an example of a perfectly correlated reconstruction with no skill at prediction. The dashed blue line is level at the mean temperature and has an r2 and a CE that are both zero. The blue and green reconstructed lines both have a CE of 0.50. For either of these reconstructions to be better than just the mean, they must exhibit some degree of correlation with the temperatures. In this case, r2 is 0.68 for the blue line and 0.51 for the green line.
Despite a common CE, these two reconstructions match the temperature series in different ways. The blue curve is more highly correlated with the short-term fluctuations, and the green curve tracks the longer term variations of the temperature series. The difference between the blue and green lines illustrates that the CE statistic alone does not contain all the useful information about the reconstruction error.
The combination of a high RE and a low CE or r2 means that the reconstruction identified the change in mean levels between the calibration and validation periods reasonably well but failed to track the variations within the validation period. One way that this discrepancy can occur is for the proxies and the temperatures to be related by a common trend in the calibration period. When the trend is large this can result in a high RE. If the validation period does not have as strong a trend and the proxies are not skillful at predicting shorter timescale fluctuations in temperature, then the CE can be substantially lower. For example, the reconstructions may only do as