J. Ross, M. Mõttus Agricultural and Forest Meteorology 100 2000 89–102 91
Fig. 2. Sunfleck indicator.
The objective of this paper is to study different statistical parameters of umbra length distribution,
umbra fractional area, number of umbrae, mean um- bra length, etc. in different canopy layers as the func-
tions of the optical depth τ = Lsin h for both Salix viminalis and Salix dasyclados coppices. For this pur-
pose, a new instrument, the sunfleck indicator Fig. 2, constructed by M. Sulev, was used. Moving in the
horizontal direction at different canopy depths, this instrument measures the length of sunflecks and
umbrae.
2. Materials and methods
Radiation and phytometrical measurements were carried out during the vegetation period of 1997 in
a 4-year-old willow coppice of S. viminalis, clone 78021, and S. dasyclados, clone 81090, located
at Tartu Observatory, Tõravere latitude 58
◦
16
′
N, longitude 26
◦
28
′
E, altitude 70 m above sea level, Estonia.
The plantation was established in May 1993 on the flat top of a hillock on light pseudopodzolic soil
Planosol. Cuttings were planted in double row, the distance between plants in a row being 0.5 m. The
azimuth angle of rows was 75
◦
, planting density was 20,000 cuttings per ha.
A special measurement system was designed for ex- perimental study of the variability of radiation charac-
teristics within the willow coppice Ross et al., 1998. The measurement system Fig. 3 consisted of a 6-m
long horizontal bar placed perpendicularly to the rows inside the willow plantation with a sensor carriage
moving along it at 30 mm s
−1
. Two Reemann pyra- nometers TR-3 for measuring downward and up-
ward fluxes of global radiation, two LI-COR quan- tum sensors LI-190SA for measuring downward and
upward fluxes of PAR, a miniature Reemann net ra- diometer MB-1 for measuring net radiation, and a
sunfleck indicator for detecting sunfleck and umbra were mounted on the carriage.
The sunfleck indicator Fig. 2 is, in principle, a miniature actinometer with an angle of view of 10
◦
in the vertical direction and 15
◦
in the horizontal direc- tion. Such an angle of view guarantees that the sun
will remain completely in the field of view for 6 min. A silicone photodiode was used as a sensor, and the
instrument was calibrated on the pyrheliometric scale using a reference actinometer. Due to different spec-
tral sensitivities of receivers and a special configura- tion of the field of view, this calibration provides only
approximate values in energy units.
The sunfleck indicator has polar mounting and must be directed manually to the sun before each scan. The
accuracy of determination of the linear dimensions of sunflecks and umbrae is ± 5 mm.
The height of the horizontal bar inside coppice can be changed from 0.4 to 6 m, the measurement heights
used on selected days are given in Table 1. One measurement scan consisted of a transit of the
carriage from one end of the bar to the other and back with a total scan length of about 12 m. Due to leaf
flutter caused by wind the data obtained from the two
Table 1 Radiation measurement heights and the corresponding values of
leaf area index Lz in a willow coppice on selected days 30 June 1997; Salix dasyclados
Height z cm 45 200
280 350
450 Lz
5.25 5.20
4.30 2.05
21 July 1997; Salix viminalis Height z cm 62
228 330
392 470
532 Lz
5.20 5.20
4.75 3.60
1.65 0.55
92 J. Ross, M. Mõttus Agricultural and Forest Meteorology 100 2000 89–102
Fig. 3. Radiation measurement system within willow coppice. M — drive, C — carriage, 1 — sunfleck indicator, 2 — pyranometers, 3 — quantum sensors, 4 — net radiometers.
transits were not identical; to increase the statistical reliability of the sample the two transits were merged
into one measurement. The passage took about 400 s, and during each scan 2400 readings were recorded for
every sensor.
Radiation measurements were carried out at differ- ent solar elevations with a clear sky. Simultaneously
with radiation measurements, air temperature and hu- midity inside and outside coppice, surface tempera-
ture beneath coppice, broadband direct solar radia- tion, photosynthetically active direct solar radiation
S
, broadband global radiation, global PAR, and wind speed above the canopy were recorded.
The data acquisition system consisted of a multi-channel data logger Delta-T Devices and a
PC. Voltage readings from the sunfleck indicator were converted to the metric system W m
−2
using the approximate calibration coefficient.
