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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.

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emergent constraints on earth system sensitivities
Emergent Constraints on Earth System Sensitivities

Peter Cox

Professor of Climate System Dynamics

University of Exeter

slide2

How can we constrain

long-term Earth System Projections

using short-term Observations ?

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?

The Timescale Problem in the Evaluation of Earth System Models
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
emergent constraints1
Emergent Constraints:

Using ESMs to identify the relationships between observable contemporary variability

and future sensitivity

an emergent constraint on carbon loss from tropical land under climate change
An Emergent Constraint on Carbon Loss from Tropical Land under Climate Change

published in February

slide9
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

slide10

DCL = b. DCO2 +g. DTL

CO2 Fertilization

Climate impact on land C

Change in

Land Carbon

=

+

x Change in CO2

x Change in Temperature

slide11

(a) Climate Impact on Tropical Land Carbon, gLT

GtC/K

  • How can we constrain this sensitivity?
rationale
The growth-rate of atmospheric CO2 varies significantly from year-to-year, and this variation is largely due to tropical land.Rationale
slide14

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

rationale1
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
rationale2
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
relationship between co 2 growth rate and tropical temperature observations1
Relationship between CO2 Growth-rate and Tropical Temperature - Observations

dCO2/dt (GtC/yr) = 5.1+/-0.9 dT (K)

slide21

Probability Density Function for

Climate Sensitivity of Tropical Forest

CO2-driven dieback in HadCM3LC

After IAV

Constraint

Prior C4MIP

PDF

slide22

Toy Model

to show variability constraint

on Climate Sensitivity

climate sensitivity to doubling co 2 remains uncertain1
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

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

historical increase in atmospheric co 2
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) ) }

Solution for Global Warming to Date

Dynamic solution lags the quasi equilibrium solution

observational constraints on effective climate parameters
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)

variability in d q 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

Variability in DQ (Hasselmann, 1976)

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
Power Spectra of Atmosphere and Ocean(North Atlantic Oscillation)

“White-noise” from

Atmosphere…..

…“reddened” by ocean

red noise spectrum
Red-noise Spectrum

Long-term

Sensitivity

of the

system

dT/dt ~ DQ/C

High-frequency limit

observational constraints on effective climate parameters1
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)

conclusions
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
slide33

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

slide34

Thanks!

Any Questions?

slide35

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