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 Kaiman 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.
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References
Aldrin, M.: 1988a, ‘Gaula Monitoring — Estimation of Pollution Indicators’. Report No. STAT/02/88, Norwegian Computing Center, Oslo (in Norwegian).
Aldrin, M.: 1988b, ‘Statistical Estimation of Pollution Components in Gaula, South-Trondelag’. Report No. STAT/10/88, Norwegian Computing Center, Oslo (in Norwegian).
Harrison, P. J. and Stevens, C.F.: 1976, ‘Bayesian Forecasting’, J. Roy. Stat. Soc, Ser. B 38, 205–228.
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.
Kohn, R. and Ansley, C. F.: 1986, ‘Estimation, Prediction and Interpolation for ARIMA Models with Missing Data’, J. Am. Stat. As. 81, 751–761.
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.
Sæbø, H. V.: 1987, ‘Gaula Monitoring — Some Statistical Problems’. Report No. STAT/15/87, Norwegian Computing Center, Oslo (in Norwegian).
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© 1989 Kluwer Academic Publishers
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Aldrin, M., Damsleth, E., Sæbø, H.V. (1989). Time Series Analysis of Unequally Spaced Observations - With Applications to Copper Contamination of the River Gaula in Central Norway. In: Chapman, D.T., El-Shaarawi, A.H. (eds) Statistical Methods for the Assessment of Point Source Pollution. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1960-0_8
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DOI: https://doi.org/10.1007/978-94-009-1960-0_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7376-9
Online ISBN: 978-94-009-1960-0
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