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Investigating forced transient chaos in monsoon using Echo State Networks

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Abstract

Forecasting Indian Summer Monsoon Rainfall (ISMR) is a formidable task due to its intricate variability. This study harnesses the power of machine learning (ML) to decipher the chaotic trajectory within ISMR, drawing inspiration from ML's success in predicting analogous systems. By utilizing ERA-interim data, the method dissects ISMR's chaotic nature through correlation dimension-based techniques. Employing the Lorenz-96 model on daily rainfall data, trained with an Echo State Network (ESN), the technique discerns patterns within a span of 1 model time slightly trailing its performance in other systems. This discrepancy could stem from the intricacies of observational data and the training process involving 500 initial conditions. Notably, this method achieves accuracy in slightly over 50% of cases. Despite its current limitations, this approach exhibits promise in shedding light on the chaotic behaviour enforced in ISMR. As a result, it contributes to the advancement of monsoon forecasting techniques.

Plain language summary

Predicting Indian Summer Monsoon Rainfall is a challenging task because it is highly variable. This study uses machine learning to better recognize the complex chaotic patterns in ISMR, using a type of data called ERA-interim. Apply a mathematical model called the Lorenz-96 model to daily rainfall data and train it using a neural network called an Echo State Network. This method can identify patterns in ISMR with up to about 1 model time unit, which is slightly less accurate compared to its performance in predicting other systems. This difference may be due to the complexities of the data used and the training process, which involves 500 initial conditions. Importantly, this approach is successful in predicting ISMR accurately in slightly over 50% of cases. While it has some limitations, this method shows promise in helping us recognize the chaotic behaviour of ISMR and may be used in improving monsoon forecasting techniques in future.

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References

  • Ashok K, Saji NH (2007) On the impacts of ENSO and Indian Ocean dipole events on sub-regional Indian summer monsoon rainfall. Nat Hazards 42:273–285

    Article  Google Scholar 

  • Ashok K, Guan Z, Yamagata T (2001) Impact of the Indian Ocean dipole on the relationship between the Indian monsoon rainfall and ENSO. Geophys Res Lett 28(23):4499–4502

    Article  Google Scholar 

  • Basu S, Andharia HI (1992) The chaotic time series of Indian monsoon rainfall and its prediction. Proceed Indian Acad Sci-Earth Planet Sci 101:27–34

    Article  Google Scholar 

  • Borah N, Sahai AK, Chattopadhyay R, Joseph S, Abhilash S, Goswami BN (2013) A self-organizing map–based ensemble forecast system for extended range prediction of active/break cycles of Indian summer monsoon. J Geophys Res: Atmos 118(16):9022–9034

    Article  Google Scholar 

  • Brenowitz ND, Bretherton CS (2018) Prognostic validation of a neural network unified physics parameterization. Geophys Res Lett 45(12):6289–6298

    Article  Google Scholar 

  • Casdagli M (1989) Nonlinear prediction of chaotic time series. Phys D Nonlin Phenom 35(3):335–356. https://doi.org/10.1016/0167-2789(89)90074-2

    Article  Google Scholar 

  • Chattopadhyay A, Hassanzadeh P, Subramanian D (2020) Data-driven predictions of a multiscale Lorenz-96 chaotic system using machine-learning methods: Reservoir computing, artificial neural network, and long short-term memory network. Nonlin Process Geophys 27(3):373–389

    Article  Google Scholar 

  • Goswami BN (1997) Chaos and predictability of the Indian summer monsoon. Pramana 48:719–736

    Article  Google Scholar 

  • Goswami BN, Xavier PK (2005) Dynamics of internal interannual variability of the Indian summer monsoon in a GCM. J Geophys Res. https://doi.org/10.1029/2005JD006042

    Article  Google Scholar 

  • Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9(1–2):189–208

    Article  Google Scholar 

  • Hassanibesheli F, Kurths J, Boers N (2022) Long-term ENSO prediction with echo-state networks. Environ Res Clim 1(1):011002

    Article  Google Scholar 

  • Jaeger H, Lukoševičius M, Popovici D, Siewert U (2007) Optimization and applications of echo state networks with leaky-integrator neurons. Neural Netw 20(3):335–352

    Article  Google Scholar 

  • Kantz H, Schreiber T (2004): Nonlinear time series analysis, Cambridge university press 7

  • Leyffer SS, et al. (2016): Doing Moore with Less–Leapfrogging Moore’s Law with Inexactness for Supercomputing, arXiv, arXiv:1610.02606

  • Liu Z (2010) Chaotic time series analysis. nonlinear time series: computations and applications. Math Probl Eng. https://doi.org/10.1155/2010/720190

