Decomposition of solute dispersion in watersheds across a spectrum of spatio-temporal scales

Abstract:

To quantify different dispersion phenomena affecting solute transport in a watershed may be difficult because the governing mechanisms responsible for the concentration fluctuations span a wide range of temporal and spatial scales. Heterogeneities along and between transport pathways together with the fact that dispersive processes often occur on different spatial and temporal scales generally require complex explanatory models. Here we propose a novel methodology that includes a spectral decomposition of the watershed solute response using a distributed solute transport model with spatially variable parameters applied to the network of transport pathways in surface and sub-surface water. Closed-form solutions of the transport problem in both the Laplace and Fourier domains are used to derive formal expressions of: I) the central temporal moments of a solute pulse response, and II) the power spectral response of a solute concentration time series. The latter attributes the watershed’s solute response in specific intervals of frequencies to governing processes and spatial regions within the watershed. From a set of high-frequency long-term hydrochemical data collected in Upper Hafren, Wales, we observed a systematic damping of the solute concentration in the output signal compared with the input signal. Further, we linked the watershed dispersion mechanisms to the damping of the concentration fluctuations in selected frequency intervals reflecting various environments responsible for the damping. Thus, the estimates of the same model parameters differ between the pathways contributing to different concentration fluctuations, and the specific findings include a 100 times greater typical transit time of chloride and a 3 times greater retardation of sodium for the lowest frequency fluctuations of the concentration time series compared with the highest frequency fluctuations. The frequency-dependent parameters indicate that different environments dominate the response at different temporal scales.