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

1. 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

2. Methodology: Training phase Transfer Function 20th century observations 20th century model simulations

3. Methodology: Projection phase Transfer Function ? 21sr century projection 21st century model simulations

4. Neural Networks and Bayesian statistics Two classes of error: Error on the weights Model-Data fit error

5. Neural 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:

6. 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

7. 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

8. Observations and models • Observations: • CRU data interpolated onto a 2.5°x2.5° grid • Models:

9. Too warm Temperature analysis

10. Too zonal Temperature analysis

11. Mean Temperature MWIs IPSL CNRM MPI UKMO NCAR GFDL MIROC

12. Four 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

13. MLP validation

14. MLP Validation for extrapolation

15. SRES A1B SRES A2 SRES B1

16. SRES A2 SRES A1B SRES B1

17. SSA: South of 30°S NSA: North of 30°S LPB: La Plata Basin SRES A2 SRES A1B SRES B1

19. MWIs

20. SRES A1B SRES A2 SRES B1

22. General 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).

23. Temperature: 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)

24. Temperature: 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

25. Precipitation-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.

26. General 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.

28. Sensitivity to MLP architecture

29. Likelihood Prior 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

30. Neural Networks Multi-layer Perceptron

31. Neural Networks Multi-layer Perceptron

32. Prior Likelihood Prior Distribution Likelihood Neural Networks and Bayesian statistics Density of parameters for a given data set D

33. To optimize Prior Distribution Model-Data fit error Neural Networks and Bayesian statistics Posterior Distribution as a function of the hyperparameters

34. JJA MAM SON Four seasons DJF

36. Precipitation: 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

37. 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.