Long-range memory in Earths climate response and its implications for future global warming

Atmospheric CO2 traps some of the heat radiated from the Earth surface, and a rapid supply of this greenhouse gas leads to a temporary imbalance where the Earth receives more energy from solar radiation than it loses to space in the form of radiated heat. The Earth avoids being heated indefinitely by this energy flux because the outgoing radiation increases when the surface temperature increases. The conventional wisdom has therefore been that the response to increased CO2 concentration will be a rapid temperature rise which comes to a halt when a new energy balance has been established. This view is contested by modern climate models that describe ocean dynamics more realistically. They show that it may take a long time to restore the energy balance. The solar influx does not only heat the upper layers of the oceans; there is also a slow vertical heat transport driven by ocean circulation. This mean that if the net energy influx has a rapid increase due to human-caused CO2 emissions, then a rapid increase of the surface-layer temperature will be followed by a slower temperature rise lasting for centuries. In mathematical terms we describe this phenomenon as long-range memory. In the period when this slow warming takes place, the planet will receive more energy than it emits to space, and this will have long-term implications. The global temperature has already increased about one degree C during the last 150 years. Calculations we have published in Journal of Climate demonstrate that even if the CO2 concentration were kept constant on today?s level the temperature would rise another degree up to year 2100. In a world without emission restrictions we can expect one percent increase in CO2 concentrations per year, and this will lead to another three degrees within year 2100 and eight degrees within 2200. Our estimates are based on statistical long-range memory in the observed temperature records, but they agree very well with what we observe in climate models. In our project we replaced the extremely complex general circulation climate models by simple linear response models. They turn out to give similar projections and similar uncertainties of the global mean surface temperature as the complex climate models. We cannot claim they give better estimates, but they demonstrate that for the global temperature most of the information and costly computation of the complex models are idle. What is important are the strength and memory structure of the climate response, which is reflected in the linear response function. Complex carbon cycle models indicate that a linear long-memory response function may be an appropriate approximation of how the climate system responds to a sudden release of CO2 to the atmosphere. Using such a law to compute the projected CO2 concentration and corresponding forcing, and inserting this forcing into the temperature response model, yield a closed model for the projected temperature in any given emission scenario. Computations take seconds on a laptop, which allows costless play with scenarios and makes the model very suitable as a climate module in integrated economic models. The model is also very suitable as a pedagogical tool, since one can study interactively the effect of various scenarios and the effect of varying parameters in the model, and hence get a grip on the effect of model uncertainty. The long memory in the climate response is expressed mathematically as a power-law function. Such a function has the property of being scale invariant, i.e. the function takes the same form independent on which scale we are looking at. Many researchers interpret this scaling as a signature of a turbulent cascade resulting from the nonlinear nature of the equations describing the climate dynamics. We have demonstrated, however, that this interpretation is unreasonable as an explanation of scaling in global temperature and have shown that the scaling can result from linear interaction between different parts of the climate system with different response times, such as different layers of the oceans. In our modeling, the internal natural variability of the climate system can be described as a long-memory response to the atmospheric short-memory weather noise. The resulting long-memory noise has been shown to prevail as a background noise also during ice ages, interrupted by sudden intervals of warmer climate called Dansgaard-Oeschger events. Using this fact we have been able to develop a method that allows detection of early-warning signals and hence prediction of these events. The generality of the method expands the prospect of predicting tipping points in the climate system and other complex systems.

The Earth's climate is a driven complex system which responds to a variable radiative forcing on a vast range of time scales. This response is influenced by fast and slow feedbacks involving a large number of interacting subsystems encompassing atmosphe re, ocean mixed layer, thermohaline ocean circulations, snow and vegetation cover, sea ice and ice sheets, hydrosphere and lithosphere. The project explores the hypothesis that the temporal global temperature response can be modeled as a long-range memo ry (LRM) stochastic process on time scales from months to millennia, driven by both deterministic and random forcing. The LRM is a mathematical representation of the multitude of response times associated with the various subsystems. The project add resses the serious implications of such memory effects on future global warming due to the stronger disturbance of the Earth's energy balance under sustained forcing. Long-range memory leads to periods of apparent drift in the global temperature, which is random in nature, but often incorrectly interpreted as trends driven by external forcing. Thus, the long-range memory hypothesis leads to larger uncertainties in estimated trends in the temperature record, and suggests that many acclaimed cycles and t rends should rather be considered as inherent fluctuations of the climate system. The team will make an effort to improve our understanding of the physical dynamics underlying the long-range memory effects. This effort includes systematic analysis of instrumental and and paleoclimatic records for forcing and response, and data from a broad range of climate models; from simple conceptual models to sophisticated Earth-system models. A particular task will involve millennium-long runs of the state-of-t he-art NorESM. The project will announce one postdoc and one PhD fellowship to specialize on paleo-data and model data, respectively, and procure R&D services for statistical analysis and runs of NorESM.