Multi-Model Data Fusion for Hydrological Forecasting Linda See 1 and Bob Abrahart 2 1 Centre for Computational Geography, University of Leeds, UK 2 School of Earth and Environmental Sciences, University of Greenwich, UK

What is Data Fusion? process of combining information from multiple sensors and/or data sources RESULT = 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 Technologies e.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 Different Model Forecasts Simple Statistics, Neural Networks Improved Model Forecast??

Study Areas Two contrasting sites: Ê Upper River Wye at Cefn Brywn (Wales, UK) –small, flashy catchment Ë the River Ouse at Skelton (Yorkshire, UK) –stable regime at the bottom of a large catchment

Individual Forecasting Models

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 model Naïve predictions Output (Skelton) Level at t+6 Hidden Layer

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) Data

MMF_2 forecasts for Skelton: 30 Oct :00

MMF_2 forecasts for Skelton: 4 Jan :00

MMF_2 forecasts for Cefn Brywn: 20 Nov :00

MMF_2 forecasts for Cefn Brywn: 27 Dec :00

MMF_2 forecasts for Cefn Brywn: 7 Oct :00

MMF_7 forecasts for Cefn Brywn: 7 Oct :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