Table 1. Mean and sdev (standard deviation, in parentheses) of stem diameter (d1.3), height (h), crown diameter (dcr), and age.
Variable Pine
N = 5914 		Spruce
N = 7105 		Birch
N = 2169
d1.3, cm 20.1 (6.5) 20.3 (7.9) 15.1 (6.7)
h, m 17.5 (4.1) 18.1 (5.8) 16.4 (5.3)
dcr, m 2.8 (0.9) 2.9 (0.9) 2.6 (0.9)
Age, years 59.5 (25.3) 66.4 (28.7) 47.0 (24.6)
1

Fig. 1. Illustration of perspective imaging of a ‘forest scene’. A frame camera image on the left has white rectangles depicting the nadir- and backward viewing lines of the ADS40. Sections of the nadir (N00) and backward viewing (B16) images are shown on the right. The flying direction is upwards and it is 25° off with respect to the direction to the Sun.

Table 2. Characteristics of the ADS40 data acquisition by each four-color image. ‘Trees lost’ is the percentage of trees occluded or shaded by clouds in the image coverage.
Flying altitude
[km] 		Start time
[GMT] 		Flight path azimuth
[°] 		Sun azimuth
[°] 		Sun
elevation
[°] 		Tree
observations 		Trees lost
[%] 		Integration
time
[ms] 		Active CCD lines
1 0656 349 119.3 27.1 48 - 1.94 N00
1 0703 169 121.0 27.8 6345 8 1.94 N00
1 0711 349 123.1 28.6 9027 24 1.94 N00
1 0718 169 124.9 29.3 - - 1.94 N00
1 0725 349 126.7 30.0 6867 - 1.94 N00
1 0733 169 128.8 30.7 6917 - 1.94 B16
2 0745 349 132.0 31.8 8844 3 2.77 N00
2 0753 169 134.2 32.5 11332 8 2.77 N00
2 0800 349 136.1 33.1 7550 17 2.77 B16
2 0808 169 138.3 33.7 11077 5 2.77 B16
3 0818 349 141.1 34.4 13571 2 4.16 N00
3 0818 349 141.1 34.4 14876 0 4.16 B16
3 0825 169 143.1 35.0 12045 16 4.16 N00
3 0825 169 143.1 35.0 11280 8 4.16 B16
3 0833 260 145.4 35.5 8742 28 4.16 N00
3 0833 260 145.4 35.5 9694 35 4.16 B16
4 0843 169 148.3 36.1 13531 4 5.54 N00
4 0843 169 148.3 36.1 12073 0 5.54 B16
4 0852 260 151.0 36.7 12352 6 5.54 N00
4 0852 260 151.0 36.7 12941 11 5.54 B16
2

Fig. 2. Illustration of sidelit spruce crowns that were sampled for image data in a 1-km B16 BLU image. Points not self-occluded were superimposed. Colors depict the assigned illumination class: white = sunlit (Su), yellow = self-shaded (Se), blue = neighbor-shaded, magenta = neighbor- and self-shaded. Green points are occluded by a neighboring tree.

Table 3. Mean reflectance factors of pine, spruce and birch crowns at nadir. BLU (blue), GRN (green), RED (red), NIR (near-infrared). Se = self-shaded, Su = sunlit illumination class.
Illumination – Species BLU GRN RED NIR
Se – Pine 0.037 0.041 0.030 0.169
Se – Spruce 0.035 0.035 0.024 0.155
Se – Birch 0.038 0.044 0.031 0.227
Su – Pine 0.040 0.051 0.037 0.220
Su – Spruce 0.038 0.047 0.032 0.224
Su – Birch 0.042 0.060 0.043 0.322
3

Fig. 3. Distribution of all image observations in the xy view-illumination geometry (Eq. 1). The x coordinate is negative in the forward-scattering geometry (back-lit trees dominate) and positive in the backscattering geometry, in which front-lit trees dominate the view.

4

Fig. 4. Examples of directional R anisotropy models for the GRN band in the Su illumination class showing the response along the solar principal plane (y = 0°). The principal plane (view) zenith angle ranges from –32° (forward scattering) to +32 (back­scatter­ing), i.e. from back-lit to front-lit trees. The R of pine deviates somewhat from spruce and birch as a function of the view zenith angle, which constitutes the directional ‘signature’.

