Environmental Engineering Reference
In-Depth Information
such as the RIV algorithm introduced earlier, or
nonlinear State-Dependent Parameter versions of
this (Young 2001b). This process is repeated for
selected values of the large model parameters, and
the relationship between these parameters and the
DEM model parameters is inferred, using some
suitable mapping method, so as to produce the
complete DEM that behaves like the large model
over the whole range of selected model values.
In order to validate the model, further simula-
tions are then carried out and the ability of the
DEM to emulate the large model behaviour under
these changed circumstance is evaluated. A typi-
cal example of DEM validation is shown in
Figure 9.2, which is taken from recent papers by
Beven et al. (2008) and Young et al. (2009) and
concerns the emulation of the HEC-RAS model.
The DEM is in the form of a simple, nonlinear,
dominant-mode DBM model identified and esti-
mated from dynamic experimental data of the
kind mentioned above. The output of the DEM is
compared with HEC-RAS model validation data
based on its response to a newset of upstreamlevel
data. As we see, the DEM outputs are very similar
to the HEC-RAS model outputs at the six sites
selected for emulation.
If the DEM is able to emulate the large model
well, then it is clear that it can replace it for a
variety of purposes, such as data assimilation,
forecasting, automatic control and sensitivity
analysis, for which the concept of emulation
modelling was originally conceived: see, for ex-
ample, Conti et al. (2007).Moreover, because it is a
low-order, well-parameterized and identifiable
model, it can be updated in real time using recur-
sive estimation algorithms such as RIV and RPE.
Although research on dynamic emulation model-
ling is at an early stage, the initial results are
promising and it clearly represents a potential
approach to catchment modelling that allows for
fairly straightforward real-time updating.
e.g., Julier et al. 2000, and the prior references
therein). Instead of linearizing using Jacobian ma-
trices, as in the EKF, the UKF uses a deterministic
'sigma point filter' sampling approach to capture
themeanandcovarianceestimateswithaminimal
set of sample points. It has some similarities with
the EnKF but the random sampling strategy of the
EnKF is replaced by this deterministic approach,
whichwill bemore efficient both computationally
and statistically when its assumptions are satis-
fied. The UKF appears to be a powerful nonlinear
estimation technique and has been shown to be a
superior alternative to the EKF in a variety of
applications includingstateestimationandparam-
eter estimation for time series modelling. So it
clearly has potential relevance to rainfall-flow
modelling and forecasting, although it is not clear
whether it has been evaluated yet in this context.
However, a dual-UKF method involving state and
parameter estimation is described by Tian
et al. (2008) in relation to the design of a system
for assimilating satellite observations of soilmois-
ture using the NCAR Community Land Model.
Dynamic Emulation Modelling
Onenewapproachto real-timeupdating inthecase
of large and complex system models is the devel-
opment of a Dynamic Emulation Model (DEM).
Here, a large, and normally over-parameterized
dynamic simulationmodel is emulated by a much
smaller and identifiable 'dominant mode' model,
suchasaDBMmodel (Rattoetal. 2007a;Youngand
Ratto 2008). The process of emulation is shown
diagrammatically in Figure 9.1. The large simula-
tion model is first subjected to planned dynamic
experiments and the data so obtained are used to
identify and estimate the low order 'dominant
mode' model (Young 1999a). For instance, a flood
routing model such as ISIS or HEC-RAS (Hydro-
logicEngineeringCenterRiverAnalysis System) is
run in an unsteady flow mode and forced with an
upstream boundary condition defined by specified
flowinputs. Thewater surface level fieldgenerated
by the unsteady simulation run is then used as a
dataset for identification and estimation of a
'nominal' DEM, using an estimation algorithm,
The Model and Its Parametric Identifiability
In the previous sections, it has been assumed that
the catchment model used for forecasting is
