Some Initial Experiments with Neural Network Models of Flood Forecasting on the River Ouse L. See, S. Corne, M. Dougherty† and S. Openshaw School of Geography, University of Leeds, United Kingdom † Centre for Research on Transportation and Society, Högskolan Dalarna, Sweden E-mail:
[email protected] Presented at the second annual conference of GeoComputation ‘97 & SIRC ‘97, University of Otago, New Zealand, 26-29 August 1997
Summary
proaches, on the other hand, offer real prospects for a
This paper presents results and conclusions from a set of
cheaper, yet more flexible, less assumption-dependent and
experiments designed to assess the potential for using ar-
adaptive methodology well suited to modelling flood proc-
tificial neural networks in real-time flood forecasting, and
esses, which by their nature are inherently complex, non-
which highlight the principal benefits and limitations of using
linear and sometimes life critical. At a time when global
the technology in this context. The emphasis on hybrid
climatic change would seem to be increasing the risk of
approaches reflects the need to integrate existing conven-
historically unprecedented changes in river regimes, it
tional methods with alternative artificial intelligence tech-
would appear to be appropriate that alternative represen-
niques in order to produce better and more cost-effective
tations for flood forecasting should be considered. How-
forecasting systems.
ever, these new types of models will need to be less dependent on historical data and rely more on real-time ad-
1 Introduction
aptation to actual flood events, some of which may be unlike anything seen before. It has also emerged that a criti-
Neural networks are widely regarded as a potentially effective approach for handling large amounts of dynamic, non-linear and noisy data, especially in situations where the underlying physical relationships are not fully understood. They are now increasingly being employed to model complex problems as both substitutes for, and in association with, more conventional mathematical and statistical models. Neural networks are also particularly well suited to modelling systems on a real-time basis, and this could greatly benefit operational flood forecasting systems which
cal factor in achieving good model performance is disaggregation of the data. This allows the model builder to draw upon aspects of domain knowledge whilst retaining the advantages of a data driven approach. Hybrid approaches, which supplement conventional methods with artificial intelligence, may well provide both a better and more robust forecasting system, capable of adapting to changing conditions once their construction is better understood and their performance demonstrated on off-line data.
aim to predict the flood hydrograph for purposes of flood warning and control. Existing flood forecasting models
The purpose of this paper is to present a set of empirical
are highly data specific and based on complex and expen-
experiments which are part of a larger, on-going feasibility
sive-to-maintain mathematical models. Performance is
study to assess the potential use of neural networks for
related to accurate real-time data inputs, the quality of the
real-time flood forecasting. A subset of historical water
knowledge used to specify, build and operate the models,
level data from the Ouse River catchment in the United
and the ability of the models to respond to dynamic and
Kingdom was used to build neural network models for
sometimes rapidly changing events. Soft computing ap-
two prediction points in the catchment. Assessment is
Proceedings of GeoComputation ‘97 & SIRC ‘97
15
based on the performance of these models relative to
3 Artificial Neural Networks
benchmark statistical models and naive predictions evalu-
Artificial neural networks offer a significant departure from
ated according to goodness of fit, although in practice the
the conventional approach to problem-solving and have
performance of flood forecasting systems is based on the
been applied successfully to a variety of application areas
number of correct warnings issued and not merely on the
including pattern recognition, classification, optimisation
accuracy of predicted water levels. Additional customised
problems and dynamic modelling. Although neural net-
evaluation measures and the certainty of forecast levels
works were historically inspired by the biological function-
are discussed.
ing of the human brain, in practice the connection is more loosely based on a broad set of characteristics which they
2 Conventional Methods of Flood Forecasting
both share, such as the ability to learn and generalise, dis-
There are currently two main approaches employed in hy-
Openshaw (1997) for an overview of neural networks.
drological forecasting. The first is a mathematical model-
The basic function of a neural network, which consists of a
ling approach. It is based on modelling the physical dy-
number of simple processing nodes or neurons, is to map
namics between the principal interacting components of
information from an input vector space onto an output
the hydrological system. In general, a rainfall-runoff model
vector space. These neurons are distributed in layers which
is used to transform point values of rainfall, evaporation
can be interconnected in a variety of architectural con-
and flow data into hydrograph predictions by considering
figurations. Information is delivered to each neuron via
the spatial variation of storage capacity. A channel flow
the weighted connections between them. Information
routing model is then used to calculate water movement
processing within each neuron normally comprises two
down river channels using kinematic wave theory. A
stages. In the first stage, all incoming information is con-
snowmelt model is also customary in colder climates. An
verted into an activation, where the most common activa-
example of this type of deterministic modelling is the River
tion function is simply the sum of the weighted inputs. In
Flow Forecasting Model (RFFS), a large scale operational
the second stage, a transfer function, such as the sigmoid,
system currently employed on the Ouse River catchment
converts the activation into an output value.
