Application of stochastic models to rational management of water resources at the Damasi Titanos karstic aquifer in Thessaly Greece

  • A. Manakos
  • P. Georgiou
  • I. Mouratidis
Part of the Environmental Earth Sciences book series (EESCI)

Abstract

Several stochastic models, known as Box and Jenkins or SARIMA (Seasonal Autoregressive Integrated Moving Average) have been used in the past for forecasting hydrological time series in general and stream flow or spring discharge time series in particular. SARIMA models became very popular because of their simple mathematical structure, convenient representation of data in terms of a relatively small number of parameters and their applicability to stationary as well as nonstationary process. The application of SARIMA model to the Mati spring’s monthly discharge time series for the period 1974-2007 at Damasi Titanos karst system yielded the following results. The stationary is obtained by logarithmic transformation and the suitable model (2,0,0)(0,1,1)12 is selected by different criteria. This type of model is suitable for the Damasi Titanos karst aquifer simulation and can be utilised as a tool to forecast monthly discharge values at Mati spring for at least a 4 year period. SARIMA model seem to be capable of simulating both runoff and groundwater flow conditions on a karst system and also easily adapt to their natural conditions.

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References

  1. Ahn H, Salas JD, (1997) Groundwater head sampling based on stochastic analysis. Water Resour. Res. 33(12), 2769-2780CrossRefGoogle Scholar
  2. Akaike H, (1974) A new look at the statistical model identification. IEEE Trans. Autom. Control. AC-19(6), 716-723Google Scholar
  3. Box GEP, Jenkins GM, (1976) Time Series Analysis: Forecasting and Control. Revised Edition. Holden Day, Inc., San Francisco, Calif., 532 pGoogle Scholar
  4. Box GEP, Pierce DA, (1970) Distribution of autocorrelations in autoregressive integrated moving average time series models. J. Amer. Stat. Assoc, 180Google Scholar
  5. Hannan EL, Quinn BG, (1979) The determination of the order of an autoregression. J. Roy. Stat. Soc. B., 41, 190-195Google Scholar
  6. Hipel KW, McLeod AI, (1994) Time Series Modelling of Water Resources and Environmental Systems. Elsevier Science B.V., Developments in Water Science, No 45, 1013CrossRefGoogle Scholar
  7. Manakos A, (1999) Hydrogeological behavior and stochastic simulation of Krania Elassona karstic aquifer Thessaly. PhD Thesis, Aristotle University of Thessaloniki, 214 p. (in Greek)Google Scholar
  8. Manakos A, Dimopoulos G (2004) Contribution of stochastic models to the sustainable water management. The example of Krania Elassona karstic aquifer in Thessaly. Proceedings of the 10th International Conference of Greek Geol. Society, April 15-17, Thessaloniki, 361-368 (in Greek)Google Scholar
  9. Manakos A, Georgiou P, (2009) Time series modeling of groundwater head using seasonal stochastic models SARIMA. Proceedings of the common Conference of the 11th Hellenic Hydrotechnical Society and of the 7th Conference of the Hellenic Committee of Water Management, 27-30 May, Volos, 709-716 (in Greek)Google Scholar
  10. Mohan S, Vedula S, (1995) Multiplicative seasonal arima model for longterm forecasting of inflows. Water Res Manag 9, 115-126Google Scholar
  11. Papamichail DM, Antonopoulos VZ, Georgiou PE (2000) Stochastic models for Strymon river flow and water quality parameters. Proceedings of the International Conference “Protection and Restoration of the Environment V”, Thassos, Greece, Vol. I, 219-226Google Scholar
  12. Papamichail DM, Georgiou PE, (2001) Seasonal ARIMA inflow models for reservoir sizing. J. Amer. Water Res. Assoc. 37(4), 877-885Google Scholar
  13. Schwartz G, (1978) Estimating the dimension of a model. Ann. Statist, 6, 461-464CrossRefGoogle Scholar
  14. Yurekli K, Kurunc A, Oztrurk F (2005) Application of linear stochastic models to monthly flow data of Kelkit Stream. Ecol. Mod. 183, 67-75CrossRefGoogle Scholar
  15. Voudouris K, Georgiou P, Stiakakis E, Monopolis D, (2010) Comparative analysis of stochastic models for simulation of discharge and chloride concentration in Almyros Karstic Spring in Greece. e-Proceedings of the 14th Annual Conference of the International Association of Mathematical Geosciences, IAMG 2010, Budapest, Hungary, 15 pGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • A. Manakos
    • 1
  • P. Georgiou
    • 2
  • I. Mouratidis
    • 3
  1. 1.IGMEThessalonikiGreece
  2. 2.Department of Hydraulics, Soil Science and Agricultural Engineering, Faculty of AgricultureAristotle University of ThessalonikiThessalonikiGreece
  3. 3.VoulgaroktonouKozaniGreece

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