Advertisement

Homogeneous Climate Regions Using Learning Algorithms

  • Mathilde Mougeot
  • Dominique Picard
  • Vincent Lefieux
  • Miranda Marchand
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 254)

Abstract

Climate analysis is extremely useful to understand better the differences of electricity consumption within the French territory and to help electricity consumption forecasts. Using a large historical data base of 14 years of meteorological observations, this work aims to study a segmentation of the French territory based on functional time series of temperature and wind. In a first step, 14 clustering instances, one for each year, have been performed using, for each instance, one year of data. Each year, the clustering exhibits several homogeneous and spatially connected regions. Benefits of this approach let to study the stability of the previous regions over the years and to highlight the inter-annual variability of the French climate. A final aggregation of all clustering instances shows a segmentation map in easily interpretable, geographically connected climate zones over the last years. Especially, we observe that the number of clusters remains extremely stable through the years. Exhibiting stable homogeneous regions bring then some valuable knowledge for potentially installing new wind or solar farms on the French territory.

Keywords

Climate segmentation Graph partitioning Clustering 

Notes

Acknowledgements

The authors thank RTE for the financial support through one industrial contract, LPSM for hosting our researches and Agence Nationale de la Recherche (ANR-14-CE05-0028) through the FOREWER project.

References

  1. 1.
    A. Antoniadis, X. Brossat, J. Cugliari, J.-M. Poggi, Une approche fonctionnelle pour la prevision non-parametrique de la consommation d’electricite. Journal de la Société Française de Statistique 155(2), 202–219 (2014)MathSciNetzbMATHGoogle Scholar
  2. 2.
    M. Bador, P. Naveau, E. Gilleland, M. Castellà, T. Arivelo, Spatial clustering of summer temperature maxima from the CNRM-CM5 climate model ensembles & E-OBS over europe. Weather Clim. Extrem. 9, 17–24 (2015)CrossRefGoogle Scholar
  3. 3.
    J.D. Banfield, A.E. Raftery, Model-based Gaussian and non-Gaussian clustering. Biometrics 803–821 (1993)MathSciNetCrossRefGoogle Scholar
  4. 4.
    T. Caliński, J. Harabasz, A dendrite method for cluster analysis. Commun. Stat. Theory Methods 3(1), 1–27 (1974)MathSciNetCrossRefGoogle Scholar
  5. 5.
    J. Friedman, T. Hastie, R. Tibshirani, The Elements of Statistical Learning. Springer Series in Statistics, vol. 1 (Springer, New York, 2001)Google Scholar
  6. 6.
    M. Girolami, Mercer kernel based clustering in feature space. IEEE Trans. Neural Netw. (2001)Google Scholar
  7. 7.
    J.A. Hartigan, M.A. Wong, Algorithm as 136: a k-means clustering algorithm. J. R. Stat. Soc. Ser. C (Appl. Stat.) 28(1), 100–108 (1979)zbMATHGoogle Scholar
  8. 8.
    A.K. Jain, M. Narasimha Murty, P.J. Flynn, Data clustering: a review. ACM Comput. Surv. (CSUR) 31(3), 264–323 (1999)CrossRefGoogle Scholar
  9. 9.
    G.M. James, T.J. Hastie, C.A. Sugar, Principal component models for sparse functional data. Biometrika 87(3), 587–602 (2000)MathSciNetCrossRefGoogle Scholar
  10. 10.
    W.J. Krzanowski, Y.T. Lai, A criterion for determining the number of groups in a data set using sum-of-squares clustering. Biometrics 23–34 (1988)MathSciNetCrossRefGoogle Scholar
  11. 11.
    J. Mairal, F. Bach, J. Ponce, Sparse modeling for image and vision processing. Found. Trends® Comput. Graph. Vis. 8(2–3), 85–283 (2014)CrossRefGoogle Scholar
  12. 12.
    S. Mika, B. Scholkopf, A. Smola, K.-R. Müller, M. Scholz, G. Ratsch, Kernel PCA and de-noising in feature spaces, in Advances in Neural Information Processing Systems 11 (MIT Press, Cambridge, 1999), pp. 536–542Google Scholar
