Skip to main content
SpringerLink
Log in

An ARMA(1,1) model for monthly stream flows

  • Original Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

An Erratum to this article was published on 16 February 2017

Abstract

The partial auto-correlation coefficients of most of the series of monthly stream flows recorded in Turkey of lag greater than one are within the 99% confidence band while the lag-one partial correlation coefficient is highly significant. An ARMA(1,1) model to compute synthetic monthly flows up to 5000 years is developed, which is different from the ones presented in relevant sources. Having observed mostly skewed standardized variates, they are normalized by the 3-parameter log-normal distribution whose parameters are computed by the method of maximum-likelihood (LN3-ML). The two parameters of the ARMA(1,1) model are computed so as to minimize the sum of squares of differences of the observed and computed standardized–normalized variates rather than minimizing the sum of squares of the random component terms. Application of the developed model on the 64-year-long monthly flow series of the unregulated Kızılırmak River in Turkey is given here as an example, which reveals plausible results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Box GEP, Jenkins GM, Reinsel GC (2008) Time series analysis forecasting and control, Fourth edn. John Wiley & Sons Inc., Hoboken, New Jersey, USA

    Google Scholar 

  • Can I, Yerdelen C (2005) Auto-regressive moving-average (ARMA) modeling of monthly flows of M Kemalpasa River, Susurluk Basin. Journal of Faculty of Engineering and Architecture of Selcuk University 20(3):25–34

    Google Scholar 

  • Karabörk MÇ, Kahya E (1999) Multivariate stochastic modeling of monthly streamflow of rivers in Sakarya Basin (in Turkish). Turk J Eng Environ Sci 23(1999):133–147

    Google Scholar 

  • Kottegoda (1980) Stochastic water resources technology. The MacMillan Press Ltd., Hong Kong

    Book  Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in Fortran 77, the art of scientific computing, Second edn. Cambridge University Press, UK

    Google Scholar 

  • WMO (2009) Guide to Hydrological Practices, Volume II, Management of Water Resources and Application of Hydrological Practices, WMO–No. 168. Sixth Edition, World Meteorological Organization, 7 bis, avenue de la Paix, CH-1211 Geneva 2, Switzerland.

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Erciyes University, Kayseri, Turkey

    Tefaruk Haktanir & M Bircan Kara

Authors
  1. Tefaruk Haktanir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M Bircan Kara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tefaruk Haktanir.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s12517-017-2884-5.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Haktanir, T., Bircan Kara, M. An ARMA(1,1) model for monthly stream flows. Arab J Geosci 10, 52 (2017). https://doi.org/10.1007/s12517-017-2833-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12517-017-2833-3

Keywords

Search

Navigation