Table 4. Partition of reflectance factor (R) variance between the terms of the mixed-effects models (Eq. 3). Percentages (%) of total R variance. Su refers to the directly illuminated canopy and Se to self-shaded canopy in diffuse illumination. BLU (blue), GRN (green), RED (red), NIR (near-infrared).
Band BLU GRN RED NIR
Illumination Su Se Su Se Su Se Su Se
  Directional anisotropy
Pine 51 36 41 19 42 15 4 1
Spruce 43 21 36 10 37 10 13 0
Birch 41 29 20 9 18 8 4 0
Mean 45 29 32 13 33 11 7 0
  Tree effect
Pine 13 12 35 38 35 41 58 60
Spruce 14 13 39 42 37 42 58 67
Birch 26 15 54 44 55 44 70 65
Mean 18 13 43 41 42 42 62 64
  Image effect
Pine 28 42 6 14 5 11 9 2
Spruce 33 54 5 17 5 15 3 1
Birch 20 41 3 10 3 9 6 2
Mean 27 46 5 14 4 12 6 2
  Residual
Pine 8 10 18 29 18 33 29 37
Spruce 10 12 21 30 21 32 26 32
Birch 13 15 22 38 23 39 20 33
Mean 10 13 20 32 21 35 25 34
Table 5. Classification performance when the training and validation data were from the same image. The sdevs of the overall accuracy values varied from 0.4 to 0.7% in 100 trials with randomized training data.
Image Height,
km 		Accuracy
% 		Kappa Pine
% 		Spruce
% 		Birch
%
0753_N00 2 78.7 0.657 80.6 78.2 75.9
0808_B16 2 80.4 0.683 84.0 79.5 73.7
0818_N00 3 75.6 0.604 75.5 76.4 73.5
0825_N00 3 74.3 0.582 75.8 74.2 70.0
0833_N00 3 75.7 0.610 74.9 77.0 73.6
0843_N00 4 77.8 0.641 80.7 76.9 72.8
Table 6. QDA classification performance when the train­ing and validation data were from different 3 km images in the same strip. Tests with nadir normalized (Rnadir, *) data are included.
Training Validation Accuracy % Kappa Pine Spruce Birch
0818_B16 0818_N00 66.3 0.480 73.6 56.7 77.2
* * 69.6 0.510 64.6 74.2 68.3
0825_B16 0825_N00 62.8 0.386 38.6 83.7 66.5
* * 58.2 0.341 58.9 54.0 70.4
0833_B16 0833_N00 72.5 0.575 80.4 64.8 78.6
* * 70.4 0.540 75.6 65.4 74.5
5

Fig. 5. xy observation geometry (Eq. 1) of eight N⇔S-oriented strips and 16 images. ϕSun changed from 140 to 161° with 3° intervals. The V- and L-shaped patterns represent observations in the nadir and backward viewing images, respectively.

