Agriculture Reference
In-Depth Information
In addition, we have to deal with uncertainty, because the pattern if the contaminant were
released on a spot a few meters away, might look similarly irregular but not exactly the
same! It might be slightly deeper or shallower, moved to the left or right, and have another
shape. Whereas for contaminated sites, it may be meaningful to know the exact pattern, for
making predictions, the precise shape of the plume becomes less important: a calculation for
another spot would look always more or less different. For this reason, we need more robust
measures to quantify the transport behaviour, than the pictures of Figure 3.
4.2 Spatial moments
To this aim, we explain the moment theory, with which such quantification is feasible at
different levels of detail. Using this moment theory, it is feasible to illustrate the profound
impact of spatial variability on contaminant transport in terms of pollution front,
breakthrough time, and of course remediation efficiency.
If soil and aquifer properties are spatially variable, two limiting situations may arise. These
two limiting situations are related with those of point source pollution and of diffuse source
pollution, respectively. The point source pollution problem can be defined as the situation
where the source is relatively small (or of similar order of magnitude) compared with the
scale of (random) heterogeneity. In that case, the source of contaminants might be visualized
as being in a spot of large or of small hydraulic conductivity. In the first case, contaminants
may readily spread in the environment, whereas in the latter case, this occurs slowly. For
the point source pollution event, it is difficult to predict whether the source will be at in
contact with the fast or the slow route of transport, which leads to high uncertainty. In the
diffuse source pollution case, contaminants enter the soil or aquifer over a large surface, and
both fast and slow transport routes are 'sampled'. In that case, uncertainty is much smaller,
and heterogeneity leads to large spatial variability of fluxes. This distinction of two limiting
situations is illustrative, but in view of the nested scales of heterogeneity of soil and
aquifers, many real situations will be somewhere in between.
Fig. 4. Photo of a heterogeneous soil profile.
It is clear from Fig. 4, that the thickness and intensity of soil horizons varies in the horizontal
plane. As soil genesis processes involve longer time periods, spatial variability must be due
