On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change

Ezéchiel Obada; Eric Adéchina Alamou; Eliezer I. Biao; Abel Afouda

doi:doi:10.11648/j.hyd.20160404.11

| Peer-Reviewed

On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change

Ezéchiel Obada, Eric Adéchina Alamou, Eliezer I. Biao, Abel Afouda

Published in Hydrology (Volume 4, Issue 4)

Received: 28 June 2016 Accepted: 8 July 2016 Published: 28 July 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Climate Change hypothesis pushed the scientific community to question the characteristics of the classical statistics such as mean, variance, standard deviation, covariance, etc. in the hydroclimatic field. Many studies have revealed that the climate has always changed and that these changes are closely related to the Hurst phenomenon detected in long hydroclimatic time series and in stochastic term which is equivalent to a simple scaling behavior of climate variability on the time scale. A new statistical framework taking into account the climatic variability is now applied. Most studies are at annual scale where variability at finer scales is not taken into account. This paper proposes to verify the validity of the new statistical framework at finer time scale: the daily time scale. Twelve (12) daily time series of flows, rainfalls and temperatures with 18,628 observations, each one, were studied. Four different methods, such as Rescaled range Statistic (R/S) method, R/S modified method, Aggregate Variances method and Aggregated Standard Deviation (ASD) were applied to determine the Hurst exponent (H). All methods lead to the conclusion that the investigated time series have a long-term persistence phenomenon. Contrary to annual time series where variability corresponds to a Simple Scaling Stochastic (SSS) process, the daily time series seem to correspond to a process having both a SSS component and a deterministic component.

Published in	Hydrology (Volume 4, Issue 4)
DOI	10.11648/j.hyd.20160404.11
Page(s)	35-45
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Climate Change, Hurst Phenomenon, Hydroclimatic, Persistence, Uncertainty

