  Uncertainty in estimation of Drake Passage transport is analyzed in a
Hessian-based uncertainty quantification (UQ) framework. The approach extends
the adjoint-based ocean state estimation method to provide formal error bounds
functionality. Mechanisms of uncertainty propagation in an idealized barotropic
model of the Antarctic Circumpolar Current are identified by analysis of
Hessian and Jacobian derivative operators, generated via algorithmic
differentiation (AD) of the MIT ocean general circulation model (MITgcm).
Inverse and forward uncertainty propagation mechanisms are identified,
projecting uncertainty between observation, control and state variable domains.
Time resolving analysis of uncertainty propagation captures the dynamics of
uncertainty evolution and reveals transient and stationary uncertainty regimes.
The UQ system resolves also the dynamical coupling of uncertainty across
different physical fields, as represented by the off-diagonal posterior
covariance structure. The spatial patterns of posterior uncertainty reduction
and their temporal evolution are explained in terms of barotropic ocean
dynamics. Global uncertainty teleconnection mechanisms are associated with
barotropic wave propagation. Uncertainty coupling via data assimilation is
demonstrated to dominate the reduction of Drake Passage transport uncertainty,
highlighting the importance of correlation between different oceanic variables
on the large scale.
