**2:00 PM / Tuesday, February 13, 1996**
### Invited Presentation 4

Applications of Computational Differentiation in Numerical Modelling of the Atmospheric and Oceanic Circulation

Numerical modelling of the atmospheric and oceanic circulation is based on codes that compute the evolution of the flow from given initial and lateral boundary conditions. Computational differentiation is used in this context for optimization and sensitivity studies with respect to the initial and boundary conditions, as well as with respect to the various parameters of the model. A basic tool in this context is the adjoint code of the model. One major application of computational differentiation is variational assimilation of observations, in which one looks for the model solution that fits best, in the sense of an objectively defined scalar functional, a set of observations distributed in time. Another application consists of a posteriori sensitivity studies, with respect to the initial conditions of the forecast, of the observed error in a numerical meteorological forecast.
The needs of the numerical simulation of atmospheric and oceanic circulation have strongly stimulated the develoment of automatic differentiators that produce the adjoint of a given code.

**Olivier Talagrand**

Laboratoire de Meteorologie Dynamique, Ecole Normale Superieure, France

MEM, 12/28/95