J. Ross, M. Mõttus Agricultural and Forest Meteorology 104 2000 215–231 217
The accuracy of determination of the linear dimen- sions of sunflecks and umbrae is ±5 mm. The height
of the horizontal bar inside coppice on which the sen- sor is mounted, can be changed from 0.4 to 6 m. One
measurement scan consisted of a transit of the carriage perpendicular to willow rows from one end of the bar
to the other and back with a total scan length of about 12 m. Because of leaf flutter caused by the wind, the
data obtained from the two transits were not identi- cal; to increase the statistical reliability of the sample,
the data from the two transits were considered as one measurement. The passage took about 400 s, and dur-
ing each scan 2400 readings were recorded.
As an example, Fig. 2 shows the recordings of the sunfleck sensor on a cloudless day, 14 September
1998, at three heights relative heights zz
U
0.85 a, 0.65 b and 0.36 c, with the coppice height z
U
= 3.1 m. Fig. 2 shows how the large variation in the
recordings of the sunfleck sensor depend on measur- ing height within the coppice.
3. Coppice architecture
As mentioned above, measurements with the sun- fleck sensor were performed during 1995–1998. The
years 1995, 1996, 1997 were the third, fourth and fifth growing years, respectively. At the end of 1997, the
plants were cut and 1998 was the first growing year after cutting.
Some phytometrical characteristics of the planta- tion Fig. 3 show the growth dynamics of coppice
architecture. The architecture of willow coppice is de- scribed in more detail in Ross and Ross 1998, Ross
and Mõttus 2000 and Ross et al. 2000, where it was demonstrated that it would be reasonable to di-
vide willow coppice into three layers.
The upper foliage layer z
U
− z
V
consists of current- year stems and branches modelled as differently ori-
ented foliage cylinders with leaves distributed along their axes; we assume random spatial distribution of
cylinders. Cylinders start growing from the apices of previous-year stems and branches. In the first year, this
layer consists of nearly vertical foliage cylinders, in the following years, of shoot and branch foliage cylin-
ders of the current year. So, starting from the second growing year, the character and structure of the upper
foliage cylinder layer does not change considerably. The lower foliage layer z
U
− z
A
consists of branch and shoot foliage cylinders with greatly varied orien-
tations and dimensions. This layer is almost homo- geneous, and for its architecture, the turbid medium
model Ross, 1981 will be used. The architecture of this layer is characterised by the vertical distribution
of the leaf area density u
L
z and probability distribu- tion function of the leaf area orientation g
L
rrr
L
2π . The spatial distribution of leaves is assumed to be ran-
dom. Since in both foliage layers the share of stems, branches and twigs is less than 10 of that of leaves,
their area will be neglected.
The lowest leafless coppice layer consists of nearly vertical stems Fig. 4a. Orientation of cylindrical
branches Fig. 4b varies over a wide range, the domi- nant inclination angles ϑ
S
being between 10
◦
and 30
◦
. In accordance with the measurements performed by
Ross in 1997 and 1998, an S. viminalis plantation is characterised by a large number of leaves per stem and
a great variability of leaf length Fig. 5a and leaf area S
L
Fig. 5b. In midsummer, an S. viminalis stem with a height of 500 cm has about 7000 leaves, the area of
the smallest leaves being 0.3 cm
2
and the area of the largest ones, 27 cm
2
. The size of a leaf depends on its age: the smallest leaves are the youngest, located
at the top of the shoot, and the largest ones are about 50 cm lower down the stem.
