Visual techniques for the detection of water quality trends: Double-mass curves and cusum functions

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Abstract
There is a great need for quantitative techniques to assess changes in water quality related to progressive watershed land-use developments, water-related impoundments or to evaluate the impact of recent sanitation programs. In choosing a physically representative variate for the water quality of the run-off, both concentrations and fluxes of pollutants must be taken into account. The importance of the climatic seasonal and hydrological factors associated with unstable event-related contributions of point and non-point pollution sources of the pollutants has lead us to simultaneously study water-discharge and pollutant flux time-series. The mass-discharge time-series are, in practice, far from being ideal for the application of classical trend analysis: they are relatively short and inaccurate: their distribution, orginating from mixed parent populations is very often highly skewed; they show a high level of serial dependence and the seasonal effects represent a large percentage of the variance, concealing possible long-term trends. Faced with the poor structure of these series which prohibits the use of statistical tests, experiments have been carried out with progressive-regressive inertial techniques, which imply the stationarity of water discharges. The double-mass technique was developed originally as a visual technique, to assess the homogeneity of precipitation records and was extended to study variations in sediment transport in modified watersheds. More recently confidence ‘rails’ and slope change detection have rendered its use more quantitative. Based on the same inertial principles, the Cumulative Sum (CUSUM) functions allow simultaneous evaluation of the covariability of the two series. An example involving weekly sampled nitrate concentrations and continuously monitored water discharges is developed.

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