Modeling the dispersion of atmospheric pollution using cubic splines and chapeau functions

Knowledge of the inaccuracies inherent in each method are necessary prior to their use in modeling the dispersion of atmospheric pollutants. The accuracy and amount of artificial diffusion and dispersion of each method can be easily visualized by conducting a simple test: A cosine hill distribution of concentration with a peak value of 100 is advected in a clockwise direction. The peak value and distribution should remain constant throughout the rotation. Hence, a measure of the accuracy of a method lies in its ability to transport the distribution without change. This test was used by Long and Pepper in analyzing six numerical schemes for advecting pollutant concentrations. A part of their analysis is shown here