Long-Range Dependence in Millennial-Scale Climate Models

Many past studies have concluded that many Earth system processes, including in weather, show “long-range dependence” (LRD): excessive temporal dependence in widely separated events. For example, William Hurst showed in a classic 1951 study that Nile river levels showed unexpected correlation over long time intervals, providing valuable practical information for the development of reservoir sizes. However, it has remained an outstanding question whether natural processes truly show this statistical behavior, or whether the appearance of LRD in environmental time series is an artifact of evolving forcing over the timescale of the record. The recent production of millennial-scale climate model runs under stable forcing conditions now allows us to gain insight into the long-term statistical behavior of the climate system. In this study, we apply and compare several techniques to estimate LRD in the time series of surface temperature from millennial-scale climate model runs under constant forcing, in both pre-industrial or elevated-CO2 simulations. In contrast to studies based on real historical time series, we find that LRD, while present in some locations, is generally small over land. In pre-industrial simulations with the CCSM3 model, for example, the mean Hurst exponent over N. America is only 0.494 (0.5 would indicate no LRD). Preliminary results suggest that LRD may increase under conditions of enhanced CO2, although minor non-stationarity in the data may affect the estimation. Such an increase would imply a decrease in long-term variability in a warmer climate. Although results are necessarily based only on models, they can provide insight into plausible statistical properties of the Earth system.