ECM3730: Mathematics of Climate Change

14. Climate Tipping Points and Dangerous Climate Change

Prof Peter Cox Harrison Room 336p.m.cox@exeter.ac.uk

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 PointThe tipping point is the .critical point ..at which the future state of the systemcan 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)

A Mathematician Explains Tipping Points

Initial equilibrium state Small Perturbation Return to Initial equilibrium stateDavid Stephenson University of Exeter

A Mathematician Explains Tipping Points

Initial equilibrium state Large Perturbation Flip to New equilibrium stateNot very sustainable in this case

Typical Characteristics of Systems with 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.

Tipping Points and Multiple EquilibriaClimate State Variable(e.g. Temperature, Ice-mass)Climate Control Variable(e.g. CO2 Concentration)

Tipping Points and Multiple EquilibriaClimate State Variable(e.g. Temperature, Ice-mass)Climate Control Variable(e.g. CO2 Concentration)Stable Climate:Climate Change proportional to forcingand reversible

Tipping Points and Multiple EquilibriaClimate State Variable(e.g. Temperature, Ice-mass)Climate Control Variable(e.g. CO2 Concentration)UnstableEquilibriumTIPPING POINT

Tipping Points and Multiple EquilibriaClimate State Variable(e.g. Temperature, Ice-mass)Climate Control Variable(e.g. CO2 Concentration)Abrupt Climate Change:System moves spontaneouslyto a new state independent of forcing

Typical Characteristics of Systems with 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 densityLenton T. M. et.al. PNAS 2008;105:1786-17932008 by National Academy of Sciences Tipping Points (Lenton et al., 2008)

Amazon Dieback: See last lecture and video tomorrowGreening of the SaharaGulf-streamCollapseHydrate Destabilization

Greening of the Sahara

Rock Painting from Tassili NAjjerEvidence of Fertile Sahara 6-9 kyr ago

NO VEGETATION FEEDBACK ON ATMOSPHEREClaussen and Gayler, 1997Multiple States arise from Atmosphere-Vegetation Interaction in mid-HoloceneArid SaharaGreen SaharaWITH VEGETATION FEEDBACK

Summer insolationB,C CLIMBER-2 results (Claussen et al., 1999) D proxy data (deMenocal et al., 2000)Eolian dustDynamic Simulation of Sahara through Holocene Vegetation fractionRainfall

Collapse of the Thermohaline Circulation (Gulf Stream)

Could the Gulf Stream CollapseUnder Global Warming ?

wouldnt be quite as dramatic as the Hollywood version.

but serious nonetheless

Salinity > 36 Salinity < 34 Deep Water Formation(Rahmstorf, Nature 2002)SurfaceDeepBottomThermohaline Circulation

Phase Diagram for Thermohaline CirculationRahmstorf, Climatic Change (2000)On StateOff State

Interglacial-mode of the Thermohaline CirculationHeat Transport by the THC keeps the north Atlantic up to 6oC warmer than it would otherwise beSlide Courtesy of Stefan Rahmsdorf

Glacial-mode of the Thermohaline CirculationDeep-water formation further south and a cold, ice-covered North AtlanticCould human-induced climate change lead to a similar shutdown of the THC ?Slide Courtesy of Stefan Rahmsdorf

Evidence of THC Instability ? :Dansgaard-Oeshger EventsGISP2 ice core, GreenlandSediments, subtropical AtlanticSST (C)d18O (per mil)Millennia before presentUp to 10 C warming within a decadeOther events: Heinrich events, 8k event, Younger DryasSlide Courtesy of Stefan Rahmsdorf

Source: IPCC TARWeakerGulf Streammost climate models predict a weakening but not a collapse of the Gulf Stream

Destabilization ofMethane Hydrates

Methane HydratesA crystalline solid in which water molecules form a cage-like structure around a methane moleculeOnly stable at high-pressures and low temperatures

Methane Hydrates and Climate Change

Global reserves of hydrates are not well known but could amount to 10,000 GtC in the ocean, i.e. about x2 fossil fuel reserves and 400 GtC under Arctic permafrost (MacDonald 1999).

Hydrates can be destabilised by reduced pressure or increased temperature.

