Environmental Engineering Reference
In-Depth Information
2 =0.869
2 =0.865
Third Order Model: R T
Seventh Order Model: R T
2.5
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1
1
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−2
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−2.5
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1954
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Date
Date
Fig. 9.7 The effect of imposing Bayesian prior constraints on the seventh-order model: no constraint with diffuse prior
(left panel); tight constraint with Bayesian prior (right panel). (See the colour version of this Figure in Colour Plate
section.)
1944 km 2 located north of Collins, Mississippi,
USA. These data have been selected because they
have been used as the basis for recent research on
the application of some of the newest methods of
data assimilationmentioned previously: the EnKF
and the PF (Moradkhani et al. 2005a, 2005b; Smith
et al. 2006). Consequently, the results presented
below can be viewed in the context of these pre-
vious studies and themethods that they describe. 7
For simplicity of presentation and in order that
more detailed aspects of the model estimation and
forecasting system design process can be empha-
sized, the example concerns only a single model
relationship between rainfall and flow at a single
site on the Leaf River. When this methodology is
illusory; it only occurs because very tight prior
constraints have been imposed on the operation of
the recursive estimation algorithm, implying
much more confidence than justified in the a
priori assumed values of the parameter estimates.
There are, of course, numerous high-order
catchment simulation models used in hydrology,
and so the Bayesian approach to estimating the
parameters in suchmodels is appealing and can be
quite useful, provided it is applied with care, rec-
ognizing that it is very dependent on the validity of
the assumed prior knowledge. Unfortunately, this
does not always seem to be the case.
Data Assimilation and Adaptive Forecasting:
An Illustrative Tutorial Example
7 Note that, in these papers, the term 'residence time' is used
incorrectly when referring to the inverse of the residence time,
with inverse time units (d 1 ); the residence time referred to in the
present section is defined in the standard manner, with daily
time units.
As pointed out earlier, this example is concerned
with daily rainfall-flow data from the Leaf River
catchment, a humid watershed with an area of
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