for the deep ocean from the Global Data Analysis Project, Version 2. CYCLOCIM’s control parameters include: (i) a seasonally varying 3-D field of unresolved eddy-stress divergences that appear in the horizontal momentum equations, (ii) seasonally varying 2-D correction fields for the surface heat and freshwater fluxes, and (iii) a constant scaling factor for the air–sea flux of CFCs. The influence of initial conditions on a fully spun-up ocean model vanishes. Thus, unlike other 4-D variational assimilation systems, CYCLOCIM does not include initial conditions as control parameters. A Bayesian procedure is used to formulate the inverse problem, which is solved by finding the maximum of the posterior probability distribution. The optimization process used to find the maximum includes a forward simulation to calculate the flow velocities and tracer distributions followed by a backward (“adjoint” ) simulation to compute the gradient of the posterior. A quasi-Newton search algorithm is used to find the set of parameters to maximize the posterior probability. We find that by resolving the seasonal cycle the model is able to better fit the observations in the upper ocean compared to a previous steady-state version of the model. The main output from CYCLOCIM is a set of 12 data-constrained monthly tracer transport matrices that will provide a useful circulation model for global marine biogeochemical cycle studies.