PREDICTION OF THE EVOLUTION OF THE VARIANCE IN A BAROTROPIC MODEL

Tile Schmidt decomposition is applied to the evolution operator of the linearized barotropic equation on a sphere (in the following referred to as the barotropic propagator) to study the evolution of the varian ce, that is, of the collective evolution of a cloud of trajectories ce ntered around the initial condition. The variance can give reliable in formation on the tendency that some initial conditions may have to gen erate large spreads in the subsequent time evolution, especially when many modes with similarly large amplifying rates exist. It appears lat her arbitrary, under these circumstances, to pick a particular mode ju st because it happens to have the largest rate for that particular num erical formulation and resolution setting. It is also shown that the G olden-Thompson generalized inequality and other indicators can be used to estimate the linear variance from the analysis of the initial cond ition itself, without the need for performing the costly explicit calc ulation of the propagator. Numerical experiments performed on a set of initial conditions obtained from a simulation experiment and from obs ervations show that in a barotropic model a spread index based on an i ndicator of non-self-adjointness, as the Golden-Thompson index, is cap able of detecting with good reliability initial conditions with a tend ency to produce large spreads.