Agriculture Reference
In-Depth Information
5. Implications for management strategies
5.1 Simplified modeling approach
For decision making, we propose to first make an approximate assessment based on several
simplifications. Thus, diffusion-dispersion is considered to be of secondary importance and
flow is assumed to be steady state (as a first step). For groundwater quality protection,
particularly the leached fraction of applied or spilled contaminant is of interest, because that
quantity will control the concentration in the annual recharge of the topmost aquifer. For a
particular year, both the leached fraction and the recharge (precipitation minus
evapotranspiration) may be difficult to predict, which is an example of lack of ergodicity in
time. However, if the interest is primarily for long term predictions as is the case with de-
icing chemicals applied every winter, rather than for incidental spill events, then the
uncertainty becomes considerably smaller. Regular leaching leads in that case to repetitive
concentration jumps in the upper groundwater aquifer, and whether these jumps lead to a
gradual building up of concentrations in groundwater, can be analysed according to the
method of Beltman et al. (1996) and Van der Zee et al. (2010).
In those papers, we showed how the regular leaching of contaminant can result in a
building up of concentrations in groundwater, depending on the capacity of the soil to
degrade the contaminant: Figure 7. Whereas Beltman et al. (1996) focused on degradation
and transport in an aquifer, Van der Zee et al. (2010) considered leaching from a mixed
reservoir analogous of the unsaturated soil. In essence, the mathematical formulation does
not depend on whether the first order kinetics of the contaminant transport and removal are
due to transport processes or to degradation. Hence, in analogy to the approach of Van der
Zee et al. (2010), we can consider an unsaturated soil volume, that looses contaminant to the
groundwater. The quantity that is lost, we consider below, but if the lost quantity is equal to
M and the volume of water in the unsaturated soil zone equals V, then
∆
(5)
∆
For the maximum concentrations of the resulting saw tooth pattern of concentrations, where
j is the water flux leaching from the unsaturated soil, n is the number of applications of the
contaminant, and the time step is for one year. Observe that the minimum concentrations of
this pattern are given by C-M/V.
Fig. 7. Saw tooth patterns of concentration for an application of contaminant every year for
two different values of CEC (cation exchange capacity), which controls concentration
buffering. From: Van der Zee et al. (2010).
