An alternative to specious linearization of environmental models

The solution of a number of environmental models is incorrectly obtained by linearizing a nonlinear analytical solution. The linearization can yield a model that includes a common variable on both sides of the equal sign (i.e., ratio analysis), which in calibration causes highly inflated goodness-of-fit statistics. These specious practices continue likely because of tradition, i.e., “that is the way it is done”. Goodness-of-fit statistics that result from these erroneous practices do not accurately reflect the actual prediction accuracy of the model. Additionally, the linearly calibrated coefficients can be poor estimators of the true coefficients. The goal of this paper is to demonstrate the pitfalls of models based on ratio analyses. Several environmental models are used to demonstrate the erroneous procedure. Monte Carlo simulation is used to show the distribution of the true correlation coefficient and compare it to the distribution that results from the erroneous linearization. Linearization can produce correlation coefficients above 0.9 when the actual correlation is near 0. Nonlinear least squares algorithms can be used to more accurately fit nonlinear data to nonlinear models.