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

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

Climate Sensitivity to Doubling CO 2 remains uncertain…. Murphy et al., 2005

The Timescale Problem in the Evaluation of Earth System Models 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?

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

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

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

Uncertainty in Future Land Carbon Storage in Tropics (30 o N-30 o S) C 4 MIP Models (Friedlingstein et al., 2006) Models without climate affects on Carbon Cycle Models with climate affects on Carbon Cycle  C L =  CO 2 +  T L  C L =  CO 2

 C L =  CO 2 +  T L Change in Land Carbon CO 2 Fertilization x Change in CO 2 Climate impact on land C x Change in Temperature + =

(a) Climate Impact on Tropical Land Carbon,  LT GtC/K  How can we constrain this sensitivity?

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

Rationale  The growth-rate of atmospheric CO 2 varies significantly from year-to-year, and this variation is largely due to tropical land.

Updated from Le Quéré et al. 2009, Nature Geoscience; Data: NOAA 2010, CDIAC 2010 Interannual Variability in CO 2 Growth-rate Evolution of the fraction of total emissions that remain in the atmosphere Total CO 2 emissions Atmosphere CO 2 Partitioning (PgC y -1 ) Time (y)

Rationale  The growth-rate of atmospheric CO 2 varies significantly from year-to-year, and this variation is largely due to tropical land.  These variations are driven by climate variability especially ENSO.

Relationship between CO 2 Growth-rate and Tropical Temperature - Observations

Rationale  The growth-rate of atmospheric CO 2 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 CO 2 growth-rate as a constraint on the sensitivity of tropical land carbon to climate change ?

Relationship between CO 2 Growth-rate and Tropical Temperature - Observations dCO 2 /dt (GtC/yr) = 5.1+/-0.9 dT (K)

(a) Climate Impact on Tropical Land Carbon,  LT GtC/K (b) Sensitivity of CO 2 Growth-Rate to Tropical Temperature GtC/yr/K Observed

Observational Constraint IAV of dCO 2 /dt – Excellent Predictor of Sensitivity

Probability Density Function for Climate Sensitivity of Tropical Forest Prior C 4 MIP PDF After IAV Constraint CO 2 -driven dieback in HadCM3LC

Toy Model to show variability constraint on Climate Sensitivity

Climate Sensitivity to Doubling CO 2 remains uncertain…. Murphy et al., 2005 Due to uncertainties in climate feedbacks….

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

Historical Increase in Atmospheric CO 2 Near-exponential rise in CO 2 concentration  near-linear increase in Radiative Forcing….

Solution for Global Warming to Date C. d  T/dt + .  T = .t Initial condition; dT(0)=0.0   T =  / { t – C / ( 1 - exp(- /C.t) ) } Dynamic solution lags the quasi equilibrium solution

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

Variability in  Q (Hasselmann, 1976) The radiative forcing,  Q (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 Relates the response of the system at different frequencies/timescales to the characteristic timescale of the system

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

Red-noise Spectrum Long-term Sensitivity of the system dT/dt ~  Q/C High-frequency limit

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

Conclusions  The observed year-to-year variability in atmospheric CO 2 has been found to give a 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……

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

Thanks! Any Questions?

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