The impact of spatial correlation and incommensurability on model evaluation

Standard evaluations of air quality models rely heavily on a direct comparison of monitoring data matched with the model output for the grid cell containing the monitor's location. While such techniques may be adequate for some applications, conclusions are limited by such factors as the sparseness of the available observations (limiting the number of grid cells at which the model can be evaluated) and the incommensurability between volume-averages and pointwise observations. We examine several sets of simulations to illustrate the effect of incommensurability in a variety of cases distinguished by the type and extent of spatial correlation present. Block kriging, a statistical method which can be used to address the issue, is then demonstrated using the simulations. Lastly, we apply this method to actual data and discuss the practical importance of understanding the impact of spatial correlation structure and incommensurability.