Estimating the Probability of Thermohaline Collapse and Rapid Climate Change

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Estimating the Probability of Thermohaline
Collapse and Rapid Climate Change

• Peter Challenor
• Southampton Oceanography Centre
• and
• Tyndall Centre for Climate Change Research
• UK

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• With thanks to Bob Marsh and
• Jamie Banasik

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Outline

• What is the thermohaline circulation?
• How might it collapse?
• Can it happen?

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Why is Europe warmer than Alaska?

• Is it the Gulf Stream?

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Why is Europe warmer than Alaska?

• Is it the Gulf Stream?
• No. The Kuroshio is a very similar current in the
  Pacific
• There is something else going on

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The Thermohaline Circulation

• The Gulf Stream and Kuroshio are components of
  the ocean circulation driven by the wind
• There is another component of the circulation
  driven by differences of density (density in the
  ocean is a function of temperature and salinity,
  hence thermohaline circulation)

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Summary

• Dense water sinks in the North Atlantic and moves
  south at the bottom of the ocean.
• This pulls warm water north at the surface.
• In the Atlantic the strength of the circulation
  is about 20 Sv (1 Sv106 m3s-1)

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A Simple Model

• The Stommel model

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Multiple equilibria of the THC (Stommel model)
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Thermohaline collapse

• In this very simple model it is possible to move
  from the current situation (with a thermohaline
  circulation) to a circulation without the
  Northward transport of heat.
• Is it possible for this to happen in real life?

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The Historical Evidence

• Ice core data
• Temperature inferred from air trapped in ice

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Temperature in central Greenland
Courtesy of Richard Alley
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Should we be worried?

• Global warming
• Change in fresh water flux to the ocean

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Model THC changes due to global warming
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Surface air temperature change 20-30 years after
THC shutdown by large freshwater input. THC
recovers after 120 years (Vellinga Wood, 2002).
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What is the risk?

• What is the probability of thermohaline collapse
  and hence rapid climate change?
• UK Rapid Climate Change Programme (20M over 5
  years, including a monitoring system)
• Similar programmes in other countries e.g.
  NORCLIM in Norway

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Estimating the probability of THC collapse

• Need to use a numerical model of the climate
  system
• Definition of THC collapse
• Develop methods for large climate models
• SACCO (statistical analysis of computer code
  outputs) method

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C-GOLDSTEIN

• Intermediate complexity climate model
• 36x36 grid
• 10 longitude 3-20 latitude
• 8 ocean depths

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C-GOLDSTEIN continued

• The atmosphere is an energy balance model
• This has some problems
• Zonal wind speeds are prescribed and we need to
  make some corrections to the freshwater fluxes

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Monte Carlo Method

• Simulate inputs
• Run the model
• Estimate the pdf of strength of the THC
• BUT the model is very expensive to run

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Bayesian method (Tony O'Hagan)

• Treat the model as an unknown function
• Model the unknown function as a Gaussian Process
• Estimate the properties of this function with a
  limited number of model runs

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Gaussian Processes

• Model our knowledge of an unknown function with a
  continuous stochastic process
• This has a Gaussian distribution everywhere.
• Mean function m(x)
• Variance v(x)
• And covariance function C(x1,x2)

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Prior

• m(x)h(x)Tb
• h(.) is a known vector of regressor functions
• b is a vector of unknown parameters
• v(x1,x2)s2c(x1-x2)
• c(x1,x2)exp(-(x1-x2)2)
• p(b,s2) ??s-2

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Posterior distribution of h

• E(h(x))m(x)h(x)Tb't(x)TA-1(y-Hb')
• b'(HTA-1H)-1HTA-1y
• yih(xi)
• H is the matrix h(x1)h(xn)T
• T(x)C(x,x1),C(x,xn)T
• And a variance given by
• Distribution is tn-q

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Estimating the smoothing parameters

• The function C(.,.) is not dealt with in a fully
  Bayesian way
• We need to estimate the parameters of C
• Use cross-validation.

