Changing Box–Cox transformation parameter as an early warning signal for abrupt climate change

There are some critical thresholds in many complex dynamic systems. When a system approaches its critical threshold, the probability density distribution of the system might be changed. In view of this, we presented a new early warning indicator of an abrupt climate change based on the Box–Cox transformation, namely, the changing Box–Cox transformation parameter (BCTP). A significant increasing or decreasing trend in BCTP can always be found before the onset of an abrupt change in different folding models. Based on the Greenland paleotemperature data reconstructed through Greenland Ice Sheet Project II, we found that BCTP showed an increasing trend about 2800 years before the onset of Bølling–Allerød warming. The trends of BCTP are statistically significant at a significant level of of α = 0.05 for both artificial abrupt changes and Greenland paleotemperature. Compared with kurtosis coefficient and skewness coefficient, BCTP can present an effectively early warning in some cases of abrupt change where kurtosis coefficient or skewness coefficient showed a poor warning performance. In general, the variation magnitudes of BCTP are greater than that of kurtosis coefficient and skewness coefficient, and BCTP shows a better warning performance in most of cases. These results indicate that changing BCTP could be a good new indicator for warning upcoming abrupt changes.