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Exploring the Indian summer monsoon rainfall through multifractal detrended fluctuation analysis and the principle of entropy maximization

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Abstract

The present paper reports a rigorous study of the Indian Summer Monsoon Rainfall (ISMR) through Multifractal Detrended Fluctuation Analysis (MF-DFA). It has been observed that the ISMR is characterized by multifractality and Hurst Exponent above 0.5. It has been interpreted from the Hurst Exponent value that the ISMR time series is characterized by long term positive auto-correlation. Studying the strong correlation between the qthorder fluctuation and the length scale the multifractality has been confirmed within the ISMR time series. Finally, the entropy associated with ISMR has been computed using the principle of entropy maximization and the potential of entropy maximizing principle has been established over conventional fitting of normal distribution to ISMR.

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References

  • Acharya N, Robertson AW, Munoz A, Goddard LM (2019). Experimental real-time sub-seasonal to seasonal (S2S) forecast for indian summer monsoon 2018 over Bihar: a forecast application for risk management in agriculture. In: AGU fall meeting abstracts, vol 2019, pp A23U–3023

  • Aghakouchak A (2014) Entropy–copula in hydrology and climatology. J Hydrometeorol 15(6):2176–2189

    Article  Google Scholar 

  • Robertson AW, Acharya N, Goddard L, Pattanaik DR, Sahai AK, Singh KK, Ghosh K, Agarwal A, Buizer JL (2019a) Subseasonal forecasts of the 2018 Indian summer monsoon over Bihar. J Geophys Res Atmos 124(24):13861–13875

    Article  Google Scholar 

  • Robertson AW, Moron V, Vigaud N, Acharya N, Greene AM, Pai DS (2019b) Multi-scale variability and predictability of Indian summer monsoon rainfall. Mausam 70:277–292

    Google Scholar 

  • Zhang T, Wang T, Krinner G, Wang X, Gasser T, Peng S, Piao S, Yao T (2019) The weakening relationship between Eurasian spring snow cover and Indian summer monsoon rainfall. Sci Adv 5(3):eaau8932

    Article  Google Scholar 

  • Bhatt BC, Nakamura K (2005) Characteristics of monsoon rainfall around the Himalayas revealed by TRMM precipitation radar. Mon Weather Rev 133(1):149–165

    Article  Google Scholar 

  • Brunsell NA (2010) A multiscale information theory approach to assessspatial-temporal variability of daily precipitation. J Hydrol 385:165–172

    Article  Google Scholar 

  • Biazar SM, Fard AF, Singh VP, Dinpashoh Y, Majnooni-Heris A (2020) Estimation of evaporation from saline-water with more efficient input variables. Pure Appl Geophys 177(11):5599–5619

    Article  Google Scholar 

  • Chattopadhyay S (2006) Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India. arXiv preprint nlin/0609014

  • Chattopadhyay S (2007) Feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India. Acta Geophys 55(3):369–382

    Article  Google Scholar 

  • Chattopadhyay S, Chattopadhyay G (2018) Conjugate gradient descent learned ANN for Indian summer monsoon rainfall and efficiency assessment through Shannon-Fano coding. J Atmos Solar Terr Phys 179:202–205

    Article  Google Scholar 

  • Chattopadhyay G, Midya SK, Chattopadhyay S (2021) Information theoretic study of the ground-level ozone and its precursors over Kolkata, India, during the summer monsoon. Iran J Sci Technol Trans A Sci 45(1):201–207

    Article  Google Scholar 

  • Cracknell AP, Varotsos CA (2011) New aspects of global climate-dynamics research and remote sensing. Int J Remote Sens 32(3):579–600

    Article  Google Scholar 

  • Cui H, Sivakumar B, Singh VP (2018) Entropy applications in environmental and water engineering

  • Efstathiou MN, Varotsos CA (2012) Intrinsic properties of Sahel precipitation anomalies and rainfall. Theoret Appl Climatol 109(3):627–633

    Article  Google Scholar 

  • Efstathiou MN, Varotsos CA (2010) On the altitude dependence of the temperature scaling behaviour at the global troposphere. Int J Remote Sens 31(2):343–349

    Article  Google Scholar 

  • Ghosh S, Luniya V, Gupta A (2009) Trend analysis of Indian summer monsoon rainfall at different spatial scales. Atmos Sci Lett 10(4):285–290

    Google Scholar 

  • Jadhav D, Meshram J, Bhusari M, Shendre M, Bahadure P, Sangode P (2020) Prediction of Indian summer monsoon by using Artificial Neural Network (ANN)

  • Jin Q, Wang C (2017) A revival of Indian summer monsoon rainfall since 2002. Nat Clim Chang 7(8):587–594

    Article  Google Scholar 

  • Kantelhardt JW, Koscielny-Bunde E, Rego HH, Havlin S, Bunde A (2001) Detecting long-range correlations with detrended fluctuation analysis. Physica A 295(3–4):441–454

    Article  Google Scholar 

  • Karmakar S, Goswami S, Chattopadhyay S (2019) Exploring the pre-and summer-monsoon surface air temperature over eastern India using Shannon entropy and temporal Hurst exponents through rescaled range analysis. Atmos Res 217:57–62

    Article  Google Scholar 

  • Koutsoyiannis D (2006) An entropic-stochastic representation of rainfall intermittency: the origin of clustering and persistence. Water Res Res 42(1):W01401

    Article  Google Scholar 

  • Liu Y, Liu C, Wang D (2011) Understanding atmospheric behaviour interms of entropy: a review of applications of the second law ofthermodynamics to meteorology. Entropy 13:211–240

