Projection of future climate change conditions using IPCC

simulations, neural networks and Bayesian statistics.

Temperature and Precipitation mean state and seasonal cycle

in South America.

Projection of future climate change conditions using IPCC

simulations, neural networks and Bayesian statistics.

Temperature and Precipitation mean state and seasonal cycle

in South America.

Jean-Philippe Boulanger*, Fernando Martinez** and Enrique C. Segura**

*LOCEAN, UMR CNRS/IRD/UPMC, Tour 45-55/Etage 4/Case 100, UPMC, 4 Place Jussieu, 75252 Paris Cedex 05, France. Presently at Departamento de Ciencias de la Atmosfera y los Oceanos, University of Buenos Aires, Argentina

**Departamento de Ciencias la Computación, Facultad de Ciencias Exactas y Naturales, University of Buenos Aires, Argentina

Methodology: Training phaseMethodology: Training phase20

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Transfer Function

Methodology: Projection phaseMethodology: Projection phase21

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Transfer Function

?

Neural Networks and Bayesian statisticsNeural Networks and Bayesian statistics

Error on the weights

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exp(−Ew ) =α

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exp −α

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Model-Data fit error

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exp(−ED ) =β

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Two classes of error:

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ln p(D | α ,β ) = −αEw − βED −1

2ln A +

W

2lnα +

N

2ln β −

W + N

2ln(2π )

Neural Networks and Bayesian statisticsNeural Networks and Bayesian statistics

• The evidence procedure: a maximization problem

• Generalizing the hyperparameter concept:• Define one hyperparameter for each entry neuron• Compute a Model Weight index as:

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MWIi = (1/α i) / (1/α i)i

∑

Why using neural networks?Why using neural networks?

• The major critics to Bayesian methods is the subjective choice of the prior distribution

• Neural networks optimized by Bayesian methods define prior distributions linked to the NN architecture, not to the field or models under study (more objective)

• Most methods are based on a linear combination of model outputs (indices)

• NN optimized by Bayesian methods offer a non-linear combination of model spatial outputs (maps)

• The major limitation of NN is their reduced skill for extrapolation

What results do we expect?What results do we expect?

• A set of MWIs potentially generalized to a set of linear combination weights. • They indicate how much each model contributes to the model

mix. • To a certain extent, they should indicate a model skill (with

caution).

• A non-linear transfer function if the NN has skills for extrapolation

• A universal method based on objective definitions of the prior and likelihood distributions

Observations and modelsObservations and models

• Observations: • CRU data interpolated onto a 2.5°x2.5° grid

• Models: Model Name andInstitute

Ocean model Atmosphere model Land model Ice model

ipsl_cm4IPSL

OPA8.12x2L31

LMDZ.3- 96x72x19 ORCHIDEE1.3 LIM

cnrm_cm3Météo-France

OPA8.12x2L31

Arpege-Climat v3(T42L45, cy 22b+)

TRIP Gelato 3.10

mpi_echam5MPI

(1x1L41) ECHAM5 (T63L32) ECHAM5

ukmo_hadcm3UKMO

1.25 x 1.25 2.5 x 3.75 MOSES1

ncar_ccsm3_0NCAR

POP1.4.3, gx1v3 CAM3.0, T85L26 CLM3.0, gx1v3 CSIM5.0,T85

gfdl_cm2_1GFDL

OM3.1(mom4p1p7_om3p5,tripolar360x200L50)

AM2.1 (am2p13fv,M45L24)

LM2 SIS

miroc3_2_medresMIROC

COCO3.3256x192 L44

AGCM5.7b, T42 L20 MATSIRO T42 COCO3.3,256x192L44

Temperature analysisTemperature analysis

Too warm

Temperature analysisTemperature analysis

Too zonal

Mean Temperature MWIsMean Temperature MWIs

IPSL CNRM MPI UKMO NCAR GFDL MIROC

Four season MWIsFour season MWIs

IPSL CNRM MPI UKMO NCAR GFDL MIROC

IPSL CNRM MPI UKMO NCAR GFDL MIROC

IPSL CNRM MPI UKMO NCAR GFDL MIROC

IPSL CNRM MPI UKMO NCAR GFDL MIROC

MLP validationMLP validation

MLP Validation for extrapolationMLP Validation for extrapolation

SRES A2

SRES A1B

SRES B1

SRES A2SRES A1BSRES B1

SSA:South of 30°S

NSA:North of 30°S

LPB:La Plata Basin

SRES A2

SRES A1B

SRES B1

MWIs

SRES A2

SRES A1B

SRES B1

General Conclusions-MethodGeneral Conclusions-Method

• NN optimized by Bayesian method may allow:• Computing MWIs representative of model skills• Evaluating an optimal linear combination of climate models• Defining an objective prior distrbution independent on the

problem under study

• BUT their skill in extrapolating is case-dependent and leads to very different behavior and conclusions.

