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Figure 4.11. Flow paths (red lines) and
potential surfaces simulated by a three-
dimensional groundwater model for the
aquifer on the Arabian peninsula. Vertical
lines are the bore holes for which
groundwater level data are available.
From
Rink et al. (2012)
.
Beven and Kirkby (
1979
) to predict zones of saturation.
The wetness index is based on four assumptions (Blöschl
and Sivapalan,
1995
): (i) the lateral subsurface flow rate is
proportional to the local slope, tan
hydrology, climate, geomorphology and ecology, and so
topographic indices may have a certain level of predictive
power that goes beyond the mere application of Darcy
s
law. In this more holistic approach, different units in a
catchment (e.g.,
'
of the terrain. This
implies kinematic flow, small slopes and that the water-
table is parallel to the topography; (ii) hydraulic conduct-
ivity decreases exponentially with depth and storage
deficit is assumed to be distributed linearly with depth;
(iii) recharge is assumed to be spatially uniform and (iv)
steady-state conditions apply, so the lateral subsurface
flow rate is proportional to the recharge and the area
drained per unit contour length at a point. From these
assumptions the wetness index can be derived as the loga-
rithm of the ratio of contributing area and local slope.
Other indices (Barling et al.,
1994
; Borga et al.,
2002
;
Richardson et al.,
2009
) differ in terms of their assump-
tions but in essence they are similar in that they are effect-
ively simplified distributed hydrological models based on
mass balance, application of Darcy
β
; Hack and
Goodlett,
1960
; England and Holtan,
1969
; Krasovskaia,
1982
) may have different functions and are typically
formed by different processes (Blöschl and Sivapalan,
1995
). An example of this approach is the landscape clas-
sification idea of Winter (
2001
), who subdivided the con-
tinental USA into hydrological landscape units (upland,
valley side and lowland), exploiting the combination of
topographic, geological and climatic conditions. Based on
similar concepts, Rennó et al.
2008
) proposed the
'
'
nose
'
,
'
slope
'
and
'
hollow
'
(HAND) model, in
which topography is normalised according to the local
relative heights found along the drainage network. Field
data are needed to calibrate the modelled predictions,
e.g., by expert knowledge, reconnaissance field trips, or
short-term measurements to assess the groundwater table
(
Figure 4.12
). The soil water maps from this type of terrain
index can assist in parameterising distributed models or
can be directly used to discern surface and subsurface flow
paths in the landscape. Savenije (
2010
) and Gharari et al.
(
2011
) noted that this type of approach may capture feed-
back processes between water flow and geomorphic and
vegetation processes.
Height Above the Nearest Drainage
'
s law and several add-
itional assumptions. These indices have been tested by a
number of authors (e.g., Rodhe and Seibert,
1999
; Western
et al.,
2001b
), showing in many cases that they can predict
the spatial soil moisture patterns well, provided the main
assumptions are satisfied. This suggests that it is indeed
possible to reduce the complexity of distributed models to
representation of simple topographic indices if one focuses
on the dominant processes that are actually operative in a
particular landscape. However, for them to work, these
need to be already known in ungauged catchments.
The second paradigm does not start from the local equa-
tions but examines flow paths at the landscape scale.
The underlying idea is that landscapes have evolved in a
co-evolutionary way with diverse feedbacks between
'
4.4.3 Methods based on proxy data
Another class of methods starts from field-scale irrigation
experiments, reconnaissance field trips and other hydro-
logical measurements to infer the runoff mechanisms at
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