Generalized Four-Dimensional Variational Data Assimilation for Ocean Modeling

Traditional four-dimensional variational data assimilation (4D-Var) requires the development of the tangent linear (TL) and adjoint models, derived from the non-linear forecast model, and represent a significant investment in resources and time. Often, when a new forecast model is developed, the previous TL and adjoint models are discarded and new versions developed. However, newer forecast models typically represent a different numerical implementation of the same dynamical equations used in the previous generation model. In this case, the previous versions of the TL and adjoint models can be considered linearized dynamical operators for a common dynamical equation set. If true, this would allow the continued use of the same TL and adjoint models over time as the forecast models are upgraded or replaced. In this work, this hypothesis is tested using the US Navy’s Hybrid Coordinate Ocean Model (HYCOM) as the forecast model and the Navy Coastal Ocean Model 4D-Var (NCOM-4DVAR) as the data assimilation system. NCOM and HYCOM are both based on the Navier-Stokes equations for fluid motion, but have different numerical implementations, most notably in the specification of the vertical grid (fixed for NCOM, varying in time with HYCOM). Here the TL model for NCOM will be shown to be a good approximation of the HYCOM TL, where the HYCOM TL is derived exactly as the difference between two HYCOM non-linear model solutions (different in a small perturbation to the model initial conditions). Further, the NCOM-4DVAR is used to derive analysis corrections based on a HYCOM background forecast and a set of ocean observations. This analysis, and its resulting forecast using HYCOM, are compared to a companion run where the analysis is generated using the Navy’s Coupled Ocean Data Assimilation (NCODA) system using 3D-Var. The improvement in the analysis and forecast using the 4D-Var approach is shown by comparison to available observations.