Biogeochemical Filtering of Solute Signals During Transport Through Hillslopes
N.B. Basu1, P.S.C. Rao2 and S. Zanardo2,3
1
University of Iowa, Civil and Environmental Engineering
Purdue University, School of Civil Engineering
3
Dept. IMAGE, University of Padova, Padova, via Loredan 20, I-35131, Italy
2
The filtering of water and solute pulses transport through the hillslopes can be considered as
equivalent to a shot-noise process with non-linear dynamics and spatial heterogeneity controlling
the temporal patterns of observed signals at the watershed outlet. The stochastic behavior of the
contaminant loads generated from hillsopes was modeled using the Mass Response Functions
(MRF) approach (Rinaldo et al., 2006). MRF model was able to capture nitrate and atrazine
dynamics at the outlet of the Little Vermillion River basin (~400 km2) in Illinois. The primary
assumption of this model is that the evolution of solute concentration in the water pulses depends
only on the residence time and not on its trajectory; thus, space is replaced by time. The hillslope is
conceptualized as an immobile source zone, in which first-order biogeochemical reactions
(degradation rate constant, ke) alter the solute mass, in contact with multiple mobile rainfall pulses
exchanging mass (following linear kinetics). The MRF model is thus, analogous to the
mobile/immobile zone model used previously to describe contaminant transport in the saturated
domain (that have been explored using fractal ADEs), with a range of mass-transfer constants that
describe the observed power-law breakthrough curves. In contrast, in MRF model, there is one
mass-transfer rate constant, but multiple contact times corresponding to multiple rainfall pulses.
Interesting clustering behaviour was observed in the output signal as a function of the dynamics of
the solute source function in the immobile zone, and degradation during transport in the hillslope. In
a recent work (Botter et al 2006), stream discharge probability density function (pdf) has been
described as a generalized Gamma distribution with few climate and landscape parameters, such as
the rainfall frequency and mean depth, and the mean travel time through the hillslope. Given the
direct relationship between discharge and solute loads, the pdfs for intra-annual variations in solute
loads are also expected to follow a Gamma distribution. What are the alternate stochastic treatments
and physical conceptualizations that can decsribe the filtering of the rainfall Poisson distribution to
generate the stream flow and load pdfs?.