No Access Submitted: 27 April 2020 Accepted: 13 July 2020 Published Online: 03 August 2020
Chaos 30, 083108 (2020); https://doi.org/10.1063/5.0012059
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We present a hybrid framework appropriate for identifying distinct dynamical regimes and transitions in a paleoclimate time series. Our framework combines three powerful techniques used independently of each other in time series analysis: a recurrence plot, manifold learning through Laplacian eigenmaps, and Fisher information metric. The resulting hybrid approach achieves a more automated classification and visualization of dynamical regimes and transitions, including in the presence of missing values, observational noise, and short time series. We illustrate the capabilities of the method through several pragmatic numerical examples. Furthermore, to demonstrate the practical usefulness of the method, we apply it to a recently published paleoclimate dataset: a speleothem oxygen isotope record from North India covering the past 5700 years. This record encodes the patterns of monsoon rainfall over the region and covers the critically important period during which the Indus Valley Civilization matured and declined. We identify a transition in monsoon dynamics, indicating a possible connection between climate change and the decline of the Indus Valley Civilization.
This work was supported by RIT’s Grant Writers’ Boot Camp for 2019.
  1. 1. P. J. Webster, V. O. Magana, T. Palmer, J. Shukla, R. A. Tomas, M. Yani, and T. Yasunari, “Monsoons: processes, predictability, and the prospects for prediction,” J. Geophys. Res. 1031, 14451–14510, https://doi.org/10.1029/97JC02719 (1998). https://doi.org/10.1029/97JC02719, Google ScholarCrossref
  2. 2. H. Flohn, “Large-scale aspects of the “summer monsoon” in South and East Asia,” J. Meteor Soc. Jpn. 75, 180–186 (1957). https://doi.org/10.2151/jmsj1923.35A.0_180, Google ScholarCrossref
  3. 3. S. Pincus and R. E. Kalman, “Irregularity, volatility, risk, and financial market time series,” Proc. Natl. Acad. Sci. U.S.A. 101, 13709–13714 (2004). https://doi.org/10.1073/pnas.0405168101, Google ScholarCrossref
  4. 4. T. M. Cronin, Paleoclimates: Understanding Climate Change Past and Present (Columbia University Press, 2009). Google Scholar
  5. 5. J. E. H. Davidson, D. B. Stephenson, and A. A. Turasie, “Time series modeling of paleoclimate data,” Environmetrics 27, 55–65 (2016). https://doi.org/10.1002/env.2373, Google ScholarCrossref
  6. 6. M. Mudelsee, Climate Time Series Analysis: Classical Statistical and Bootstrap Methods, 2nd ed. (Springer, 2014). Google Scholar
  7. 7. N. Malik, Y. Zou, N. Marwan, and J. Kurths, “Dynamical regimes and transitions in Plio-Pleistocene Asian monsoon,” Europhys. Lett. 97, 40009 (2012). https://doi.org/10.1209/0295-5075/97/40009, Google ScholarCrossref
  8. 8. H. H. Lamb, Climate: Present, Past and Future. Fundamentals and Climate Now (Routledge Revivals, 1972), Vol. 1. Google Scholar
  9. 9. H. A. Dijkstra, Nonlinear Climate Dynamics (Cambridge University Press, 2013). Google ScholarCrossref
  10. 10. E. N. Lorenz, “Deterministic nonperiodic flow,” J. Atmospheric Sci. 20, 130–148 (1963). https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2, Google ScholarCrossref
