Monte Carlo simulations and forecasting of Radium-226, Thorium-232, and Potassium-40 radioactivity concentrations

Abstract

This study depicts the radioactivity time series levels of 226Ra, 232Th, and 40K prospectively by Monte Carlo simulations (MCSs). Three ARIMA stationary stochastic processes are used with measurement records statistical parameter conservation. The MCSs by means of the ARIMA stochastic processes, the statistical characteristics of the radionuclide data are determined and the future simulation forecasts are made for different periods (time between two measurements, i.e. 1 week). Future concentrations of radionuclides with MCS are estimated for the first time. The results obtained on the transport, control and management of radionuclides can also reach similar gains for other different materials.

Graphical abstract

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References

  1. 1.

    Aközcan S, Külahcı F, Mercan Y (2018) A suggestion to radiological hazards characterization of 226Ra, 232Th, 40K and 137Cs: spatial distribution modelling. J Hazard Mater 353:476–489

    Article  Google Scholar 

  2. 2.

    Korkulu Z, Özkan N (2013) Determination of natural radioactivity levels of beach sand samples in the black sea coast of Kocaeli (Turkey). Radiat Phys Chem 88:27–31

    CAS  Article  Google Scholar 

  3. 3.

    Külahcı F (2011) A risk analysis model for radioactive wastes. J Hazard Mater 191(1–3):349–355

    Article  Google Scholar 

  4. 4.

    Celik N, Cevik U, Celik A, Koz B (2009) Natural and artificial radioactivity measurements in Eastern Black Sea region of Turkey. J Hazard Mater 162(1):146–153. https://doi.org/10.1016/j.jhazmat.2008.05.017

    CAS  Article  PubMed  Google Scholar 

  5. 5.

    Sabiha J, Tufail M, Asghar M (2010) Hazard of NORM from phosphorite of Pakistan. J Hazard Mater 176(1–3):426–433. https://doi.org/10.1016/j.jhazmat.2009.11.047

    CAS  Article  Google Scholar 

  6. 6.

    Gorur FK, Camgoz H (2014) Natural radioactivity in various water samples and radiation dose estimations in Bolu province, Turkey. Chemosphere 112:134–140. https://doi.org/10.1016/j.chemosphere.2014.02.074

    CAS  Article  PubMed  Google Scholar 

  7. 7.

    Uǧur A, Özden B, Filizok I (2011) Spatial and temporal variability of 210Po and 210Pb in mussels (Mytilus galloprovincialis) at the Turkish coast of the Aegean Sea. Chemosphere 83(8):1102–1107. https://doi.org/10.1016/j.chemosphere.2011.01.032

    CAS  Article  PubMed  Google Scholar 

  8. 8.

    Hassan AK, Fares S, Abd El-Rahma M (2013) Natural radioactivity levels and radiation hazards for gypsum materials used in Egypt. J Environ Sci Technol 7(1):56–66. https://doi.org/10.3923/jest.2014.56.66

    CAS  Article  Google Scholar 

  9. 9.

    Menezes M, Maia ECP, Filho SS, Albinati C (2002) Assessment of occupational exposure and contamination by means of airborne particulate matter and biomonitors using k(0) instrumental neutron activation analysis. J Radioanal Nucl Chem 254(3):499–507. https://doi.org/10.1023/a:1021638021157

    CAS  Article  Google Scholar 

  10. 10.

    Borylo A (2013) Determination of uranium isotopes in environmental samples. J Radioanal Nucl Chem 295(1):621–631. https://doi.org/10.1007/s10967-012-1900-1

    CAS  Article  Google Scholar 

  11. 11.

    Yucel H, Karadeniz H, Cetiner MA, Demirel H, Turhan S (2003) Measurement of absolute intensity of 1001 keV gamma-ray of (234) mPa. J Radioanal Nucl Chem 258(2):445–447. https://doi.org/10.1023/a:1026226930151

    Article  Google Scholar 

  12. 12.

    Abbasi A, Hassanzadeh M (2017) Measurement and Monte Carlo simulation of γ-ray dose rate in high-exposure building materials. Nucl Sci Technol. https://doi.org/10.1007/s41365-016-0171-x

    Article  Google Scholar 

  13. 13.

