Time Series Analysis of Unequally Spaced Observations - With Applications to Copper Contamination of the River Gaula in Central Norway

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.