. It is possible to
handle single files interactively or to process
several files as a batch.Different methods have been published to estimate the leaf area index LAI from the transmission of light measured either directly under a canopy or on hemispherical photographs. Some of these methods also estimate an average leaf angle in the canopy. See the original references of these methods for more details or see Thimonier et al., 2010 for a synthesis. Here is short comparative table:
| Common features | All methods used in Hemisfer are based on the classification
of pixels to either white (=sky) or black (=canopy) by applying a brightness
threshold to the analysed picture. The light
transmission is then calculated as the proportion of white pixels within
analysis rings, i.e. as a discrete function of the zenith
angle Θ (theta). The next step is to calculate the average number of
times that a light ray would touch the canopy when travelling a distance equal
to the thickness of the canopy. This number is called contact number, or K. K = -cos Θ ln T The K values are finally integrated over the rings to give the LAI, but this step differs among methods. |
|---|---|
| Miller (1967) | This method is based on the fact that (ideally) the effect of the leaf angle disappears when integrated over all viewing angles of the hemisphere. This method is simple, but it is biased if it is not possible to analyse the picture down to the horizon, for example if there are mountains around. Reducing the total angle covered by the analysis rings will thus produce errors, but these errors will be small as long as the foliage is neither too planophile (low leaf angle) nor too erectophile (high leaf angle). If the leaf angle is close to α = 1 rad = 57°, then the K values are approximately constant over zenith angles and Miller's method is accurate even if calculated only over a limited number of rings. |
| Li-Cor LAI-2000 / 2200 | The standard method used by the plant canopy analyser
Li-Cor LAI-2000 or 2200 is
based on Miller's equations. The difference is that the contact points of the
lowest analysed ring is extrapolated down to the horizon.
If the analysis is done over all zenith angles (Θ from 0 to 90°), then
both methods are identical. An estimation of the leaf angle is also implemented in the software of the LAI-2000. To this purpose, the regression slope of K against Θ is calculated and used to estimate the leaf angle. This method is optimised for the rings of the LAI-2000/2200 (5 x 15°). It tends to give often very high of very low leaf angles, but this does not affect the LAI calculated by this LAI-2000 method (both parameters are estimated independently). |
| Lang (1987) | At a zenith angle of Θ = 1 rad = 57°, the K values are almost unaffected by the leaf angle. Lang thus proposed to estimate the value of K at 1 rad by a linear regression against Θ, i.e. the same regression as used by the LAI-2000 method to calculate the leaf angle. Lang's LAI is easy to calculate and quite reliable. |
| Gonsamo et al. (2018) | Gonsamo et al. used the same idea as Lang (1987), but with a robust regression based on least absolute deviations instead of a least-square regression. They found that this method gives one of the most reliable estimates of LAI, even when the hemispherical pictures are not perfect. |
| Norman & Campbell (1989) | Norman & Campbell proposed to estimate jointly the
LAI and the leaf angle because both
parameters are unknown and interdependent. This method is based on the ellipsoidal
model of leaf angle distribution (ELAD). The
algorithm searches for a combination of LAI and α which gives transmission
values as close as possible to the measured light transmissions. This is
calculated with a least-square method: the sum of the squared differences is
minimised over the zenith angles of the rings. Norman
& Campbell's method is unweighted, each ring receiving the same weight in the
calculations. The LAI and leaf angle calculated with this method make it possible to estimate the light transmission in a vertical projection for the canopy on the photograph (vertical total gap fraction, Fmv), as well as the large gaps in vertical projection (Frv) as given by the gap separation procedure of Chen & Cihlar (1995) (see below). |
| Weighted ellipsoidal method (Thimonier et al, 2010) | This method was developed with the Hemisfer
software. It is based on the same approach as Norman & Campbell's algorithm
with the following exceptions: (1) it minimises the errors on the K values rather
than on the light transmission and (2) the rings are
weighted according to their area, more precisely to the area they would have in
an azimuthal equidistant projection (i.e. with a linear lens geometry). The LAI and leaf angle calculated with this method make it possible to estimate the light transmission in a vertical projection for the canopy on the photograph (vertical total gap fraction, Fmv), as well as the large gaps in vertical projection (Frv) as given by the gap separation procedure of Chen & Cihlar (1995) (see below). |
The following corrections are implemented in Hemisfer and can be applied on all methods mentioned above. They are applied separately, except for the first two which can be combined.
| Non-linearity correction (Schleppi et al., 2007) | The light transmission varies with the zenith angle Θ (theta).
