multi-model data fusion for hydrological forecasting linda see 1 and bob abrahart 2 1 centre for...
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Multi-Model Data Fusion for Hydrological Forecasting
Linda See1 and Bob Abrahart2
1Centre for Computational Geography, University of Leeds, UK
2School of Earth and Environmental Sciences, University of Greenwich, UK
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What is Data Fusion?• process of combining information from multiple sensors and/or data
sourcesRESULT = a more accurate solution
OR one which could not otherwise be obtained
• analogous to the way humans and animals use multiple senses + experience + reasoning to improve their chances of survival
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Is Now a Practical Technology due to:
• provision of data from new types of sensors• development of advanced algorithms:
– Bayesian inference– Dempster-Shafer theory– neural networks
– rule-based reasoning systems • high performance computing• advances in communication
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Areas of Use
Military applications:– automated target recognition (e.g. smart weapons)– guidance for autonomous vehicles– remote sensing– battlefield surveillance
Nonmilitary applications:– robotic navigation– law enforcement– medical diagnosis
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Data Fusion• two main categories of data fusion:
– low level: fusion of raw information to provide an output
– higher level: fusion of raw + processed information to provide outputs including higher level decisions
• RESULT = a lack of standard terminology• differentiation by application domain, objective,
types of data/sensors used, degree of fusion
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Data Fusion Framework
• flexible characterisation provided by Dasarathy (1997)
• divides inputs/outputs into data, features and higher level decisions– e.g. feature might be the shape of an
object + range to give volumetric size of the object
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Simple Data-In Data-Out (DIDO) Strategy
Data Inputs
Amalgamation Technologiese.g., Bayesian inference,
neural networks,rule-based systems, etc.
Data Outputs
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Relevance to Hydrological Forecasting
• many different hydrological modelling strategies
• may benefit from being combined
DifferentModel
Forecasts
Simple Statistics, Neural Networks
ImprovedModel
Forecast??
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Study Areas
Two contrasting sites: Upper River Wye at Cefn Brywn (Wales,
UK)– small, flashy catchment
the River Ouse at Skelton (Yorkshire, UK)– stable regime at the bottom of a large
catchment
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Individual Forecasting ModelsUpper River Wye River Ouse
TOPMODEL Hybrid Neural Network (HNN)Feedforward Neural Network
(NN1)ARMA[1,2] model
NN1 + weight-based pruning(NN2)
Rule-based f uzzy logic model(FLM)
NN1 + node-based pruning(NN3)
Naïve predictions
ARMA[1,2] model -Naïve predictions -
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Simple Statistics for Combining Forecasts
#1: Arithmetic Mean– on the basis that different models might have
different residual patterns– averaging out might cancel out highly
contrasting patterns
#2: Median– might work better if the range of predicted
values are skewed
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NN-based Data Fusion Strategies
#MMF_1: Inputs (Skelton)
Hybrid Neural Network (HNN)Fuzzy Logic Model (FLM)ARMA modelNaïve predictions
Output (Skelton)Level at t+6
HiddenLayer
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NN Strategies cont’d
#MMF_2: MMF_1 but using differenced data
#MMF_3: MMF_2 + arithmetic mean of the three predictions
#MMF_4: MMF_2 + standard deviation
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NN Strategies cont’d
#MMF_5: Inputs from MMF_2 to predict model weightings based on best performance
e.g., if model_1 > model_2 & model_3 then
the models were assigned weights of 1, 0, 0
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More NN Strategies
#MMF_6: used outputs from MMF_5 + differenced predictions from the models
#MMF_7: MMF_6 + actual level at time t
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RMSE for Training (T) and Validation (V) DataCefn Brwyn (m3/hx104) Skelton (m)
Approach Model V(1984)
T(1985)
V(1986)
V40%
T60%
HNN - - - 0.056 0.051
FLM - - - 0.110 0.109
TOPMODEL 1.518 1.417 1.182 - -
NN1 Individual 0.611 0.461 0.582 - -
NN2 0.453 0.538 0.638 - -
NN3 0.475 0.575 0.705 - -
ARMA 0.398 0.668 0.706 0.098 0.082
PERSISTENCE 0.369 0.886 0.975 0.159 0.165
MEAN 0.424 0.528 0.516 0.086 0.087
MEDIAN 0.364 0.534 0.613 0.085 0.086
MMF_1 1.350 0.660 1.900 0.011 0.017
MMF_2 0.652 0.402 0.577 0.010 0.014
MMF_3 Multi- model 0.620 0.400 0.580 0.010 0.014
MMF_4 0.620 0.410 0.560 0.010 0.014
MMF_5 0.403 0.462 0.520 0.041 0.042
MMF_6 0.519 0.439 0.509 0.013 0.016
MMF_7 0.533 0.398 0.488 0.011 0.015
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MMF_2 forecasts for Skelton: 30 Oct 1991 21:00
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MMF_2 forecasts for Skelton: 4 Jan 1992 03:00
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MMF_2 forecasts for Cefn Brywn: 20 Nov 1984 06:00
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MMF_2 forecasts for Cefn Brywn: 27 Dec 1996 16:00
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MMF_2 forecasts for Cefn Brywn: 7 Oct 1994 10:00
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MMF_7 forecasts for Cefn Brywn: 7 Oct 1994 10:00
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Conclusions
• can extend data fusion to many new areas including hydrological modelling
• data fusion, at the simplest DIDO level, can result in improvements in prediction but requires further testing
• also has potential relevance at higher decision making levels for flood forecasting and warning systems