Applications of adjoint models

The ability to efficiently linearize CFD codes is a crucial element in the analysis of the predictability of fluid flow. Predictability is limited by three fundamentally different factors; understanding of each is greatly enhanced by the use of linearized fluid codes:

1. Initial conditions Skillful prediction of flow evolution is possible only when the initial conditions are determined with sufficient accuracy. An improved estimate of the state of the fluid can be obtained by combining observations from a certain time period with a model, which performs interpolation and extrapolation in space and time. Very large-scale problems can be solved through a minimization approach using the adjoint to the CFD code. MITgcm is being used by us to synthesize the WOCE observations.
2. The physical model must represent all important processes influencing flow evolution, either by resolving them explicitly or parametrically. Testing a fluid code against observations and determining parameters in parameterizations of unresolved flow scales both lead to very large optimization problems, which can be solved very efficiently using the adjoint to the CFD code.
3. Hydrodynamic instabilities lead to rapid growth of small perturbations and, via the same mechanisms, of error growth. It is crucial to identify the fastest growing flow perturbations and how they are triggered. The tangent-linear model and its adjoint permit the computation of the singular vectors of the the linearized operator describing flow evolution, which often describe the most rapid growth of perturbations and forecast error. The availability of the linearized operator also facilitates the construction of bifurcation diagrams by continuation methods - a powerful tool in the analysis of the onset of hydrodynamic instability or the establishment of flow regimes in the vicinity of unstable critical points.