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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
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
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
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
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
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
Simple Data-In Data-Out (DIDO) Strategy
Data Inputs
Amalgamation Technologiese.g., Bayesian inference,
neural networks,rule-based systems, etc.
Data Outputs
Relevance to Hydrological Forecasting
• many different hydrological modelling strategies
• may benefit from being combined
DifferentModel
Forecasts
Simple Statistics, Neural Networks
ImprovedModel
Forecast??
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
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 -
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
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
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
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
More NN Strategies
#MMF_6: used outputs from MMF_5 + differenced predictions from the models
#MMF_7: MMF_6 + actual level at time t
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
MMF_2 forecasts for Skelton: 30 Oct 1991 21:00
MMF_2 forecasts for Skelton: 4 Jan 1992 03:00
MMF_2 forecasts for Cefn Brywn: 20 Nov 1984 06:00
MMF_2 forecasts for Cefn Brywn: 27 Dec 1996 16:00
MMF_2 forecasts for Cefn Brywn: 7 Oct 1994 10:00
MMF_7 forecasts for Cefn Brywn: 7 Oct 1994 10:00
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