References

[1]	Koutsoyiannis, D., 2013a. Hydrology and change, Hydrological Sciences Journal, 58: 6, 1177–1197.
[2]	Koutsoyiannis, D., 2003. Climate change, the Hurst phenomenon, and hydrological statistics. Hydrological Sciences Journal, 48 (1), 3–24.
[3]	Koutsoyiannis, D., 2010. HESS Opinions “A random walk on water”. Hydrology and Earth System Sciences, 14, 585 601.
[4]	Von Storch, H., von Storch, J-S. & Müller, P. (2001) Noise in the climate system—ubiquitous, constitutive and concealing. In: Mathematics Unlimited—2001 and Beyond (ed. by B. Engquist & W. Schmid). Springer, Berlin, Germany.
[5]	Hurst, H. E., 1951. Long term storage capacities of reservoirs. Transactions of the American Society of Civil Engineers, 116, 776–808.
[6]	Koutsoyiannis, D., 2002. The Hurst phenomenon and fractional Gaussian noise made easy. Hydrological Sciences Journal, 47 (4), 573–595.
[7]	Koutsoyiannis, D., 2011a. Hurst-Kolmogorov dynamics as a result of extremal entropy production. Physica A: Statistical Mechanics and its Applications, 390 (8), 1424–1432.
[8]	Koutsoyiannis, D., 2011b. Hurst-Kolmogorov dynamics and uncertainty. Journal of the American Water Resources Association, 47 (3), 481–495.
[9]	Mesa, O. J. & Poveda, G. (1993) The Hurst effect: the scale of fluctuation approach. Water Resour. Res. 29 (12), 3995– 4002.
[10]	Haslett, J. & Raftery, A. E. (1989) Space–time modelling with long-memory dependence: assessing Ireland’s wind power resource. Appl. Statist. 38 (1), 1–50.
[11]	Bloomfield, P. (1992) Trends in global temperature. Clim. Change 21, 1–16.
[12]	Eltahir, E. A. B. (1996) El Niño and the natural variability in the flow of the Nile River. Water Resour. Res. 32 (1) 131–137.
[13]	Radziejewski, M. & Kundzewicz, Z. W. (1997) Fractal analysis of flow of the river Warta. J. Hydrol. 200, 280–294.
[14]	Montanari, A., Rosso, R. & Taqqu, M. S. (1997) Fractionally differenced ARIMA models applied to hydrologic time series. Water Resour. Res. 33 (5), 1035–1044.
[15]	Stephenson, D. B., Pavan, V. & Bojariu, R. (2000) Is the North Atlantic Oscillation a random walk? Int. J. Climatol. 20, 1–18.
[16]	Klemeš, V., 1974. The Hurst phenomenon: a puzzle? Water Resources Research, 10 (4), 675–688.
[17]	Le Barbé L., Alé G., Millet B., Texier H., Borel Y. (1993). Monographie des ressources en eaux superficielles de la République du BENIN. Paris, ORSTOM, 540 pages.
[18]	Totin V. S. H., Boko M., Ogouwale E., 2002. Dynamique de la mousson Ouest africaine, régime hydrologique et gestion de l’eau dans le bassin supérieur de l’Ouémé. LECREDE, 12 pages.
[19]	Biao I. E., Gaba C., Alamou A. E. and Afouda A., 2015. Influence of the uncertainties related to the Random Component of Rainfall Inflow in the Ouémé River Basin (Benin, West Africa). International Journal of Current Engineering and Technology. Vol 3, N°3.
[20]	Mandelbrot B. B. et Wallis J. (1968). Noah, Joseph and Operational Hydrology. Water Resources Research, vol 4, pp. 909-918.
[21]	Beran, J., 1994. Statistics for long-memory processes. New York: Chapman and Hall.
[22]	Taqqu M. S., Teverovsky V. et Willinger W., 1995. "Estimators for Long-Range Dependence: An Empirical Study", Preprint, Boston University.
[23]	Lo A. W., 1991. Long-term memory in stock market prices. Econometrica, vol. 59, No. 5, 1279-1313.
[24]	Mandelbrot B. B. et Wallis J. (1969). "Robustness of the Rescaled Range R/S in the Measurement of Noncyclic Long-Run Statistical Dependence", Water Resources Research, vol. 5, pp. 967-988.
[25]	Mandelbrot, B. B., 1972. "Statistical Methodology for Non Periodic Cycles: From the Covariance to R/S Analysis", Annals of Economic and Social Measurement, vol. 1, pp. 259-290.
[26]	Mandelbrot, B. B. et Taqqu, M. S., 1979. "Robust R/S Analysis of Long-Run Serial Correlation". Bulletin of the International StatisticalInstitute, vol. 48, pp 69-104.
[27]	Davies, R. B. and Harte, D. S., 1987. “Tests for Hurst effect”, Biometrika, 74, 95 − 101.
[28]	Mandelbrot, B. B., 1973. "Le problème de la réalité des cycles lents et le syndrome de Joseph". Economie Appliquée, vol. 26, pp. 349-365.
[29]	Newey, W. and West, K.., 1987. A simple positive definite, heteroscedasticity and autocorrelation consistent covariance matrix. Econometrica, vol 55, pp. 703-705.
[30]	Lo, A., And Mackinlay, C., 1989. “The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation,”, Journal of Econometrics, 40, 203 − 238.
[31]	Andrews, D., 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation", Econometrica, vol. 59, pp. 817-858.
[32]	Koutsoyiannis, D. and Montanari, A., 2007. Statistical analysis of hydroclimatic time series: uncertainty and insights. Water Resources Research, 43 (5), W05429, doi: 10.1029/2006WR005592.
[33]	Koutsoyiannis, D., 2013b. Encolpion of stochastics: fundamentals of stochastic processes [online]. Athens: National Technical University of Athens. Available from: http://itia.ntua.gr/1317/ [Accessed 6 May 2013].
[34]	Tyralis, H., and D. Koutsoyiannis, 2010. Simultaneous estimation of the parameters of the Hurst- Kolmogorov stochastic process, Stochastic Environmental Research & Risk Assessment, DOI: 10.1007/s00477-010-0408-
[35]	Koutsoyiannis, D., Yao, H., and Georgakakos, A., 2008. Medium-range flow prediction for the Nile: a comparison of stochastic and deterministic methods. Hydrological Sciences Journal, 53 (1), 142–164.

