Geoscience Reference
In-Depth Information
form of Figure 4.6a, with discharge as the wetness index variable, has been found to be quite
useful in a number of studies). Figure B4.3.2 shows an example of the predictions of the DBM
catchment model with the nonlinearities estimated in this way.
SDP estimation of the nonlinearity has now been used in a number of different catchment
modelling studies (e.g. Young, 2000, 2001, 2003), in developing DBMflood forecasting models
(Young, 2002, 2011b; Romanowicz
et al.
, 2006, 2008; Leedal
et al.
, 2008; see also Section 8.4)
and in the emulation of hydraulic models using the upstream water level as the index variable
(Beven
et al.
, 2008b; Young
et al.
, 2009). Once the
form
of the state dependency is identified,
then the complete model of nonlinearity and transfer function is generally re-estimated in a
final step. For the interested reader, Young (2011b) gives a good explanation of state dependent
parameter estimation with a variety of examples to show the power of the methodology.
A further important use of time variable parameter estimation is in adaptive real-time flood
forecasting (see Section 8.4). In this case, errors due to the nonlinearities in the runoff generation
processes and limitations in the measurements of both rainfall and flow can be allowed for by
using an adaptive gain parameter (Lees
et al.
, 1994; Young, 2002, 2011b). In this case, only the
forward pass Kalman filtering step is normally used, since observations are only available up
to time
t
. The parameter estimates
p
t
are then used to make predictions into the future, before
being updated as new data is received at the next time step. The NVR is normally chosen so as
to give a relatively long estimator memory, so that the parameters (and consequent forecasts)
do not change too rapidly from time step to time step.
