STATISTICAL TREATMENT OF THE PAR VARIABILITY AND ITS APPLICATION TO WILLOW COPPICE

For characterization of spatial variability of the global photosynthet ically active radiation (PAR) Q at different depths in a plant canopy a new statistical treatment has been developed. II is based on the use of the irradiance probability density function (IPDF) which is divide d into three parts: IPDF for umbra f(Q)(u), for penumbra f(Q)(P) and f or sunflecks f(Q)(s). In umbra, IPDF was approximated by a normal dist ribution, in penumbra by the Beta-distribution, and in sunflecks, by a normal distribution. Statistical treatment has been applied for the f ast growing willow coppice. In the umbra area the mean value Q(I) of g lobal PAR decreases exponentially with the optical path length of the direct solar radiation inside the canopy tau=L/sinh with small values of the standard deviation sigma(u). In the sunfleck area the mean valu e Q(II) decreases linearly with tau with small values of the standard deviation. In the penumbra area agreement with experimental data is in ferior to that in umbra and sunfleck areas. Inside the canopy, the sun fleck fractional area k(s), fitted by a second order polynomial, decre ases with tau up to tau=3.3. The umbra fractional area k(u) increases nearly linearly with depth tau starting from tau=0.8. The fractional a rea of the penumbra k(p) increases rapidly with tau, reaches the maxim um value (k(p)=0.6-0.8) at tau=3 and then decreases nearly linearly. ( C) 1998 Elsevier Science B.V. All rights reserved.