Cite This Article

Plain Text BibTeX RIS

APA Style

Ezéchiel Obada, Eric Adéchina Alamou, Eliezer I. Biao, Abel Afouda. (2016). On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change. Hydrology, 4(4), 35-45. https://doi.org/10.11648/j.hyd.20160404.11

Copy | Download

ACS Style

Ezéchiel Obada; Eric Adéchina Alamou; Eliezer I. Biao; Abel Afouda. On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change. Hydrology. 2016, 4(4), 35-45. doi: 10.11648/j.hyd.20160404.11

Copy | Download

AMA Style

Ezéchiel Obada, Eric Adéchina Alamou, Eliezer I. Biao, Abel Afouda. On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change. Hydrology. 2016;4(4):35-45. doi: 10.11648/j.hyd.20160404.11

Copy | Download

@article{10.11648/j.hyd.20160404.11,
  author = {Ezéchiel Obada and Eric Adéchina Alamou and Eliezer I. Biao and Abel Afouda},
  title = {On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change},
  journal = {Hydrology},
  volume = {4},
  number = {4},
  pages = {35-45},
  doi = {10.11648/j.hyd.20160404.11},
  url = {https://doi.org/10.11648/j.hyd.20160404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.hyd.20160404.11},
  abstract = {Climate Change hypothesis pushed the scientific community to question the characteristics of the classical statistics such as mean, variance, standard deviation, covariance, etc. in the hydroclimatic field. Many studies have revealed that the climate has always changed and that these changes are closely related to the Hurst phenomenon detected in long hydroclimatic time series and in stochastic term which is equivalent to a simple scaling behavior of climate variability on the time scale. A new statistical framework taking into account the climatic variability is now applied. Most studies are at annual scale where variability at finer scales is not taken into account. This paper proposes to verify the validity of the new statistical framework at finer time scale: the daily time scale. Twelve (12) daily time series of flows, rainfalls and temperatures with 18,628 observations, each one, were studied. Four different methods, such as Rescaled range Statistic (R/S) method, R/S modified method, Aggregate Variances method and Aggregated Standard Deviation (ASD) were applied to determine the Hurst exponent (H). All methods lead to the conclusion that the investigated time series have a long-term persistence phenomenon. Contrary to annual time series where variability corresponds to a Simple Scaling Stochastic (SSS) process, the daily time series seem to correspond to a process having both a SSS component and a deterministic component.},
 year = {2016}
}

Copy | Download

TY - JOUR
T1 - On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change
AU - Ezéchiel Obada
AU - Eric Adéchina Alamou
AU - Eliezer I. Biao
AU - Abel Afouda
Y1 - 2016/07/28
PY - 2016
N1 - https://doi.org/10.11648/j.hyd.20160404.11
DO - 10.11648/j.hyd.20160404.11
T2 - Hydrology
JF - Hydrology
JO - Hydrology
SP - 35
EP - 45
PB - Science Publishing Group
SN - 2330-7617
UR - https://doi.org/10.11648/j.hyd.20160404.11
AB - Climate Change hypothesis pushed the scientific community to question the characteristics of the classical statistics such as mean, variance, standard deviation, covariance, etc. in the hydroclimatic field. Many studies have revealed that the climate has always changed and that these changes are closely related to the Hurst phenomenon detected in long hydroclimatic time series and in stochastic term which is equivalent to a simple scaling behavior of climate variability on the time scale. A new statistical framework taking into account the climatic variability is now applied. Most studies are at annual scale where variability at finer scales is not taken into account. This paper proposes to verify the validity of the new statistical framework at finer time scale: the daily time scale. Twelve (12) daily time series of flows, rainfalls and temperatures with 18,628 observations, each one, were studied. Four different methods, such as Rescaled range Statistic (R/S) method, R/S modified method, Aggregate Variances method and Aggregated Standard Deviation (ASD) were applied to determine the Hurst exponent (H). All methods lead to the conclusion that the investigated time series have a long-term persistence phenomenon. Contrary to annual time series where variability corresponds to a Simple Scaling Stochastic (SSS) process, the daily time series seem to correspond to a process having both a SSS component and a deterministic component.
VL - 4
IS - 4
ER -