In Fig. 4, two recordings of the sunfleck indicator are presented. In the coppice with height h
c
= 475 cm, at the height of z = 350 cm, zh
c
= 0.74 a, sunflecks, penumbra and umbra are all present, with umbra occu-
pying 42 of scan length. The situation is totally dif- ferent at the height of z = 45 cm, zh
c
= 0.09 b. Sun- flecks have disappeared and the part of penumbra is
relatively small as umbra occupies 80 of scan length. In the statistical processing of the sunfleck indica-
tor’s recordings, two methodological problems must be solved: i how to determine the irradiance S
FS
separating sunflecks from penumbra sunfleck thresh- old, and ii how to determine the irradiance S
FU
sep- arating umbra from penumbra umbra threshold.
For two uppermost measurement levels, sunfleck fractional areas K
S
were calculated using different val- ues of S
FS
S
F
, where S
F
is the sunfleck indicator’s reading above canopy.
Analogously, for two lower measurement levels the sunfleck indicator’s recordings were cut at different
values of S
FU
S
F
, and the corresponding umbra frac- tional areas were calculated.
Fig. 5a shows that umbra fractional area increases rapidly with umbra threshold until S
FU
S
F
≈ 0.005 and then remains almost constant. Sunfleck fractional
area Fig. 5b depends strongly on S
FS
S
F
at S
FS
S
F
values larger than 0.98. This is probably due to fluc- tuations of direct solar irradiation above the canopy
S
F
as well as due to measurement uncertainties. At lower values of S
FS
S
F
the slope of k
S
is much smaller.
To eliminate noise and fluctuations of S
F
in further data analysis, sunfleck threshold was chosen to be 0.95
and umbra threshold 0.007.
J. Ross, M. Mõttus Agricultural and Forest Meteorology 100 2000 89–102 93
Fig. 4. Sunfleck indicator readings in a S. dasyclados coppice on two scans on 30 June 1997. a
b height z, cm
350 45
coppice height h
c
, cm 475
475 zh
c
0.74 0.09
leaf area index L 2.05
5.25 solar elevation h,
35.6 51.0
optical path length τ 3.52
6.76 umbra fractional area k
U
42 80
94 J. Ross, M. Mõttus Agricultural and Forest Meteorology 100 2000 89–102
Fig. 5. Umbra and sunfleck discrimination level in S. viminalis: a umbra fractional area k
U
as a function of umbra threshold S
FU
S
F
at two measurement heights, 470 and 228 cm; b sunfleck fractional area k
S
as a function of sunfleck threshold at 470 left-hand axis and 532 cm right-hand axis as a function of sunfleck threshold S
FS
S
F
. The measuring heights 228, 470 and 532 cm constitute 0.37, 0.77 and 0.87 of the coppice height h
c
= 610 cm, respectively.
2.1. Phytometrical characteristics of willow coppice The architecture of a willow coppice during the first
three growing years is characterized more in detail in Ross and Ross 1998.
The coppice can be divided into three layers: 1. The uppermost layer is made up of almost vertical
branches that can be described as foliage cylinders with a length of about 60 cm and a diameter of
about 10 cm.
J. Ross, M. Mõttus Agricultural and Forest Meteorology 100 2000 89–102 95
Table 2 Coppice height h
c
, leaf area index L, and layer thicknesses on selected days
Salix dasyclados Salix viminalis
Date 30 June 97
21 July 97 h
c
cm 475
610 L
5.2 5.2
Layer thickness cm i
200 240
ii 65
120 iii
210 250
2. The middle foliage layer can be modelled as a horizontally homogeneous turbid plate medium
where individual branches are indistinguishable. 3. The lowest foliage layer is almost leafless and
contains mostly cylindrical, nearly vertical stems. Some phytometrical characteristics of S. viminalis
and S. dasyclados coppices, measured on selected days, are given in Table 2.
The vertical distribution of leaf area density u
L
z for both subspecies shows that in the upper layer with a
thickness of about 200 cm, leaf area density increases almost linearly, accounting for 60–80 of total leaf
area.
Compared with S. dasyclados, S. viminalis leaves are longer and narrower. The mean area of a S. vim-
inalis leaf is about 4.0 cm
2
, that of a S. dasyclados leaf, about 4.9 cm
2
. The variability of leaf dimensions is large for both subspecies and can be approximated
by lognormal distribution Ross and Ross, 1998. The stems of a S. viminalis shoot can be modelled as
nearly vertical cylinders, unlike the stems of S. dasy- clados which are less vertical and more convex.
3. Statistical treatment
