Correlation methods in fingerprint detection studies

This investigation addresses two general issues regarding the role of pattern similarity statistics in greenhouse warming detection studies: normalization, and the relative merits of centered versus uncentered statistics. A pattern correlation statistic is used to search for the greenhouse warming signals predicted by five different models in the observed records of land and ocean surface temperature changes. Two forms of this statistic were computed: R (t), which makes use of nonnormalized data, and (t), which employs point-wise normalized data in order to focus the search on regions where the signal-to-noise ratio is large. While there are no trends in the R (t) time series, the time series of (t) show large positive trends. However, it is not possible to infer from the (t) results that the observed pattern of temperature change is, in fact, becoming increasingly similar to the model-predicted signal. This is because point-wise normalization of the observed and simulated mean change fields by a single common field introduces a common factor effect, which means that the quantities being compared should show some similarity a priori. This does not necessarily make normalization inapplicable, because the detection test involves seeking a trend in the similarity statistic. We show, however, that trends in (t) must arise almost completely from the observed data, and cannot be an indicator of increasing observed data/signal similarity. We also compare the information provided by centered statistics such as R(t) and the uncentered C(t) statistic introduced by Barnett. We show that C(t) may be expressed as the weighted sum of two terms, one proportional to R(t) and the other proportional to the observed spatial mean. For near-surface temperatures, the spatial average term dominates over the R(t) term. In this case the use of C(t) is equivalent to the use of spatial-mean temperature. We conclude that at present, the most informative pattern correlation statistic for detection purposes is R(t), the standard product-moment correlation coefficient between the observed and model fields. Our failure to find meaningful trends in R(t) may be due to the fact that the signal is being obscured by the background noise of natural variability, and/or because of incorrect model signals or sensitivities.