Statistical treatment of umbra length inside willow coppice

Measurements of the statistical characteristics of umbra and sunflecks at different depths inside a willow coppice — Salix viminalis and Salix dasyclados — were carried out at Tartu Observatory, Tõravere, Estonia, in 1997. A new instrument, the sunfleck indicator, constructed by M. Sulev, was used. This instrument, moving perpendicularly to rows in the horizontal direction, counts the number and length of sunflecks and umbrae at a level where downward cumulative leaf area index is L. During statistical data processing, several umbra characteristics — umbra length distribution function, mean number of umbrae, mean umbra length, fractional area of umbra, etc. — were calculated at different measurement heights as the functions of the optical path length τ = L/sin h, where h is the solar elevation. The number of umbrae NU increases rapidly at small τ , has a maximum at τ ≈ 3–4 and decreases slowly with further increase in τ . This interrelationship was fitted by an exponential function. Umbra length distribution function can be divided into three regions: small umbrae (0–10 cm in length), medium-length umbrae (10–20 cm) and long umbrae (up to 100 cm). At all depths the number of small umbrae exceeds the number of medium-length and long umbrae by 3–10 times. The fractional area of umbra kU(τ ) increases with τ and was approximated by a rectangular hyperbola. In lower layers (τ = 8–12) kU(τ ) reaches 0.85–0.90 and these layers are dominated by umbra. ©2000 Elsevier Science B.V. All rights reserved.