Cascading water and solute transport through the vadose zone: advection, dispersion, and
transformations in highly non-steady flow.
Ciaran Harman1,Suresh Rao2, Nandita Basu3, Murugesu Sivapalan1,4
1
University of Illinois at Urbana-Champaign, Civil and Environmental Engineering
Purdue University, School of Civil Engineering
3
The University of Iowa, Civil and Environmental Engineering
4
University of Illinois at Urbana-Champaign, Geography
2
The transport of a sorbing, degrading solute (such as Atrazine) through the soil is largely driven
by infiltrating water from storms or irrigation, and so depends on the interactions between the timing
and characteristics of the rainfall or irrigation events, the properties of the solute, soil characteristics
(e.g, porosity, macropore density etc.), and the antecedent soil moisture conditions. This interaction
causes the time series inputs of the solute to be “filtered” prior to reaching the watertable, so that the
timing, frequency and magnitude of output events is altered. This filtering is similar in kind to “shot
noise”, but richer due to the non-linearities of unsaturated transport, and the effects of
evapotranspiration on the transmission through unsaturated zone. While many previous studies have
examined the movement of solutes through soils for a particular site, few have examined the nature of
this filtering in more general terms.
In this work we present an elegant 1-D model of solute transport through the soil, driven by
random episodes of infiltration events, that is designed to examine this filtering effect. The model
simulates transport through the soil using a Lagrangian framework, allowing simple implementation of
Fickian and non-Fickian transport through the soil. A unique feature of this model is the event-scale
time-stepping and decoupling of hydrologic and biogeochemical processes. By assuming that
infiltration and redistribution processes occur instantaneously during an event, while degradation,
mobilization, and evapotranspiration are the only important processes occurring between storms,
analytical expressions can be derived for the event-to-event transformations of the input signal within
the system. Solutes can be surface applied in recalcitrant and labile forms, with first-order mass transfer
between the pools, and linear reversible sorption. Infiltrating water mobilizes the labile dissolved
solute, generating a point load that moves through the soil with wetting fronts generated by storm
events. The retardation and first-order decay of the point-loads eventually decouples them from the
wetting fronts they first entered with, allowing solutes to concentrate in the profile. Because only one
timestep is required per storm, the model runs very fast, allowing us to examine the effect of different
parameter combinations on the filtering.
The results show that, particularly in shallow soils, solute delivery events exhibit an intriguing
clustering behavior both in time and in a phase space plot with solute inputs and initial conditions. This
clustering is caused by events that flush significant amounts of solute from the system, which occur
more rarely when soils are deeper, or degradation rates are higher.