On the numerical accuracy of trajectory models for long‐range transport of atmospheric pollutants

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Abstract
A method to evaluate the accuracy of trajectory models for the Long‐Range Transport of Atmospheric Pollutants (LRTAP) is described. The method involves derivation of horizontally non‐divergent wind fields from streamfunctions that are dependent on latitude and longitude. Appropriate choice of seven adjustable parameters enables a fairly realistic simulation of frictionless flow to be made. The differential equations for trajectories in these analytically specified flows are solved numerically with a high degree of accuracy, giving a standard against which results from trajectory models may be compared. Theoretical estimates suggest that an important source of error in LRTAP trajectory models is horizontal interpolation of wind data. This error is significantly reduced through use of a cubic interpolation scheme. Theory also indicates that truncation error in the trajectory equation can be made almost negligible in comparison with observational errors by using a “constant‐acceleration” scheme. A linear scheme for temporal interpolation of wind data is shown to be sufficiently accurate, if observational and horizontal interpolation errors are considered. Likewise, an assumption of constant map‐scale factor during each time step is shown to give errors that are negligible except in cases of strong meridional circulation. An example of an application of the method to a trajectory model is used to confirm the theoretical conclusions regarding horizontal interpolation of wind data.

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