It has been suggested that a number of past climate changes may have been associated with hydrate release, e.g. rapid warming 55 Myr ago, glacial terminations.

How will hydrates respond to future climate change?

Late Palaeocene Thermal Maximum (55 million yrs ago)Zachos et al., 2001Release of 1500-3000 GtC of light carbon5 to 7 oCWarming

Stability of Marine Hydrates (stable at low temperatures and high pressures)StableUnstable

Stability of Marine Hydrates (stable at low temperatures and high pressures)T = 2 oCat 500mT = 5 oCat 500mOcean Bottom at 500mGeothermal TemperatureGradient Through SedimentStableUnstable

Stability of Marine Hydrates (stable at low temperatures and high pressures)Potentially stable hydrate before warmingPotentially stable hydrate after warmingOcean Bottom at 500mGeothermal TemperatureGradient Through SedimentStableUnstableT = 2 oCat 500mT = 5 oCat 500m

Estimate of thickness of potentially stable hydrate layer (1)Depth of Hydrate phase boundary (Dickens and Quinby-Hunt, 1994):

D = K1 exp {K2 / (273.15 + T)} (1)

where K1, K2 are constants and T is temperature in oC, and D is the depth in equivalent metres of water.

Equation (1) is well approximated by a quadratic expansion about T = 0 oC

D ~ D0 {1 + c1 T + c2 T} (2)

Where D0, c1 and c2 are constants.

The geothermal temperature gradient, a, determines how T varies with depth through the sediment:

D Dbot = (T Tbot) / a (3)

Where Dbot is ocean depth, Tbot is ocean bottom temperature (i.e. at top of sediment), and a is the geothermal temperature gradient (~0.02 K/m)

Estimate of thickness of potentially stable hydrate layer (2)The boundaries at which hydrates are marginally stable are the depths at which the geothermal temperature profile (equation 3) intercepts the hydrate phase boundary (equation 2). Equating D as given by (2) and (3) gives a quadratic for the temperatures at these boundaries:a D0 c2 T2 + {c1 a D0 -1} T + Teff + a D0 = 0 (4)Where Teff = Tbot - a Dbot depends on both the ocean temperature and the ocean depth (i.e. pressure).The difference between the two roots of equation (4) represents the thickness of the potentially stable hydrate layer:H = H0 { 1 ( Teff + a D0 ) / ( Tcrit + a D0 )}0.5 (5)

Where Tcrit ~ -4.6 oC is the value of Teff at which no hydrate is stable, and H0 is a constant representing the potential hydrate thickness when Teff = - a D0

Potential Hydrate Thickness as a Function of Ocean Depth and TemperatureOcean bottom TGeothermal T gradientOcean depthCritical Conditionfor destabilisation as a function of ocean bottom temp and ocean depthWhere are the hydrates and how close are they to this threshold?

WikipediaMap of Known Hydrate Stores

ConclusionsThe notion of dangerous anthropogenic interference in the climate system, is most obviously defined with respect to threholds or tipping points in the response of the climate system to forcing factors.

Many potential Tipping Points have been identified, e.g.:Collapse of the Thermohaline Circulation (THC)Greening of the SaharaDestabilization of Methane HydratesDieback of the Amazon Rainforest.

These events can be considered as High-impact, Low Probability events.

..but we do not know the probability of crossing the relevant thresholds under future global warming.

*Map of potential policy-relevant tipping elements in the climate system, updated from ref. 5 and overlain on global population density. Subsystems indicated could exhibit threshold-type behavior in response to anthropogenic climate forcing, where a small perturbation at a critical point qualitatively alters the future fate of the system. They could be triggered this century and would undergo a qualitative change within this millennium. We exclude from the map systems in which any threshold appears inaccessible this century (e.g., East Antarctic Ice Sheet) or the qualitative change would appear beyond this millennium (e.g., marine methane hydrates). Question marks indicate systems whose status as tipping elements is particularly uncertain.*****Lets look at what such an ice core shows.This put out a major challenge to climatologists how can such abrupt changes happen?This is what my group studies, with the help of model simulations. We developed a theory for the DO events, and it works like this.*