Universal fractal scaling in stream chemistry and its implications for solute transport and water quality trend detection

Abstract

The chemical dynamics of lakes and streams affect their suitability as aquatic habitats and as water supplies for human needs. Because water quality is typically monitored only weekly or monthly, however, the higher-frequency dynamics of stream chemistry have remained largely invisible. To illuminate a wider spectrum of water quality dynamics, rainfall and streamflow were sampled in two headwater catchments at Plynlimon, Wales, at 7-h intervals for 1–2 y and weekly for over two decades, and were analyzed for 45 solutes spanning the periodic table from H + to U. Here we show that in streamflow, all 45 of these solutes, including nutrients, trace elements, and toxic metals, exhibit fractal 1/ f α scaling on time scales from hours to decades (α = 1.05 ± 0.15, mean ± SD). We show that this fractal scaling can arise through dispersion of random chemical inputs distributed across a catchment. These 1/ f time series are non–self-averaging: monthly, yearly, or decadal averages are approximately as variable, one from the next, as individual measurements taken hours or days apart, defying naive statistical expectations. (By contrast, stream discharge itself is nonfractal, and self-averaging on time scales of months and longer.) In the solute time series, statistically significant trends arise much more frequently, on all time scales, than one would expect from conventional t statistics. However, these same trends are poor predictors of future trends—much poorer than one would expect from their calculated uncertainties. Our results illustrate how 1/ f time series pose fundamental challenges to trend analysis and change detection in environmental systems.