Environmental Engineering Reference
In-Depth Information
momentum loss. The second is that when rough-
ness is back-calculated from velocity profiles, it is
done so assuming that the flow is steady and
uniform, but the model is then used to predict
non-uniform flows in floods. [There is a third
reason that isworthmentioning inpassing.Nearly
all hydraulic routing models based on the
St-Venant equations make use of the Manning
uniformflow equations in defining roughness and
calculating momentum loss. In his original papers
on equations for uniform flow (Manning 1891,
1895), Manning himself rejected that equation in
favour of somethingmore complicated but dimen-
sionally more consistent.] This is a clear example
of where
effective
values of the parameters, appro-
priate at the discretization element scale, are
required to get good predictions for both hydrolog-
ical and hydraulicmodels. In fact this concept also
needs to be extended to effective values of the
input and boundary condition variables to get good
predictions. Calibration of these effective values is
an important issue in the practical application of
distributed models.
Monaghan 2005; Rodriguez-Paz and Bonet 2005;
Liu and Liu 2006).
The computational requirements of full 2D and
3D solutions are still demanding, so there have
also been attempts to link simpler 1D channel
flow solutions to simpler representations of the
distributed floodplain. Thus LISFLOOD (Bates
and de Roo 2000; Hunter et al. 2006) and JFLOW
(Bradbrook 2006) both use a diffusion wave sim-
plification of the St-Venant equations over the
floodplain, while the 1DMIKE 11 and ISIS models
can both be used with floodplain embayment ele-
ments that treat parts of the floodplain just as a
volume-filling problem. Run times for the simpli-
fied JFLOW have also been reduced significantly
(by a factor of up to 100) by making use of the
highly parallel structure on Graphics Processing
Units developed for supporting computer games
(Lamb et al. 2009). Current use of distributed
models in hydraulics to support flood mitigation
is explored in more detail in Chapter 12.
Here we will concentrate on calibration and
data assimilation issues in relation to uncertainty
estimation indistributedhydrological andhydrau-
lic models. The accuracy of hydraulic models has
been improved in recent years by the availability of
much finer-resolution data for the geometry of the
floodplain. However, distributed hydraulic mod-
els also are subject to issues of parameter defini-
tion. Normally, the most important parameters
are the channel and floodplain roughness coeffi-
cients, but these can be allowed to vary for every
element in the solution domain. Roughness is
something that can be back-calculated, of course,
from measurements of point velocity profiles.
Within a cross-section, velocity profiles are nor-
mally averaged to allow the back-calculation of a
roughness value for that cross-section. But such
point values are not what might be required for the
model to provide good predictions, for two reasons.
The first is that themodel predictions aremade for
elements (or groups of elements when roughness
is assumed constant over larger numbers of ele-
ments) within which the geometry and boundary
characteristicsmay be changing andwithinwhich
internal eddying caused by secondary currents and
lateral velocity gradients might lead to additional
Simplified Distributed Models
These unavoidable uncertainties in model struc-
ture, parameter values and boundary conditions
have meant that there has been plenty of scope for
the use of simpler models that do not pretend to
have such a theoretical basis as the Freeze and
Harlan blueprint or the REW concepts. Some of
these models have been around for some time and
were developed when computational limitations
were much more severe, but with the aim of
making use of GIS and remote-sensing databases.
Others have been aimed at large-scale (national or
global) prediction systems, when large numbers of
spatial elements might be required and computa-
tion time remains an issue. They may be subdi-
vided into a number of broad categories in several
ways: herewewill distinguishmodels that neglect
transfers between distributed elements (except
in the channel network); models that treat such
transfers implicitly or analytically; and models
that
treat
such transfers
explicitly. More
