Research Article
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Persistence of Rainfall Time Series: Kırşehir Case Study

Year 2022, Volume 14, Issue 1, 246 - 255, 31.01.2022
https://doi.org/10.29137/umagd.868317

Abstract

This study examines the persistence and long-term correlation of monthly and seasonal rainfall time series of Kırşehir for the period of 1960-2019, with widely used Hurst exponent and Detrended Fluctuation Analysis (DFA) analyses. Both Hurst exponent and DFA analyses could be used to detect the long-term memory and correlation that can be assessed as a reference of predictability. To support the analyses results Augmented Dickey Fuller and Mann-Kendall tests also applied to time series. Within various rainfall series, evidence of persistence and long-term correlation was identified. According to H exponent values of simple R/S and corrected R/S methods, 10 out of 12 months and winter, spring (only simple R/S), summer (only corrected R/S) and autumn season and according to DFA scaling exponent values 4 out of 12 months and winter and autumn seasons exhibit long term correlation. On the other hand, when the H exponent and DFA scaling exponent values compared only four monthly and two seasonal rainfall series concluded to be consistent with both H exponent and DFA scaling exponent results.

References

  • Agbazo, M., N’Gobi, G.K., Alamou, E., Kounouhewa, B., & Afouda, A. (2019). Fractal Analysis of the Long-Term Memory in Precipitation over Bénin (West Africa). Advances in Meteorology, 2019, 1-12.
  • Ahmad, I., Tang, D., Wang, T., Wang, M., and Wagan, B. (2015) Precipitation Trends over Time Using Mann-Kendall and Spearman’s rho Tests in Swat River Basin, Pakistan. Advances in Meteorology. 2015, 1-15.
  • Anderson BT, Gianotti JS, Guido S, Jason F (2016) Dominant time scales of potentially predictable precipitation variations across the continental United States. J Clim 29(24):8881–8897. https://doi.org/10.1175/JCLI-D-15-0635.1
  • Barbulescu, A., Serban, C., & Maftei, C. (2010). Evaluation of Hurst exponent for precipitation time series.
  • Bozoglu M, Başer U, Alhas Eroglu N, Kılıc Topuz B (2019) Impacts of Climate Change on Turkish Agriculture. Journal of International Environmental Application and Science, 14:97-103 . Retrieved from https://dergipark.org.tr/tr/pub/jieas/issue/48886/560710
  • Bryce, R., & Sprague, K. (2012). Revisiting detrended fluctuation analysis. Scientific Reports, 2.
  • Bu, L., & Shang, P. (2014). Scaling analysis of stock markets. Chaos, 24 2, 023107.
  • Chandrasekaran, S., Poomalai, S., Saminathan, B., Suthanthiravel, S., Sundaram, K., & Hakkim, F.F. (2019). An investigation on the relationship between the Hurst exponent and the predictability of a rainfall time series. Meteorological Applications, 26, 511-519.
  • Chen, Y., Guan, Y., Shao, G., & Zhang, D. (2016). Investigating Trends in Streamflow and Precipitation in Huangfuchuan Basin with Wavelet Analysis and the Mann-Kendall Test. Water, 8(3), 77. MDPI AG. Retrieved from http://dx.doi.org/10.3390/w8030077