tributed processing and robustness; see Openshaw &
(Moore et al., 1994). A neural network learns to solve a problem by modifying
16
The second main approach to flood forecasting is model-
the values of the weighted connections through either
ling the statistical relationship between the hydrologic in-
supervised or unsupervised training. In supervised train-
puts and outputs without explicitly considering the physi-
ing, neural networks are provided with a training set con-
cal process relationships that exist between them. Exam-
sisting of a number of input patterns together with the
ples of stochastic models used in hydrology are the
expected output, and adjustments to the weights are based
autoregressive moving average models (ARMA) of Box &
on the differences between observed and expected out-
Jenkins (1976) and the Markov method (Yakowitz, 1985;
put values. These adjustments are calculated using a gradi-
Yapo et al., 1993). ARMA models work on the assumption
ent descent algorithm (optionally modified for higher per-
that an observation at a given time is predictable from its
formance with refinements such as a momentum or sec-
immediate past, i.e., a weighted sum of a series of previous
ond derivative term). Currently, the most widely applied
observations. Markov methods also rely on past observa-
network is the multilayer perceptron using a supervised
tions but the forecasts consist of the probabilities that the
training algorithm, known as backpropagation. Once
predicted flow will be within specified flow intervals, where
trained, the network is validated with a testing dataset to
the probabilities are conditioned on the present state of
assess how well it can generalise to unseen data. In unsu-
the river.
pervised training, the artificial neural network attempts to
Proceedings of GeoComputation ‘97 & SIRC ‘97
identify relationships inherent in the data without knowl-
required for the practicalities of flood protection (e.g., alert-
edge of the outputs and is often used in classification prob-
ing the police, issuing of warnings to industries and house-
lems.
holds in the vicinity, protection of property, etc.) precludes
To date there have only been a handful of neural network applications that address the hydrological forecasting problem. Research has shown that neural networks have great potential as substitutes for rainfall-runoff models (Abrahart & Kneale, 1997; Minns & Hall, 1996; Smith & Eli, 1995), and Yang (1997) has demonstrated the success of neural networks, trained with a genetic algorithm, in predicting daily river levels on the Yangtze River at Yichang in China. The question now is how well can they perform when asked
lead times of less than six hours. In fact, a six hour forecast is generally too short for large scale floods but in real-time operational flood forecasting, the catchment is monitored continually and accurate six hour predictions would still be a useful source of management information. More critical is an accurate twelve hour forecast which would allow flood control teams to respond to imminent flood conditions and operate warning systems for the public as well as industries. Water levels of 3 and 2.5 metres at Skelton and Kilgram, respectively, currently trigger standby
to make short-term predictions of river flow.
4 Empirical Experiments
alarms to duty officers monitoring the catchment. If the levels continue to increase, site specific operational instructions are issued such as shutting flood gates and other
4.1 Prediction Points and Forecasting Horizons
engineering measures. In parallel, warnings of varying se-
The Ouse River catchment in Northern England is subject
inform residents and businesses in the affected areas.
verity related to flood risk are issued to authorities who
to seasonal flood events and is the focus of attention because of the availability of historical data. It is fairly typical
4.2 Establishing Benchmarks
of a UK catchment, with a mix of urban and rural land
Neural network models need to be tested and compared
uses, and is 3286 km in size. There are three main tribu-
with benchmarks provided by conventional methods. An
taries: the Nidd, the Swale and the Ure. Gauging stations
initial benchmarking exercise was undertaken to assess
are distributed throughout the catchment, on each of the
the performance of the RFFS model (MAFF Project
tributaries that flow into the River Ouse toward the city
OCS967P, 1997), currently used by the Environment
of York. Two gauging stations were chosen as prediction
Agency. The RFFS was used to predict five flood events at
points: Skelton, located just north of York on the River
forecast horizons of six, twelve, eighteen and twenty-four
Ouse, and Kilgram, located further upstream from York on
hours for two stations: Viking, located at York, and
the River Ure. A map of the study area is given in Figure 1.