    Abdollahnejad H, Vosoughi N, Zare MR (2016) Design and fabrication of an in situ gamma radioactivity measurement system for marine environment and its calibration with Monte Carlo method. Appl Radiat Isot 114:87–91. https://doi.org/10.1016/j.apradiso.2016.05.013

    CAS  Article  PubMed  Google Scholar 

  14. 14.

    Ba VN, Loan TTH, Huy NQ (2018) Evaluation of characteristics of the peak-to-valley ratio versus material thickness in transmission gamma spectra by Monte Carlo simulation. J Radioanal Nucl Chem 317(3):1455–1461. https://doi.org/10.1007/s10967-018-6035-6

    CAS  Article  Google Scholar 

  15. 15.

    Çelik N (2012) Monte Carlo modelling of human body for dose conversion coefficients of 137Cs in soil of the Eastern Black Sea region of Turkey. Isot Environ Health Stud 48(2):280–285. https://doi.org/10.1080/10256016.2012.647815

    CAS  Article  Google Scholar 

  16. 16.

    Külahcı F (2020) Environmental distribution and modelling of radioactive lead (210): a Monte Carlo simulation application. In: Gupta DK, Chatterjee S, Walther C (eds) Lead in plants and the environment. Springer, Berlin, pp 15–32

    Google Scholar 

  17. 17.

    Sang TT, Chuong HD, Tam HD (2019) Simple procedure for optimizing model of NaI(Tl) detector using Monte Carlo simulation. J Radioanal Nucl Chem 322(2):1039–1048. https://doi.org/10.1007/s10967-019-06787-0

    CAS  Article  Google Scholar 

  18. 18.

    Yoo DH, Shin WG, Lee J, Yeom YS, Kim CH, Chang BU, Min CH (2017) Development of an effective dose coefficient database using a computational human phantom and Monte Carlo simulations to evaluate exposure dose for the usage of NORM-added consumer products. Appl Radiat Isot 129:42–48. https://doi.org/10.1016/j.apradiso.2017.07.064

    CAS  Article  PubMed  Google Scholar 

  19. 19.

    Rashed-Nizam QM, Tafader MK, Zafar M, Rahman MM, Bhuian AKMSI, Khan RA, Kamal M, Chowdhury MI, Alam MN (2016) Radiological risk analysis of sediment from Kutubdia island, Bangladesh due to natural and anthropogenic radionuclides. Intl J Radiat Res 14(4):373–377. https://doi.org/10.18869/acadpub.ijrr.14.4.373

    Article  Google Scholar 

  20. 20.

    Kawakami H, Honda MC, Watanabe S, Sino T (2014) Time-series observations of 210Po and 210Pb radioactivity in the western North Pacific. J Radioanal Nucl Chem 301(2):461–468. https://doi.org/10.1007/s10967-014-3141-y

    CAS  Article  Google Scholar 

  21. 21.

    Loos M, Krauss M, Fenner K (2012) Pesticide nonextractable residue formation in soil: insights from inverse modeling of degradation time series. Environ Sci Technol 46(18):9830–9837. https://doi.org/10.1021/es300505r

    CAS  Article  PubMed  Google Scholar 

  22. 22.

    Yamanishi H, Miyake H (2003) Separation of natural background by using correlation of time-series data on radiation monitoring. J Nucl Sci Technol 40(1):44–48. https://doi.org/10.1080/18811248.2003.9715331

    CAS  Article  Google Scholar 

  23. 23.

    Zhang Y-J, Hu L-S, Bai T (2017) Online estimation of radionuclide transportation in water environment. J Radioanal Nucl Chem 314(2):1237–1244. https://doi.org/10.1007/s10967-017-5484-7

    CAS  Article  Google Scholar 

  24. 24.

    Hu Y, Wang Z, Wen J, Li Y (2016) Stochastic fuzzy environmental risk characterization of uncertainty and variability in risk assessments: a case study of polycyclic aromatic hydrocarbons in soil at a petroleum-contaminated site in China. J Hazard Mater 316:143–150. https://doi.org/10.1016/j.jhazmat.2016.05.033

    CAS  Article  PubMed  Google Scholar 

  25. 25.

