Effect of correlated observation error on parameters, predictions, and uncertainty

Water Resources Research
By:  and 



Correlations among observation errors are typically omitted when calculating observation weights for model calibration by inverse methods. We explore the effects of omitting these correlations on estimates of parameters, predictions, and uncertainties. First, we develop a new analytical expression for the difference in parameter variance estimated with and without error correlations for a simple one-parameter two-observation inverse model. Results indicate that omitting error correlations from both the weight matrix and the variance calculation can either increase or decrease the parameter variance, depending on the values of error correlation (ρ) and the ratio of dimensionless scaled sensitivities (rdss). For small ρ, the difference in variance is always small, but for large ρ, the difference varies widely depending on the sign and magnitude of rdss. Next, we consider a groundwater reactive transport model of denitrification with four parameters and correlated geochemical observation errors that are computed by an error-propagation approach that is new for hydrogeologic studies. We compare parameter estimates, predictions, and uncertainties obtained with and without the error correlations. Omitting the correlations modestly to substantially changes parameter estimates, and causes both increases and decreases of parameter variances, consistent with the analytical expression. Differences in predictions for the models calibrated with and without error correlations can be greater than parameter differences when both are considered relative to their respective confidence intervals. These results indicate that including observation error correlations in weighting for nonlinear regression can have important effects on parameter estimates, predictions, and their respective uncertainties.
Publication type Article
Publication Subtype Journal Article
Title Effect of correlated observation error on parameters, predictions, and uncertainty
Series title Water Resources Research
DOI 10.1002/wrcr.20499
Volume 49
Issue 10
Year Published 2013
Language English
Publisher Wiley
Contributing office(s) National Research Program - Western Branch
Description 17 p.
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Water Resources Research
First page 6339
Last page 6355
Online Only (Y/N) Y
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