The ability of the model to reproduce the pattern in the observations can be measured using the correlation coefficient:

N^- X)(y - y} (22.3) R = —-, where ax and are the standard deviations of the model and observations respectively.

The correlation coefficient provides information about whether the patterns in the model are similar to the patterns of the observations, but not about the amplitude of variation in the two fields. It reaches a value of 1 when the two fields have the same centred pattern of variation, a value of -1 when the two fields vary in the opposite sense to each other, and a value of zero when no correlation exists between the two fields. The square of the correlation coefficient, R2, is also a useful quantity as it provides information on the fraction of the variance explained.

When the dominant source of variability in a field is a large scale signal, for instance the seasonal cycle, most ocean models would easily reproduce the signal, resulting in high values of R. However, ocean forecasting systems produce infor-

x ~ y mation at smaller temporal and spatial scales. To assess these, it is instructive to calculate the anomaly correlation coefficient:

y i=i i=i which provides information about the ability of the model forecast to reproduce the observational information when the seasonally varying climate signal, denoted C, has been removed.

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