• Further analysis are required, with a larger ensemble of models and over different regions of the world (more regional approach).

Temperature: conclusions-1Temperature: conclusions-1

• MLP optimized by Bayesian methods lead to estimate the optimal set of weights for combining linearly IPCC climate models

• MLP skill for extrapolation is low due to the common and large trend of temperature among models, which make future values be out of present climate data distribution

• MLP projection allows deriving a level of confidence in the projection, which summarizes linear model combination error and model dispersion (or disagreement in future changes)

Temperature: conclusions-2Temperature: conclusions-2

• Large temperature increase over most of the continent with a seasonal cycle modulation• SRES A2 displays the largest warming. • SRES A1B projects a warming 80% that of SRES A2 in late 21st

century. • SRES B1 reaches about 60% of SRES A2 warming. All display the

same patterns.

• NSA: about 4°C increase with larger amplitudes over the Chilean and Peruvian coasts, the central Amazons and the Colombia-Venezuela-Guiana region. Amplitude of the seasonal cycle would be reduced.

• SSA: about 3°C increase, but the penalizing function is close to zero in the southern tip. Amplitude of the seasonal cycle would increase

Precipitation-ConclusionsPrecipitation-Conclusions

• In SRES A2, annual mean precipitation would decrease over Colombia-Venezuela-Guyana as well as part of the Amazons and the Chilean coasts, while it would increase at the equator on the Pacific side and between 20°S and 35°S along the Atlantic coasts.

• In the northern part of South America, precipitation increases in summer and decreases in winter. During austral summer, the South American Monsoon would be weaker. Nordeste would receive less precipitation in austral summer and fall, but more precipitation in winter and spring.

• Other scenarios (A1B and B1) strongly resemble the SRES A2 trends but with weaker amplitudes.

General Conclusions-ResultsGeneral Conclusions-Results• In a much warmer climate as the one projected, it is

likely that changes in winter conditions may increase the risk of development of Dengue southward of its actual position.

• This is only one example of potential climate impact on society, there is no doubt that other diseases as well as crop yields may also be affected in such conditions.

• The study of such impacts in South America is under analysis in the framework of the European CLARIS Project (http://www.claris-eu.org).

• Our results must be compared to other methods to evaluate whether they all converge toward similar projections.

Sensitivity to MLP architectureSensitivity to MLP architecture

Multi-model ensemble and Bayesian methods

Multi-model ensemble and Bayesian methods

• Optimally combine models based on their skills in simulating present climate conditions

• Works by Giorgio et al. (2001), Giorgi and Mearns (2002) and Tebaldi et al. (2004) based on Bayesian statistics offers an interesting method to project climate indices

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p(λ i | Mn{ }n=1,N

) =p(M = Data | λ i) p(λ i)

p(M = Data)PriorLikelihood

Neural NetworksNeural Networks

Multi-layer Perceptron

Neural NetworksNeural Networks

Multi-layer Perceptron

Neural Networks and Bayesian statisticsNeural Networks and Bayesian statistics

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p(w | D) =p(D | w)p(w)

p(D)Density of parameters for a given data set D

Prior Distribution

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p(w) =α

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Likelihood

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p(D | w) =β

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exp −β

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Prior

Likelihood

Neural Networks and Bayesian statisticsNeural Networks and Bayesian statistics

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p(w | D) = p(w,α ,β | D)dαdβ∫∫p(w | D) ≈ p(w |α MP ,β MP ,D) p(α ,β | D)dαdβ∫∫

Prior Distribution

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p(w) =α

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Model-Data fit error

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p(D | w) =β

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Posterior Distribution as a function of the hyperparameters

To optimize

Four seasonsFour seasons

DJF

MAM

JJA

SON

Precipitation: A different fieldPrecipitation: A different field

• Climate models poorly simulate the precipitation fields (mean and variability)

• Climate models strongly disagree in simulating future changes

BUT

• Most of the climate models project future mean precipitation values similar or close to the range of present climate distribution

What can we expect?What can we expect?

• MWIs are unlikely to be useful to create an optimal linear combination.

BUT• MWIs may represent the model skills in

simulating the large scale structures.

• The MLPs may actually be used directly to project climate change model outputs optimally combining the models and correcting the model biases.