Low Order Uncertainty Dynamics in Ocean State Estimation: Reduced Hessian Method for Constraining Barotropic Drake Passage Transport

Abstract:

Uncertainty Quantification (UQ) is of central practical and theoretical importance in Ocean State Estimation, enabling estimation of error bounds of model outputs as well as new dynamical insight by analyzing information propagation in ocean models. Key effort in developing UQ techniques applicable to realistic large scale ocean models is numerical scalability for high dimensionality imposed by high resolution discretization of infinite dimensional PDEs governing ocean dynamics. This scalability requirement conflicts with the "curse of dimensionality" restricting current non-Gaussian UQ approaches to low dimensional idealized problems. On the other hand, practical progress in large scale UQ was enabled by Hessian-based methodologies, relying on a Gaussian approximation of the nonlinear state-space statistics. Validity of this approximation is rooted in the experience that for many large scale ocean problems the dynamics are smooth and not chaotic, supported by the expectation that small scale turbulence cancels out in aggregate converging to asymptotic normality on the large scale. Here, the dynamics of large scale uncertainty is addressed directly by explicit analysis of propagation of assimilated information in a global ocean model. It is demonstrated that for the case of barotropic Drake Passage transport separate uncertainty propagation mechanisms can be identified on small and large scales, with aggregate balances governed by simple low order dynamics. Reduced order Hessian is derived to approximate the dominant uncertainty evolution patterns, explaining the physical mechanisms of uncertainty propagation and reduction in a global ocean model.