4. Statistical treatment
Let N
S
L, h be the number of sunflecks per metre of scan at the depth L, where L is the downward cumu-
lative leaf area index and h is the solar elevation; these sunflecks have different lengths varying from zero to
l
S
max
, and their lengths are statistically distributed in the interval [0, l
S
max
]. Let n
S
l
S
be the sunfleck length distribution function, i.e. the number of sunflecks with
a length between l
S
and l
S
+ 1l
S
per metre of scan and
l
Smax
X
l
S
=
n
S
l
S
= N
S
. 1
In our case, the distance between two consecutive mea- surements, 1l
S
= 0.7 cm. Mean sunfleck length is
h l
S
i = P
l
Smax
l
S
=
l
S
n
S
l
S
N
S
2
218 J. Ross, M. Mõttus Agricultural and Forest Meteorology 104 2000 215–231
Fig. 2. Examples of the sunfleck sensor’s recordings at different heights inside the willow coppice on a cloudless day, 14 September 1998, at coppice height z
U
= 310 cm: a h=35
◦
, z=2.60, zz
U
= 0.84, τ =0.1; b h=35
◦
, z=2.00, zz
U
= 0.65, τ =2.1; and c h=32
◦
, z=1.10, zz
U
= 0.36, τ =5.5. h, solar elevation; z, measurement height; zz
U
, relative height; τ , pathlength of the direct solar radiation beam through the coppice.
J. Ross, M. Mõttus Agricultural and Forest Meteorology 104 2000 215–231 219
Fig. 3. a Development of three vegetation layers of a willow coppice during the growing seasons of 1996–1998. z
U
— coppice height, z
V
— height of the surface located between the upper foliage cylinder layer 1 and the lower foliage turbid medium layer 2, z — height of the lowest leafless stem layer 3. b Variation in the leaf area index LAI during the same periods.
and the fractional area of sunflecks inside the coppice equals sunfleck length per metre of scan:
k
S
=
l
Smax
X
l
S
=
l
S
n
S
l
S
. 3
From 2 and 3 it follows that k
S
= h l
S
i N
S
. 4
For analysis of sunfleck length variability, the sun- fleck length distribution function n
S
l
S
and the cumu- lative sunfleck fractional area F
S
l
S
are used. F
S
l
S
denotes the fraction of the transect occupied by sun- flecks larger than l
S
, or the fractional area of sunflecks with length from l
S
to l
S
max
: F
S
l
S
=
l
max
X
l=l
S
ln
S
l, or in the integral form
F
S
l
S
= Z
l
Smax
l
S
ln
S ∗
l dl, 5
where n
S ∗
l
S
= lim
1l
S
→
n
S
l 1l
S
.
220 J. Ross, M. Mõttus Agricultural and Forest Meteorology 104 2000 215–231
Fig. 4. Probability histogram of stem a and branch b inclination angle, fitted by a lognormal distribution, measured in 1997 and 1998.
From 3 and 4 it follows that F
S
0 = k
S
, F
S
l
S
max
= 0. 6
Analysis of F
S
and n
S
shows that for upper layers it is reasonable to divide the interval between 0 and l
S
max
into two parts Fig. 6a and b: 1. A
SS
, interval of short sunflecks [0, l
SS
], k
SS
L, h=F
S
0−F
S
l
SS
; 2. A
SL
, interval of long sunflecks [l
SS
, l
S
max
], k
SL
L, h=F
S
l
SS
. The fractional sunfleck area for the intervals k
SS
and k
SL
is defined so that k
S
= k
SS
+ k
SL
. 7
It should be noted that the location of point l
SS
sep- arating the intervals and, consequently, the fractional
areas k
SS
and k
SL
is somewhat arbitrary and subjective. It is appropriate to assume that short sunflecks are
caused by the gaps between individual leaves at least in upper canopy layers and are hence determined by
the effective diameter of a leaf, while the length of long sunflecks is determined by the distance between
shoot cylinders. Large sunflecks occur only in upper canopy layers, where the distance between neighbour-
ing shoots is large.
Analysis of experimental data shows that the char- acteristics of sunfleck length are largely determined
by three factors: solar elevation h, depth of the mea- surement level characterised by Lz, and characteris-
J. Ross, M. Mõttus Agricultural and Forest Meteorology 104 2000 215–231 221
Fig. 5. Probability histogram of leaf length a and leaf area b, fitted by a lognormal distribution, measured by Ross in 1997 and 1998.
tics of leaf, shoot, plant and canopy architecture. The first two factors determine the pathlength of the direct
solar radiation beam in the plant canopy, τ =Lsin h. Hereafter, sunfleck length characteristics will be con-
sidered as functions of pathlength τ , assuming that it is the key factor determining the absorption pattern of
direct sunlight.
5. Results and discussion
