Estimating Trends in Stream Water Quality with a Time-varying Flow Relationship
DOI:
https://doi.org/10.17713/ajs.v27i1&2.528Abstract
The concentration of many elements in stream water depends in some way on the discharge. When looking for trends in these concentrations it is helpful to allow for this dependency. There are two advantages to this: the noise due to varying flow can be removed and thus the trend more clearly seen, especially if there are large variations in the flow over time (e.g. wet and dry years), and if the changes in the flow relationship arecorrectly modelled trends in high and low flow water can be investigated separately. This paper proposes an exploratory model in which the logarithm of the concentration is linearly related to that of the flow, but in which the slope of this relationship is allowed to vary smoothly through time, both with a long term trend and seasonally. The model also fits a trend in the intercept, which is also allowed to vary seasonally. The seasonal pattern is
fixed, but the amplitude of the seasonal variations is allowed to vary smoothly through time. Thus the model is very flexible, and allows more aspects of the changes in water quality to be investigated than is the case with simpler models. For example, by predicting the concentrations at 95 and 5 percentile flow, the trends in high and low flow water quality can be investigated, even though these flows are rarely achieved in most data sets.
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