Contributions to surface air temperature trends estimated from climate time series: Medium-term causalities.

Contributions of various natural and anthropogenic factors to trends of surface air temperatures at different latitudes of the Northern and Southern hemispheres on various temporal horizons are estimated from climate data since the 19th century in empirical autoregressive models. Along with anthropogenic forcing, we assess the impact of several natural climate modes including Atlantic Multidecadal Oscillation, El-Nino/Southern Oscillation, Interdecadal Pacific Oscillation, Pacific Decadal Oscillation, and Antarctic Oscillation. On relatively short intervals of the length of two or three decades, contributions of climate variability modes are considerable and comparable to the contributions of greenhouse gases and even exceed the latter. On longer intervals of about half a century and greater, the contributions of greenhouse gases dominate at all latitudinal belts including polar, middle, and tropical ones.

Relating Granger causality to long-term causal effects.

In estimation of causal couplings between observed processes, it is important to characterize coupling roles at various time scales. The widely used Granger causality reflects short-term effects: it shows how strongly perturbations of a current state of one process affect near future states of another process, and it quantifies that via prediction improvement (PI) in autoregressive models. However, it is often more important to evaluate the effects of coupling on long-term statistics, e.g., to find out how strongly the presence of coupling changes the variance of a driven process as compared to an uncoupled case. No general relationships between Granger causality and such long-term effects are known. Here, we pose the problem of relating these two types of coupling characteristics, and we solve it for a class of stochastic systems. Namely, for overdamped linear oscillators, we rigorously derive that the above long-term effect is proportional to the short-term effects, with the proportionality coefficient depending on the prediction interval and relaxation times. We reveal that this coefficient is typically considerably greater than unity so that small normalized PI values may well correspond to quite large long-term effects of coupling. The applicability of the derived relationship to wider classes of systems, its limitations, and its value for further research are discussed. To give a real-world example, we analyze couplings between large-scale climatic processes related to sea surface temperature variations in equatorial Pacific and North Atlantic regions.

From Granger causality to long-term causality: application to climatic data.

Quantitative characterization of interaction between processes from time series is often required in different fields of natural science including geophysics and biophysics. Typically, one estimates "short-term" influences, e.g., the widely used Granger causality is defined via one-step-ahead predictions. Such an approach does not reveal how strongly the "long-term" behavior of one process under study is affected by the others. To overcome this problem, we introduce the concept of long-term causality, which extends the concept of Granger causality. The long-term causality is estimated from data via empirical modeling and analysis of model dynamics under different conditions. Apart from mathematical examples, we apply both approaches to find out how strongly the global surface temperature (GST) is affected by variations in carbon dioxide atmospheric content, solar activity, and volcanic activity during the last 150 years. Influences of all the three factors on GST are detected with the Granger causality. However, the long-term causality shows that the rise in GST during the last decades can be explained only if the anthropogenic factor (CO2) is taken into account in a model.

Explaining the eventual transient saturation of climate-carbon cycle feedback.

BACKGROUND: Coupled climate-carbon cycle simulations generally show that climate feedbacks amplify the buildup of CO2 under respective anthropogenic emission. The effect of climate-carbon cycle feedback is characterised by the feedback gain: the relative increase in CO2 increment as compared to uncoupled simulations. According to the results of the recent Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP), the gain is expected to increase during the 21st century. This conclusion is not supported by the climate model developed at the A.M. Obukhov Institute of Atmospheric Physics at the Russian Academy of Sciences (IAP RAS CM). The latter model shows an eventual transient saturation of the feedback gain. This saturation is manifested in a change of climate-carbon cycle feedback gain which grows initially, attains a maximum, and then decreases, eventually tending to unity. RESULTS: Numerical experiments with the IAP RAS CM as well as an analysis of the conceptual framework demonstrate that this eventual transient saturation results from the fact that transient climate sensitivity decreases with time. CONCLUSION: One may conclude that the eventual transient saturation of the climate-carbon cycle feedback is a fundamental property of the coupled climate-carbon system that manifests itself on a relevant time scale.