  11. 11. R. Bradley, Paleoclimatology: Reconstructing Climates of the Quaternary, 3rd ed. (Academic Press, 2015). Google Scholar
  12. 12. W. F. Ruddiman, Earth’s Climate: Past and Future, 3rd ed. (W. H. Freeman, 2014). Google Scholar
  13. 13. G. Kathayat, H. Cheng, A. Sinha, L. Yi, X. Li, H. Zhang, H. Li, Y. Ning, and R. L. Edwards, “The Indian monsoon variability and civilization changes in the Indian subcontinent,” Sci. Adv. 3, e1701296 (2017). https://doi.org/10.1126/sciadv.1701296, Google ScholarCrossref
  14. 14. N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence plots for the analysis of complex systems,” Phys. Rep. 438, 237–329 (2007). https://doi.org/10.1016/j.physrep.2006.11.001, Google ScholarCrossref
  15. 15. B. Erem, R. M. Orellana, D. E. Hyde, J. M. Peters, F. H. Duffy, P. Stovicek, S. K. Warfield, R. S. MacLeod, G. Tadmor, and D. H. Brooks, “Extensions to a manifold learning framework for time-series analysis on dynamic manifolds in bioelectric signals,” Phys. Rev. E 93, 042218 (2016). https://doi.org/10.1103/PhysRevE.93.042218, Google ScholarCrossref
  16. 16. A. L. Mayer, C. W. Pawlowski, and H. Cabezas, “Fisher information and dynamic regime changes in ecological systems,” Ecol. Model. 195, 72–82 (2006). https://doi.org/10.1016/j.ecolmodel.2005.11.011, Google ScholarCrossref
  17. 17. J.-P. Eckmann, S. O. Kamphorst, and D. Ruelle, “Recurrence plots of dynamical systems,” Europhys. Lett. 4, 973–977 (1987). https://doi.org/10.1209/0295-5075/4/9/004, Google ScholarCrossref
  18. 18. M. Belkin and P. Niyogi, “Laplacian eigenmaps and spectral techniques for embedding and clustering,” in Advances in Neural Information Processing Systems (MIT Press, 2001), Vol. 14, pp. 585–591. Google Scholar
  19. 19. A. T. Karunanithi, H. Cabezas, R. Frieden, and C. W. Pawlowski, “Detection and assessment of ecosystem regime shifts from Fisher information,” Ecol. Soc. 13, 22 (2008). http://www.ecologyandsociety.org/vol13/iss1/art22/. Google ScholarCrossref
  20. 20. E. Konig, H. Cabezas, and A. L. Mayer, “Detecting dynamic system regime boundaries with Fisher information: The case of ecosystems,” Clean Technol. Environ. Policy 21, 1471–1483 (2019). https://doi.org/10.1007/s10098-019-01718-9, Google ScholarCrossref
  21. 21. N. Ahmad, D. S. T. Eason, and H. Cabezas, “Using Fisher information to track stability in multivariate systems,” R. Soc. Open Sci. 3, 160582 (2016). https://doi.org/10.1098/rsos.160582, Google ScholarCrossref
  22. 22. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, 1997). Google Scholar
  23. 23. H. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1996). Google ScholarCrossref
  24. 24. H. Whitney, “Differentiable manifolds,” Ann. Math. 37, 645–680 (1936). https://doi.org/10.2307/1968482, Google ScholarCrossref
  25. 25. F. Takens, “Detecting strange attractors in turbulence,” in Lecture Notes in Mathematics (Springer Verlag, Berlin, 1981), Vol. 898, pp. 366. https://doi.org/10.1007/BFb0091924, Google ScholarCrossref
  26. 26. D. Aeyels, “Generic observability of differentiable systems,” SIAM J. Control Optim. 19, 595–603 (1981). https://doi.org/10.1137/0319037, Google ScholarCrossref
  27. 27. N. Packard, J. Crutchfield, J. Farmer, and R. Shaw, “Geometry from a time series,” Phys. Rev. Lett. 45, 712–715 (1980). https://doi.org/10.1103/PhysRevLett.45.712, Google ScholarCrossref