    Article  Google Scholar 

  • Lorenz EN (1984) Irregularity. a fundamental property of the atmosphere. Tellus 36(A):98–110

    Google Scholar 

  • Lorenz E (1967) The nature and theory of the general circulation of the atmosphere. World Meteorol Org 161

  • Lukoševičius M (2012) A practical guide to applying echo state networks. In: Montavon G, Orr GB, Müller K-R (eds) Neural networks tricks of the trade. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 659–686

    Chapter  Google Scholar 

  • Machicao J, Bruno OM, Baptista MS (2021) Zooming into chaos as a pathway for the creation of a fast, light and reliable cryptosystem. Nonlin Dyn 104:753–764. https://doi.org/10.1007/s11071-021-06280-y

    Article  Google Scholar 

  • Materassi M, Alberti T, Migoya-Orué Y, Radicella SM, Consolini G (2023) Chaos and Predictability in Ionospheric Time Series. Entropy 25(2):368

    Article  Google Scholar 

  • McDermott PL, Wikle CK (2019) Bayesian recurrent neural network models for forecasting and quantifying uncertainty in spatial-temporal data. Entropy 21(2):184

    Article  Google Scholar 

  • Mishra V, Smoliak BV, Lettenmaier DP, Wallace JM (2012) A prominent pattern of year-to-year variability in Indian Summer Monsoon Rainfall. Proc Natl Acad Sci 109(19):7213–7217

    Article  CAS  Google Scholar 

  • Palmer TN (1994) Chaos and predictability in forecasting the monsoon. In Proc Indian Nat Sci Acad 60:57–66

    Google Scholar 

  • Panis R, Martin K, Zdenek S (2020) Detection of chaotic time series, Proceedings of RAGtime, 20–22

  • Pathak J, Hunt B, Girvan M, Lu Z, Ott E (2018) Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach. Phys Rev Lett 120(2):024102

    Article  CAS  Google Scholar 

  • Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686–707

    Article  Google Scholar 

  • Rasp S, Pritchard MS, Gentine P (2018) Deep learning to represent subgrid processes in climate models. Proc Natl Acad Sci 115(39):9684–9689

    Article  CAS  Google Scholar 

  • Sahai AK, Grimm AM, Satyan V, Pant GB (2003) Long-lead prediction of Indian summer monsoon rainfall from global SST evolution. Clim Dyn 20:855–863

    Article  Google Scholar 

  • Satyan V (1988) Is there an attractor for the Indian summer monsoon? Proceed Indian Acad Sci Earth Planet Sci 97:49–52

    Article  Google Scholar 

  • Sikka DR (1980) Some aspects of the large scale fluctuations of summer monsoon rainfall over India in relation to fluctuations in the planetary and regional scale circulation parameters. Proceed Indian Acad Sci Earth Planet Sci 89:179–195

    Article  Google Scholar 

  • Vlachas PR, Wonmin B, Wan Zhong Y, Sapsis Themistoklis P, Koumoutsakos P (2018) Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc R Soc A 474:20170844

    Article  Google Scholar 

  • Walker JM, Bordoni S, Schneider T (2015) Interannual variability in the large-scale dynamics of the South Asian summer monsoon. J Clim 28(9):3731–3750

    Article  Google Scholar 

  • Xie T, Li J, Chen K, Zhang Y, Sun C (2021) Origin of Indian Ocean multidecadal climate variability: role of the North Atlantic Oscillation. Clim Dyn 56:3277–3294

    Article  Google Scholar 

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Acknowledgements

The authors are thankful to the European Centre for Medium-Range Weather Forecasts (ECMWF) for reanalysis data. This work is supported by the Indian Institute of Geomagnetism (IIG), Department of Science and Technology, India.

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Authors and Affiliations

  1. Indian Institute of Geomagnetism, Mumbai, 410218, India

    Chandan Kapil, Vasundhara Barde & Gopi K. Seemala

  2. School of Environmental Science, Jawaharlal Nehru University, New Delhi, India

    A. P. Dimri

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  1. Chandan Kapil
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  2. Vasundhara Barde
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  3. Gopi K. Seemala
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  4. A. P. Dimri
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Contributions

APD has conceived this idea; APD and CK has discussed; CK has made major computations and APD and CP has written the ms and discussed with GS.

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Correspondence to A. P. Dimri.

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Kapil, C., Barde, V., Seemala, G.K. et al. Investigating forced transient chaos in monsoon using Echo State Networks. Clim Dyn (2024). https://doi.org/10.1007/s00382-024-07174-6

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