Introduction - Runoff Prediction in Ungauged Basins: Synthesis across Processes, Places and Scales - page 3

1.2 Runoff predictions in ungauged basins are
difficult
So, how can one predict runoff at the catchment scale?
Unfortunately, there are currently no universal theories
or equations applicable for predicting runoff at the catch-
ment scale. Most of the knowledge we have of processes
that occur within the catchment has been derived at the
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range of hydrological situations, such as under much higher
precipitation. The underlying equations are universal, so
should be applicable everywhere at all times. This is
appealing since it will generate generalisable knowledge.
Also, there are many examples from sister disciplines, such
as the atmospheric sciences and river hydraulics, where
distributed models are the universal currency.
However, there are three problems with the Newtonian
approach for predicting catchment runoff. When subdivid-
ing the catchment into computational units, it is necessary
to characterise the system through which the water flows
for every single element. In principle, this may appear to be
a trivial task, but in practice it turns out to be very difficult.
In essence, the medium through which the water flows is
unknown. It is difficult to identify the spatial (and depth)
distribution of the flow parameters, such as the hydraulic
conductivity that describes how easily water moves
through a medium such as soil or rock. The runoff esti-
mated by the models is usually very sensitive to these
parameters, and even a small change will produce a big
change in runoff. It is not feasible to measure these param-
eters everywhere in a catchment, even in a research catch-
ment, let alone in routine applications needed in water
resources management, where almost always there are
strict resource and time limitations. Second, even if we
were able to characterise parameters such as hydraulic
conductivity and roughness for every pixel within a catch-
ment, computational resources currently do not allow us to
actually use laboratory-scale computational elements

or laboratory scale (Dooge, 1986 ; Blöschl, 2005b ).
The equations of flow of water are essentially valid at the
laboratory scale. Similarly, theories of infiltration we cur-
rently use are point-scale equations, and overland flow is
clearly defined at the hydrodynamic scale, developed in
hydraulic laboratories where turbulent processes are very
well researched. The challenge for predictions is to move
from the well-researched point-scale equations to the
catchment scale, something termed the upscaling problem.
One way of addressing the upscaling problem is to divide
the catchment into smaller elements, which are small
enough to apply these point-scale equations, and then
assemble these pieces together to form a model of the
entire catchment to make the required runoff predictions.
This approach could work, in principle

point '

geometrically the
catchment can be easily decomposed into sufficiently uni-
form elements. This so-called reductionist approach is then
the most logical way of building predictive models. For
estimating runoff in ungauged catchments the approach
will then lead to a form of distributed process-based hydro-
logical models that solve the governing equations for mass,
momentum and energy in a spatially explicit way, drawing
on as much laboratory-scale process understanding as
possible. In this topic we will call this the Newtonian
approach, as the essence of such models is based on
Newtonian physics or mechanics.
The Newtonian approach has numerous strengths. First
and foremost, it is based on cause-and-effect relationships.
If you change an input or a parameter of the model at some
location, there is a clearly defined response of the runoff to
this change. This is very important for many applications,
in particular for those related to change prediction. Land
use change effects can be directly simulated by these types
of models and, similarly, the approach lends itself naturally
for climate impact analyses. Second, these models are
spatially explicit and have the potential to represent pro-
cesses within the catchment in much detail, such as spatial
patterns in the infiltration characteristics, the exact channel
shape or the presence of any hydraulic structures. Again,
there is considerable benefit in the spatial representation, as
any detailed knowledge one may have about the catchment
can be fully exploited. Third, the underlying equations,
such as Darcy

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at
least a trillion elements would be needed for a catchment of
practical interest. Because of this, the elements or building
blocks of distributed processes-based hydrological models
are usually much larger, at least tens of metres. This leads
to the problem of quantifying the flow processes within
such elements, i.e., how to parameterise the effects of
subgrid variability. This parameterisation is not very well
understood either. Preferential flow phenomena may lead
to flow dynamics that are very different from those at the
laboratory scale. Third, many of the processes controlling
catchment runoff are in fact not physical processes but
chemical and biological processes. For example, soil
chemical processes may strongly affect the infiltration
characteristics. Biological activity of earth worms and
plants may alter the hydraulic conductivity considerably.
Stream

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aquifer interactions are often controlled by bio-
logical activity at their interface and transpiration is, of
course, a biologically driven process. So, while the flow
processes per se are physical phenomena, they are con-
trolled by many other processes that cannot be quantified
by means of Newtonian physics.
Because of these issues, distributed process-based
hydrological models often tend to produce biased results
when applied to real catchments. To reduce bias in the

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s equation are known to
work at the laboratory scale for a wide range of flow condi-
tions, so it should be possible to extrapolate them to a wide

s law or Manning