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Sampling from the model output

• We can derive statistics by sampling from the
  distribution of the outputs
• To improve sampling efficiency use sampling
  design points (Oakley and OHagan, 2000)

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Sampling design points

• Add to the design extra points
• At these points sample from ?
• Use these sampled points as if they were extra
  data
• Resample at the sample design points
• Repeat

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The Experiment

• Look at probabilities of THC collapse under
  future GHG scenarios
• Increase CO2 at a constant rate (compound
  interest)
• After some time mitigate gases at a percentage
• All the time the natural system is removing CO2

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Initial conditions

• The model is spun up for 2000 years
• This gives us initial conditions of approximately
  2000 AD with an atmospheric CO2 concentration of
  350 ppm

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Parameters to vary

• Rate of CO2 increase
• Rate of CO2 mitigation
• Time mitigation starts
• Natural time scale for the removal of CO2
• Two parameters that modify the Atlantic-Pacific
  freshwater flux
• Equator to pole temperature difference
• Equator to pole humidity difference

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The Latin Hypercube

• We have d inputs and we want to run the model
  only n times
• Divide the range for each input parameter into n
  intervals of equal probability
• Randomly select a value for each input in each of
  the intervals
• For inputs 2d shuffle the order

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Parameters to vary

• Rate of CO2 increase 0, 3
• Rate of CO2 mitigation 0, 3
• Time mitigation starts 0, 150
• Time scale for the removal of CO2 150, 300
• Two freshwater flux parameters
• Equator to pole temperature difference 10, 20
• Equator to pole humidity difference 25, 125
• The experiment is run for 1000 years

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Some results
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Building the Emulator

• Extract data at 2050, 2100, 2150, 2200, 2250 and
  2500
• NB The model failed after 2150 on two runs so we
  have 294 points not 300
• Calculate smoothing parameters by
  cross-validation

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Testing the emulator

• Test emulator with the results of a 26 factorial
• 1 2
• 0.3 1
• 50 100
• 150 300
• 5 10
• 50 100

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A future climate scenario

• We need to build some future climate scenarios
  before we can estimates the probability of THC
  collapse
• The SRES (IPCC) scenarios are not suitable

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Scenario 1

• CO2 rise age U(0,2)
• age mitigation U(1,3)
• Start time mitigation U(25,75)
• Time scale for CO2 removal U(150,350)
• fwfsens1 U(10,20)
• fwfsens2 U(45,105)

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Simulations

• Time fixed at 100 years
• 300 sampling design points in separate Latin
  Hyper Cube
• Sampling design points sampled 100 times
• Inputs sampled 100 times for each set of design
  points
• 100x100 points sampled in total

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Probability of reduced THC strength
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Scenario 2

• CO2 rise age log N(-3.89,2.93)
• Mean 1.5 and 95thile 2.5
• age mitigation log N(-3.43,2.34)
• Mean 0.5 and 95thile 1.5
• Start time mitigation N(50,10)
• Time scale for CO2 removal N(250,50)
• fwfsens1 N(15,2)
• fwfsens2 N(75,15)

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• P(THC lt5)0.048
• THC strengths less than zero are possible
• The min here -2177 Sv is impossible (as is the
  max 117 Sv)
• We are extrapolating too far outside our original
  hypercube

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What next?

• Model uncertainty
• Better future scenarios
• Better way of dealing with time
• How good is the model?
• How does the model relate to reality?

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Model Uncertainty

• So far we have only included uncertainty on two
  model parameters (fwfsens1, fwfsens2)
• There are at least nineteen others we need to
  look at.

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What next?

• Model uncertainty
• Better future scenarios
• Better way of dealing with time
• How good is the model?
• How does the model relate to reality?

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Better Future Scenarios

• Expert opinion
• Integrated assessment models

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What next?

• Model uncertainty
• Better future scenarios
• Better way of dealing with time
• How good is the model?
• How does the model relate to reality?

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Better way of dealing with time

• At the moment we take time slices
• Better to look at output as a function of time
  and parameterise that function
• Functional data analysis

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What next?

• Model uncertainty
• Better future scenarios
• Better way of dealing with time
• How good is the model?
• How does the model relate to reality?

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How good is the model?

• The results depend on C-GOLDSTEIN
• How good is it?
• We know the atmosphere is very poor
• Does that matter?
• If we get todays THC right but nothing else is
  that OK?
• Calibrate the model

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Ocean data

• We dont have much oceanographic data
• It is impossible to directly measure the strength
  of the THC
• We may be able to measure the Meridional
  Overturning Circulation (MOC) which is related

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Monitoring the Atlantic MOC at 26.5N
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Test one model against another

• It is common in climate work to
  validate/calibrate a simple model against a more
  complex one
• Somewhere we need to bring in reality

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What next?

• Model uncertainty
• Better future scenarios
• Better way of dealing with time
• How good is the model?
• How does the model relate to reality?
• Goldstein and Rougier 2003
• http//www.maths.dur.ac.uk/stats/physpred/papers/d
  irectSim.pdf