  • Cheng, L., & AghaKouchak, A. (2014). Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate. Sci. Rep. 4, 7093. doi:10.1038/srep07093
  • Corrêa, C.S., Schuch, D., Queiroz, A.P., Fisch, G., Correa, F., & Coutinho, M.M. (2017). The Long-Range Memory and the Fractal Dimension: a Case Study for Alcântara. Journal of Aerospace Technology and Management, 9, 461-468.
  • Dellal Đ, McCarl BA, Butt T (2011) The Economic Assessment of Climate Change on Turkish Agriculture, Journal of Environmental Protection and Ecology 12:376-385.
  • "Dickey DA and Fuller WA (1979), ""Distribution of the Estimators for Autoregressive Time Series with a Unit Root"", Journal of the American Statistical Association 74:427-431."
  • Dudu H, Çakmak EH (2018) Climate change and agriculture: an integrated approach to evaluate economy-wide effects for Turkey. Climate and Development, 10:275-288. https://doi.org/10.1080/17565529.2017.1372259
  • Fuller, W. A. (1996). Introduction to Statistical Time Series, second ed., New York: John Wiley and Sons.
  • Gilbert, R.O. (1987) Statistical Methods for Environmental Pollution Monitoring. Wiley New York NY. USA. pp. 336
  • Golinska, A. (2013). Detrended Fluctuation Analysis ( DFA ) in biomedical signal processing : selected examples.
  • Hacinliyan, A., & Kandıran, E. (2015). Fractal Analysis of Stock Exchange Indices in Turkey. AJIT‐e: Online Academic Journal of Information Technology, 6, 7-19.
  • Hardstone, R., Poil, S., Schiavone, G., Jansen, R., Nikulin, V., Mansvelder, H., & Linkenkaer-Hansen, K. (2012). Detrended Fluctuation Analysis: A Scale-Free View on Neuronal Oscillations. Frontiers in Physiology, 3.
  • Hurst, H. (1951). Long term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers , 6: 770-799.
  • Yue, J., Zhao, X., & Shang, P. (2010). Effect of Trends on Detrended Fluctuation Analysis of Precipitation Series. Mathematical Problems in Engineering, 2010, 1-15.
  • Kantelhardt J.W. (2015) Fractal and Multifractal Time Series. In: Meyers R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_221-3
  • Kendall, M.G. (1975) Rank Correlation Methods, 4th ed., Charles Griffin, London, UK. pp. 202
  • Koutsoyiannis, D.: Revisiting the global hydrological cycle: is it intensifying?, Hydrol. Earth Syst. Sci., 24, 3899–3932, https://doi.org/10.5194/hess-24-3899-2020, 2020.
  • Kurnaz, M. (2004). Application Of Detrended Fluctuation Analysis To Monthly Average Of The Maximum Daily Temperatures To Resolve Different Climates. Fractals, 12, 365-373.
  • López-Lambraño, A., Fuentes, C., López-Ramos, A., Ramírez, J., & López-Lambraño, M. (2018). Spatial and temporal Hurst exponent variability of rainfall series based on the climatological distribution in a semiarid region in Mexico. Atmosfera, 31, 199-219.
  • Mall RK, Gupta A, Singh R, Singh RS, Rathore LS (2006) Water resources and climate change: an Indian perspective. Curr Sci 90:1610-1626.
  • Mandelbrot-Wallis. (1969). Robustness of the rescaled range R/S in the measurement of noncyclic longrun statistival dependence. Water Resources Research , 5: 967-988.
