1. Rate-dependent Tipping Points in the Earth System Peter Cox Cat Luke, Owen Kellie-Smith University of Exeter

2. United Nations Framework Convention on Climate Change (UNFCCC) The ultimate objective [is]…. stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system… Introduces the notion of Dangerous Climate Change… ….but how can this be defined ?

3. Definitions of Tipping Point The tipping point is the ….critical point..at which the future state of the system…can be switched into a qualitatively different state by small perturbations (based on Lenton et al., 2008) when the climate system is forced to cross some threshold, triggering a transition to a new state at a rate determined by the climate system itself and faster than the cause (Abrupt Climate Change, NAS, 2002)

4. Tipping Points and Multiple Equilibria Climate State Variable (e.g. Temperature, Ice-mass) Climate Control Variable (e.g. CO 2 Concentration)

5. Tipping Points and Multiple Equilibria Stable Climate: Climate Change proportional to forcing and reversible Climate State Variable (e.g. Temperature, Ice-mass) Climate Control Variable (e.g. CO 2 Concentration)

6. Tipping Points and Multiple Equilibria Unstable Equilibrium TIPPING POINT Climate State Variable (e.g. Temperature, Ice-mass) Climate Control Variable (e.g. CO 2 Concentration)

7. Tipping Points and Multiple Equilibria Climate State Variable (e.g. Temperature, Ice-mass) Climate Control Variable (e.g. CO 2 Concentration) Abrupt Climate Change: System moves spontaneously to a new state independent of forcing

8. Characteristics of Systems with Classical Tipping Points Have more than one equilibrium state. Current equilibrium becomes unstable at the Tipping Point (gain >1) Magnitude and rate of change at the Tipping Point is a system feature and is independent of the forcing. Crossing a Tipping Point may result in a new stable state, implying a degree of irreversibility or hysteresis. Many possible climate Tipping Points have now been identified.

9. Map of potential policy-relevant tipping elements in the climate system, updated from ref. 5 and overlain on global population density Lenton T. M. et.al. PNAS 2008;105:1786-1793 ©2008 by National Academy of Sciences Tipping Points (Lenton et al., 2008)

10. Characteristics of Systems with Classical Tipping Points Have more than one equilibrium state. Current equilibrium becomes unstable at the Tipping Point (gain >1) Magnitude and rate of change at the Tipping Point is a system feature and is independent of the forcing. Crossing a Tipping Point may result in a new stable state, implying a degree of irreversibility or hysteresis. Many possible climate Tipping Points have now been identified. In some cases these have been used to estimate dangerous global warming or dangerous levels of CO 2 ….

11. It may make more sense to think about Dangerous Rates of Change, because: The impacts of climate change depend on the ability of natural and human system to adapt, and this depends fundamentally on how fast the change occurs. Although the long-term equilibrium climate change is uncertain, rates of climate change are more strongly constrained by contemporary observations. Focusing on rates of change may allow a more adaptive climate mitigation policy. There are potential Tipping Points which are related more to the rate of change that its ultimate magnitude in the long- term….

12. Rate-dependent Tipping Points FLUX SLOW VARIABLE FAST VARIABLE + Fast +ve feedback Slow –ve feedback - Forcing of Fast Loop Tipping point can occur if forcing is faster than the slow negative feedback loop

13. Map of potential policy-relevant tipping elements in the climate system, updated from ref. 5 and overlain on global population density Lenton T. M. et.al. PNAS 2008;105:1786-1793 ©2008 by National Academy of Sciences Tipping Points (Lenton et al., 2008)

14. Stability of Peatlands Peatland soils are estimated to contain 400-1000 GtC Peatland carbon and hydrology are tightly coupled, giving the possibility of two-equilibrium states and tipping points. Could Peatland soils may also be destabilized by Biochemical Heat Release from decomposition ?

15. Compost-Bomb Instability SOIL CARBON SOIL TEMPERATURE + Fast +ve feedback Slow –ve feedback - Global Warming See Poster by Catherine Luke..... SOIL RESPIRATION Depletion of Soil Carbon Biochemical Heat Release

16. Numerical Solutions for Constant Rate of Global Warming C s (0) = 50 kg C m -2, W m -2 K -1 R sref = 0.5 kg C m -2 yr -1, q 10 = 2.5 Luke and Cox, in press T a forcing 6K 10K 8K T s Response Time (yrs)

17. Numerical Solutions for Dangerous Rate of Global Warming Luke and Cox, in press Dangerous Rate of Warming C s (0) = 50 kg C m -2, W m -2 K -1 R sref = 0.5 kg C m -2 yr -1, q 10 = 2.5

18. Stability of the Climate-Economy System Economies have a tendency to grow….. Economic growth has been correlated with global CO 2 emissions. Global CO 2 emissions lead to climate change. Climate change impacts imply damages to the economy. How might this climate impact on the economy affect the dynamics of the coupled Climate-Economy system ?

19. Climate-Economy Coupling CO 2 Emissions GLOBAL WEALTH Slow –ve feedback How fast can the global economy grow and still have a soft landing for the climate-economy system ? Economic Growth Carbon Intensity of Economy Investment Climate Damages

20. Simple Climate-Economy Model Background CO 2 Emissions Growth-rate of 1% and 4% Without climate impacts on economy Economic Depression due to Environmental change

21. Dynamical Regimes in the Simple Climate-Economy Model

22. Conclusions Many potential climate Tipping Points have been identified. There have been attempts to use these Tipping Points to define dangerous levels of global warming or CO 2 concentrations. The ability of human and natural systems to adapt depends much more on the rate at which climate changes. We have identified two very different examples of rate- dependent instabilities in the Earth system. These may represent a generic class of rate-dependent Tipping Points.

23. Climate Change Projection SOCIOECONOMICS GHG EMISSIONS CLIMATE CHANGE IMPACTS IPCC WG3 IPCC WG1 IPCC WG2 CLIMATE IMPACTS ON THE ECONOMY

24. Impact of Biochemical Heat Release Decomposition self-heating is an essential process to account for, capable of fostering a self-sustainable mobilization of soil carbon… Khvorostyanov et al., 2008 Without decomposition heating With decomposition heating Response to a Step Perturbation in T

25. Simple Model of Impact of Soil Biochemical Heat Release The stability of the soil is determined by the Zimov Number : This represents the increase in biochemical heating per unit warming divided by the increase in heat loss per unit warming. Soils are potentially unstable if :

26. Stability Diagram for Peat Soils R sref = 0.5 kg C m -2 yr -1, q 10 = 2.5 STABLE UNSTABLE Warming Drying Luke and Cox, in prep. …not a sufficient condition for instability- also depends on rate of warming