Boroughbridge, situated upstream. The results showed that
Due to its location far from the headwaters, Skelton has a
forecast performance degraded appreciably with an in-
relatively stable regime while Kilgram, situated further
crease in forecast horizon, indicating that neural networks
upstream and hence closer to the headwaters, has a re-
could be used to supplement forecasts at these longer
gime that is flashier, with corresponding flood types that
time scales. Since the RFFS has not yet been configured to
are more difficult to predict. All data were originally re-
output historical forecast data, direct statistical compari-
corded at 15 minute intervals but to reduce the amount
son was not possible. In the future, as performance is
of data and thereby determine whether coarser resolu-
evaluated on additional measures available as model out-
tion data were sufficient for prediction, hourly averages
put, including peak prediction and time-to-peak, additional
were used. No data were missing in this subset.
benchmark runs will be undertaken at all prediction points
2
For prediction purposes, operational forecasting horizons of six and twelve hours are needed. The length of time
for a comprehensive comparison. For this exercise, benchmarks were produced for a six
Proceedings of GeoComputation ‘97 & SIRC ‘97
17
and twelve hour forecast at each station by (1) fitting ARMA
ence is less pronounced for Kilgram. This may reflect
models to the data, and (2) by making naive predictions.
the generally lower observed levels at Kilgram than
Naive predictions substitute the last known figure as the
Skelton;
current prediction and are a good bottom line benchmark.
c) low flows are much easier to predict than high ones
ARMA models use a weighted linear combination of pre-
yet it is the flood events which trigger alarms and warn-
vious values and shocks. Five years of hourly water level data (1982-1986) using the measurement at time t and the previous five hourly observations as inputs were used to
ings that are of greatest importance; d) naive predictions are 30 to 40% worse on average than the ARMA model forecasts for all levels; and,
fit ARMA models to the data using software developed by
e) validation results are generally lower than the training
Masters (1995). Three years of testing data (1987-1988)
results indicating that there must be fewer storm events
were then used to validate the model performance. Table
or storms of a lower magnitude in the validation dataset.
1 lists the RMS errors of the ARMA models and naive
Therefore, alternative performance measures are
predictions for each station and forecasting horizon. In
needed in addition to global goodness of fit statistics
addition, RMS errors are given for low flow levels and lev-
which can be used to assess overall flood-related per-
els above which the initial alarms are triggered according
formance rather than performance averaged out on
to the operational definitions developed by the Environ-
all levels.
ment Agency (1996) in forecasting floods on the Ouse
Neural networks could be used to improve the forecasts
catchment (1996).
of the higher flow levels and the longer forecasting horizons where the performance of the ARMA models is the
The following observations can be made from the model results given in Table 1: a) the errors for Kilgram are higher then Skelton, reflecting the flashier nature of the upstream station;
poorest.
4.3 Neural Network Models A feedforward backpropagation neural network model was
b) levels for the longer forecasting horizon are more dif-
initially developed for predicting levels at Skelton with a
ficult to predict at both stations, although the differ-
six hour forecasting horizon using the Stuttgart Neural
Table 1: RMS errors in metres for the ARMA models and naive predictions ARMA
18
Naive Prediction
Station
Levels
Testing
Validation
Testing
Validation
Skelton
All levels
0.119
0.094
0.187
0.167
6 hr
Low flows
0.082
0.067
0.174
0.154
prediction
Alarms
0.228
0.138
0.476
0.437
Skelton
All levels
0.240
0.201
0.341
0.309
12 hr
Low flows
0.181
0.166
0.319
0.286
prediction
Alarms
0.622
0.498
0.926
0.862
Kilgram
All levels
0.194
0.184
0.299
0.275
6 hr
Low flows
0.131
0.137
0.194
0.195
prediction
Alarms
0.795
0.734
0.954
0.864
Kilgram
All levels
0.224
0.204
0.329
0.300
12 hr
Low flows
0.203
0.187
0.293
0.271
prediction
Alarms
1.188
1.094
1.329
1.202
Proceedings of GeoComputation ‘97 & SIRC ‘97
Table 2: RMS errors in metres for high level events for both the neural network and ARMA models Station
Levels
Testing
Validation
Skelton
ARMA
0.228
0.138
6 hr prediction
Neural net
0.129
0.118
Skelton
ARMA
0.662
0.498
12 hr prediction
Neural net
0.343
0.280
Kilgram
ARMA
0.795
0.734
6 hr prediction
Neural net
0.321
0.370
Kilgram
ARMA
1.187
1.094
12 hr prediction
Neural net
0.440
0.567
Network Simulator package (SNNS Group, 1990-95). The
changes in previous measurements. Since the number of
same data inputs as used for the ARMA model and naive
low level events is much larger than flood events, both
predictions were employed for testing and validation of
models become good at recognising small changes, but
the neural network. A variety of different architectures
when large changes in level were encountered under a
was examined, and the best result was an overall RMS er-
flood situation, the resulting predictions were highly exag-
ror of 0.108 metres, obtained with a fully connected
gerated. This also indicates that a global model for pre-
multilayer neural network containing 24 neurons in each
dicting all river levels is inappropriate.
