Predicting the expected rainfall given the SST is not a deterministic prediction problem, such as forecasting the trajectory of a rocket around a planet. It is more analogous to the following situation. Consider a sloping surface with a divider at the bottom (Fig 2.4) and consider the apparatus to be placed outside on a table. Imagine releasing a light ball down the surface, starting it at the top, perfectly in line with the divider point at the bottom. You release the ball ten times in a situation with no wind. All things being equal, we expect the ball to fall about five times into the left hand divide and five times into the right hand divide. You return the next day, and there is a gentle (2m/s) but randomly gusting breeze blowing from left to right across the table. You repeat the experiment of releasing the ball ten times, and this time, on some occasions, the wind catches the ball and pushes it into the right hand divide. Overall, you may have a situation where the ball drops on seven occasions into the right hand divide and on three occasions into the left hand divide. Maybe you return the next day and the wind is a little stronger (4m/s) but still gusting randomly. Of course, this time you expect the ball to be more often taken into the right hand divide. The experiment may result in the ball falling to the right side on 9 out of 10 occasions. Trying to predict which way the ball will drop based on the breeze blowing across the table is analogous to predicting whether the rainfall will be above or below normal, given the prevailing SST. For example, consider you made a ball drop experiment on a windy day, and after ten experiments, the ball had dropped nine times into the right divide and once into the left divide. What is your forecast if you now make an 11th ball release, assuming the level of wind is the same as was operating during your experiment? Your best estimate forecast would be for the ball to drop into the right and divide, and based on your experiment, you attach a 9 in 10 likelihood of the ball drop into the right hand divide. For the climate system, the General Circulation Model (GCM) makes the calculation of the ball dropping down the ramp. For the GCM, it is the prevailing SST that may alter the likelihood of the rainfall falling into the above normal or below normal rainfall category. One issue is how many experiments we need to make to get a good estimate of the likelihood of the rainfall occurring in each category. This is a sampling problem, that can be explored by using the animation in Fig. 2.4. The strength of wind blowing across the apparatus alters the likelihood of the ball falling into the left or right hand bin. But it can be seen that it takes a relatively large sample to arrive at a reliable estimate of the extent to which a wind of, say, 2m/s, alters the likelihood. If you have a very large sample, then you will find that a wind of 2m/s creates a likelihood of 70% for the right hand bin.

In fact, the analogy is even better if we imagine a motor inside the ball which fires in random directions as the ball falls down the surface. Furthermore, this time we consider the left-to-right wind to be a perfectly steady force on the ball. Now, the random directions the ball takes as a result of its internal motor is analogous to the internal mechanisms of climate variability in the GCM, while the steady wind forcing on the ball as it falls down the slope is analogous to the SST constantly trying to push the GCM's atmosphere into an anomalous state. If the wind force on the ball dominates its random directions of movement, we will be able to predict with high confidence that the ball will fall into the right hand divide. If the wind force is trivial compared to the random movements created by the motor in the ball, we will not be able to say much different from a 50-50 chance of the balling falling into the left or right hand divide.