Except in very planophile canopies, it decreases from the zenith down to the
horizon. This is because the light has to travel a longer way through the canopy.
The calculation of the contact number K takes this into account (cos Θ
in the formula above), but only between rings. Within rings, the same effect can
produce a negative bias on the calculation of K if K, Θ and the
ring width are all large. A method was thus developed
along with Hemisfer to correct this effect. Notes: if a ground slope is set, then the non-linearity is always corrected! This method can be combined with the next one. |
|---|---|
| Canopy clumping (Chen & Cihlar, 1995) | Canopy gaps can be recognised as those patches of sky that would not be
expected to be so large in a canopy with random foliage distribution. The method
proposed by Chen & Cihlar thus consists in separating the statistically unlikely
large sky patches (considered gaps) from the rest of the canopy (including the
smaller, statistically expectable sky patches). This method estimates the
clumping index Ω (omega) and the corrected
value of LAI (beside the apparent LAIe). In the original method, gap sizes are measured on the light patches along transects on the ground, i.e. in the parallel projection produced by the sun rays. In a hemispherical photograph, however, the gap size in pixels cannot be directly related to the width of individual leaves or twigs, as would be necessary in Chen & Cihlar's method. In Hemisfer, circles around the zenith are used instead of transects. A representative foliage width is then estimated interactively, within analysis rings, based also on the statistical distribution of gap sizes. The estimated foliage element widths can also be displayed as results. The user can further chose the probability at which a gap is treated as such: if its probability is less than the tolerance, then it is considered as gap, in the other case it is part of the rest of the canopy. We found good results with a tolerance of 0.02 when applying the developed algorithm on constructed canopy pictures. Note: this method can be combined with the previous one. |
| Slope correction (Walter & Torquebiau, 2000) | This method divides the pictures both in zenith rings and in azimuth sectors.
In each cell defined by their intersection, an average angle of incidence can be
calculated according to the ground slope. The LAI is estimated per sector
according to both this angle of incidence and the zenith angle (the first because
it affects the geometry of the whole canopy, the second because it statistically
determines the angles at which the single leaves are seen). An average between
the sectors is then taken as the LAI of the picture. Note: this method cannot be combined with the other corrections listed in this table. |
| Clumping correction (Lang & Xiang, 1986) | This method also divides the pictures both in zenith rings and in azimuth
sectors. The LAI is first estimated over a group of m sectors (this
parameter m can be chosen in the options).
Sector by sector, the analysis per group is then repeated around the whole
picture. The LAI of the picture is finally calculated as average of the groups.
Because of the logarithmic relation between LAI and light transmission, this
averaging method is affected by the scale at which the transmission varies, either
within or between sectors and sector groups. The LAI of clumped canopy is better
estimated if the foliage can be considered as randomly distributed within the
groups, while the clumping makes differences between groups. Note: this method cannot be combined with the other corrections listed in this table. |
In some cases, especially if there are large gaps either close to the zenith
or low over the horizon, the calculation after Norman
& Campbell (1989) and our weighted ellipsoidal method
(Thimonier et al, 2010) can give extreme
leaf angles. While the original method of
Norman & Campbell (1989) is implicitely limited
to angles between 10° and 86°, our method can sometimes yield values of either
0° or 90°. The average leaf inclination angle, however, is in reality never 0
or 90° because it never happens that leaves are either all absolutely flat or
all absolutely vertical. It is therefore also possible to explicitely constrain
these methods to a range of leaf angles that appears plausible. Both the
minimum and the maximum can be chosen as: min ≤ α ≤ max. These
limits don't apply to the LAI-2000 method because in this case the LAI
calculation is independent of the leaf angle (see above).
To allow all angles (no constraint), simply chose 0 ≤ α ≤ 90.
Note: taking enough pictures per site and calculating a
synthesis per site yields more robust values
for the leaf angle compared to results from single pictures.
Once the methods for calculating the threshold and the
LAI are set, the analysis is run via the File menu or by
clicking on the button . It is possible to
handle single files interactively or to process
several files as a batch.