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