    Li J, He L, Lu H, Fan X (2014) Stochastic goal programming based groundwater remediation management under human-health-risk uncertainty. J Hazard Mater 279:257–267. https://doi.org/10.1016/j.jhazmat.2014.06.082

    CAS  Article  PubMed  Google Scholar 

  26. 26.

    Li X, Li H, Liu Y, Xiong W, Fang S (2018) Joint release rate estimation and measurement-by-measurement model correction for atmospheric radionuclide emission in nuclear accidents: an application to wind tunnel experiments. J Hazard Mater 345:48–62. https://doi.org/10.1016/j.jhazmat.2017.09.051

    CAS  Article  PubMed  Google Scholar 

  27. 27.

    Külahci F, Şen Z (2009) Potential utilization of the absolute point cumulative semivariogram technique for the evaluation of distribution coefficient. J Hazard Mater 168(2–3):1387–1396. https://doi.org/10.1016/j.jhazmat.2009.03.027

    CAS  Article  PubMed  Google Scholar 

  28. 28.

    Külahcı F, Şen Z (2009) Spatio-temporal modeling of 210Pb transportation in lake environments. J Hazard Mater 165(1–3):525–532. https://doi.org/10.1016/j.jhazmat.2008.10.026

    CAS  Article  PubMed  Google Scholar 

  29. 29.

    Hyndman RJ, Khandakar Y (2008) Automatic time series forecasting: the forecast package for R. J Stat Softw 27(3):1–22. https://doi.org/10.18637/jss.v027.i03

    Article  Google Scholar 

  30. 30.

    Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175

    Article  Google Scholar 

  31. 31.

    Box GE, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. Wiley, New York

    Google Scholar 

  32. 32.

    Suganthi L, Samuel AA (2012) Energy models for demand forecasting—a review. Renew Sustain Energy Rev 16(2):1223–1240. https://doi.org/10.1016/j.rser.2011.08.014

    Article  Google Scholar 

  33. 33.

    Adamowski J, Chan HF (2011) A wavelet neural network conjunction model for groundwater level forecasting. J Hydrol 407(1–4):28–40. https://doi.org/10.1016/j.jhydrol.2011.06.013

    Article  Google Scholar 

  34. 34.

    Valipour M, Banihabib ME, Behbahani SMR (2013) Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. J Hydrol 476:433–441. https://doi.org/10.1016/j.jhydrol.2012.11.017

    Article  Google Scholar 

  35. 35.

    Quintela-del-Rio A, Francisco-Fernandez M (2011) Nonparametric functional data estimation applied to ozone data: prediction and extreme value analysis. Chemosphere 82(6):800–808. https://doi.org/10.1016/j.chemosphere.2010.11.025

    CAS  Article  PubMed  Google Scholar 

  36. 36.

    Duenas C, Fernandez MC, Canete S, Carretero J, Liger E (2005) Stochastic model to forecast ground-level ozone concentration at urban and rural areas. Chemosphere 61(10):1379–1389. https://doi.org/10.1016/j.chemosphere.2005.04.079

    CAS  Article  PubMed  Google Scholar 

  37. 37.

    Rubinstein RY, Kroese DP (2016) Simulation and the Monte Carlo method, vol 10. Wiley, New York

    Google Scholar 

  38. 38.

    Aalizadeh R, Nika MC, Thomaidis NS (2019) Development and application of retention time prediction models in the suspect and non-target screening of emerging contaminants. J Hazard Mater 363:277–285. https://doi.org/10.1016/j.jhazmat.2018.09.047

    CAS  Article  PubMed  Google Scholar 

  39. 39.

    Sechopoulos I, Rogers DWO, Bazalova-Carter M, Bolch WE, Heath EC, McNitt-Gray MF, Sempau J, Williamson JF (2018) RECORDS: improved reporting of Monte Carlo radiation transport studies: report of the AAPM Research Committee Task Group 268. Med Phys 45(1):e1–e5. https://doi.org/10.1002/mp.12702

    Article  PubMed  Google Scholar 

  40. 40.

