Process realism: flow paths and storage - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 64

1000 1000 1000

100 100 100

10

10 10

c)

a) b)

1

1 1

1 1.5 2 2.5 3 3.5 4 4.5

Drainage density (km/km 2 )

0 300 600 900 1200 1500 0.0 0.2 0.4 0.6 0.8 1.0

Proportion responsive soil (-)

L/G (m)

Figure 4.10. Mean transit times (MTT) from stable isotope analysis plotted against (a) ratio of flow paths length and gradient (L/G) for catchments in
Oregon. After McGuire et al.( 2005 ). (b, c) Proportion of responsive soils and drainage density for catchments in Scotland. After Hrachowitz et al.
( 2009 ).

4.4 Estimating flow paths and storage
in ungauged basins
4.4.1 Distributed process-based models
Mathematical modelling provides a powerful method for
estimating flow paths in catchments based on a bottom-up
approach. The modelling can take many forms, including
lumped models and spatially explicit (distributed) models
of catchment surface and subsurface response (Grayson
and Blöschl, 2001 ). The general idea behind distributed
models is usually Newtonian mechanics, i.e., start from the
laboratory-scale constitutive relations such as Darcy

For ungauged catchments, distributed models can still
be very useful provided the uncertainty associated with the
predictions of flow paths, storage and ultimately runoff is
analysed and documented. The models can be used as a
quantification of the perceptual model the analyst has
developed on the basis of the subsurface catchment struc-
ture, the flow paths and the permeability of soils, and how
these relate to the dynamic catchment response. The mod-
elling may include combined groundwater - surface water

-

models to infer stream aquifer interactions, as illustrated

by Massuel et al.( 2011 ) for a catchment in south-west
Niger. Some of the variables needed for the hydrological
modelling (depth to bedrock, average hydraulic resistances
and retention properties of the soils) can be estimated from
proxy data within some (admittedly wide) limits of uncer-
tainty. Even in the absence of runoff data, such a model
can be tested by ad hoc field surveys (e.g., seismic surveys,
spot sampling of streamflow and soil moisture) and
more qualitative methods of reading the landscape (see
Chapter 3 ). Because of these issues, and for computational
convenience, several index methods have been developed
as alternatives to estimate flow paths and storage in
ungauged catchments.

s law
and combine them with balance equations (e.g., mass
balance, momentum balance etc.) and additional assump-
tions about hydrological processes and their spatial vari-
ability. The fundamental belief behind this approach is that
these small-scale governing equations can be combined on
the basis of an a-priori concept of how catchments work.
The approach usually adopts a mechanistic concept that a
catchment is composed of many hillslopes (or smaller
elements, in some cases), each of which consists of soil
profiles, and the hillslopes (or other smaller building
blocks) are connected by stream paths (Zehe et al.,
2007 ). For groundwater flow and transport problems such
distributed models are the obvious choice, since spatial
groundwater level data are often available ( Figure 4.11 ).
For runoff simulations, however, several challenges have
been recognised in early work (Freeze and Harlan, 1969 );
they are mostly related to scale issues, and the lack of
unifying governing equations representing the various flow
paths at the catchment scale (Beven, 2001 ). The debate of
the 1980s and early 1990s about the relative merits of
models of different levels of complexity has now largely
subsided, as it has been realised that the value of such
distributed models really hinges on the degree to which
they can be validated in a spatially distributed way (Gray-
son et al., 2002 ).

'

4.4.2 Index methods
Simplified representations of hydrological processes
within a catchment where topography is the most import-
ant control can be achieved by topographic indices (Moore
et al., 1991 ). Such indices provide the water storage avail-
able in different parts of the catchment, as well as the
partitioning of surface and subsurface flow paths, and can
therefore be used as the basis for estimating runoff in
ungauged basins. There are two alternative paradigms cur-
rently in operation for representing topographic controls on
hydrological processes. The first is Newtonian, and the
classic example is the topographic wetness index of