Measures of Flow Variability for Great Lakes Tributaries

Design of monitoring programs for load estimation is often hampered by the lack of existing chemical data from which to determine patterns of flux variance, which determine the sampling program requirements when loads are to be calculated using flux-dependent models like the Beale Ratio Estimator. In contrast, detailed flow data are generally available for the important tributaries. For pollutants from non-point sources there is often a correlation between flow and pollutant flux. Thus, measures of flow variability might be calibrated to flux variability for well-known watersheds, after which flow variability could be used as a proxy for flux variability to estimate sampling needs for tributaries for which adequate chemical observations are lacking. Three types of measures of flow variability were explored: ratio measures, which are of the form q x /q y , where q x is the flow corresponding to the percentile x, and y=100-x; spread measures, of the form (q x -q y )/q m , where q m is the median flow; and the coefficient of variation of the logs of flows. In the latter, flows are log transformed because flow distributions are often approximately log-normal. Three ratio measures were evaluated, based on the percentiles (10,90), (20,80), and (25,75). The analogous spread measures were also evaluated; the spread measure based on percentiles (25,75) is derived from the commonly used fourth spread of non-parametric statistics. The ratio measures and the spread measures are scale independent, and thus are measures only of the shape of the distribution. The coefficient of variation is also scale independent, but in log space. Values of these measures of flow variability for 120 Great Lakes tributaries are highly intercorrelat-ed, although the relationship is often non-linear. The coefficient of variation of the log of the flows is also well correlated with the coefficient of variation of fluxes of suspended solids, total phosphorus, and chloride, for a smaller set of rivers where the existence of abundant chemical data allows comparison. Tributaries with abnormal distributions often show up as outliers when one measure of flow variability is plotted against another. Several examples are discussed.