Uncertainty Analysis of First Order Decay Model

Abstract

Relationships to estimate confidence intervals for linear regressions were presented to determine the uncertainty of estimates obtained from firstorder models, when the concentration in grab samples of the parameter studied has a lognormal distribution. This uncertainty is a function of the number of samples on which the model was calibrated, the locations where these samples were taken, and the variance of the grab sample. Also shown is an estimate of the probability that the true value of the predicted parameter lies above a given critical value, even though its estimate is below that value. This probability can be used as a criterion to determine if the model's results are adequate for the modeler's purposes, or to estimate how many additional samples are required to reduce this probability to levels that are acceptable, or both. As a consequence, sampling, modeling, and decision making based on the model's output is presented as one cycle within an iterative process.