Rate-dependent Tipping Points
in the Earth System
Peter Cox
Cat Luke, Owen Kellie-Smith
University of Exeter
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 ?
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)
Tipping Points and Multiple Equilibria
Climate Control Variable
(e.g. CO2 Concentration)
Climate State Variable
(e.g. Temperature, Ice-mass)
Tipping Points and Multiple Equilibria
Climate Control Variable
(e.g. CO2 Concentration)
Stable Climate:
Climate Change
proportional to forcing
and reversible
Climate State Variable
(e.g. Temperature, Ice-mass)
Tipping Points and Multiple Equilibria
TIPPING
POINT
Climate Control Variable
(e.g. CO2 Concentration)
Unstable
Equilibrium
Climate State Variable
(e.g. Temperature, Ice-mass)
Tipping Points and Multiple Equilibria
Climate Control Variable
(e.g. CO2 Concentration)
Abrupt Climate Change:
System moves spontaneously
to a new state independent of forcing
Climate State Variable
(e.g. Temperature, Ice-mass)
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.
Tipping Points
(Lenton et al., 2008)
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
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….
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 longterm….
Rate-dependent Tipping Points
Slow
–ve feedback
SLOW
VARIABLE
FLUX
Fast
+ve feedback
+
FAST
VARIABLE
Forcing of
Fast Loop
Tipping point can occur if forcing is “faster”
than the slow negative feedback loop
Tipping Points
(Lenton et al., 2008)
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
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 ?
Compost-Bomb Instability
Depletion of
Soil Carbon
Biochemical
Heat Release
SOIL
RESPIRATION
Slow
–ve feedback
-
Fast
+ve feedback
+
SOIL
CARBON
SOIL
TEMPERATURE
Global Warming
See Poster by Catherine Luke.....
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
Ts
Response
10K
8K
Ta
forcing
6K
Time (yrs)
Time (yrs)
Luke and Cox, in press
Numerical Solutions for
Dangerous Rate of Global Warming
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
Luke and Cox, in press
Stability of the
Climate-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 ?
Climate-Economy Coupling
Carbon Intensity
of Economy
Slow
–ve feedback
Economic
Growth
Climate
Damages
CO2
Emissions
Investment
GLOBAL
WEALTH
How fast can the global economy grow and still have a
‘soft landing’ for the climate-economy system ?
Simple Climate-Economy Model
Background CO2 Emissions Growth-rate of 1% and 4%
Without climate impacts
on economy
Economic Depression
due to Environmental
change
Dynamical Regimes in the Simple
Climate-Economy Model
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 ratedependent instabilities in the Earth system.
 These may represent a generic class of rate-dependent
Tipping Points.
Climate Change Projection
IMPACTS
IPCC WG2
CLIMATE CHANGE
CLIMATE IMPACTS
ON THE ECONOMY
IPCC WG1
GHG EMISSIONS
IPCC WG3
SOCIOECONOMICS
Impact of Biochemical Heat Release
Response to a Step Perturbation in T
Without decomposition heating
With decomposition heating
“Decomposition ‘self-heating’ is an essential process to account for,
capable of fostering a self-sustainable mobilization of soil carbon…”
Khvorostyanov et al., 2008
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 :
Stability Diagram for Peat Soils
Rsref = 0.5 kg C m-2 yr-1, q10 = 2.5
UNSTABLE
Warming
STABLE
Drying
Luke and Cox, in prep.
…not a sufficient condition for instability- also depends on rate of warming