Estimating Granger causality among large-scale climate processes from palaeoclimate time series including recent stalagmite-based data from Yok Balum Cave

Dmitry Smirnov

We analyze palaeoclimate data reflecting variations in solar activity (a record of 14C isotope representing a compiled archive of data from tree rings, marine sediments, and stalagmites; total solar irradiance time series reconstructed from an ice-core record of 10Be isotope) and Earth climate conditions such as temperature and moisture (stalagmite-based 13C, 18O, and 14C isotope records from Yok Balum Cave in Southern Belize). The time series available cover simultaneously the period from approximately 15 B.C. till 1950 A.D. and some of these data are characterized with non-equidistant temporal sampling and considerable dating errors.

Influences of the processes under study on each other are estimated with the aid of Granger causality approach. Different time scales for temporal averaging of the data (ranging from 5 to 25 years) are inspected, as well different trial shifts of the time series relative to each other (ranging from -60 to 60 years) are considered to allow
either for a delayed influence or a biased dating. A mathematical benchmark system in the form of coupled stochastic oscillators with measurement noise and dating errors in the time series is used to simulate the effect of the latter factors on the Granger causality estimates. Influence of solar activity on 13C and 18O variations in
the sense of Granger causality is revealed at a significance level less than 0.05. We roughly quanify also temporal changes in the strength (and characteristic time scales or time delays) of that influence using moving window analysis.