Emergent Constraints on Earth System Sensitivities

Peter CoxProfessor of Climate System Dynamics

University of Exeter

How can we constrain

long-term Earth System Projections

using short-term Observations ?

Climate Sensitivity to Doubling CO2 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 (30oN-30oS) C4MIP Models (Friedlingstein et al., 2006)

Models without climate affects on Carbon Cycle

Models with climate affects on Carbon Cycle

DCL = b. DCO2 + g. DTLDCL = b. DCO2

DCL = b. DCO2 + g. DTL

Change in

Land Carbon

CO2 Fertilizationx Change in CO2

Climate impact on land Cx Change in Temperature +=

(a) Climate Impact on Tropical Land Carbon, gLT Gt

C/K

HADLEY

IPSL MPI

CCSM1

FRCGC

LOOP

HadCM3C_st

d

HadCM3C_a

HadCM3C_h

-200

-160

-120

-80

-40

0

How can we constrain this sensitivity?

Interannual Variability as

an Emergent Constraint

..on Tropical Forest Dieback...

Rationale

The growth-rate of atmospheric CO2 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 CO2 Growth-rateEvolution of the fraction of total emissions that remain in the atmosphere

Total CO2 emissions

Atmosphere

CO2 P

artit

ioni

ng (P

gC y

-1)

1960 20101970 1990 20001980

10

8

6

4

2

Time (y)

Rationale

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.

Relationship between CO2 Growth-rate and Tropical Temperature - Observations

RationaleThe 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 ?

Relationship between CO2 Growth-rate and Tropical Temperature - Observations

dCO 2/dt (GtC/yr) = 5.1+/-0.9 dT (K)

(a) Climate Impact on Tropical Land Carbon, gLT Gt

C/K

(b) Sensitivity of CO2 Growth-Rate to Tropical Temperature

GtC/

yr/K

Observed

HADLEY

IPSL MPI

CCSM1

FRCGC

LOOP

HadCM3C_st

d

HadCM3C_a

HadCM3C_h

-200

-160

-120

-80

-40

0

HADLEY

IPSL MPI

CCSM1

FRCGC

LOOP

HadCM3C_st

d

HadCM3C_a

HadCM3C_h

Observed

0

4

8

12

16

Obs

erva

tiona

l Co

nstr

aint

IAV of dCO2/dt – Excellent Predictor of Sensitivity

Probability Density Function for Climate Sensitivity of Tropical Forest

Prior C4MIPPDF

After IAVConstraint

CO2-driven dieback in HadCM3LC

Toy Model

to show variability constraint

on Climate Sensitivity

Climate Sensitivity to Doubling CO2 remains uncertain….

Murphy et al., 2005

Due to uncertainties in climate feedbacks….

Simplest Linear Climate Model

Global warming, DT (K), due to radiative forcing, DQ (W m-2) :

C. dDT/dt + l. DT = DQ

Areal heat capacity(W yr m-2 K-1)

Climate Feedback Factor

(W 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

Historical Increase in Atmospheric CO2

Near-exponential rise in CO2 concentration near-linear increase in Radiative Forcing….

Solution for Global Warming to Date

C. dDT/dt + l. DT = a.t

Initial condition; dT(0)=0.0

DT = a / l { t – C /l ( 1 - exp(-l/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

Are

al H

eat C

apac

ity (W

yr m

-2 K

-1)

Climate Sensitivity to doubling CO2 (K)

Parameter Degeneracy

Variability in DQ (Hasselmann, 1976)

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

Relates the response of the systemat different frequencies/timescalesto the characteristic timescale of the system

Power Spectra of Atmosphere and Ocean(North Atlantic Oscillation)

“White-noise” fromAtmosphere…..

…“reddened” by ocean

Red-noise Spectrum

Long-term Sensitivity

of the system

dT/dt ~ DQ/CHigh-frequency limit

Too Much Global Warming

by now

Too Little Global Warming

by now

Observational Constraints on Effective Climate Parameters

Are

al H

eat C

apac

ity (W

yr m

-2 K

-1)

Climate Sensitivity to doubling CO2 (K)

Hypothetical Constraintfrom Interannual Variability

ConclusionsThe observed year-to-year variability in atmospheric

CO2 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 Sensitivityto Forcing

Larger Sensitivityto Forcing

StableEquilibrium

Less StableEquilibrium

Short and FastOscillations

Long and SlowOscillations

Stability, Sensitivity and Variability