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Environmental Monitoring and Assessment

, Volume 13, Issue 2–3, pp 227–243 | Cite as

Time series analysis of unequally spaced observations-with applications to copper contamination of the river gaula in central norway

  • Magne Aldrin
  • Eivind Damsleth
  • Hans Viggo Sæbø
Trend Detection

Abstract

The upper parts of the river Gaula in Central Norway are heavily contaminated by toxic metals-particularily copper (Cu).

A monitoring program for the river was established in early 1986, and the concentration of Cu, among other variables, has been measured.

There is a fairly strong temporal component in the Cu measurements, which calls for some sort of time series model. The irregular pattern of the observation times, however, makes the usual models infeasible, as they assume equi-spaced observations.

In the paper we present a simple DLM (Dynamic Linear Model) which gives a satisfactory description of the Cu concentration series. The model is fitted to the data using a Kalman filter technique which handles the irregularly spaced observations without problems.

We have utilized the model to interpolate non-observed values, estimate the net loading and to simulate alternative patterns for the Cu series, observed values and the runoff, to obtain estimates of the extreme values and the probability that the concentration has exceeded a certain limit.

Keywords

Copper Time Series Linear Model Kalman Filter Monitoring Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aldrin, M.: 1988a, ‘Gaula Monitoring-Estimation of Pollution Indicators’, Report No. STAT/02/88, Norwegian Computing Center, Oslo (in Norwegian).Google Scholar
  2. Aldrin, M.: 1988b, ‘Statistical Estimation of Pollution Components in Gaula, South-Trøndelag’. Report No. STAT/10/88, Norwegian Computing Center, Oslo (in Norwegian).Google Scholar
  3. Harrison, P. J. and Stevens, C. F.: 1976, ‘Bayesian Forecasting’, J. Roy. Stat. Soc., Ser. B 38, 205–228.Google Scholar
  4. Jones, R. H.: 1985, ‘Time Series with Unequally Spaced Data’. In Hannan, E. J. et. al. (eds.), Handbook of Statistics 5, North-Holland, Amsterdam, pp. 157–177.Google Scholar
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  6. Lingsten, L. and Sæbø, H. V.: 1987, ‘Pilot Study of the Riverine Input to Marine Waters’. Report No. 0-86201, Norwegian Institute for Water Research, Oslo.Google Scholar
  7. Sæbø, H. V.: 1987, ‘Gaula Monitoring-Some Statistical Problems’. Report No. STAT/15/87, Norwegian Computing Center, Oslo (in Norwegian).Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Magne Aldrin
    • 1
  • Eivind Damsleth
    • 1
  • Hans Viggo Sæbø
    • 1
  1. 1.Norwegian Computing CenterOslo 3Norway

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