A linear systems approach to watershed transport simulation

Models that simulate loadings of pollutants from agricultural landscapes to surface waters often operate at time scales that are relatively coarse (e.g. daily) compared with how fast water moves in streams, suggesting a commensurate physical scale that is substantially larger than typical agricultural fields. In general, as pollutants enter water and move downstream, longitudinal dispersive effects and travel time de‐synchronization tend to cause flattening and broadening of concentration peaks—an effect with implications for potential impacts on ecological and human health, and for which adequate representation is thus important for risk assessment. In‐stream transport is often approximated in practice using numerical implementation of the one‐dimensional advection–dispersion equation (ADE), with streams discretized into linked homogeneous segments. However, when a daily time step is employed, limitations inherent in the finite difference methodology may constrain simulated dispersion in lotic waters to unrepresentative or unrealistic magnitudes. In this paper, a convolution‐based approach to surface water transport is suggested as an alternative to the ADE, for use in combination with daily input loading models. This approach offers the advantage of greater flexibility in representing longitudinal mixing by using impulse response functions (IRF) to represent inter‐segment transport. Networks of stream segments are represented using nested convolutions, implemented using forward and inverse discrete Fourier transform to simplify calculations. Enhanced representational flexibility arises from the freedom afforded the modeller in selecting each segment's IRF, which may be chosen to represent dispersive regimes ranging from pure advection (plug flow) to compete mixing, and beyond to the sort of long‐tailed mixing characterized by fractal inverse frequency power‐law scaling. The approach is explored in proof‐of‐concept exercises that make use of atrazine monitoring data sets collected over common time periods from upstream and downstream locations within the same watersheds. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.