    Article  Google Scholar 

  • Nebot A, Mugica V, Escobet A (2008) Ozone prediction based on meteorologicalvariables: a fuzzy inductive reasoning approach. Atmos Chem Phys Discuss 8:12343–12370

    Google Scholar 

  • Pal S, Dutta S, Nasrin T, Chattopadhyay S (2020) Hurst exponent approach through rescaled range analysis to study the time series of summer monsoon rainfall over northeast India. Theoret Appl Climatol 142(1):581–587

    Article  Google Scholar 

  • Papalexiou SM, Koutsoyiannis D (2012) Entropy based derivation of probability distributions: a case study to daily rainfall. Adv Water Resour 45:51–57

    Article  Google Scholar 

  • Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49:1685

    Google Scholar 

  • Popuri SK, Neerchal NK, Mehta A, Mousavi A (2020) Density estimation using entropy maximization for semi-continuous data. arXiv preprint arXiv:2011.08475

  • Poveda G (2011) Mixed memory,(non) Hurst effect, and maximum entropy of rainfall in the tropical Andes. Adv Water Resour 34(2):243–256

    Article  Google Scholar 

  • Parthasarathy B, Kumar KR, Munot AA (1993) Homogeneous Indian monsoon rainfall: variability and prediction. Proc Indian Acad Sci Earth Planet Sci 102(1):121–155

    Google Scholar 

  • Roulston MS, Smith LA (2002) Evaluating probabilistic forecasts using information theory. Mon Weather Rev 130(6):1653–1660

    Article  Google Scholar 

  • Ray SN, Chattopadhyay S (2021) Analyzing surface air temperature and rainfall in univariate framework, quantifying uncertainty through Shannon entropy and prediction through artificial neural network. Earth Sci Inf 14(1):485–503

    Article  Google Scholar 

  • Saha S, Chattopadhyay S (2020) Exploring of the summer monsoon rainfall around the Himalayas in time domain through maximization of Shannon entropy. Theoret Appl Climatol 141(1):133–141

    Article  Google Scholar 

  • Sahai AK, Soman MK, Satyan V (2000) All India summer monsoon rainfall prediction using an artificial neural network. Clim Dyn 16(4):291–302

    Article  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(7):855–863

    Article  Google Scholar 

  • Singh VP (1997) The use of entropy in hydrology and water resources. Hydrol Process 11(6):587–626

    Article  Google Scholar 

  • Singh VP (2011) Hydrologic synthesis using entropy theory. J Hydrol Eng 16(5):421–433

    Article  Google Scholar 

  • Shrestha AB, Wake CP, Dibb JE, Mayewski PA (2000) Precipitation fluctuations in the Nepal Himalaya and its vicinity and relationship with some large scale climatological parameters. Int J Climatol 20(3):317–327

    Article  Google Scholar 

  • Singh VP, Zhang L, Rahimi A (2012) Probability distribution of rainfall-runoff using entropy theory. Trans ASABE 55(5):1733–1744

    Article  Google Scholar 

  • Singh VP, Sivakumar B, Cui H (2017) Tsallis entropy theory for modeling in water engineering: a review. Entropy 19(12):641

    Article  Google Scholar 

  • Singh P (2018) Indian summer monsoon rainfall (ISMR) forecasting using time series data: a fuzzy-entropy-neuro based expert system. Geosci Front 9(4):1243–1257

    Article  Google Scholar 

  • Thapaliyal V (1981) ARIMA model for long-range prediction ofmonsoon rainfall in Peninsular India. India Meteorol DeptMonogr Climatology, 12/81

  • Tzanis CG, Koutsogiannis I, Philippopoulos K, Kalamaras N (2020) Multifractal detrended cross-correlation analysis of global methane and temperature. Remote Sens 12(3):557

    Article  Google Scholar 

  • Varotsos CA, Efstathiou MN, Cracknell AP (2013) On the scaling effect in global surface air temperature anomalies. Atmos Chem Phys 13(10):5243–5253

    Article  Google Scholar 

  • Wu Z, Huang NE, Long SR, Peng CK (2007) On the trend, detrending, and variability of nonlinear and nonstationary time series. Proc Natl Acad Sci 104(38):14889–14894

    Article  Google Scholar 

  • Xu Q (2007) Measuring information content from observations for dataassimilation: relative entropy versus shannon entropy difference. Tellus A Dyn Meteorol Oceanogr 59:198–209

    Article  Google Scholar 

  • Yeh HC, Chen YC, Chang CH, Ho CH, Wei C (2017) Rainfall network optimization using radar and entropy. Entropy 19(10):553

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the anonymous reviewers for the insightful suggestions. The data of ISMR have been obtained from the website of Indian Institute of Tropical Meteorology (IITM), Pune (https://www.tropmet.res.in/DataArchival-51-Page).

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Authors and Affiliations

  1. Department of Mathematics, Amity University Kolkata, Major Arterial Road, Action Area-II, Newtown, Kolkata, 700135, India

    Sombit Chakraborty & Surajit Chattopadhyay

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  1. Sombit Chakraborty
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  2. Surajit Chattopadhyay
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Correspondence to Surajit Chattopadhyay.

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Communicated by: H. Babaie

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Chakraborty, S., Chattopadhyay, S. Exploring the Indian summer monsoon rainfall through multifractal detrended fluctuation analysis and the principle of entropy maximization. Earth Sci Inform 14, 1571–1577 (2021). https://doi.org/10.1007/s12145-021-00641-2

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