    Ahmadzadeh F (2018) Change point detection with multivariate control charts by artificial neural network. Int J Adv Manuf Technol 97(9–12):3179–3190. https://doi.org/10.1007/s00170-009-2193-6

    Article  Google Scholar 

  41. 41.

    Schuhmacher M, Meneses M, Xifro A, Domingo JL (2001) The use of Monte-Carlo simulation techniques for risk assessment: study of a municipal waste incinerator. Chemosphere 43(4–7):787–799. https://doi.org/10.1016/s0045-6535(00)00435-5

    CAS  Article  PubMed  Google Scholar 

  42. 42.

    Toros H, Erdun H, Çapraz Ö, Özer B, Daylan EB, Öztürk Aİ (2013) Air Pollution and quality levels in metropolitans of turkey for sustainable life. EJOSAT Eur J Sci Technol 1(1):12–18

    Google Scholar 

  43. 43.

    MTA (2018) General directorate of mineral research and explorations. Available via MTA. http://www.mta.gov.tr/eng/. Accessed 27 Dec 2018

  44. 44.

    Aközcan S (2014) Annual effective dose of naturally occurring radionuclides in soil and sediment. Toxicol Environ Chem 96(3):379–386

    Article  Google Scholar 

  45. 45.

    Ediger VŞ, Akar S (2007) ARIMA forecasting of primary energy demand by fuel in Turkey. Energy Policy 35(3):1701–1708

    Article  Google Scholar 

  46. 46.

    Kumar U, Jain V (2010) ARIMA forecasting of ambient air pollutants (O3, NO, NO2 and CO). Stoch Environ Res Risk Assess 24(5):751–760

    Article  Google Scholar 

  47. 47.

    Cholette PA (1982) Prior information and ARIMA forecasting. J Forecast 1(4):375–383

    Article  Google Scholar 

  48. 48.

    Xu X, Qi Y, Hua Z (2010) Forecasting demand of commodities after natural disasters. Expert Syst Appl 37(6):4313–4317

    Article  Google Scholar 

  49. 49.

    Li C, Chiang T-W (2013) Complex neurofuzzy ARIMA forecasting—a new approach using complex fuzzy sets. IEEE Trans Fuzzy Syst 21(3):567–584

    Article  Google Scholar 

  50. 50.

    MathWorks I (1996) MATLAB: application program interface guide, vol 5. MathWorks, Natick

    Google Scholar 

  51. 51.

    Adam AM, Junior PO (2017) Financial econometrics: an example-based handbook. An example-based handbook. Financial Econometrics. Nova Science Publishers Inc, New York

    Google Scholar 

  52. 52.

    Chatfield C (2016) The analysis of time series: An introduction. The Analysis of Time Series: An Introduction, 6th edn. CRC Press, Boca Raton

    Google Scholar 

  53. 53.

    Ozcan T, Küçükdeniz T, Sezgin FH (2016) Comparative analysis of statistical, machine learning, and grey methods for short-term electricity load forecasting. In: Nature-inspired computing: concepts, methodologies, tools, and applications, vol 2–3. IGI Global, Hershey, pp 1161–1183. https://doi.org/10.4018/978-1-5225-0788-8.ch044

  54. 54.

    Ramarao NV, Babu PYY, Ganesh S, Rajendran C (2017) Multiobjective forecasting: time series models using a deterministic pseudo-evolutionary algorithm. In: Big data analytics using multiple criteria decision-making models. CRC Press, Boca Raton, pp 135–153. https://doi.org/10.1201/9781315152653

  55. 55.

    Fattah J, Ezzine L, Aman Z, El Moussami H, Lachhab A (2018) Forecasting of demand using ARIMA model. Int J Eng Bus Manag. https://doi.org/10.1177/1847979018808673

    Article  Google Scholar 

  56. 56.

    Ongbali SO, Igboanugo AC, Afolalu SA, Udo MO, Okokpujie IP (2018) Model selection process in time series analysis of production system with random output. Institute of Physics Publishing, Bristol. https://doi.org/10.1088/1757-899x/413/1/012057

    Google Scholar 

  57. 57.

