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Quantification of the predictive uncertainty of artificial neural network based river flow forecast models
Published in
2013
Volume: 27
   
Issue: 1
Pages: 137 - 146
Abstract
The meaningful quantification of uncertainty in hydrological model outputs is a challenging task since complete knowledge about the hydrologic system is still lacking. Owing to the nonlinearity and complexity associated with the hydrological processes, Artificial neural network (ANN) based models have gained lot of attention for its effectiveness in function approximation characteristics. However, only a few studies have been reported for assessment of uncertainty associated with ANN outputs. This study uses a simple method for quantifying predictive uncertainty of ANN model output through first order Taylor series expansion. The first order partial differential equations of non-linear function approximated by the ANN with respect to weights and biases of the ANN model are derived. A bootstrap technique is employed in estimating the values of the mean and the standard deviation of ANN parameters, and is used to quantify the predictive uncertainty. The method is demonstrated through the case study of Upper White watershed located in the United States. The quantitative assessment of uncertainty is carried out with two measures such as percentage of coverage and average width. In order to show the magnitude of uncertainty in different flow domains, the values are statistically categorized into low-, medium- and high-flow series. The results suggest that the uncertainty bounds of ANN outputs can be effectively quantified using the proposed method. It is observed that the level of uncertainty is directly proportional to the magnitude of the flow and hence varies along time. A comparison of the uncertainty assessment shows that the proposed method effectively quantifies the uncertainty than bootstrap method. © 2012 Springer-Verlag.
About the journal
JournalStochastic Environmental Research and Risk Assessment
ISSN14363240
Open AccessNo
Concepts (34)
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    AVERAGE WIDTH
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    BOOTSTRAP METHOD
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    BOOTSTRAP TECHNIQUE
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    FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
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    FIRST-ORDER TAYLOR SERIES
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    FLOW DOMAINS
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    FORECAST MODEL
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    Function approximation
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    HYDROLOGIC SYSTEMS
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    HYDROLOGICAL MODELS
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    HYDROLOGICAL PROCESS
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    MODEL OUTPUTS
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    Nonlinear functions
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    Predictive uncertainty
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    Quantitative assessments
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    River flow
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    Simple method
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    Standard deviation
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    UNCERTAINTY ASSESSMENT
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    Uncertainty bounds
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    Neural networks
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    Partial differential equations
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    Taylor series
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    Uncertainty analysis
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    Artificial neural network
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    Bootstrapping
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    Flow field
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    Flow modeling
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    Forecasting method
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    Numerical model
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    Prediction
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    Quantitative analysis
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    United states
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    WHITE RIVER [UNITED STATES]