  • Mann, H.B. (1945) Non-parametric tests against trend. Econometrica. 13, 245-259.
  • Márton, L., Brassai, S.T., Bakó, L., & Losonczi, L. (2014). Detrended Fluctuation Analysis of EEG Signals. Procedia Technology, 12, 125-132.
  • Meshram, S., Kahya, E., Meshram, C., Ghorbani, M.A., Ambade, B., & Mirabbasi, R. (2020). Long-term temperature trend analysis associated with agriculture crops. Theoretical and Applied Climatology, 140, 1139-1159.
  • Onyutha, C. (2020). Graphical-statistical method to explore variability of hydrological time series. Hydrology Research.
  • Osborn, T. J., Gosling, S., Wallace, C., & Dorling, S. (2015). The Water Cycle in a Changing Climate. 7th World Water Forum. Faircount Media Group, London, 14–19.
  • Palmer MA, Reidy Liermann CA, Nilsson C, Flörke M, Alcamo J, Lake PS, Bond N (2008) Climate change and the world's river basins: anticipating management options. Frontiers in Ecology and the Environment, 6:81-89. https://doi.org/10.1890/060148.
  • Papagiannaki, K., Lagouvardos, K., Kotroni, V., & Bezes, A. (2015). Flash flood occurrence and relation to the rainfall hazard in a highly urbanized area, Nat. Hazards Earth Syst. Sci., 15, 1859-1871
  • Peng, C. K., Buldyrev, S. V., & Simons, M. "Nature and Fractals." Physics Rev, 1994: 168.
  • Peters EE. 1994. Fractal Market Analysis: Applying Chaos Theory to Investment and Economic. John Wiley and Sons: New York, NY.
  • Raimundo, M.S., & Okamoto, J. (2018). Application of Hurst Exponent (H) and the R/S Analysis in the Classification of FOREX Securities. International Journal of Modeling and Optimization, 8, 116-124.
  • Said E and Dickey DA (1984), ""Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order"", Biometrika 71:599-607.
  • Taqqu MS, Teverovsky V, Willinger W. 1995. Estimators for long range dependence: an empirical study. Fractals 3: 785– 788.
  • Tatli, H. (2015), Detecting persistence of meteorological drought via the Hurst exponent. Met. Apps, 22: 763-769. https://doi.org/10.1002/met.1519
  • Weron, R. (2001). Estimating long range dependence: finite sample properties and confidence intervals. HSC Research Reports.
  • Xie, F., Yuan, N., Qi, Y. et al. Is long-term climate memory important in temperature/precipitation predictions over China?. Theor Appl Climatol 137, 459–466 (2019). https://doi.org/10.1007/s00704-018-2608-0
  • Yuan N, Fu Z, Liu S (2013) Long-term memory in climate variability: a new look based on fractional integral techniques. J Geophys Res 118(23):12962–12969.
  • Yuan N, Fu Z, Liu S (2014) Extracting climate memory using fractional integrated statistical model: a new perspective on climate prediction. Sci Rep 4:6577.
  • Zhou, Q., Arnbjerg-Nielsen, K., Mikkelsen, P. S., Nielsen, S. B., & Halsnæs, K. (2012). Urban drainage design and climate change adaptation decision making. Kgs. Lyngby: DTU Environment
  • Zhu X, Fraedrich K, Liu Z, Blender B. (2010). A demonstration of long‐term memory and climate predictability. J. Clim. 23: 5021– 5029.