  13. 13.
    M. Mougeot, D. Picard, V. Lefieux, L. Maillard-Teyssier, Forecasting intra day load curves using sparse functional regression, in Modeling and Stochastic Learning for Forecasting in High Dimensions (Springer, Berlin, 2015), pp. 161–181CrossRefGoogle Scholar
  14. 14.
    K.P. Murphy, Machine Learning: A Probabilistic Perspective (MIT Press, Cambridge, 2012)Google Scholar
  15. 15.
    J. Najac, J. Boé, L. Terray, A multi-model ensemble approach for assessment of climate change impact on surface winds in france. Clim. Dyn. 32(5), 615–634 (2009)CrossRefGoogle Scholar
  16. 16.
    A.Y. Ng, M.I. Jordan, Y. Weiss, On spectral clustering. Adv. Neural Inf. Process. Syst. 2, 849–856 (2002)Google Scholar
  17. 17.
    C. Radhakrishna Rao, The use and interpretation of principal component analysis in applied research. Sankhyā Indian J. Stat. Ser. A (1961–2002) 26(4), 329–358 (1964)MathSciNetzbMATHGoogle Scholar
  18. 18.
    J.O. Ramsay, B.W. Silverman, Applied Functional Data Analysis: Methods and Case Studies, vol. 77 (Springer, New York, 2002)CrossRefGoogle Scholar
  19. 19.
    J.O. Ramsay, B.W. Silverman, Springer Series in Statistics (Springer, Berlin, 2005)Google Scholar
  20. 20.
    J. Rissanen, Minimum Description Length Principle (Wiley Online Library, London, 1985)Google Scholar
  21. 21.
    P.J. Rousseeuw, Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)CrossRefGoogle Scholar
  22. 22.
    B. Schölkopf, A.J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (MIT Press, Cambridge, 2002)Google Scholar
  23. 23.
    J. Shi, J. Malik, Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRefGoogle Scholar
  24. 24.
    M. Stefanon, F. D’Andrea, P. Drobinski, Heatwave classification over Europe and the Mediterranean region. Environ. Res. Lett. 7(1), 014023 (2012)CrossRefGoogle Scholar
  25. 25.
    Syndicat des Énergies Renouvelables, Panorama de l’électricité renouvelable en 2015. Technical report, Syndicat des Énergies Renouvelables, 2015Google Scholar
  26. 26.
    R. Tibshirani, G. Walther, T. Hastie, Estimating the number of clusters in a data set via the gap statistic. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 63(2), 411–423 (2001)MathSciNetCrossRefGoogle Scholar
  27. 27.
    P.-J. Trombe, P. Pinson, H. Madsen, Automatic classification of offshore wind regimes with weather radar observations. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 7(1), 116–125 (2014)CrossRefGoogle Scholar
  28. 28.
    V.N. Vapnik, The Nature of Statistical Learning Theory (Springer, New York, 1995)CrossRefGoogle Scholar
  29. 29.
    U. Von Luxburg, A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)MathSciNetCrossRefGoogle Scholar
  30. 30.
    M. Vrac, Modélisions statistiques à différentes échelles climatiques et environnementales. HDR, Université Orsay, 2012Google Scholar
  31. 31.
    M. Vrac, A. Chédin, E. Diday, Clustering a global field of atmospheric profiles by mixture decomposition of copulas. J. Atmos. Ocean. Technol. 22(10), 1445–1459 (2005)CrossRefGoogle Scholar
  32. 32.
    J.H. Ward Jr., Hierarchical grouping to optimize an objective function. J. Am. Stat. Assoc. 58(301), 236–244 (1963)MathSciNetCrossRefGoogle Scholar
  33. 33.
    D. Yan, A. Chen, M.I. Jordan, Cluster forests. Comput. Stat. Data Anal. 66, 178–192 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mathilde Mougeot
    • 1
  • Dominique Picard
    • 1
  • Vincent Lefieux
    • 2
  • Miranda Marchand
    • 3
  1. 1.Université Paris Diderot, LPSM UMR 8001, Sorbonne Paris CitéParisFrance
  2. 2.RTE-EPT & UPMC-ISUPLa Défense CedexFrance
  3. 3.RTE-R&DILa Défense CedexFrance

Personalised recommendations