Sensitivity analysis in variational data assimilation

A model of the evolution of the state of the ocean or of the atmosphere makes sense in and only in presence of data. Any sensitivity analysis have to take into account the data. In this paper we will show the general principle of sensitivity analysis and the use of the adjoint model in order to derive the sensitivity. In presence of data this analysis must be carried out not on the model itself but on the optimality system. Two examples are shown, firstly we study the sensitivity of a variable governed by a simple ordinary differential equation, a realization being imperfectly observed, with respect to one of the parameter of the governing equation. In a second example we will estimate the sensitivity with respect to surface observations of retrieved kinetic energy of the bottom layer in a quasigeostrophic model of oceanic circulation. Both examples clearly show that a correct sensitivity have to take into account the second order terms.