of two hidden layers. The network was trained for about 17,000 epochs using a momentum of 0.5 and a gain of 0.2. An improvement of just over 9% relative to the ARMA model was obtained. However, after disaggregating the data into low levels and flood events, the results indicated that all the neural network improvements over the benchmarks were gained on the low level events, and the ARMA model and naive predictions outperformed the neural network at the higher levels. Given that the low level events comprised more than 90% of all observations in the dataset,
Therefore, a subset of the data comprising only high level events (as defined above by the levels at which alarms and warnings are triggered), was used to train a feedforward backpropagation neural network for each station and forecasting horizon. Network architecture was reexamined, and smaller neural networks with two hidden layers of 6 and 12 neurons were finally chosen. Convergence varied between 40,000 and 70,000 epochs using a momentum of 0.6 and a learning coefficient of 0.8. Results from the neural networks and the ARMA models are listed above in
the neural network appeared to be concentrating most learning efforts on low level events and was not able to
Table 2.
learn the high level events satisfactorily, regardless of net-
The results show that there were significant improvements
work size or training time. The final trained neural net-
in overall performance of high level event prediction with
work also seemed to converge on a similar solution to the
the neural network, especially for the flashier upstream
ARMA model, i.e., both models exhibited similar devia-
station and for the longer forecasting horizons. However,
tions from the actual observations. In general the devia-
given that the input data included only previous measure-
tions were small oscillations about a very smooth observed
ments, the neural network models were not able to learn
level record and these oscillations were generally more
those situations where the hydrograph was starting to fall,
pronounced at higher levels, accounting for the poorer
resulting in peak hydrograph overprediction. This can be
performance. This indicates that both the ARMA and neu-
seen in Figure 2, which shows flood events over a period
ral network models are extremely sensitive to small
of one month in 1988 (part of the validation dataset). The
Proceedings of GeoComputation ‘97 & SIRC ‘97
19
neural network is only predicting higher levels at which
ral network (Kohonen, 1984). The idea is to produce a
alerts and warnings are triggered as defined above, and
series of characteristic event types, for example, low level
ARMA predictions are substituted at the remaining lower
events with little rainfall, rising hydrograph events with high
levels for graphing purposes. Looking at only higher level
amounts of rainfall, etc., and build a neural network for
events, the amount of overprediction is slightly less for the
each event type similar to the approach undertaken by
neural network models than it is for the ARMA models.
Van der Voort et al. (1996) in forecasting traffic flow. The
The amount of overpredicton is also more pronounced at
main advantage of this approach is that each network can
longer forecasting horizons. A degree of oscillating behav-
concentrate on learning only a small task so that training
iour is still apparent by the neural network models at the
is quick; moreover, the antecedent conditions of a wet or
higher flows, and this behaviour can clearly be seen by
dry catchment or high levels of evaporation can be incor-
looking at the ARMA model predictions at lower levels.
porated into the models, thereby capturing some of the
Having established that neural networks can improve performance, additional data inputs such as rainfall and upstream level data appropriately lagged to account for travel times between stations could be incorporated into the simple neural network model. These extra variables should allow the network to learn the rising and falling limbs of the hydrograph more accurately and then more comprehensive evaluation measures such as the peak prediction and the time-to-peak prediction can be employed to assess the performance of the models. As mentioned previously, additional benchmarks from the Environment Agency’s own RFFS model will then be used to compare per-
physical properties of flood events which is analogous to the model states of a large-scale hydrodynamic modelling system. A disadvantage of this approach is the large number of models which need to be built because the total forecasting will eventually cover 15 prediction points scattered throughout the catchment. However, since training times are quick, which could be a critical factor in adaptive neural networks, overall development time should still be relatively minor compared to the development times associated with large-scale physical hydrodynamic flood forecasting systems. The individual flood prediction models will eventually be linked via a fuzzy logic model that will recommend which sub-network model to use at the current
formance.
