Rate-dependent Tipping Points in the Earth System

Peter CoxCat 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 State Variable(e.g. Temperature, Ice-mass)

Climate Control Variable(e.g. CO2 Concentration)

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)

Tipping Points and Multiple Equilibria

UnstableEquilibrium

TIPPINGPOINT

Climate State Variable(e.g. Temperature, Ice-mass)

Climate Control Variable(e.g. CO2 Concentration)

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

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.

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)

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 long-term….

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

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)

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

SOILCARBON

SOILTEMPERATURE

+

Fast +ve feedback

Slow –ve feedback

-

Global Warming

See Poster by Catherine Luke.....

SOILRESPIRATION

Depletion ofSoil Carbon

BiochemicalHeat Release

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)

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

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 ?

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

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 rate-dependent instabilities in the Earth system.

These may represent a generic class of rate-dependent Tipping Points.

Climate Change Projection

SOCIOECONOMICS

GHG EMISSIONS

CLIMATE CHANGE

IMPACTS

IPCC WG3

IPCC WG1

IPCC WG2

CLIMATE IMPACTSON THE ECONOMY

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

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 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