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 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
DCL = b. DCO2
Models with
climate affects on Carbon Cycle
DCL = b. DCO2 + g. DTL
DCL = b. DCO2
Change in
Land Carbon
=
CO2 Fertilization
x Change in CO2
+
+
g. DTL
Climate impact on land C
x Change in Temperature
-200
(a) Climate Impact on Tropical Land Carbon,
GtC/K
-160
-120
-80
-40
0
 How can we constrain this sensitivity?
gLT
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.
Interannual Variability in CO2 Growth-rate
CO2 Partitioning (PgC y-1)
Evolution of the fraction of total emissions that remain in the atmosphere
10
Total
CO2 emissions
8
6
4
Atmosphere
2
1960
1970
1980
1990
Time (y)
Updated from Le Quéré et al. 2009, Nature Geoscience; Data: NOAA 2010, CDIAC 2010
2000
2010
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
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.
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
-200
(a) Climate Impact on Tropical Land Carbon,
gLT
GtC/K
-160
-120
-80
-40
0
GtC/yr/K
16
12
8
4
0
(b) Sensitivity of CO2 Growth-Rate to Tropical Temperature
Observational
Constraint
IAV of dCO2/dt – Excellent Predictor of Sensitivity
Probability Density Function for
Climate Sensitivity of Tropical Forest
CO2-driven dieback in HadCM3LC
After IAV
Constraint
Prior C4MIP
PDF
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
Areal Heat Capacity (W yr m-2 K-1)
Observational Constraints on
Effective Climate Parameters
Too Little
Global Warming
by now
Too Much
Global Warming
by now
Climate Sensitivity to doubling CO2 (K)
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 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
High-frequency limit
dT/dt ~ DQ/C
Areal Heat Capacity (W yr m-2 K-1)
Observational Constraints on
Effective Climate Parameters
Too Little
Global Warming
by now
Hypothetical Constraint
from Interannual Variability
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 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……
Hybrid approach to find
Emergent Constraints
Underlying Simple Model
FDT
Variability
Sensitivity
Is this relationship confirmed in ESMs?
YES
Emergent Constraint
NO
Revise Simple Model
Thanks!
Any Questions?
Stability, Sensitivity and Variability
Stable
Equilibrium
Less Stable
Equilibrium
Small Sensitivity
to Forcing
Short and Fast
Oscillations
Larger Sensitivity
to Forcing
Long and Slow
Oscillations