time t based on similar inputs used in the clustering exercise. This is a variation of an approach used by Dougherty
20
5 Towards an Operational Hybridised Flood Forecasting System
(1997) in which a simple Bayesian technique is used to
The initial results of the neural network models for Skelton
fuzzy logic approach will be a more generalised version of
and Kilgram indicate that there are improvements in per-
the Bayesian one. When transitions between event types
formance to be gained by using neural networks as an ad-
occur, the fuzzy logic model will be able to recommend
ditional tool for flood forecasting. As a global model, neu-
more than one model but to differing degrees and the
ral networks perform worse than statistical models on
resulting prediction will be a weighted average of the sug-
the important flood events but by simply disaggregating
gested models. In this way, the imprecision associated with
the data into low and high level events, the neural net-
event types that occur over a broad spectrum of behav-
works can concentrate their efforts on learning a smaller
iour will be captured directly in the modelling system.
number of similar patterns and thus significantly improve
Other possibilities include integrating ARMA models and
their forecast accuracy. Experiments with a more intelli-
predictions from the conventional hydrodynamic system
gent disaggregation scheme have already been undertaken
(RFFS) currently employed by the Environment Agency into
as part of the ongoing feasibility study, whereby previous
the controlling fuzzy logic model to improve forecasts in
level measurements, rainfall data and information about
situations where conventional models may still outperform
day length have been clustered with a self-organising neu-
the neural networks or for low flow forecasting which is
Proceedings of GeoComputation ‘97 & SIRC ‘97
switch between different forecasting methods although the
less important for flood control. In addition to improving forecasts, a hybridised system will need to produce certainty measures, i.e., an indication of the certainty of the forecast which operational staff can use in determining whether to issue a flood warning. As PCs and workstations become more powerful, it will be feasible to bootstrap the forecasts and the resulting confidence intervals can then be used as a means of assessing the quality of the forecasts being made. There is no sug-
under their Open Contracting System under MAFF grant OCS967P. The opinions expressed in this paper are those of the authors and do not reflect Ministry policy.
References Abrahart, R.J. and Kneale, P.E. (1997). Exploring neural network rainfall-runoff modelling, paper submitted to the Sixth National Hydrological Symposium, University of Salford, Manchester, 15-18 September, 1997.
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placed by machines but there is every indication that they
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by automated, adaptive, smart flood forecasting methods that they can learn to trust.
6 Conclusions Initial results of an assessment of neural networks for realtime flood forecasting indicate that significant improvements in performance can be gained over conventional statistical models and naive forecasts. A critical factor to
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good model performance is in disaggregation of the data, as a global model appears to be inappropriate for forecasting all event types. Neural networks in combination with conventional methods and other artificial intelligence technologies have the potential to deliver hybridised solutions that can produce more cost effective and accurate forecasting systems, which can be used as part of a flood warning decision support system. This allows the model builder to draw upon aspects of domain knowledge whilst retaining the advantages of a data driven approach. These
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Acknowledgments Smith, J., and Eli, R.N. (1995). Neural network models of Level data for the Ouse river catchment were kindly provided by the Environment Agency. The research has been
rainfall-runoff process, Journal of Water Resources Planning and Management, 121, 499-509.
funded by the Ministry of Agriculture, Fisheries and Food
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SNNS Group, (1990-95). SNNS User Manual v.4.1, Institute for Parallel and Distributed High-Performance Systems (IPVR), University of Stuttgart, Stuttgart. Van der Voort, M., Dougherty, M.S., and Watson S.M. (1996). Combining Kohonen maps with ARIMA time series models to forecast traffic flow. Transportation Research C, 4(5), 307-318. Yakowitz, S.J. (1985). Markov flow models and the flood warning problem, Water Resources Research, 21, 81-88. Yang, R. 1997. Application of Neural Networks and Genetic Algorithms to Modelling Flood Discharges and Urban Water Quality. Unpublished PhD thesis, University of Manchester. Yapo, P., Sorooshian, S., and Gupta,V. (1993).A Markov chain flow model for flood forecasting, Water Resources Research, 29, 2427-2436.
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