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Iterative multiscale dynamic time warping (IMs-DTW): a tool for rainfall time series comparison

  • Mohamed Djallel DilmiEmail author
  • Laurent Barthès
  • Cécile Mallet
  • Aymeric Chazottes
Regular Paper
  • 27 Downloads

Abstract

In many domains, such as weather forecasting, hydrology or civil protection, it is an important issue to characterize rainfall variability and intermittency in, either or both, a given time period or area. A variety of sensors, for instance, rain gauges, weather radars and satellites, are widely used for this purpose. Techniques to establish the similarity between rainfall time series are commonly based on the comparison of some extracted characteristic parameters (cumulative rainfall height, extreme values, rain occurrence, mean rain rate, etc.). The present study focuses on the development of a tool allowing to compare directly rainfall time series at a fine temporal scale. It allows quantifying the dissimilarity between the time series and determining a nonlinear relationship between their time axes. This study presents an algorithm based on a multiscale dynamic time warping approach, and it is based on the DTW algorithm applied on an iterative multiscale framework called IMs-DTW. This proposed algorithm is well suited for rain time series allowing point-to-point pairing between pairs of rainfall time. It takes the intermittency and the non-stationarity of the precipitation process into account. An application to measurements observed by four pluviometers located in the Paris area makes it possible to interpret the obtained results and to compare the IMs-DTW with more usual statistical features.

Keywords

Multiscale dynamic time warping Rain gauges network Time series comparison Precipitations Warping path Measure of dissimilarity Spatiotemporal variability of the rain 

Notes

Acknowledgements

This work was supported by the CNES/TOSCA ATMEAU_GPM project. The authors gratefully acknowledge Météo France for providing rain gauges data from their Radome network.

