Geoscience Reference
In-Depth Information
be a useful threshold in terms of process (Bull and Kirkby,
1997; Kirkby and Bracken, 2009). In particular, as flow
concentrates so that it becomes sufficiently competent to
produce sediment detachment and thus the formation of
rills (and gullies), flow depths and erosion rates typically
increase by an order of magnitude, modifying the nature
of feedbacks to the infiltration and runoff processes. The
principal characteristic of overland flows on hillslopes is
the high relative roughness of the surface compared to
the flow depth. This roughness significantly affects the
pathways and rates of flow transfers and the scientific and
methodological basis for understanding these processes is
still relatively young. Recent attempts to combine all of
the relevant information have been within a connectivity
framework.
more completely (Neuman, 1977; Hassanizadeh, 1986).
Standard methods exist for determining
K
s
as a function
of particle-size data, based on laboratory testing of homo-
geneous materials (e.g. Campbell, 1985), but most arid
region soils are rather heterogeneous in nature.
Most dryland soils are rarely saturated, but condi-
tions of unsaturated infiltration were addressed in the
early twentieth century by Buckingham (1907) and more
conceptually by Richards (1931), who coupled Darcy's
equation to a one-dimensional continuity equation. The
Richards
equation
exists
in
several
forms,
the
most
straightforward of which is
K
(
)
1
∂θ
∂
∂
∂
+
∂ψ
(
θ
)
t
=
θ
(11.2)
z
∂
z
11.2
Infiltration processes
is the volumetric soil-moisture content [L
3
/L
3
],
where
θ
K
(
) is the hydraulic conductivity [L/T], i.e. the hydraulic
conductivity as a function of the moisture content of the
soil (and equal to
K
s
when the soil is saturated), and
θ
Infiltration is the critical threshold for understanding
runoff generation and thus flooding and related geomor-
phic processes. This importance is reflected by the amount
of research carried out to evaluate and predict infiltration
rates under specific conditions. Yet, in many cases, the
definition of this threshold is far from simple and many
applications result in unhelpful calibrations of models so
that any understanding achieved through measurement is
undone. The difficulties in making such predictions lie in
part in the use of simplified conceptual models, which are
problematic in a range of conditions that pertain in dry-
lands. The standard model for infiltration starts off with
an exposition of Darcy's 'law':
)
is the soil suction as a function of the moisture content [L].
At saturation,
K
(
ψ
(
θ
θ
=
K
s
by definition, and the soil suction
is zero, so that Equations (11.1) and (11.2) can be seen to
be equivalent at this point. Soil suction is a highly nonlin-
ear and hysteretic function of soil moisture, which is one
reason why the Richards equation is extremely difficult
to solve in practice (see Baird, 2003). Simplified approx-
imations
K
(
)
), usually ignoring the hysteresis,
have been developed from laboratory testing (e.g. Brooks
and Corey, 1964; Van Genuchten, 1980). Where soils are
layered, the values of the parameters can be estimated for
each layer, but this approach does not overcome lateral
heterogeneity, which is another important characteristic
of dryland soils.
The steady-state assumption of the Darcy-Richards ap-
proach is also rarely met in dryland conditions, not least
because of the high temporal variability of rainfall when
it does occur. Not only will the rainfall input be chang-
ing dramatically but also will the pressure head. Unsteady
flows may also develop from feedbacks within the system.
De Rooij (2000) reviewed the literature on infiltration that
occurs as discrete fingers rather than as a uniform wetting
front and suggested that unsteady infiltration is likely to
occur when there is acceleration of the flow through the
profile. In dryland soils, a higher flow rate just below the
surface is likely to occur in soils that have high stone cov-
ers (especially at times when vesicular horizons have de-
veloped below the stones), mechanical or microbial crusts,
or water-repellent layers developed from burning (see be-
low). Furthermore, the temperature of the surface will also
θ
) and
ψ
(
θ
K
s
dH
dz
=−
q
(11.1)
where
q
is the rate of flow [L/T],
K
s
is a constant usu-
ally called the saturated hydraulic conductivity [L/T] and
d
H
/d
z
[L/L] is the pressure gradient. The negative sign
relates to the convention of measuring the pressure gra-
dient negative downwards. It is informative to recognise
that the law is not a strict one scientifically, but was based
on empirical observations (Henri Darcy was an engineer
responsible for the water supply in the French city of Di-
jon, who was interested in characterising the rates of flow
through beds of sand used to filter the water). It is based
on a number of assumptions, specifically homogeneity
of material, saturated flow, steady-state conditions and
relatively low rates of viscous flow. Indeed, when these
conditions are met, the equation can be derived from the
Navier-Stokes equations, which describe fluid motions
