Constrained multivariate trend analysis applied to water quality variables

Constrained multivariate regression analysis is used to model trends and seasonal effects in time series measurements of water quality variables. The constraint used ensures that when identifying trends the scientifically important charge balance of model-fitted concentrations is maintained, while accounting for between variable dependencies. The analysis is a special case of linear reduction of dimensionality which preserves the integrity of a subset of the original variables, while allowing the remainder to be identified as linear combinations of this subset. The technique is applied to water quality measurements made at the outflow from Loch Grannoch, an acid-sensitive loch in Scotland. A reduction in marine ion concentrations is observed in water samples collected four times a year over the period 1988-2000. This is identified with long term variability in the marine component in rainfall. Separation of the non-marine component of the solute load shows a reduction in non-marine sulphate and calcium concentrations, and an increase in the non-marine sodium concentration. There is no significant change in either alkalinity or acid neutralizing capacity over the period. The reduction in non-marine sulphate is consistent with reductions in atmospheric inputs of sulphate. However, the reduction in sulphate, has not been accompanied by a reduction in the acidity of water samples from Loch Grannoch, but with a reduction in calcium concentration and an apparent increase in organic acids, as evidenced by increased dissolved organic carbon concentrations, with possible increases in nitrate and non-marine sodium concentrations. Copyright (C) 2002 John Wiley Sons, Ltd.