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Emergent Constraints on Earth System Sensitivities
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Emergent Constraints on Earth System Sensitivities
Peter CoxProfessor of Climate System Dynamics
University of Exeter
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How can we constrain
long-term Earth System Projections
using short-term Observations ?
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Climate Sensitivity to Doubling CO2 remains uncertain….
Murphy et al., 2005
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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?
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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.
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Emergent Constraints:
Using ESMs to identify the relationships between observable
contemporary variability and future sensitivity
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Archetypal Example of an Emergent Constraint
Hall & Qu (2006)
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An Emergent Constraint on Carbon Loss from Tropical Land
under Climate Change
published in February
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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
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DCL = b. DCO2 + g. DTL
Change in
Land Carbon
CO2 Fertilizationx Change in CO2
Climate impact on land Cx Change in Temperature +=
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(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?
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Interannual Variability as
an Emergent Constraint
..on Tropical Forest Dieback...
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Rationale
The growth-rate of atmospheric CO2 varies significantly from year-to-year, and this variation is largely due to tropical land.
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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)
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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.
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Relationship between CO2 Growth-rate and Tropical Temperature - Observations
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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 ?
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Relationship between CO2 Growth-rate and Tropical Temperature - Observations
dCO 2/dt (GtC/yr) = 5.1+/-0.9 dT (K)
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(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
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Obs
erva
tiona
l Co
nstr
aint
IAV of dCO2/dt – Excellent Predictor of Sensitivity
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Probability Density Function for Climate Sensitivity of Tropical Forest
Prior C4MIPPDF
After IAVConstraint
CO2-driven dieback in HadCM3LC
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Toy Model
to show variability constraint
on Climate Sensitivity
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Climate Sensitivity to Doubling CO2 remains uncertain….
Murphy et al., 2005
Due to uncertainties in climate feedbacks….
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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
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Historical Increase in Atmospheric CO2
Near-exponential rise in CO2 concentration near-linear increase in Radiative Forcing….
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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
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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
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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
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Power Spectra of Atmosphere and Ocean(North Atlantic Oscillation)
“White-noise” fromAtmosphere…..
…“reddened” by ocean
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Red-noise Spectrum
Long-term Sensitivity
of the system
dT/dt ~ DQ/CHigh-frequency limit
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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
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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……
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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
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Thanks!
Any Questions?
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Small Sensitivityto Forcing
Larger Sensitivityto Forcing
StableEquilibrium
Less StableEquilibrium
Short and FastOscillations
Long and SlowOscillations
Stability, Sensitivity and Variability