Geoscience Reference
In-Depth Information
(see Box 5.4). All such relationships are defined by a number of parameter values. Parameter values need
to be specified for every element in the mesh. A variety of functional forms for describing the soil mois-
ture characteristics have been proposed. All require a number of different parameters to be specified.
Most are “singled-valued” relationships, i.e. each value of
θ
is associated with a unique value of
ψ, K
(
θ
)
and
C
(
ψ
). Not all soils show such single-valued relationships, however. The appropriate curves for a
soil that is wetting may be different to the appropriate curves for a soil that is drying. This is known as
soil moisture hysteresis. The appropriate values of
ψ, K
(
θ
) and
C
(
ψ
) then depend on the changes in
θ
over time. There are some models of hysteretic soil moisture characteristics available (see, for example,
the review by Jaynes, 1990), but they tend to rely on idealised representations of the soil to simplify the
problem of keeping track of the wetting and drying history of each node. Most models of this type have
tended to neglect hysteresis of the soil moisture characteristics in actual applications.
Measuring the soil moisture characteristics, whether in the field or on samples brought back to the
laboratory, is time-consuming and expensive and, in heterogeneous soils, the values obtained on one
sample may not be representative of the effective grid element values needed in the model. One tech-
nique that has been developed to solve this problem is the use of what have been called
pedotransfer
functions
, which attempt to provide estimates of the parameter values in mathematical descriptions of
the soil moisture characteristics curves in terms of variables, such as soil texture variables, that are more
easily measured (see Box 5.5). The idea is fine in principle but may need to be applied with some circum-
spection in practice since the pedotransfer functions currently available have generally been developed
from data obtained from small sample experiments. The parameter values estimated in this way may,
then, not necessarily be appropriate at the model grid scale. Most pedotransfer functions are based on
regression analysis of soil characteristic parameters against the texture variables. The resulting estimates
can therefore be associated with a standard error of estimation as a measure of the uncertainty associated
with the estimates.
A further method for deriving the parameter values for soil moisture characteristic functions is to
calibrate a model of the functions within a Richards equation solution algorithm, so as to best simulate
a set of soil moisture and capillary potential data. Where this method is applied to a laboratory soil
column, discharge from the column can also be used in calibration. This is also called the
inverse
method
. There is a huge literature on inverse methods for groundwater problems involving only saturated
flows (see, for example, Hill and Tiedeman, 2007) and one of the most widely used groundwater flow
packages, MODFLOW2000, is now available from the USGS with a parameter optimisation routine as
MODFLOWP (Poeter and Hill, 1997). MODFLOW has also been integrated into more general catchment
rainfall-runoff models with more conceptual representations of near-surface processes, such as GSFLOW
(Markstrom
et al.
2008) and the Integrated Hydrological Modelling System (IHMS; Ragab and Bromley,
2010; Ragab
et al.
, 2010).
For unsaturated flows, the inverse method has been reviewed by Kool
et al.
(1987) and an application
to the determination of hysteretic soil moisture characteristics has been made by Sim unek
et al.
(1999).
In general, the calibration of subsurface flow parameters is not a well-posed inverse problem; there is
often inadequate information about the flow domain and estimated parameter values may be sensitive
to errors in model structure, boundary conditions and observations. Particularly in the nonlinear case
of unsaturated flow, it may be difficult to obtain a clear optimum set of parameter values (e.g. Abeliuk
and Wheater, 1990; Hollenbeck and Jensen, 1998). Parameter calibration is discussed more generally
in Chapter 7.
A number of computer packages, such as the now commercial HYDRUS2D and HYDRUS3D finite
element programs (see Appendix A) for flow and transport calculations, are available for solving the
Richards equation in one, two or three dimensions under the assumption that effective parameter values
for the Darcy flow law can be specified at the element scale ( Sim unek
et al.
, 1996; Sim unek and van
Genuchten, 2008). These also include models that use a two-domain approach to the prediction of pref-
erential flow e.g. CHAIN-2D (Mohanty
et al.
, 1998); the MACRO model (Jarvis
et al.
1991); HYDRUS
