An equation for irregular distributions of leaf azimuth density

The von Mises equation was modified to describe numerically irregular distributions of leaf azimuth density. The new equation has three indexes: T (describing distribution elongation), S (describing number of azimuth preferences), and R (describing general canopy azimuth position). The equation was tested on two contrasting canopies: sunflower and maize. In 1998, the diurnal variation of leaf azimuths was measured weekly beginning 66 days after planting for 5 weeks. The equation was tested again in 1999. The equation characterised the leaf azimuth densities accurately (mean absolute estimation error of 0.05). For sunflower, R index was linearly related to sun azimuth, and sunflower generally tracked the sun in the same way for both years because they had almost equal R at a given sun azimuth. However, the azimuth density distribution in 1999 was slightly more clumped than in 1998, and that sunflower canopies in 1998 would fluctuate between one to two azimuth preferences, but sunflower in 1999 generally showed one azimuth preference. For maize, mean T, S and R for 1998 and 1999 were similar to each other. These values agreed with field observations, where maize canopies were usually elongated, having two azimuth preferences that were perpendicular to planting row direction. Logistic regression showed that these indexes were descriptive enough to differentiate between sunflower and maize canopies with an accuracy greater than 80%. The most important index to differentiate between canopy types was T, S, then R.