Summary

The tentative conclusions are as follows:

Individual ENSO events evolve by the so-called (linear) delayed oscillator physics (see, e.g., Battisti 1988), which is described uniquely by the evolution of a single cyclic pattern of the coupled system which we will call the ENSO mode (mathematically, this is an eigenmode). The ENSO events are best described as linear transient growth of the ENSO mode.

Results indicate that the future state of the tropical climate system largely depends on two things: how the integrated noise (i.e., uncoupled variability) had projected onto the ENSO mode up to the forecast time (defining the initial conditions for the forecast), and how the (unpredictable) future noise projects onto the ENSO mode These facts imply that the forecast skill will be less sensitive to subtle changes in the initialization of the model, than to the details of the statistics of the projection of the (unpredictable) noise onto the ENSO mode during the forecast period. Hence, the inherent predictability should be determined primarily by the characteristics of the noise in the system. For our present mean climate state, our best estimate of the (theoretical) upper limit of predictability of ENSO is somewhere between one year and 15 months.

Description of the Panels in Fig. 1

Top Panel

We have plotted the time series of Nino 3 from the a coupled model of the tropical Pacific atmosphere/ocean system (the heavy line). The model is a variant of the Cane/Zebiak (C/Z) mode. Here, the model has been linearized and the numerical scheme used to solve the system of equations follows Hirst (1988). Changes have also been made to the ocean mechanical damping and the reflection efficiency of the western boundary, to bring the model more in-line with observational constraints. As a result, the coupled model is stable to perturbations: it does not support oscillations unless an external forcing is applied to the model. Here, external is defined as variability in the system that is associated with uncoupled phenomenon inherent to the atmosphere or ocean.

The light solid line is the Nino 3 index when the same noise that was used in the control run is instead projected onto the ENSO mode and then integrated forward. The difference between these lines is very small and demonstrates that almost all of what is happening in the full coupled atmosphere/ocean model is accounted for by "noise" ; more specifically, the component of the noise that projects onto the model's ENSO.

Not shown are the statistical properties of the output of this model (e.g., the annual cycle of the model's variance in SST, EOFS, etc.) when the model is forced by uncoupled noise that is assumed to be white. In brief, the model is a credible model for the tropical Pacific climate system.

Panels in Second Row

In these panels we show the pattern of SST anomaly (left panel) that is most efficient for growing (over 6 months) the peak phase of the ENSO mode (right panel). [The thermocline and current portion of the "optimal" are not shown.] Analogous structures (optimals) exist for all phases of the ENSO mode. These optimal structures contain all the deterministic physics that is required to carry the system into the distant future (i.e., for times longer than about four months).

Third Row Panel

In this panel we show the observed Nino 3 time series (solid line). Also shown (line with circles) is the Nino 3 index from six month forecasts made using the model described above. The forecast time series is constructed by stringing together the Nino 3 from each six month forecast, made each month starting from July 1949. The initialization of the model is described elsewhere. Forecasts were made through 1990 (not shown).

The raw skill of the model (uncorrected for biases, etc) is comparable to other coupled dynamical models being used.

Last Panel

This panel starts to hint at the important implications of our study, in which we are staring to get a handle on the upper limit of predictability of ENSO. This figure illustrates the main points.

The model described above is employed to make a large ensemble of forecast, with each forecast starting from a perfect initialization. This is accomplished by saving the state variables of the system for each month of the control integration of the coupled model. Then, the model is restarted with each of these initial conditions, and integrated forward (the forecast). Unpredictable (uncoupled) noise acting on the system during these forecast integrations will be different from that in the control integration, and thus the forecasts will diverge from the control integration.

Traditional yardsticks for measuring the divergence between the forecasts and control integration are correlation coefficient and root mean square (RMS) error for a large ensemble of forecasts. Here we only show correlation as a function of the duration of the forecast. The solid line with circles is for the model described above. This plot and the structure of the RMS error (not shown) suggest the limit of predictability is 12-15 months.

The remaining lines on the last panel indicate the skill of different coupled models - models in which the character of the dynamics of the system is different from the modified C/Z model. The solid and dashed lines are for coupled systems in which the ratio of normal mode (i.e., eigenmode) growth to transient growth is greater than that in modified C/Z model (described above). These climate systems are much less susceptible to noise compared to the the modified C/Z model. Hence, the predictability of these climate systems is enhanced compared to our "best guess" model physics (circles). In contrast, when the ratio of normal mode (eigenmode) growth to transient growth is less than that in modified C/Z model, the limit of predictability is significantly reduced (starred curve). In effect, the predictability of the system increases as the the first eigenmode (i.e., the delayed oscillator mode) becomes more prominent.