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Rate-dependent Tipping Points in the Earth System
Peter CoxCat Luke, Owen Kellie-Smith
University of Exeter
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United Nations Framework Convention on Climate Change (UNFCCC)
“The ultimate objective [is]….
stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system…”
Introduces the notion of “Dangerous” Climate Change…
….but how can this be defined ?
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Definitions of Tipping Point
“The tipping point is the ….critical point ..at which the future state of the system…can be switched into a qualitatively different state by small perturbations”
(based on Lenton et al., 2008)
“when the climate system is forced to cross some threshold, triggering a transition to a new state at a rate determined by the climate system itself and faster than the cause”
(Abrupt Climate Change, NAS, 2002)
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Tipping Points and Multiple Equilibria
Climate State Variable(e.g. Temperature, Ice-mass)
Climate Control Variable(e.g. CO2 Concentration)
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Tipping Points and Multiple Equilibria
Stable Climate:Climate Change proportional to forcingand reversible
Climate State Variable(e.g. Temperature, Ice-mass)
Climate Control Variable(e.g. CO2 Concentration)
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Tipping Points and Multiple Equilibria
UnstableEquilibrium
TIPPINGPOINT
Climate State Variable(e.g. Temperature, Ice-mass)
Climate Control Variable(e.g. CO2 Concentration)
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Tipping Points and Multiple Equilibria
Climate State Variable(e.g. Temperature, Ice-mass)
Climate Control Variable(e.g. CO2 Concentration)
Abrupt Climate Change:System moves spontaneously
to a new state independent of forcing
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Characteristics of Systems with “Classical” Tipping Points
Have more than one equilibrium state.
“Current” equilibrium becomes unstable at the Tipping Point (gain >1)
Magnitude and rate of change at the Tipping Point is a system feature and is independent of the forcing.
Crossing a Tipping Point may result in a new stable state, implying a degree of irreversibility or hysteresis.
Many possible climate Tipping Points have now been identified.
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Map of potential policy-relevant tipping elements in the climate system, updated from ref. 5 and overlain on global population density
Lenton T. M. et.al. PNAS 2008;105:1786-1793
©2008 by National Academy of Sciences
Tipping Points (Lenton et al., 2008)
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Characteristics of Systems with “Classical” Tipping Points
Have more than one equilibrium state.
“Current” equilibrium becomes unstable at the Tipping Point (gain >1)
Magnitude and rate of change at the Tipping Point is a system feature and is independent of the forcing.
Crossing a Tipping Point may result in a new stable state, implying a degree of irreversibility or hysteresis.
Many possible climate Tipping Points have now been identified.
In some cases these have been used to estimate dangerous global warming or dangerous levels of CO2….
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It may make more sense to think about Dangerous Rates of Change, because:
The impacts of climate change depend on the ability of natural and human system to adapt, and this depends fundamentally on how fast the change occurs.
Although the long-term “equilibrium” climate change is uncertain, rates of climate change are more strongly constrained by contemporary observations.
Focusing on rates of change may allow a more adaptive climate mitigation policy.
There are potential Tipping Points which are related more to the rate of change that its ultimate magnitude in the long-term….
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Rate-dependent Tipping Points
FLUX
SLOW VARIABLE
FAST VARIABLE
+
Fast +ve feedback
Slow –ve feedback
-
Forcing of Fast Loop
Tipping point can occur if forcing is “faster” than the slow negative feedback loop
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Map of potential policy-relevant tipping elements in the climate system, updated from ref. 5 and overlain on global population density
Lenton T. M. et.al. PNAS 2008;105:1786-1793
©2008 by National Academy of Sciences
Tipping Points (Lenton et al., 2008)
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Stability of Peatlands
Peatland soils are estimated to contain 400-1000 GtC
Peatland carbon and hydrology are tightly coupled, giving the possibility of two-equilibrium states and tipping points.
Could Peatland soils may also be destabilized by Biochemical Heat Release from decomposition ?
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Compost-Bomb Instability
SOILCARBON
SOILTEMPERATURE
+
Fast +ve feedback
Slow –ve feedback
-
Global Warming
See Poster by Catherine Luke.....
SOILRESPIRATION
Depletion ofSoil Carbon
BiochemicalHeat Release
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Numerical Solutions for Constant Rate of Global Warming
Cs (0) = 50 kg C m-2, W m-2 K-1
Rsref = 0.5 kg C m-2 yr-1, q10 = 2.5
Luke and Cox, in press
Ta
forcing6K
10K
8K
Ts
Response
Time (yrs) Time (yrs)
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Numerical Solutions for Dangerous Rate of Global Warming
Luke and Cox, in press
Dangerous Rate of Warming
Cs (0) = 50 kg C m-2, W m-2 K-1
Rsref = 0.5 kg C m-2 yr-1, q10 = 2.5
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Stability of theClimate-Economy System
Economies have a tendency to grow…..
Economic growth has been correlated with global CO2 emissions.
Global CO2 emissions lead to climate change.
Climate change impacts imply damages to the economy.
How might this climate impact on the economy affect the dynamics of the coupled Climate-Economy system ?
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Climate-Economy Coupling
CO2 Emissions
GLOBALWEALTH
Slow –ve feedback
How fast can the global economy grow and still have a ‘soft landing’ for the climate-economy system ?
EconomicGrowth
Carbon Intensity of Economy
InvestmentClimateDamages
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Simple Climate-Economy Model
Background CO2 Emissions Growth-rate of 1% and 4%
Without climate impacts on economy
Economic Depression due to Environmental
change
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Dynamical Regimes in the Simple Climate-Economy Model
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Conclusions
Many potential climate Tipping Points have been identified.
There have been attempts to use these Tipping Points to define dangerous levels of global warming or CO2 concentrations.
The ability of human and natural systems to adapt depends much more on the rate at which climate changes.
We have identified two very different examples of rate-dependent instabilities in the Earth system.
These may represent a generic class of rate-dependent Tipping Points.
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Climate Change Projection
SOCIOECONOMICS
GHG EMISSIONS
CLIMATE CHANGE
IMPACTS
IPCC WG3
IPCC WG1
IPCC WG2
CLIMATE IMPACTSON THE ECONOMY
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Impact of Biochemical Heat Release
“Decomposition ‘self-heating’ is an essential process to account for, capable of fostering a self-sustainable mobilization of soil carbon…”
Khvorostyanov et al., 2008
Without decomposition heating
With decomposition heating
Response to a Step Perturbation in T
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Simple Model of Impact of Soil Biochemical Heat Release
The stability of the soil is determined by the “Zimov Number” :
This represents the increase in biochemical heating per unit warming divided by the increase in heat loss per unit warming.
Soils are potentially unstable if :
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Stability Diagram for Peat SoilsRsref = 0.5 kg C m-2 yr-1, q10 = 2.5
STABLE
UNSTABLE
Warming
Drying
Luke and Cox, in prep.
…not a sufficient condition for instability- also depends on rate of warming