Data assimilation: combining ocean models and data:

There are many available observations of the oceanic circulation from research ships, satellites, and moored instruments.  However, very often quantities of interest for climate purposes cannot be measured directly.  For example, we know quite well the temperature field of the ocean and function of season, geographical location and depth.  But there are no direct data of the amount of heat carried by ocean currents from the equator to the poles, which is an important climate unknown.  Ocean models may be used to bridge between the available data and desired information.  We have been developing a sophisticated method for the assimilation of ocean data into models and for the extraction of the needed climate information.  The method is known as the "adjoint method" and is based on "optimal control" theory. The method requires a model that is based on the adjoint equations of the ocean model to which data is assimilated...

In order to predict climate phenomena such as El Nino, one needs to initialize a model of the coupled Pacific ocean and atmosphere with the available data and then run it in a prediction mode.  The adjoint method is again useful for this initialization, and in this context is often referred to as "4d variational data assimilation".  See also here.

Adjoint models can also be used for sensitivity and generalized stability studies, and some relevant results are shown in the figure below.

Sensitivity of east pacific basic stratification to temperature in the equatorial Pacific (thanks to Eli Galanti...)