Copy | Download

Author Information

Ezéchiel Obada

International Chair in Mathematical Physics and Applications (ICMPA - UNESCO CHAIR), University of d’Abomey-Calavi (UAC), Cotonou, Benin
Eric Adéchina Alamou

School of Roads and Buildings, Polytechnic University of d’Abomey (UPA), Abomey, Benin
Eliezer I. Biao

West African Science Service Center on Climate Change and Adapted Land Use, GRP Water Resources University of d’Abomey-Calavi (UAC), Cotonou, Benin
Abel Afouda

West African Science Service Center on Climate Change and Adapted Land Use, GRP Water Resources University of d’Abomey-Calavi (UAC), Cotonou, Benin

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Ezéchiel Obada, Eric Adéchina Alamou, Eliezer I. Biao, Abel Afouda. (2016). On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change. Hydrology, 4(4), 35-45. https://doi.org/10.11648/j.hyd.20160404.11

Copy | Download

ACS Style

Ezéchiel Obada; Eric Adéchina Alamou; Eliezer I. Biao; Abel Afouda. On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change. Hydrology. 2016, 4(4), 35-45. doi: 10.11648/j.hyd.20160404.11

Copy | Download

AMA Style

Ezéchiel Obada, Eric Adéchina Alamou, Eliezer I. Biao, Abel Afouda. On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change. Hydrology. 2016;4(4):35-45. doi: 10.11648/j.hyd.20160404.11

Copy | Download

@article{10.11648/j.hyd.20160404.11,
  author = {Ezéchiel Obada and Eric Adéchina Alamou and Eliezer I. Biao and Abel Afouda},
  title = {On the Use of Simple Scaling Stochastic (SSS) Framework to the Daily Hydroclimatic Time Series in the Context of Climate Change},
  journal = {Hydrology},
  volume = {4},
  number = {4},
  pages = {35-45},
  doi = {10.11648/j.hyd.20160404.11},
  url = {https://doi.org/10.11648/j.hyd.20160404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.hyd.20160404.11},
  abstract = {Climate Change hypothesis pushed the scientific community to question the characteristics of the classical statistics such as mean, variance, standard deviation, covariance, etc. in the hydroclimatic field. Many studies have revealed that the climate has always changed and that these changes are closely related to the Hurst phenomenon detected in long hydroclimatic time series and in stochastic term which is equivalent to a simple scaling behavior of climate variability on the time scale. A new statistical framework taking into account the climatic variability is now applied. Most studies are at annual scale where variability at finer scales is not taken into account. This paper proposes to verify the validity of the new statistical framework at finer time scale: the daily time scale. Twelve (12) daily time series of flows, rainfalls and temperatures with 18,628 observations, each one, were studied. Four different methods, such as Rescaled range Statistic (R/S) method, R/S modified method, Aggregate Variances method and Aggregated Standard Deviation (ASD) were applied to determine the Hurst exponent (H). All methods lead to the conclusion that the investigated time series have a long-term persistence phenomenon. Contrary to annual time series where variability corresponds to a Simple Scaling Stochastic (SSS) process, the daily time series seem to correspond to a process having both a SSS component and a deterministic component.},
 year = {2016}
}

Copy | Download