Distributed Models and Uncertainty in Flood Risk Management - Flood Risk Science and Management - page 291

changing parameter values until a good (or at least
acceptable) fit is obtained between observed
and predicted values. Clearly this is much more
difficult to do with a distributed model. We might
suspect that the model results will be more sen-
sitive to some parameters than others, but even
a small number of sensitive parameters can be
varied in many different ways to achieve the same
type of behaviour. In particular, in distributed
models, raising the value of a parameter in one
part of the domain might be compensated by
decreasing the value of that same parameter in
another part of the domain. Once interactions
with other parameters start to be considered, then
there will be many many different combinations
of parameters that might give similarly acceptable
predictions (Beven 2006b).
There are three obvious ways around this prob-
lem. The first is to measure the parameter values
at the sites where they are needed. This approach
has significant limitations: partly because of the
expense that would be involved in measuring
parameters everywhere; partly because subsurface
parameters cannot generally be measured by
non-destructive methods; partly because most
measurement techniques provide point measure-
ments of parameters, whichmay be different from
the effective values required by the model. The
parameters may have the same name, but may not
have the same meaning (they may not be
commensurate).
The second way is to specify parameter values on
the basis of the physical characteristics of an ele-
ment, as related to past experience in applying the
modelling concepts. This might be soil texture in
specifying soil hydraulic characteristics; it might be
vegetation cover in specifying evapotranspiration
parameters; it might be vegetation density in spec-
ifying the surface roughness of a floodplain. There
are existing databases that facilitate this process
such as the pedo-transfer functions for estimating
soil hydraulic conductivities; for example, the
US Department of Agriculture (USDA) Rosetta sys-
tem (see http://www.ars.usda.gov/Services/docs.
htm?docid ¼ 8953; Schaap et al. 1998); the US Geo-
logical Survey (USGS) website (http://wwwrcamnl
.wr.usgs.gov/sws/fieldmethods/Indirects/nvalues/

the DVSHM of Wigmosta et al. (1994); the Inter-
Agency Object Modelling System (OMS) of
Leavesley et al. (2002); and the Grid to Grid model
of Bell et al. (2007; Cole and Moore 2008). A
modification of this approach to avoid the compu-
tational burden of a large number of spatial ele-
ments is to route the runoff between hydrological
response units. The dynamic version of Topmodel
(Beven and Freer 2001b) is of this type, implement-
ing explicit routing between elements to relax the
steady-state assumption of the original Topmodel.
There is an interesting question about how
accurate these types of simplified distributedmod-
els might be in reproducing the actual character-
istics of hydrological processes. In general, they
will have an advantage of computational effic-
iency over numerical solutions of the full-contin-
uum partial differential equations of the Freeze
and Harlan blueprint. However, as noted earlier,
there are real issues about whether the Freeze and
Harlan blueprint, despite its theoretical rigour, is a
good description of the actual hydrological pro-
cesses. There is also a real lack of distributed
datasets with which to test the spatial predictions
of any distributed model. Thus, it follows that it
might be rather difficult to distinguish whether
one form of distributed model is more 'realistic'
than another (Beven 2008). We will return to this
issue below (see 'Prediction uncertainty in distri-
buted models').

Calibration Issues in Using
Distributed Models

In the previous sectionwe highlighted the fact that
distributed models in both hydrology and hydrau-
lics require very large numbers of parameter
values and that any model will require effective
values of those parameters to provide good
simulations. In principle a distributed model can
use different values of the parameters for every
element in the discretization. Since there may be
thousands of elements, there can be many thou-
sands of parameter values required. With lumped
models involving only a small number of para-
meters it is normal practice to calibrate amodel by