An analysis of solar beam penetration through circular gaps in canopies of uniform thickness

A model for direct solar beam penetration through a canopy gap is presented. A canopy gap is assumed to be a circular opening in a canopy of uniform thickness. Distinct seasonal patterns of T_ps (daily duration of possible sunshine) under a model gap were revealed: long T_ps was found during seasons with high solar altitudes at noon, and short T_ps during those with low solar altitudes. Latitude showed profound effects on both the seasonal pattern of T_ps and gap-size dependency of T_ps; with increasing latitude, the seasonal variation of T_ps was enhanced and the beam penetration through a small gap decreased.The aspect of the slope of the ground influenced the seasonal pattern of T_ps, especially at higher latitudes. In the earth's northern hemisphere, solar beam penetration was enhanced on a south-aspect slope, but reduced on a north-aspect slope during the seasons of lower solar altitudes.On the ground below the model gap, the area where T_ps0 was an oblique ellipse extending east-west. The area moved in the north-south direction during the year. In regions of the northern hemisphere out of the tropics, the northern part of the gap projection on the ground showed much higher T_ps than the southern part. These results suggest that the direction to, not only the distance from, the gap center greatly affects the light regime on forest floors.