Geoscience Reference
In-Depth Information
Thus, it may not be possible to predict ahead of time whether a flood stage will definitely be exceeded in
a event; it may, however, be possible to assess the risk that the flood stage will exceeded by consideration
of the distribution of (uncertain) predictions.
As noted earlier, the propensity for error in the predictions during extreme events also suggests that
it would be advantageous to use an adaptive modelling strategy, so that if a comparison of observed
and predicted discharges reveals that the model predictions are in error, then a strategy for adjusting the
model predictions can be implemented. This is clearly only possible where discharge or river stage
measurements can be made available in real time. Adaptation is also more easily implemented for
simpler models.
An early comparison of real-time forecasting methods, including adaptive schemes, was carried
out by the World Meteorological Organisation (WMO, 1975) and a review of approaches has been
given by Moore (1999). Ensemble forecasting systems have been reviewed by Cloke and Pappen-
berger (2009) including experience from the Hydrological Ensemble Prediction Experiment (HEPEX)
(Schaake
et al.
, 2007).
It is also possible to take an approach that makes no attempt at all to model runoff generation during
flood forecasting. As noted in Section 4.6, neural net models and support vector machine models have
recently been popular as a means of estimating
N
-step ahead flood discharges, using inputs that include
rainfalls and previous values of discharge or water levels and a training set of historical events (see
Figure 4.13). In discussing neural network models, however, it has already been noted that such models
are grossly over-parameterised and there has to be some concern then that methods based only on data
analysis might not be accurate in predicting events more extreme than those included in the training set.
We consider some simple strategies for real-time forecasting here. The first is an adaptive deterministic
method due to Lambert (1972) that is very difficult to beat in forecasting the response of small catchments.
This Input-Storage-Output (ISO) model has been used in a number of UK flood forecasting schemes,
particularly in the River Dee catchment in north Wales. The second is an adaptive form of the transfer
function models considered in Section 4.3.2. Adaptive transfer functions can be used for both rainfall-
runoff and upstream discharge (or stage) to downstream discharge (or stage), depending on what data
are available. The example application presented in the case study of Section 8.5 is for an operational
forecasting model for the town of Carlisle in Cumbria, that uses both rainfall-flow and discharge-
discharge transfer functions. Adaptation of such models can be implemented in a number of different
ways. In the Carlisle model, a simple adaptive gain parameter is used, i.e. the transfer function is scaled
up or down in real time without changing its form. This simple approach has proven very effective in this
and other applications. We also briefly consider the Bayesian forecasting system and quantile regressions
as other ways of adding uncertainty to the forecasts of deterministic rainfall-runoff models.
These types of model can be made part of a larger flood forecasting system that includes flood routing
components. For the River Dee catchment, for example, ISO models were developed for all the gauged
subcatchments and linked to a flood routing model. The Forecasting and Early Warning System (FEWS)
developed by Deltares in the Netherlands (e.g. Werner
et al.
, 2004) provides a unified framework for
networking different model components in this way that has been implemented in a number of other coun-
tries including the UK Environment Agency National Flood Forecasting System. The FEWS software is
freely available under licence (see Appendix A).
8.4.1 The Lambert ISO Model
The idea behind Alan Lambert's ISO model is wonderfully simple. It is based on the development of a
master recession curve for a catchment or subcatchment where a period of discharge measurements are
available, by piecing together partial recession curves from individual events. In general, the shape of
such a recession curve may not be easily represented by a simple mathematical function but Lambert
