VARIANCE OF LOAD ESTIMATES DERIVED BY PIECEWISE-LINEAR INTERPOLATION

Piecewise linear interpolation (PLI) is used frequently in environment al studies to estimate missing data. However, to evaluate the reliabil ity of these estimates, the variances of these interpolated values mus t be quantified. We propose a procedure to quantify this PLI variance, which involves establishing a semivariogram with coefficients that ar e calibrated using a cross-validation technique. Estimated values are written as a linear combination of neighboring data points and the var iance is calculated with the help of the variogram. Such interpolated values are unaffected by the variance quantification procedure. We the n use the PLI model to calculate the variance of a yearly nutrient loa d under the assumption that only the nutrient concentrations contained missing values. When these results were compared with those from an a rithmetic mean, a flow-weighted mean, and a linear regression model, t he PLI model was found to be comparable with the other three models in terms of variance. Selection of an appropriate model depends on the c haracteristics of the data set. Knowing the variance of estimated load s can help regulatory agencies make better decisions to determine whet her water quality in the environment is in compliance with established standards or criteria.