Generalization of the NCOM-4DVAR: application to HYCOM

It takes a significant investment and resources to develop a four-dimensional variational (4dvar) capability for a specific model. However not all models lend themselves to 4dvar development; this is true of the HYbrid Coordinate Ocean Model (HYCOM) with its dynamic vertical coordinate system. Most numerical ocean models are approximations of the same Navier-Stokes equations with the same fundamental hydrostatic assumption. As such, it is fair to assume that given the same forcing, initial and boundary conditions, two numerical ocean models will produce similar solutions. That is the difference between the two solutions should be small over a typical assimilation window of a few days. And by extension, both models would yield similar solutions if they are initialized with the same perturbed initial condition. The difference between a perturbed and an unperturbed solution describes the evolution of initial perturbations, which by definition approximates the tangent linear model (TLM). The latter does not exist and is difficult to develop for HYCOM. Based on the assumption above, the difference between a perturbed and unperturbed HYCOM solutions should be similar to the difference between a perturbed and unperturbed solutions of the Navy Coastal Ocean Model (NCOM), and the latter approximates the NCOM TLM (which exists). Thus, NCOM TLM approximates HYCOM TLM, and by way of consequence the NCOM adjoint approximates the HYCOM adjoint. Thus, NCOM-4DVAR can be used to compute analysis increments for HYCOM. This study investigates if such increments improve HYCOM forecasts. Preliminary results of assimilating observation in the Gulf of Mexico will be shown.