Variance of Load Estimates Derived by Piecewise Linear Interpolation
Publication: Journal of Environmental Engineering
Volume 124, Issue 11
Abstract
Piecewise linear interpolation (PLI) is used frequently in environmental studies to estimate missing data. However, to evaluate the reliability of these estimates, the variances of these interpolated values must be quantified. We propose a procedure to quantify this PLI variance, which involves establishing a semivariogram with coefficients that are calibrated using a cross-validation technique. Estimated values are written as a linear combination of neighboring data points and the variance is calculated with the help of the variogram. Such interpolated values are unaffected by the variance quantification procedure. We then use the PLI model to calculate the variance of a yearly nutrient load under the assumption that only the nutrient concentrations contained missing values. When these results were compared with those from an arithmetic mean, a flow-weighted mean, and a linear regression model, the PLI model was found to be comparable with the other three models in terms of variance. Selection of an appropriate model depends on the characteristics of the data set. Knowing the variance of estimated loads can help regulatory agencies make better decisions to determine whether water quality in the environment is in compliance with established standards or criteria.
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Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 124 • Issue 11 • November 1998
Pages: 1114 - 1120
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Nov 1, 1998
Published in print: Nov 1998
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