  28. 28. T. Sauer, J. A. Yorke, and M. Casdagli, “Embedology,” J. Stat. Phys. 65, 579–616 (1991). https://doi.org/10.1007/BF01053745, Google ScholarCrossref
  29. 29. E. Ott, T. Sauer, and J. A. Yorke, Coping with Chaos: Analysis of Chaotic Data and the Exploitation of Chaotic Systems (Wiley Interscience, 1994). Google Scholar
  30. 30. E. Bradley and H. Kantz, “Nonlinear time-series analysis revisited,” Chaos 25, 097610 (2015). https://doi.org/10.1063/1.4917289, Google ScholarScitation
  31. 31. M. Casdagli, “Nonlinear forecasting, chaos and statistics,” in Modeling Complex Phenomena, edited by L. Lam and V. Naroditsky (Springer, New York, 1992), pp. 131–152. Google Scholar
  32. 32. C. J. Cellucci, A. M. Albano, and P. Rapp, “Comparative study of embedding methods,” Phys. Rev. E 67, 066210 (2003). https://doi.org/10.1103/PhysRevE.67.066210, Google ScholarCrossref
  33. 33. R. Hegger, H. Kantz, L. Matassini, and T. Schreiber, “Coping with nonstationarity by overembedding,” Phys. Rev. Lett. 84, 4092 (2000). https://doi.org/10.1103/PhysRevLett.84.4092, Google ScholarCrossref
  34. 34. J.-P. Eckmann and D. Ruelle, “Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems,” Physica D 56, 185–187 (1992). https://doi.org/10.1016/0167-2789(92)90023-G, Google ScholarCrossref
  35. 35. R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, “Recurrence networks—A novel paradigm for nonlinear time series analysis,” New J. Phys. 12, 033025 (2010). https://doi.org/10.1088/1367-2630/12/3/033025, Google ScholarCrossref
  36. 36. Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, and J. Kurths, “Complex network approaches to nonlinear time series analysis,” Phys. Rep. 787, 1–97 (2019). https://doi.org/10.1016/j.physrep.2018.10.005, Google ScholarCrossref
  37. 37. K. Levin and V. Lyzinski, “Laplacian eigenmaps from sparse, noisy similarity measurements,” IEEE Trans. Signal Process. 65, 1988–2003 (2017). https://doi.org/10.1109/TSP.2016.2645517, Google ScholarCrossref
  38. 38. N. Malik, N. Marwan, Y. Zou, P. J. Mucha, and J. Kurths, “Fluctuation of similarity to detect transitions between distinct dynamical regimes in short time series,” Phys. Rev. E 89, 062908 (2014). https://doi.org/10.1103/PhysRevE.89.062908, Google ScholarCrossref
  39. 39. L. Cao, “Practical method for determining the minimum embedding dimension of a scalar time series,” Physica D 110, 43–50 (1997). https://doi.org/10.1016/S0167-2789(97)00118-8, Google ScholarCrossref
  40. 40. O. E. Rössler, “Continuous chaos-four prototype equations,” Ann. N. Y. Acad. Sci. 316, 376–392 (1979). https://doi.org/10.1111/j.1749-6632.1979.tb29482.x, Google ScholarCrossref
  41. 41. P. Gaspard and G. Nicolis, “Bifurcation phenomena near homoclinic systems: A two-parameter analysis,” J. Stat. Phys. 31, 499 (1983). https://doi.org/10.1007/BF01019496, Google ScholarCrossref
  42. 42. J. Bates, “The published archaeobotanical data from the Indus Civilisation, South Asia, c. 3200–1500 BC,” J. Open Archaeology Data 7, 5 (2019). https://doi.org/10.5334/joad.57, Google ScholarCrossref
  43. 43. G. L. Possehl, The Indus Civilization: A Contemporary Perspective (Altamira Press, 2002). Google Scholar
  44. 44. A. Khan and C. Lemmen, “Bricks and urbanism in the Indus Valley rise and decline,” arXiv:1303.1426 (2013). Google Scholar
