**4. Multiple feasible futures**

Clearly, forecasts are model dependent. Different models and parametrisations will determine different probable futures, all of them physically acceptable if using dynamical models. Some will behave better than others when compared with observations, depending on several factors (e.g. the adequacy of the physical phenomena description in a dynamical model or the boundary conditions employed). Therefore, useful products for decision-makers should include, aside from the forecast maps themselves, additional information about their confidence and uncertainty.

The uncertainty of the final products can be decreased if several *realizations* are used, each one corresponding to a different and independent model execution (i.e. a feasible future). The idea is to *ensemble* in a final product as many independent realizations as possible, using statistical weights for each member that are defined in terms of how well each one represents the observed values in a certain period. It is a common practice, however, to 14 Numerical Simulations

Fig. 6. The three level, two-way hierarchical information flux between climate related

. We emphasise that the same hierarchical information flux works for both weather (short-term) and climate (seasonal to long-term) simulations. Statistical, dynamical or hybrid models can

This simple and efficient structure allows higher-level (i.e. levels II and III) models to run using as *first guess* the output of the preceding level, but the opposite must be also considered. Lower-level models should also be updated as in *upscaling* applications, providing a two-way

Clearly, forecasts are model dependent. Different models and parametrisations will determine different probable futures, all of them physically acceptable if using dynamical models. Some will behave better than others when compared with observations, depending on several factors (e.g. the adequacy of the physical phenomena description in a dynamical model or the boundary conditions employed). Therefore, useful products for decision-makers should include, aside from the forecast maps themselves, additional information about their

The uncertainty of the final products can be decreased if several *realizations* are used, each one corresponding to a different and independent model execution (i.e. a feasible future). The idea is to *ensemble* in a final product as many independent realizations as possible, using statistical weights for each member that are defined in terms of how well each one represents the observed values in a certain period. It is a common practice, however, to

models. Source: (Muñoz et al., 2010)

flux that enables a feedback among the different models.

be present at any level.

**4. Multiple feasible futures**

confidence and uncertainty.

employ equally weighted members in the final ensemble. For weather applications of the ensemble methodology the reader can review (Toth & Kalnay, 1993), and for seasonal forecast applications (Li et al., 2008) and references therein.

The different realizations can be produced in several ways. For example, they can be constructed in terms of perturbations to some initial state, using different methodologies (like the ones explained in section 3.2) for the tier-1 in seasonal forecast, or even employing diverse combinations of physical parametrisations. Figure 7 sketches a two member behaviour for the SST evolution in an AGCM equatorial grid cell. Each member originally differed in the SST cell by only 10−<sup>3</sup> K. Due to the *butterfly effect*, after a few weeks we will likely see important differences in the temporal behaviour of the variable, and not only for that cell. Climate models fed with these two SST fields as boundary conditions will provide different members in the ensemble forecast.

For climate simulations, it has been shown (Li et al., 2008) that the use of different methodologies for the tier-1 offers better results (fewer uncertainties) in the final ensemble than the simulations associated with only one methodology.
