Environmental Engineering Reference
In-Depth Information
9
Real-Time Updating in Flood
Forecasting and Warning
PETER C. YOUNG
Introduction
model parameters and state variables are updated at
each sampling instant on the basis of the estimates
obtained at the previous sampling instant.
Many different recursive algorithms for both pa-
rameter and state estimation have been proposed
over the last 50 years: see, for example, the discus-
sion on this topic in the topics by Bryson and
Ho (1969), Jazwinski (1970), Maybeck (1979), Ljung
and Soderstrom (1983), Young (1984), Norton (1986),
Harvey (1989), and Durbin and Koopmans (2001). In
fact, recursive estimation dates back to the early
19th century, when Gauss first developed the Re-
cursive Least Squares (RLS) algorithm sometime
before 1826 [see Gauss (1826) and Appendix 2 of
Young (1984), where the Gauss derivation of RLS is
compared with the modern vector-matrix deriva-
tion]. RLS was rediscovered by Plackett (1950) and,
10 years later, Kalman developed his now famous
recursive state estimation 'filter' (Kalman 1960), the
core of which can be considered as a modified RLS
algorithm for estimating the time variable states of a
stochastic state space model.
Statistical methods of real-time state and pa-
rameter updating fall into two main groups:
'analytical' methods, such as the Kalman Filter
(KF), which are derived analytically and can be
solved simply using the resulting analytical ex-
pressions; and numerically intensive methods,
normally based onMonte Carlo Simulation (MCS)
analysis, where the statistical updates involve
simple but computationally expensive ensemble
averaging of some kind. Other examples of ana-
lytical recursive parameter estimation algorithms
include: the recursive Instrumental Variable (IV)
algorithm of Young (1970, 1974) and the related
Amodel-based flood warning system incorporates
a catchment model of some sort, normally defined
by a set of parameters (coefficients), together with
a forecasting engine that utilizes this model to
compute flow or level (stage) forecasts into the
future, based on telemetered rainfall and flow data
measured at various locations in the catchment
area. Real-time updating involves the continual
adaption of the model state variables, outputs and
parameters, so that the forecasts for various times
into the future are based on the latest available
information and are optimized, in some sense, to
minimize the forecasting errors. In the last few
years, this process has been absorbed into themore
comprehensive process of 'data assimilation' -
namely a computer-controlled process where the
data are assimilated into the computer systemon a
continuing basis and used to performvarious tasks
including state/parameter updating and flow fore-
casting/warning.
Since the monitored data are subject to noise
contamination and uncertainty of various kinds, it
is clear that the model should be defined in stochas-
tic terms and the process of real-time updating
should be considered from a statistical standpoint.
The most obvious statistical method of implement-
ing real-time updating is recursive estimation: see,
for example, Gelb (1974), Ljung and Soderstrom
(1983) and Young (1984). Here, the estimates of