  45. 45. K. A. R. Kennedy and G. L. Possehl, “Were there commercial communications between prehistoric Harappans and African populations?,” Adv. Anthropology 2, 169–180 (2012). https://doi.org/10.4236/aa.2012.24020, Google ScholarCrossref
  46. 46. K. Gangal, M. N. Vahia, and R. Adhikari, “Spatio-temporal analysis of the Indus urbanization,” Curr. Sci. 98, 846–852 (2010). Google Scholar
  47. 47. C. A. Petrie and F. Lynam, “Revisiting settlement contemporaneity and exploring stability and instability: Case studies from the Indus civilization,” J. Field Archaeology 45, 1–15 (2020). https://doi.org/10.1080/00934690.2019.1664848, Google ScholarCrossref
  48. 48. D. Driebe, Fully Chaotic Maps and Broken Time Symmetry (Springer, 1999). Google ScholarCrossref
  49. 49. T. Schreiber, “Detecting and analyzing nonstationarity in a time series using nonlinear cross predictions,” Phys. Rev. Lett. 78, 843–846 (1997). https://doi.org/10.1103/PhysRevLett.78.843, Google ScholarCrossref
  50. 50. R. P. Wright, The Ancient Indus: Urbanism, Economy, and Society (Case Studies in Early Societies) (Cambridge University Press, 2009). Google Scholar
  51. 51. J. McIntosh, The Ancient Indus Valley: New Perspectives (Understanding Ancient Civilizations) (ABC-CLIO, 2008). Google Scholar
  52. 52. A. Sarkar, A. D. Mukherjee, M. K. Bera, B. Das, N. Juyal, P. Morthekai, R. D. Deshpande, V. S. Shinde, and L. S. Rao, “Oxygen isotope in archaeological bioapatites from India: Implications to climate change and decline of Bronze Age Harappan civilization,” Sci. Rep. 6, 26555 (2016). https://doi.org/10.1038/srep26555, Google ScholarCrossref
  53. 53. R. L. Kovach, K. Grijalva, and A. Nur, “Earthquakes and civilizations of the Indus Valley: A challenge for archaeoseismology,” in Ancient Earthquakes (Geological Society of America, 2010). Google Scholar
  54. 54. L. Giosan, W. D. Orsi, M. Coolen, C. Wuchter, A. G. Dunlea, K. Thirumalai, S. E. Munoz, P. D. Clift, J. P. Donnelly, V. Galy, and D. Q. Fuller, “Neoglacial climate anomalies and the Harappan metamorphosis,” Climate Past 14, 1669–1686 (2018). https://doi.org/10.5194/cp-14-1669-2018, Google ScholarCrossref
  55. 55. Y. Dixit, D. A. Hodell, and C. A. Petrie, “Abrupt weakening of the summer monsoon in northwest India 4100 yr ago,” Geology 42, 339–342 (2014). https://doi.org/10.1130/G35236.1, Google ScholarCrossref
  56. 56. W. R. Boos and T. Storelvmo, “Near-linear response of mean monsoon strength to a broad range of radiative forcings,” Proc. Natl. Acad. Sci. U.S.A. 113, 1510–1515 (2016). https://doi.org/10.1073/pnas.1517143113, Google ScholarCrossref
  57. 57. A. Levermann, V. Petoukhov, J. Schewe, and H. J. Schellnhuber, “Abrupt monsoon transitions as seen in paleorecords can be explained by moisture-advection feedback,” Proc. Natl. Acad. Sci. U.S.A. 113, E2348–E2349 (2016). https://doi.org/10.1073/pnas.1603130113, Google ScholarCrossref
  58. 58. O. N. Solomina, R. S. Bradley, D. A. Hodgson, S. Ivy-Ochs, V. Jomelli, A. N. Mackintosh, A. Nesje, L. A. Owen, H. Wanner, G. C. Wiles, and N. E. Young, “Holocene glacier fluctuations,” Quater. Sci. Rev. 111, 9–34 (2015). https://doi.org/10.1016/j.quascirev.2014.11.018, Google ScholarCrossref
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