Variational data assimilation in oceanic problems with instabilities

ALexander Kurapov
COAS, Oregon State University

Emerging tangent linear (TL) and adjoint (AD) ROMS codes utilized with the variational representer-based generalized inverse method (GIM, ref.: Chua and Bennett, Ocean Modelling, 2001) will provide powerful tools for rigorous assimilation of massive data sets into the nonlinear oceanic model, allowing to correct model inputs (including forcing, initial, and boundary conditions). Using GIM, a quadratic functional penalizing model and data errors over a finite time interval is defined. Nonlinear Euler-Lagrange equations, providing necessary conditions for the minimum of the penalty functional, are solved iteratively via a series of linearized optimization problems.

In many coastal applications, energetic alongshore flows are prone to instabilities. While their growth can be constrained by nonlinear advection in the nonlinear model, it is not similarly constrained in the companion tangent linear model, potentially posing a threat to the stability of GIM. This issue is fundamental in coastal ocean data
assimilation and is relevant both for shallow-water and three-dimensional stratified flows. To address it, TL and AD codes for a shallow-water equation model have been built using algorithmic features of the two-dimensional part of ROMS and recipes for TL-AD code development shared with us by ROMS Adjoint Group (A. Moore et al.). Using these codes, GIM is applied with synthetic measurements in a study of forced-dissipative flows over variable beach bathymetry, driven by radiation stresses from shoaling waves. In cases of relatively small dissipation, in which the model exhibits instabilities (including a regular equilibrated wave pattern or "turbulent" behavior), the utility of GIM and requirements for adequate data coverage are determined.