Fitting a Circular Distribution to a Histogram

Abstract

In meteorology, wind directions are often recorded to the nearest of 16 points of the compass. When studying the diffusion of air pollutants downwind from a source, it is often desirable to have much higher resolution?on the order of 1°. To obtain such high resolution, one is essentially faced with fitting a continuous distribution to a histogram. The basic problem is one of interpolating between observed directions. On a circle, a natural first approach is to use harmonic analysis; however, this can produce negative densities. One solution to this problem is similar to the techniques of spectrum estimation, using a window function to obtain a smooth, non-negative density.