Year 2022, Volume 14, Issue 1, 246 - 255, 31.01.2022
https://doi.org/10.29137/umagd.868317

Abstract

References

  • Agbazo, M., N’Gobi, G.K., Alamou, E., Kounouhewa, B., & Afouda, A. (2019). Fractal Analysis of the Long-Term Memory in Precipitation over Bénin (West Africa). Advances in Meteorology, 2019, 1-12.
  • Ahmad, I., Tang, D., Wang, T., Wang, M., and Wagan, B. (2015) Precipitation Trends over Time Using Mann-Kendall and Spearman’s rho Tests in Swat River Basin, Pakistan. Advances in Meteorology. 2015, 1-15.
  • Anderson BT, Gianotti JS, Guido S, Jason F (2016) Dominant time scales of potentially predictable precipitation variations across the continental United States. J Clim 29(24):8881–8897. https://doi.org/10.1175/JCLI-D-15-0635.1
  • Barbulescu, A., Serban, C., & Maftei, C. (2010). Evaluation of Hurst exponent for precipitation time series.
  • Bozoglu M, Başer U, Alhas Eroglu N, Kılıc Topuz B (2019) Impacts of Climate Change on Turkish Agriculture. Journal of International Environmental Application and Science, 14:97-103 . Retrieved from https://dergipark.org.tr/tr/pub/jieas/issue/48886/560710
  • Bryce, R., & Sprague, K. (2012). Revisiting detrended fluctuation analysis. Scientific Reports, 2.
  • Bu, L., & Shang, P. (2014). Scaling analysis of stock markets. Chaos, 24 2, 023107.
  • Chandrasekaran, S., Poomalai, S., Saminathan, B., Suthanthiravel, S., Sundaram, K., & Hakkim, F.F. (2019). An investigation on the relationship between the Hurst exponent and the predictability of a rainfall time series. Meteorological Applications, 26, 511-519.
  • Chen, Y., Guan, Y., Shao, G., & Zhang, D. (2016). Investigating Trends in Streamflow and Precipitation in Huangfuchuan Basin with Wavelet Analysis and the Mann-Kendall Test. Water, 8(3), 77. MDPI AG. Retrieved from http://dx.doi.org/10.3390/w8030077
  • Cheng, L., & AghaKouchak, A. (2014). Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate. Sci. Rep. 4, 7093. doi:10.1038/srep07093
  • Corrêa, C.S., Schuch, D., Queiroz, A.P., Fisch, G., Correa, F., & Coutinho, M.M. (2017). The Long-Range Memory and the Fractal Dimension: a Case Study for Alcântara. Journal of Aerospace Technology and Management, 9, 461-468.
  • Dellal Đ, McCarl BA, Butt T (2011) The Economic Assessment of Climate Change on Turkish Agriculture, Journal of Environmental Protection and Ecology 12:376-385.
  • "Dickey DA and Fuller WA (1979), ""Distribution of the Estimators for Autoregressive Time Series with a Unit Root"", Journal of the American Statistical Association 74:427-431."
  • Dudu H, Çakmak EH (2018) Climate change and agriculture: an integrated approach to evaluate economy-wide effects for Turkey. Climate and Development, 10:275-288. https://doi.org/10.1080/17565529.2017.1372259
  • Fuller, W. A. (1996). Introduction to Statistical Time Series, second ed., New York: John Wiley and Sons.
  • Gilbert, R.O. (1987) Statistical Methods for Environmental Pollution Monitoring. Wiley New York NY. USA. pp. 336
  • Golinska, A. (2013). Detrended Fluctuation Analysis ( DFA ) in biomedical signal processing : selected examples.
  • Hacinliyan, A., & Kandıran, E. (2015). Fractal Analysis of Stock Exchange Indices in Turkey. AJIT‐e: Online Academic Journal of Information Technology, 6, 7-19.
  • Hardstone, R., Poil, S., Schiavone, G., Jansen, R., Nikulin, V., Mansvelder, H., & Linkenkaer-Hansen, K. (2012). Detrended Fluctuation Analysis: A Scale-Free View on Neuronal Oscillations. Frontiers in Physiology, 3.
  • Hurst, H. (1951). Long term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers , 6: 770-799.
  • Yue, J., Zhao, X., & Shang, P. (2010). Effect of Trends on Detrended Fluctuation Analysis of Precipitation Series. Mathematical Problems in Engineering, 2010, 1-15.
  • Kantelhardt J.W. (2015) Fractal and Multifractal Time Series. In: Meyers R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_221-3
  • Kendall, M.G. (1975) Rank Correlation Methods, 4th ed., Charles Griffin, London, UK. pp. 202
  • Koutsoyiannis, D.: Revisiting the global hydrological cycle: is it intensifying?, Hydrol. Earth Syst. Sci., 24, 3899–3932, https://doi.org/10.5194/hess-24-3899-2020, 2020.
