Statistical treatment of sunfleck length inside willow coppice

Different sunfleck characteristics, length and number of sunflecks per metre and sunfleck fractional area, were measured at different depths inside willow (Salixviminalis) canopy. All these characteristics depend on the pathlength of the direct solar radiation beam into the canopy, τ=L/sin h, where L is the downward cumulative leaf area index and h is the solar elevation. The mean sunfleck length View the MathML source decreases exponentially with τ. The maximum length of short sunflecks (length <6 cm) decreases linearly with τ, but not exponentially. Like the number of short sunflecks, the total number of sunflecks increases with τ, reaches a maximum value of 10–12 sunflecks m−1 at τ=2.5 and then decreases slowly to zero at τ=6. The vertical profiles of the sunfleck fractional area are different for long (length >6 cm) and short sunflecks. The fractional area of long sunflecks decreases with τ exponentially; the fractional area of short sunflecks, kSS, can be approximated by the formula kSS=0.19τ exp(−0.15τ2), and the fractional area of all sunflecks kS, by the formula kS=exp(−0.18τ2). Within the canopy, direct solar radiation is present in two areas — in sunflecks and in penumbra. The total flux of direct solar radiation in penumbra is smaller than it is in sunflecks and reaches its maximum value of 50% at the pathlength τ=2. There exists a good correlation with R2=0.94 between the fractional area of umbra, kU, and the fractional area of sunflecks, kS, which can be fitted by the exponential formula kU=0.63 exp(−2.30kS).