Scaling and predicting solute transport processes in streams

We investigated scaling of conservative solute transport using temporal moment analysis of 98 tracer experiments (384 breakthrough curves) conducted in 44 streams
located on five continents. The experiments span 7 orders of magnitude in discharge (10^-3 to 10^3 m^3/s), span 5 orders of magnitude in longitudinal scale (10^1 to 10^5 m), and
sample different lotic environments—forested headwater streams, hyporheic zones, desert streams, major rivers, and an urban manmade channel. Our meta-analysis of these data
reveals that the coefficient of skewness is constant over time (CSK = 1.186+/-0.08, R^2 > 0.98). In contrast, the CSK of all commonly used solute transport models decreases
over time. This shows that current theory is inconsistent with experimental data and suggests that a revised theory of solute transport is needed. Our meta-analysis also shows
that the variance (second normalized central moment) is correlated with the mean travel time (R^2 > 0.86), and the third normalized central moment and the product of the first two
are very strongly correlated (R^2 > 0.96). These correlations were applied in four different streams to predict transport based on the transient storage and the aggregated dead zone
models, and two probability distributions (Gumbel and log normal).