Emergent Constraints on Earth System Sensitivities

1. Emergent Constraints on Earth System Sensitivities Peter Cox Professor of Climate System Dynamics University of Exeter

2. How can we constrain long-term Earth System Projections using short-term Observations ?

3. Climate Sensitivity to Doubling CO2 remains uncertain…. Murphy et al., 2005

4. We need to find constraints on changes in the Earth System over the next century BUT The observational data that we have relates to shorter timescales. What can we do? The Timescale Problem in the Evaluation of Earth System Models

5. First coined in the context of climate projections by Allen & Ingram (2002) Emergent Constraint : a relationship between an Earth System sensitivity to anthropogenic forcing and an observable (or already observed) feature of the ES. Emergent because it emerges from the ensemble of ESMs. Constraint because it enables an observation to constrain the estimate of the ES sensitivity in the real world. Emergent Constraints

6. Emergent Constraints: Using ESMs to identify the relationships between observable contemporary variability and future sensitivity

7. Archetypal Example of an Emergent Constraint Hall & Qu (2006)

8. An Emergent Constraint on Carbon Loss from Tropical Land under Climate Change published in February

9. Uncertainty in Future Land Carbon Storage in Tropics (30oN-30oS) C4MIP Models (Friedlingstein et al., 2006) Models with climate affects on Carbon Cycle Models without climate affects on Carbon Cycle DCL = b. DCO2 DCL = b. DCO2 +g. DTL

10. DCL = b. DCO2 +g. DTL CO2 Fertilization Climate impact on land C Change in Land Carbon = + x Change in CO2 x Change in Temperature

11. (a) Climate Impact on Tropical Land Carbon, gLT GtC/K • How can we constrain this sensitivity?

12. Interannual Variability as an Emergent Constraint ..on Tropical Forest Dieback...

13. The growth-rate of atmospheric CO2 varies significantly from year-to-year, and this variation is largely due to tropical land. Rationale

14. 10 Total CO2 emissions 8 6 CO2 Partitioning (PgC y-1) 4 Atmosphere 2 1970 1980 2010 2000 1960 1990 Time (y) Interannual Variability in CO2 Growth-rate Evolution of the fraction of total emissions that remain in the atmosphere Updated from Le Quéré et al. 2009, Nature Geoscience; Data: NOAA 2010, CDIAC 2010

15. The growth-rate of atmospheric CO2 varies significantly from year-to-year, and this variation is largely due to tropical land. These variations are driven by climate variability especially ENSO. Rationale

16. Relationship between CO2 Growth-rate and Tropical Temperature - Observations

17. The growth-rate of atmospheric CO2 varies significantly from year-to-year, and this variation is largely due to tropical land. These variations are driven by climate variability especially ENSO. Can we use the interannual variability in the CO2 growth-rate as a constraint on the sensitivity of tropical land carbon to climate change ? Rationale

18. Relationship between CO2 Growth-rate and Tropical Temperature - Observations dCO2/dt (GtC/yr) = 5.1+/-0.9 dT (K)

19. (a) Climate Impact on Tropical Land Carbon, gLT GtC/K Observed GtC/yr/K

20. IAV of dCO2/dt – Excellent Predictor of Sensitivity Observational Constraint

21. Probability Density Function for Climate Sensitivity of Tropical Forest CO2-driven dieback in HadCM3LC After IAV Constraint Prior C4MIP PDF

22. Toy Model to show variability constraint on Climate Sensitivity

23. Climate Sensitivity to Doubling CO2 remains uncertain…. Murphy et al., 2005 Due to uncertainties in climate feedbacks….

24. Global warming, DT (K), due to radiative forcing, DQ (W m-2) : C. dDT/dt + l. DT = DQ Simplest Linear Climate Model Climate Feedback Factor (W m-2 K-1) Areal heat capacity (W yr m-2 K-1) where DQ depends on the changing concentrations of greenhouse gases and aerosols (particulates), as well as natural factors such as solar variability etc. Hasselmann , 1976

25. Historical Increase in Atmospheric CO2 Near-exponential rise in CO2 concentration  near-linear increase in Radiative Forcing….

26. C. dDT/dt + l. DT = a.t Initial condition; dT(0)=0.0  DT = a / l{ t – C /l ( 1 - exp(-l/C.t) ) } Solution for Global Warming to Date Dynamic solution lags the quasi equilibrium solution

27. Observational Constraints on Effective Climate Parameters Too Little Global Warming by now Parameter Degeneracy Areal Heat Capacity (W yr m-2 K-1) Too Much Global Warming by now Climate Sensitivity to doubling CO2 (K)

28. The radiative forcing, DQ (W m-2), can be considered as a fourier series of sinusoidal forcings: Thus the equation for each fourier mode is: The solution to this is: where: or recognising the system timescale Variability in DQ (Hasselmann, 1976) Relates the response of the system at different frequencies/timescales to the characteristic timescale of the system

29. Power Spectra of Atmosphere and Ocean(North Atlantic Oscillation) “White-noise” from Atmosphere….. …“reddened” by ocean

30. Red-noise Spectrum Long-term Sensitivity of the system dT/dt ~ DQ/C High-frequency limit

31. Observational Constraints on Effective Climate Parameters Too Little Global Warming by now Hypothetical Constraint from Interannual Variability Areal Heat Capacity (W yr m-2 K-1) Too Much Global Warming by now Climate Sensitivity to doubling CO2 (K)

32. The observed year-to-year variability in atmospheric CO2 has been found to givea very useful emergent constraint on future loss of tropical land carbon. Other emergent constraints (i.e. relationships between observable variability and sensitivity across the model ensemble) almost certainly exist, but we desperately need a theoretical basis to guide the search of the high-dimensional model archive. This suggests a hybrid approach combining underpinning theory and hypothesis testing by interrogating the ESM archive to derive Emergent Constraints…… Conclusions

33. Hybrid approach to find Emergent Constraints Underlying Simple Model FDT Sensitivity Variability Is this relationship confirmed in ESMs? YES NO Revise Simple Model Emergent Constraint

34. Thanks! Any Questions?

35. Stability, Sensitivity and Variability Small Sensitivity to Forcing Stable Equilibrium Short and Fast Oscillations Larger Sensitivity to Forcing Less Stable Equilibrium Long and Slow Oscillations