Tuesday, 11 February 2003: 2:45 PM
Percolation theoretical treatments of water retention and unsaturated hydraulic conductivity: Relevance to water and energy fluxes across land–air interface
In porous media as elsewhere, models based on self-similarity of
topology/geometry have
received increasing attention in the last 20 years, especially in view of
physical fracture
treatments, which generate fractal media, and both experimentally determined
systematic
trends of density with volume, and established power laws for water
retention, compatible with
fractal geometry. Recent treatments of fairly large soil data sets by Hunt
and Gee, 2002a,
and of Filgueira et al., 2000, have shown that particle-size data can be
used to predict the
water retention characteristics of soils over a range of moisture contents
which is typically
about 1/6 of the porosity to near saturation, but doubt has been expressed
regarding the
usefulness/appropriateness of fractal representations on account of the
deviations from
prediction, especially at low moisture content. However, in Hunt and Gee,
2002a, it is shown
that the moisture content at which this deviation occurs is typically the
same moisture
content at which solute diffusion vanishes (in a third soil data set)
Moldrup et al., 2001,
and is therefore best interpreted as the critical volume content for
percolation of capillary
flow. Using percolation theory to calculate the hydraulic conductivity of
unsaturated flow, the
fractal dimensionality of the pore space, the porosity, the saturated
hydraulic conductivity,
and the saturation (all experimentally determined) it is then possible to
predict to a high
degree of accuracy the unsaturated hydraulic conductivity, Hunt and Gee,
2002b, without
unknown parameters. The knowledge that (probably) a large fraction of the
world's soils
are fractal, and that percolation theoretical treatments explain water
retention, hydraulic
conductivity, and diffusion relationships for these media, provides
motivation for considering
new theoretical treatments of the vadose zone in land-surface inputs to
global circulation
models. Although issues of scale, "geological" heterogeneity and coverage
remain, it is suggested that
a physically-based model with the most advanced treatment of pore-scale
heterogeneity
should be an optimal starting point.
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