  • Kurnaz, M. (2004). Application Of Detrended Fluctuation Analysis To Monthly Average Of The Maximum Daily Temperatures To Resolve Different Climates. Fractals, 12, 365-373.
  • López-Lambraño, A., Fuentes, C., López-Ramos, A., Ramírez, J., & López-Lambraño, M. (2018). Spatial and temporal Hurst exponent variability of rainfall series based on the climatological distribution in a semiarid region in Mexico. Atmosfera, 31, 199-219.
  • Mall RK, Gupta A, Singh R, Singh RS, Rathore LS (2006) Water resources and climate change: an Indian perspective. Curr Sci 90:1610-1626.
  • Mandelbrot-Wallis. (1969). Robustness of the rescaled range R/S in the measurement of noncyclic longrun statistival dependence. Water Resources Research , 5: 967-988.
  • Mann, H.B. (1945) Non-parametric tests against trend. Econometrica. 13, 245-259.
  • Márton, L., Brassai, S.T., Bakó, L., & Losonczi, L. (2014). Detrended Fluctuation Analysis of EEG Signals. Procedia Technology, 12, 125-132.
  • Meshram, S., Kahya, E., Meshram, C., Ghorbani, M.A., Ambade, B., & Mirabbasi, R. (2020). Long-term temperature trend analysis associated with agriculture crops. Theoretical and Applied Climatology, 140, 1139-1159.
  • Onyutha, C. (2020). Graphical-statistical method to explore variability of hydrological time series. Hydrology Research.
  • Osborn, T. J., Gosling, S., Wallace, C., & Dorling, S. (2015). The Water Cycle in a Changing Climate. 7th World Water Forum. Faircount Media Group, London, 14–19.
  • Palmer MA, Reidy Liermann CA, Nilsson C, Flörke M, Alcamo J, Lake PS, Bond N (2008) Climate change and the world's river basins: anticipating management options. Frontiers in Ecology and the Environment, 6:81-89. https://doi.org/10.1890/060148.
  • Papagiannaki, K., Lagouvardos, K., Kotroni, V., & Bezes, A. (2015). Flash flood occurrence and relation to the rainfall hazard in a highly urbanized area, Nat. Hazards Earth Syst. Sci., 15, 1859-1871
  • Peng, C. K., Buldyrev, S. V., & Simons, M. "Nature and Fractals." Physics Rev, 1994: 168.
  • Peters EE. 1994. Fractal Market Analysis: Applying Chaos Theory to Investment and Economic. John Wiley and Sons: New York, NY.
  • Raimundo, M.S., & Okamoto, J. (2018). Application of Hurst Exponent (H) and the R/S Analysis in the Classification of FOREX Securities. International Journal of Modeling and Optimization, 8, 116-124.
  • Said E and Dickey DA (1984), ""Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order"", Biometrika 71:599-607.
  • Taqqu MS, Teverovsky V, Willinger W. 1995. Estimators for long range dependence: an empirical study. Fractals 3: 785– 788.
  • Tatli, H. (2015), Detecting persistence of meteorological drought via the Hurst exponent. Met. Apps, 22: 763-769. https://doi.org/10.1002/met.1519
  • Weron, R. (2001). Estimating long range dependence: finite sample properties and confidence intervals. HSC Research Reports.
  • Xie, F., Yuan, N., Qi, Y. et al. Is long-term climate memory important in temperature/precipitation predictions over China?. Theor Appl Climatol 137, 459–466 (2019). https://doi.org/10.1007/s00704-018-2608-0
  • Yuan N, Fu Z, Liu S (2013) Long-term memory in climate variability: a new look based on fractional integral techniques. J Geophys Res 118(23):12962–12969.
  • Yuan N, Fu Z, Liu S (2014) Extracting climate memory using fractional integrated statistical model: a new perspective on climate prediction. Sci Rep 4:6577.
  • Zhou, Q., Arnbjerg-Nielsen, K., Mikkelsen, P. S., Nielsen, S. B., & Halsnæs, K. (2012). Urban drainage design and climate change adaptation decision making. Kgs. Lyngby: DTU Environment
  • Zhu X, Fraedrich K, Liu Z, Blender B. (2010). A demonstration of long‐term memory and climate predictability. J. Clim. 23: 5021– 5029.

Details

Primary Language English
Subjects Civil Engineering
Journal Section Articles
Authors

Sertac ORUC (Primary Author)
Kırşehir Ahi Evran Üniversitesi
0000-0003-2906-0771
Türkiye

Publication Date January 31, 2022
Published in Issue Year 2022, Volume 14, Issue 1

Cite

APA Oruc, S. (2022). Persistence of Rainfall Time Series: Kırşehir Case Study . International Journal of Engineering Research and Development , 14 (1) , 246-255 . DOI: 10.29137/umagd.868317

All Rights Reserved. Kırıkkale University, Faculty of Engineering.