J. Ross, M. Mõttus Agricultural and Forest Meteorology 100 2000 89–102 101
Fig. 11. Ratio of short umbra fractional area k
US
to total umbra fractional area k
U
, k
US
k
U
vs optical path length τ fitted by a linear regression. a S. viminalis; b S. dasyclados.
a more expressed cylindrical shoot structure in upper canopy layers. Also, leaf area density function has a
wider maximum for this subspecies compared with S. dasyclados, which indicates taller shoots.
Another indicator of different canopy architecture is the ratio of the area of long umbrae to total umbra
area. Despite the fact that the average length of umbra is smaller in S. dasyclados, the species produces more
long umbra in deeper canopy layers 50–60 of total umbra area compared with S. viminalis less than 50
of total umbra area.
5. Concluding remarks
Because of the extreme complexity of natural canopies, analytical models fail to give the distribu-
tion of solar radiation in plant canopies with sufficient accuracy.
In upper canopy layers, the total number of umbrae is larger for S. viminalis than for S. dasyclados. The
initially large number of short umbrae in a S. vimi- nalis coppice decreases more rapidly with τ than in a
S. dasyclados coppice. At the same time, starting from
102 J. Ross, M. Mõttus Agricultural and Forest Meteorology 100 2000 89–102
τ = 5–6, about 60 of total umbra in S. dasyclados is contributed by long umbrae, about 10 by short
umbrae and only 30 by medium-length umbrae. On the ground under a S. dasyclados coppice, large um-
bra areas appear to be separated by intervals of short umbrae, where radiation density changes rapidly.
In a S. viminalis coppice, the amount of umbra con- tributed by medium-length shadows is larger, since
individual shoots allow sunrays to penetrate among them. However, the fractional area of short umbrae
and the absolute value of the slope of F
U
l in this in- terval decreases rapidly with τ , and in deeper canopy
layers the total number of umbrae for S. viminalis is smaller than for S. dasyclados.
It is surprising that at the same optical path length the wider leaves of S. dasyclados, located closer to the
ground, allow more penumbra to fall onto the transect than do the narrow leaves of S. viminalis. This is a
certain evidence of a major difference in the stand architecture of the two species.
Differences in the number of umbrae and in the fraction of medium-length umbrae suggest that um-
bra distribution can be used for estimation of the geo- metrical characteristics of a plant stand. However, as
the two subspecies with relatively similar characteris- tics demonstrate quite a different behaviour, correla-
tion between umbra fraction and plant architecture is not simple.
It is clear that the statistical characteristics of um- bra and sunflecks are not independent: when the frac-
tion of umbra increases, the fraction of sunflecks de- creases, and vice versa. This interrelationship is not
simple due to the existence of penumbra. For a more detailed study of canopy radiation transfer, umbra and
sunflecks should be treated simultaneously.
Whether the methodology used in this paper is ap- propriate for describing the interception of direct so-
lar radiation in dense canopies, needs to be clarified in future models where empirical coefficients will be
correlated with the characteristics of real canopies.
Acknowledgements
This research was supported by ETF grants Nos. 251 and 2668. The authors thank Madis Sulev, Peeter
Saarelaid and Enn-Märt Maasik for assistance in field measurements and Mrs. Ester Jaigma and Mrs. Viivi
Randmets for preparing the manuscript. For valuable comments and critical remarks, the authors express
their deep gratitude to the anonymous reviewers and to Dr. J. B. Stewart.
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