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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.