Geoscience Reference
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Figure 9.5 Spatial
distribution of climatological
rainfall for (a) observations
for 1997-8, (b) ensemble
mean of all models (c) model
minus observation
differences, and (d) rms
deviations from all-model
mean.
9.3.2 Pattern correlations
The performance of models can be evaluated against the similarity of the
model rainfall patterns to the observed by the pattern correlation (P cor ) and
the root-mean-square ratio (R rms ) defined by:
P r
ð X r X r Þð O r O r Þ
R rms ¼ X
O
P cor ¼
;
X O
where X is a model variable, and O is the corresponding observation. The
summation is over the spatial coordinate r, over the chosen domain, the
overbar represents the spatial average, and is the spatial standard deviation.
P cor and R rms have been computed for each ensemble member, for each
model, and for different seasons. The closer P cor and R rms are to unity, the
better is the model performance.
Figure 9.6a and b show the model ensemble mean values of P cor and R rms for
each model as bar charts, for December-January-February (DJF) and June-July-
August (JJA) for two years, over the Indo-Pacific region 308 S-308 N,
608 E-908W). The standard deviation of P cor and R rms for each model and for
each season is indicated by the vertical lines inside the bars. The all-model
ensemble mean is show in the far right column. From Figure 9.6 , the perfor-
mance of individual models can be compared with the others and to the all-model
ensemble mean. It can be seen that the mean P cor for individual models ranges
from 0.2 to 0.8 (Figure 9.6a ). The correlations seem to be higher during the
boreal winter compared to the boreal summer, indicating that the models tend to
capture the physics of the wintertime rainfall and circulation regimes better than
that for the summer. All models seem to have a higher correlation for DJF 1998,
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