    Akaike H (1976) Canonical correlation analysis of time series and the use of an information criterion. Math Sci Eng. https://doi.org/10.1016/S0076-5392(08)60869-3

    Article  Google Scholar 

  58. 58.

    Box GEP, Jenkins GM, Reinsel GC (2013) Time series analysis: forecasting and control. Time Series Analysis: Forecasting and Control, 4th edn. Wiley, New York. https://doi.org/10.1002/9781118619193

    Google Scholar 

  59. 59.

    Chatfield C (2000) Time-series forecasting. CRC Press, Boca Raton

    Google Scholar 

  60. 60.

    Lütkepohl H (2005) New introduction to multiple time series analysis. New introduction to Multiple Time Series Analysis. Springer, Berlin. https://doi.org/10.1007/978-3-540-27752-1

    Google Scholar 

  61. 61.

    Mills TC, Markellos RN (2008) The econometric modelling of financial time series. The Econometric Modelling of Financial Time Series. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511817380

    Google Scholar 

  62. 62.

    Ljung L (1987) System identification: theory for the user. Prentice-Hall, Upper Saddle River

    Google Scholar 

  63. 63.

    Chadwick MB, Herman M, Oblozinsky P et al (2011) ENDF/B-VII.1 nuclear data for science and technology: cross sections, covariances, fission product yields and decay data. NDS 112(12):2887–2996. https://doi.org/10.1016/j.nds.2011.11.002

    CAS  Article  Google Scholar 

  64. 64.

    Beringer J, Arguin JF, Barnett RM et al (2012) Review of particle physics. Particle Data Group. PhRvD 86 (1). https://doi.org/10.1103/physrevd.86.010001

  65. 65.

    Abdolhamidzadeh B, Abbasi T, Rashtchian D, Abbasi SA (2010) A new method for assessing domino effect in chemical process industry. J Hazard Mater 182(1–3):416–426. https://doi.org/10.1016/j.jhazmat.2010.06.049

    CAS  Article  PubMed  Google Scholar 

  66. 66.

    Zhao Y, Nielsen CP, Lei Y, McElroy MB, Hao J (2011) Quantifying the uncertainties of a bottom-up emission inventory of anthropogenic atmospheric pollutants in China. Atmos Chem Phys 11(5):2295–2308. https://doi.org/10.5194/acp-11-2295-2011

    CAS  Article  Google Scholar 

  67. 67.

    Robert C, Casella G (2013) Monte Carlo statistical methods. Springer, Berlin

    Google Scholar 

  68. 68.

    Akdi Y (2003) Zaman serileri analizi: Birim kökler ve kointegrasyon. Bıçaklar Kitabevi

  69. 69.

    Enders W (2008) Applied econometric time series. Wiley, New York

    Google Scholar 

  70. 70.

    Burney SA, Raza SA (2007) Monte carlo simulation and prediction of Internet load using conditional mean and conditional variance model. In: Proceedings of the 9th Islamic countries conference on statistical sciences

  71. 71.

    Hamilton J (1994) Time series analysis. Princeton University Press Princeton, Cambridge

    Google Scholar 

  72. 72.

    Faruk Y, Tüfekçí S (2017) Handbook of research on applied optimization methodologies in manufacturing systems. IGI Global, New York

    Google Scholar 

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Acknowledgements

This work was carried out using the Gamma Spectrometer Laboratory at Advanced Technologies Application and Research Center, Kirklareli University, Kirklareli, Turkey. We would like to thank Prof. Zsolt Révay for his positive scientific approach and management from the first presentation of this research to the final stage. On the other hand, both anonymous referees contributed a lot to the development of this article. We would like also to thank them for their scientific comments.

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Correspondence to Fatih Külahcı.

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Külahcı, F., Aközcan, S. & Günay, O. Monte Carlo simulations and forecasting of Radium-226, Thorium-232, and Potassium-40 radioactivity concentrations. J Radioanal Nucl Chem 324, 55–70 (2020). https://doi.org/10.1007/s10967-020-07059-y

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Keywords

  • Monte Carlo
  • Hypothesis test
  • Forecasting
  • Prediction
  • Model