Adjoint-Based Techniques for the Analysis of Large-Scale Uncertain Systems

Abstract

Despite the increased complexity in the model representations, it is often the case that comprehensive dynamical models show poor results when compared to observational data. In four-dimensional variational data assimilation (4D-Var) a minimization algorithm is used to find the value of the model parameters such that an optimal fit between the model prediction and observations, scattered in time, is achieved. For large-scale models, the minimization of the cost functional is a very intensive computational process.

The adjoint modeling is presented as a feasible tool to evaluate the sensitivity of a scalar response function with respect to a large number of model parameters. The use of a second order adjoint model to obtain Hessian information is shown to be of benefit for ill conditioned optimization problems.

A research area of major interest is the design of an adaptive observational network. Expensive field-deployed resources (facilities and people) can be utilized more effectively and science success can be maximized by an optimal allocation of the observational resources. A new adjoint approach to the adaptive observations problem is presented and its potential benefits are illustrated in a comparative analysis with traditional methods based on singular vectors and gradient sensitivity.

Numerical results are shown for nonlinear chemical reactions systems and atmospheric circulation models.