Application of the adjoint technique to processing of a standard section data set: World Ocean Circulation Experiment section S4 along 67°S in the Pacific Ocean

We present a variational data assimilation scheme designed to recover the steady state of an ocean region along a conductivity‐temperature‐depth section track. Oceanic velocity and tracer fields are assumed to satisfy simple stationary dynamical constraints, which include the equation of state of seawater, a dynamical constraint on vertical velocity, stationary tracer transfer equations, geostrophic relations for horizontal velocities, and the kinematic constraint, imposed on the net transport across the section plane. Cousin data assimilation experiments with the steady state geostrophic component of the fine resolution antarctic model have shown that in addition to the absolute cross‐section velocity component and along‐section gradients of properties, the algorithm is capable of reconstructing the cross‐section gradients of temperature, salinity, and along‐section velocity component. The algorithm can also process an arbitrary set of passive tracer fields measured at the section. These fields are coupled statistically with active tracers and between each other via the depth dependent in situ covariance matrix. Error analysis of the assimilated data set taken at 67°S in the southern Pacific has shown that the major state vector components were statistically reliable.