Abstract. A hierarchy of E1 Nifio-Southern Oscillation (ENSO) prediction schemes has been developed during the Tropical Ocean-Global Atmosphere (TOGA) program which includes statistical schemes and physical models. The statistical models are, in general, based on linear statistical techniques and can be classified into models which use atmospheric (sea level pressure or surface wind) or oceanic (sea surface temperature or a measure of upper ocean heat content) quantities or a combination of oceanic and atmospheric quantities as predictors. The physical models consist of coupled oceanatmosphere models of varying degrees of complexity, ranging from simplified coupled models of the "shallow water" type to coupled general circulation models. All models, statistical and physical, perform considerably better than the persistence forecast in predicting typical indices of ENSO on lead times of 6 to 12 months. The TOGA program can be regarded as a success from this perspective. However, despite the demonstrated predictability, little is known about ENSO predictability limits and the predictability of phenomena outside the tropical Pacific. Furthermore, the predictability of anomalous features known to be associated with ENSO (e.g., Indian monsoon and Sahel rainfall, southern African drought, and off-equatorial sea surface temperature) needs to be addressed in more detail. As well, the relative importance of different physical mechanisms (in the ocean or atmosphere) has yet to be established. A seasonal dependence in predictability is seen in many models, but the processes responsible for it are not fully understood, and its meaning is still a matter of scientific discussion. Likewise, a marked decadal variation in skill is observed, and the reasons for this are still under investigation. Finally, the different prediction models yield similar skills, although they are initialized quite differently. The reasons for these differences are also unclear.

A new parameter of dynamical system predictability is introduced that measures the potential utility of predictions. It is shown that this parameter satisfies a generalized second law of thermodynamics in that for Markov processes utility declines monotonically to zero at very long forecast times. Expressions for the new parameter in the case of Gaussian prediction ensembles are derived and a useful decomposition of utility into dispersion (roughly equivalent to ensemble spread) and signal components is introduced. Earlier measures of predictability have usually considered only the dispersion component of utility. A variety of simple dynamical systems with relevance to climate and weather prediction is introduced, and the behavior of their potential utility is analyzed in detail. For the climate systems examined here, the signal component is at least as important as the dispersion in determining the utility of a particular set of initial conditions. The simple ''weather'' system examined (the Lorenz system) exhibited different behavior with the dispersion being more important than the signal at short prediction lags. For longer lags there appeared no relation between utility and either signal or dispersion. On the other hand, there was a very strong relation at all lags between utility and the location of the initial conditions on the attractor.

An ocean general circulation model, forced with idealized, purely oscillating wind stresses over the western equatorial Pacific similar to those observed during the Madden-Julian oscillation (MJO), developed rectified low-frequency anomalies in SST and zonal currents, compared to a run in which the forcing was climatological. The rectification in SST resulted from increased evaporation under stronger than normal winds of either sign, from correlated intraseasonal oscillations in both vertical temperature gradient and upwelling speed forced by the winds, and from zonal advection due to nonlinearly generated equatorial currents. The net rectified signature produced by the MJO-like wind stresses was SST cooling (about 0.4ЊC) in the west Pacific, and warming (about 0.1ЊC) in the central Pacific, tending to flatten the background zonal SST gradient. It is hypothesized that, in a coupled system, such a pattern of SST anomalies would spawn additional westerly wind anomalies as a result of SST-induced changes in the low-level zonal pressure gradient. This was tested in an intermediate coupled model initialized to 1 January 1997, preceding the 1997-98 El Niño. On its own, the model hindcast a relatively weak warm event, but when the effect of the rectified SST pattern was imposed, a coupled response produced the hypothesized additional westerlies and the hindcast El Niño became about 50% stronger (measured by east Pacific SST anomalies), suggesting that the MJO can interact constructively with the ENSO cycle. This implies that developing the capacity to predict, if not individual MJO events, then the conditions that affect their amplitude, may enhance predictability of the strength of oncoming El Niños.

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We present a rigorous formalism of information transfer for systems with dynamics fully known. This follows from an accurate classification of the mechanisms for the entropy change of one component into a self-evolution plus a transfer from the other component. The formalism applies to both continuous flows and discrete maps. The resulting transfer measure possesses a property of asymmetry and is qualitatively consistent with the classical measures. It is further validated with the baker transformation and the Hénon map.