Table 7. Sdevs of the parameters of the reflectance calibration error functions (Eq. 5, parameters a0, a1, a2). Plausible and accurate level of errors. x ∈ [–0.6, 0.6] and y ∈ [0, 0.6] in radians. BLU (blue), GRN (green), RED (red), NIR (near-infrared).
  BLU GRN RED NIR
a0 0.20 0.10 0.10 0.075
a1 0.05 0.025 0.025 0.020
a2 0.025 0.0125 0.0125 0.010
a0 0.05 0.03 0.02 0.02
a1 0.01 0.005 0.005 0.005
a2 0.005 0.005 0.005 0.0025
Table 8. Classification performance in simulations using plausible and very accurate R calibration accuracy and directional signatures. Simulated strips were flown in N⇔S direction. Values in parentheses are CVs (%). Strip overlaps were 35% or 67% and the mean ϕSun were 90°, 135° or 180° resulting in six view-illumination geometry scenarios. In each scenario, the first line shows the results for all trees (2.9 or 4.7 image observations per tree), while the next lines show the results for trees observed in 2, 4 or 6 images.
N Plausible reflectance calibration accuracy Very accurate reflectance calibration
Accuracy Kappa Pine Spruce Birch Accuracy Kappa Pine Spruce Birch
a) 35% overlap, solar azimuth 90 (strong directional effects)
2.9 79 (5) 0.68 (8) 82 (11) 77 (11) 77 (10) 83 (1) 0.74 (2) 87 (3) 80 (4) 80 (3)
2 69 (6) 0.53 (11) 72 (22) 67 (23) 68 (12) 74 (2) 0.60 (4) 80 (6) 69 (9) 72 (5)
4 91 (5) 0.87 (7) 95 (4) 90 (6) 89 (9) 94 (1) 0.91 (2) 97 (2) 94 (2) 91 (2)
b) 67% overlap, solar azimuth 90°
4.7 87 (4) 0.80 (7) 91 (7) 86 (7) 84 (9) 89 (1) 0.84 (2) 93 (2) 88 (3) 87 (3)
2 79 (9) 0.68 (15) 82 (15) 77 (17) 77 (15) 83 (4) 0.75 (7) 89 (6) 79 (9) 82 (8)
4 80 (7) 0.71 (12) 84 (16) 78 (16) 79 (13) 84 (4) 0.76 (7) 89 (6) 82 (9) 82 (8)
6 91 (3) 0.87 (5) 95 (4) 91 (5) 88 (8) 93 (1) 0.89 (2) 96 (2) 93 (3) 90 (3)
c) 35% overlap, solar azimuth 135 (intermediate directional effects)
2.9 78 (6) 0.67 (11) 82 (14) 76 (13) 76 (10) 83 (1) 0.74 (2) 88 (3) 80 (4) 80 (3)
2 69 (7) 0.54 (14) 74 (20) 66 (21) 68 (13) 74 (2) 0.62 (4) 81 (5) 70 (8) 72 (5)
4 89 (6) 0.84 (9) 92 (10) 88 (7) 87 (8) 94 (1) 0.90 (2) 96 (2) 94 (2) 91 (3)
d) 67% overlap, solar azimuth 135°
4.7 84 (4) 0.77 (7) 89 (11) 82 (12) 82 (9) 89 (2) 0.83 (2) 93 (3) 87 (4) 86 (4)
2 71 (11) 0.57 (22) 77 (33) 67 (37) 71 (17) 80 (5) 0.70 (8) 86 (10) 77 (11) 76 (8)
4 83 (6) 0.74 (10) 87 (11) 80 (14) 81 (13) 87 (4) 0.80 (6) 92 (5) 84 (8) 84 (7)
6 89 (4) 0.84 (6) 93 (8) 88 (9) 87 (8) 92 (2) 0.88 (2) 96 (2) 92 (3) 89 (4)
e) 35% overlap, solar azimuth 180° (mild directional effects)
2.9 75 (10) 0.62 (18) 78 (24) 72 (21) 74 (10) 83 (2) 0.75 (3) 89 (4) 82 (5) 79 (3)
2 70 (9) 0.55 (16) 75 (18) 65 (18) 69 (12) 77 (2) 0.65 (4) 84 (5) 74 (7) 73 (5)
4 81 (13) 0.71 (22) 81 (33) 81 (26) 81 (11) 91 (2) 0.87 (3) 95 (4) 92 (4) 86 (3)
f) 67% overlap, solar azimuth 180°
4.7 77 (11) 0.66 (20) 78 (35) 78 (23) 76 (10) 87 (2) 0.80 (3) 92 (5) 86 (5) 82 (3)
2 68 (16) 0.52 (31) 71 (44) 67 (40) 69 (20) 81 (4) 0.71 (7) 87 (10) 78 (12) 77 (8)
4 76 (10) 0.64 (18) 79 (31) 76 (24) 73 (14) 84 (4) 0.76 (7) 91 (7) 83 (9) 79 (9)
6 81 (12) 0.71 (20) 80 (34) 82 (21) 80 (9) 89 (2) 0.84 (3) 95 (4) 89 (5) 84 (4)
Table 9. QDA classification performance in simulations using averaged R features and the same simulated data (a through f) as in Table 8. Values in paren­the­ses are CVs (%). Plausible (Pl) and accurate (vA) reflectance calibration accuracy. Strip overlaps (O-%) were 35% or 67%, giving on average 2.9 or 4.7 image observations per tree.
Case Overlap, % mean ϕsun R calibration Accuracy Kappa Pine Spruce Birch
a 35 90° Pl 78.5 (1.0) 0.677 (1.7) 84.6 (2) 74.8 (3) 76.1 (2)
vA 79.5 (0.8) 0.693 (1.4) 84.5 (2) 76.1 (2) 77.9 (2)
b 67 90° Pl 82.7 (1.1) 0.741 (1.9) 88.3 (2) 79.7 (3) 80.1 (2)
vA 83.1 (0.8) 0.747 (1.4) 88.5 (2) 80.5 (3) 80.5 (2)
c 35 135° Pl 79.1 (0.9) 0.686 (1.6) 83.7 (2) 75.4 (3) 78.2 (2)
vA 80.2 (0.8) 0.703 (1.3) 84.0 (2) 76.6 (2) 79.9 (2)
d 67 135° Pl 83.3 (1.2) 0.749 (1.9) 86.9 (2) 80.2 (2) 82.7 (2)
vA 84.3 (0.8) 0.764 (1.3) 87.2 (2) 81.7 (2) 83.9 (2)
e 35 180° Pl 82.1 (1.1) 0.732 (1.9) 84.4 (2) 79.0 (2) 83.0 (2)
vA 83.5 (0.8) 0.753 (1.4) 85.3 (2) 80.3 (2) 84.9 (2)
f 67 180° Pl 85.4 (1.2) 0.781 (2.0) 87.7 (2) 82.4 (2) 86.1 (2)
vA 86.5 (0.8) 0.797 (1.4) 88.5 (2) 83.6 (2) 87.3 (1)