Geoscience Reference
In-Depth Information
Harlan “blueprint”, and many are, in fact, simplifications of that blueprint. Even so, their blueprint is not
complete. Relative to the perceptual model of Section 1.4, several elements are missing, including the
effects of macropores and other heterogeneities of the flow processes (although attempts to introduce the
effects of macropores into hillslope and catchment scale models have been made by Zuidema, 1985; and,
since then, by Bronstert and Plate, 1997; Faeh
et al.
, 1997; and Zehe
et al.
, 2005).
As noted previously, the boundaries between different types of hydrological model have become blurred
in the last decade and there have also been many developments in distributed models that are not based on
the continuum differential equations of the Freeze and Harlan blueprint. An example is the widely used
Soil Water Assessment Tool (SWAT) model. Since these models are more explicitly semi-distributed in
nature, they are considered in Chapter 6; this chapter considers only models based on solution of partial
differential equations describing surface and subsurface flows (even then, many such models involve
conceptual representations of other processes). We concentrate on the assumptions made in formulating
the differential equations, so that other distributed modelling strategies can later be evaluated in the light
of these most “physically based” models. Initially, subsurface (soil water and groundwater) and surface
(overland and channel flow) flow components are considered separately, followed by their interactions.
In Chapter 9, these ideas are critically examined in the context of a strategy for hydrological modelling
for the future.
The last decade has seen the development of a number of models of this type, in addition to those
presented in the first edition of this topic (SHE, IHDM, TOPOG, DVHSM, HILLFLOW, KINEROS,
CASC2D). New models that have appeared include the integrated hydrological model (InHM; VanderK-
waak and Loague, 2001); the TIN-based real-time integrated basin simulator (tRIBS; Ivanov
et al.
, 2004,
2008); the Pennsylvania integrated hydrological model (PIHM; Qu and Duffy, 2007); TOUGH2 (James
et al.
, 2010); the gridded surface/subsurface hydrologic analysis (GSSHA; Downer and Ogden, 2004;
Downer
et al.
2005); CATFLOW (Zehe
et al.
, 2005; Klaus and Zehe, 2010); and the Waterloo University
earth system simulator HydroGeoSphere (Therrien
et al.
, 2006). There have also been some reviews of
the experience of using such models (Beven, 2001; Loague and VanderKwaak, 2004; Refsgaard
et al.
,
2010) and important tests against detailed field information (Loague
et al.
, 2000; Bathurst
et al.
, 2004;
Ebel
et al.
2007; James
et al.
, 2010). A lot has been learned from this decade's applications about the
practice and limitations of this type of hydrological model and the case studies in this chapter have been
changed to reflect this.
5.1.1 Subsurface Flows
The basis of all descriptions of subsurface flow used in distributed models is Darcy's law, which assumes
that there is a linear relationship between flow velocity and hydraulic gradient, with a coefficient of
proportionality which is now called the “hydraulic conductivity”. Thus,
K
d
dx
v
x
=−
(5.1)
where
v
x
is velocity in the x direction [LT
−
1
],
is the total hydraulic
head
[L] and
K
is the hydraulic
conductivity [LT
−
1
]. Originally established empirically by Henri Darcy (1856) for flow through saturated
sands, Richards (1931) generalised the use of Darcy's law for the case of unsaturated flow by making
the assumption that the same linear relationship holds but that the constant of proportionality should be
allowed to vary with soil moisture content or capillary potential. Thus,
K
(
θ
)
d
dx
v
x
=−
(5.2)
where
θ
is volumetric soil moisture. The notation
K
(
θ
) is used to indicate that
K
is now a function
of
θ
. Darcy's law can be derived from more fundamental equations of flow, called the Navier-Stokes
