On Using Model Performance Statistics in Applying Models

This paper makes the case for developing a statistical model to describe the behavior of the residuals between model estimates and corresponding observations. Using a framework that relates model estimates to corresponding observations, we show that the distribution of the residuals can be conveniently characterized by the geometric mean, mg, and the geometric standard deviation, sg, of the ratio of the observed to the model estimates of the variable of interest. We demonstrate the role of these statistics in the application of the model. Postulating a linear relationship between the residual and the model estimate allows us to separate the residual/model error into two components: one that is correlated to the model estimate and can be thus reduced in principle through model improvement, and a component that can be reduced only by expanding the model input set. The second part of the paper incorporates this description of model error into a graphical representation that builds upon that proposed by Taylor, A. (2001).