References

  1. 1.
    Wang, S., Eick, C.F.: A data mining framework for environmental and geo-spatial data analysis. Int. J. Data Sci. Anal. 5(2–3), 83–98 (2018).  https://doi.org/10.1007/s41060-017-0075-9 CrossRefGoogle Scholar
  2. 2.
    Cristiano, E., Veldhuis, M., Giesen, N.: Spatial and temporal variability of rainfall and their effects on hydrological response in urban areas—a review In Hydrol. Earth Syst. Sci. 21, 3859–3878 (2017)CrossRefGoogle Scholar
  3. 3.
    Verrier, S., de Montera, L., Barthès, L., Mallet, C.: Multifractal analysis of African monsoon rain fields, taking into account the zero rain rates problem. J. Hydrol. 389(1), 111–120 (2010)CrossRefGoogle Scholar
  4. 4.
    Verrier, S., Mallet, C., Barthès, L.: Multiscaling properties of rain in the time domain, taking into account rain support biases. J. Geophys. Res. Atmosp. (2011).  https://doi.org/10.1029/2011jd015719 Google Scholar
  5. 5.
    Llasat, M.C.: An objective classification of rainfall events on the basis of their convective features. Application to rainfall intensity in the north east of Spain. Int. J. Climatol. 21, 1385–1400 (2001)CrossRefGoogle Scholar
  6. 6.
    Eagleson, P.S.: Dynamic Hydrology. McGraw-Hill, New York (1970)Google Scholar
  7. 7.
    Brown, B.G., Katz, R. W., Murphy, A.H.: Statistical analysis of climatological data to characterize erosion potential: 4. Freezing events in eastern Oregon/Washington. Oregon Agricultural Experiment Station Spec. Rep. No. 689, Oregon State University (1984)Google Scholar
  8. 8.
    Larsen, M.L., Teves, J. B.: Identifying individual rain events with a dense disdrometer network. Adv. Meteorol. (2015).  https://doi.org/10.1155/2015/582782
  9. 9.
    Dunkerley, D.: Rain event properties in nature and in rainfall simulation experiments: a comparative review with recommendations for increasingly systematic study and reporting. Hydrol. Process. 22(22), 4415–4435 (2008)CrossRefGoogle Scholar
  10. 10.
    Dunkerley, D.: Identifying individual rain events from pluviography records: a review with analysis of data from an Australian dryland site. Hydrol. Process. 22(26), 5024–5036 (2008)CrossRefGoogle Scholar
  11. 11.
    Cassisi, C., Montalto, P., Aliotta, M., Cannata, A., Pulvirenti, A.: Similarity measures and dimensionality reduction techniques for time series data mining, advances in data mining knowledge discovery and applications. In: Adem, K. (ed.) InTech.  https://doi.org/10.5772/49941 (2012)
  12. 12.
    Keogh, E., Pazzani, M.: Scaling up dynamic time warping for datamining applications. In: Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 285–289. Boston, MA (2000)Google Scholar
  13. 13.
    Goshtasby A.A.: Similarity and dissimilarity measures. Image Registration. Advances in Computer Vision and Pattern Recognition, Book, Chapter 2. Springer-Verlag London Limited (2012).  https://doi.org/10.1007/978-1-4471-2458-0_2
  14. 14.
    van Gennip, Y., Hunter, B., Ma, A., et al.: Unsupervised record matching with noisy and incomplete data. Int. J. Data Sci. Anal. 6(2), 109–129 (2018).  https://doi.org/10.1007/s41060-018-0129-7 CrossRefGoogle Scholar
  15. 15.
    Aghabozorgi, S., Shirkhorshidi, A.S., Wah, T.H.: Time-series clustering—a decade review. Inf. Syst. 53, 16–38 (2015)CrossRefGoogle Scholar
  16. 16.
    Sarda-Espinosa, A.: Comparing Time-Series Clustering Algorithms in R Using the dtwclust Package, R package. https://cran.rproject.Org/web/packages/dtwclust/vignettes/dtwclust.pdf (2017). Accessed 18 June 2018
  17. 17.
    Pearson, K.: Mathematical contributions to the theory of evolution. III. regression, heredity, and panmixia. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 187: 253–318. ISSN 1364-503X.  https://doi.org/10.1098/rsta.1896.0007 (1896)
  18. 18.
    Sung, P., Syed, Z., Guttag, J.: Quantifying morphology changes in time series data with skew. In: Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. International Conference on Acoustics, Speech and Signal Processing, pp. 477–480 (2009)Google Scholar
  19. 19.
    Rubner, Y., Tomasi, C., Guibas, L.J.: A metric for distributions with applications to image databases. In: Proceedings of IEEE ICCV, pp. 59–66 (1998)Google Scholar
  20. 20.
    Aronov, B., Har-Peled, S., Knauer, C., Wang, Y., Wenk, C.: “Fréchet distance for curves, revisited. In: ESA’06, London, UK, pp. 52–63, Springer (2006)Google Scholar
  21. 21.
    Huttenlocher, D.P., Klanderman, G.A., Rucklidge, W.J.: Comparing images using the Hausdorff distance. IEEE Trans. PAMI 15(9), 850–863 (1993)CrossRefGoogle Scholar
  22. 22.
    Sakoe, H., Chiba, S.: Dynamic programming algorithm optimization for spoken word recognition. In: IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-26 (1978)Google Scholar
  23. 23.
    Zhanga, Z., Tavenardb, R., Baillyb, A., Tangc, X., Tanga, P., Corpetti, T.: Dynamic time warping under limited warping path length. Inf. Sci. 393, 91–107 (2017)CrossRefGoogle Scholar
  24. 24.
    Tsiporkova E.: Dynamic Time Warping Algorithm for. PPT presentation available at: http://www.psb.ugent.be/cbd/papers/gentxwarper/DTWAlgorithm.ppt, date of the last visit (2013)
  25. 25.
    Sakoe, H., Chiba, S.: A similarity evaluation of speech patterns by dynamic programming. Dig. Nat. Meeting, Inst. Electron. Comm. Eng. Japan, p. 136 (1970)Google Scholar
  26. 26.
    Sakoe, H., Chiba, S.: A dynamic programming approach to continuous speech recognition. In: Proceedings of 7th ICA, Paper 20 CI3 (1971)Google Scholar
  27. 27.
    Zinke, A., Mayer, D.: Iterative Multi Scale Dynamic Time Warping. Computer Graphics technical reports, CG-2006/1 (2006)Google Scholar
  28. 28.
    Itakura, F.: Minimum prediction residual principle applied to speech recognition. In: IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-23, pp. 52–72 (1975)Google Scholar
  29. 29.
    Bellman, R., Dreyfus, S.: Applied Dynamic Programming. Princeton University Press, New Jersey (1962)CrossRefzbMATHGoogle Scholar
  30. 30.
    Sakoe, H., Chiba, S.: Comparative study of DP-pattern matching techniques for speech recognition. Technical Group Meeting Speech, Acoust.SOC. Japan, Preprints (S73-22) (1973)Google Scholar
  31. 31.
    Muller, M., Mattes, H., Kurth, F.: An efficient multiscale approach to audio synchronization. In: Proceedings of ISMIR, Victoria, Canada, pp. 192–197 (2006)Google Scholar
  32. 32.
    De Montera, L., Barthes, L., Mallet, C., Golé, P.: The Effect of rain-no rain intermittency on the estimation of the universal multifractals model parameters. J. Hydrometeorol. Am. Meteorol. Soc. 10(2), 493–506 (2009)CrossRefGoogle Scholar
  33. 33.
    Akrour, N., Chazottes, A., Verrier, S., Mallet, C., Barthès, L.: Simulation of yearly rainfall time series at microscale resolution with actual properties: Intermittency, scale invariance, and rainfall distribution. Water Resour. Res. Am. Geophys. Union 51(9), 7417–7435 (2015)CrossRefGoogle Scholar
  34. 34.
    Chu, S., Keogh, E., Hart D., Pazzani, M.: iterative deepening dynamic time warping for time series. In: Proceedings of the Second SIAM International Conference on Data Mining, Arlington, Virginia (2002)Google Scholar
  35. 35.
    Salvador, S., Chan, P.: FastDTW: toward accurate dynamic time warping in linear time and space. Intell. Data Anal. 11(5), 561–580 (2007)CrossRefGoogle Scholar
  36. 36.
    Tokay, A., Öztürk, K.: An experimental study of the small-scale variability of rainfall. J. Hydrometeorol. 13(1), 351–365 (2012)CrossRefGoogle Scholar
  37. 37.
    Dilmi, M.D., Mallet, C., Barthes, L., Chazottes, A.: Data-driven clustering of rain events: microphysics information derived from macro-scale observations. Atmos. Meas. Tech. 10, 1–18 (2017)CrossRefGoogle Scholar
  38. 38.
    Truong, C.D., Anh, D.T.: A novel clustering based method for time series motif discovery under time warping measure. Int. J. Data Sci. Anal. 4(2), 113–126 (2017).  https://doi.org/10.1007/s41060-017-0060-3 CrossRefGoogle Scholar
  39. 39.
    Endo, Y., Toda, H., Nishida, K., et al.: Classifying spatial trajectories using representation learning. Int. J. Data Sci. Anal. 2(3–4), 107–117 (2016).  https://doi.org/10.1007/s41060-016-0014-1 CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LATMOS/CNRS/UVSQ/Université Paris-SaclayGuyancourtFrance

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