Table 1. Applied quality requirements for Scots pine sawlog.
Crookedness, curves - Max. 1 cm within 1 m distance
Technical defects (e.g. scar) - Allowed outside log cylinder
Min. length 37 dm
Min. diameter 15 cm
Max. diameter of branches:
  - Dead/dry 4 cm
  - Living 6 cm
Not allowed: - Curves on multiple directions
- Decay
- Blue stain -fungi infection
- Insect holes
- Cracks
- Internal items
Table 2. The distribution of quality assessed Scots pines by site type index. Calculated with all pines and different subsets of pines. Relative proportions in parentheses. The mean and the standard deviation of the observed relative sawlog reduction are also shown. The study area is located in boreal forest in eastern Finland.
All OMT MT VT
All pines 1235 46 787 402
Flawless pines 346 (28.0%) 4 (8.6%) 211 (26.8%) 131 (32.6%)
Partly defective pines 625 (50.6%) 21 (45.7%) 406 (51.6%) 198 (49.3%)
Fully defective pines 264 (21.4%) 21 (45.7%) 170 (21.6%) 73 (18.1%)
MeanSR 39.8 64.1 40.1 36.4
SdSR 36.9 37.8 37.0 35.6
OMT = fertile, MT = moderate, VT = poor, Sd = standard deviation, SR = sawlog reduction (%).
Table 3. Main characteristics of the studied plots (15 × 15 m, n = 164) and stands (30 × 30 m, n = 41). Stand-level values are shown in parentheses. The study area is located in boreal forest in eastern Finland.
  Min Max Mean Sd
Theoretical sawlog V (m3 ha–1) 13.7 (21.0) 742.8 (557.3) 175.1 (175.1) 129.7 (121.2)
Factual sawlog V (m3 ha–1) 0 (8) 631.9 (519.0) 124.3 (124.3) 105.6 (100.0)
Pine prop. of the theoretical sawlog V (%) 8.8 (42.5) 100.0 (100.0) 84.5 (84.6) 23.4 (18.8)
Pine prop. of the factual sawlog V (%) 0 (28.6) 100.0 (100.0) 79.4 (78.8) 28.9 (24.3)
Mean dbh (cm) 10.9 (12.0) 35.5 (28.8) 18.0 (17.6) 4.7 (4.1)
Mean h (m) 9.7 (10.8) 31.3 (25.6) 16.3 (16.1) 3.9 (3.4)
Basal area (m2 ha–1) 6.5 (10) 60.0 (45.5) 24.4 (24.4) 9.0 (7.9)
Sd = Standard deviation, V = volume, prop. = proportion, dbh = diameter at breast height, h = height.
Table 4. Airborne laser scanning (ALS) metrics derived from the ALS point cloud.
ALS metric Definition Echo type
hmax/intmax Maximum H/I F + L
hmin/intmin Minimum H/I F + L
hstd/intstd Standard deviation of H/I F + L + Interm.
hmed/intmed Median H/I F + L
hmean/intmean Mean H/I F + L + Interm.
hskew/intskew Skewness of H/I F + L
hkurt/intkurt Kurtosis of H/I F + L
hi/inti ith percentile of H/I F + L
dj Density at height j F + L
echo_prop Proportion of echoes F + L + Interm.
i = 10, 20…80, 90; j = 0.5, 2, 5, 10, 15, 20; H = height; I = intensity; F = first; L = last; Interm. = Intermediate.
Table 5. Information of the linear mixed effects models when fitted with all data, excluding the RMSE% and BIAS% values which are after leave-one-out cross-validation. For the fixed parameters, the standard error is given in parentheses. The study area is located in boreal forest in eastern Finland and it is dominated by Scots pine.
LME-1 LME-2 LME-3 LME-4 LME-5 LME-6
Response (Factual sawlog V)1/2 (Theoretical sawlog V)1/2 (Sawlog reduction)1/2
Intercept 9.140 (1.496) 7.163 (1.492) 7.379 (1.863) 5.878 (1.855) 5.192 (1.109) 5.317 (1.717)
f_h902 0.021 (0.001) 0.021 (0.001) - - - -
l_h90 - - 0.810 (0.050) 0.804 (0.050) - -
f_h30 - - - - 0.283 (0.063) 0.283 (0.066)
l_d10 –9.082 (1.663) –10.008 (1.617) –14.393 (1.649) –15.077 (1.646) - -
f_d2 - - - - –8.592 (1.710) –8.580 (1.790)
MT - 2.718 (0.772) - 2.241 (0.784) - –0.124 (1.398)
VT - 2.843 (0.829) - 2.154 (0.841) - –0.141 (1.477)
var(u) 0.9742 0.8172 0.9132 0.8162 1.5992 1.6512
var(e) 1.2842 1.2812 1.3312 1.3292 1.8352 1.8362
p(MT) - 0.001 - 0.007 - 0.93
p(VT) - 0.002 - 0.015 - 0.92
RMSE% 30.85 29.46 29.18 28.18 82.45 83.27
BIAS% –0.44 –0.91 –0.14 –0.32 3.83 3.75
V = volume, f/l denotes whether the metric is derived from the first or last echoes, h30 and h90 are the 30th and 90th height percentiles, d2 and d10 are the densities at heights of 2 and 10 m, MT and VT = site type dummy variables, var = variance, p(MT/VT) = the p-values of corresponding site type dummy variables.
Table 6. The root mean squared error (RMSE%) and BIAS% values for the predicted factual sawlog volumes with different alternatives at the stand-level (30 × 30 m) in Scots pine dominated boreal forests. Alternatives b always include the site type dummies. See Materials and Methods and Table 5 for detailed definitions.
Alt. Definition RMSE% BIAS%
1 Observed theoretical sawlog volume - SRM 29.08 –10.26
2a LME-1 factual sawlog volume 22.69 –0.44
2b LME-2 factual sawlog volume 20.92 –0.91
3a LME-3 theoretical sawlog volume - SRM 27.16 –10.19
3b LME-4 theoretical sawlog volume - SRM 25.27 –10.50
4a LME-3 theoretical sawlog volume - LME-5 sawlog reduction 25.11 –1.77
4b LME-4 theoretical sawlog volume - LME-6 sawlog reduction 23.78 –1.98
5 TL factual sawlog volume 27.31 3.20
6 TL theoretical sawlog volume - SRM 30.03 –7.98
Alt. = alternative, LME = linear mixed-effects model, TL = tree list, SRM = sawlog reduction model of Mehtätalo (2002).
1

Fig. 1. Observed vs. predicted values for the factual sawlog volume (m3 ha–1) at the stand- level (30 × 30 m). For simplicity, only the b versions of alternatives 2, 3 and 4 are shown. LME = linear mixed-effects model, TL = tree list, SRM = sawlog reduction of Mehtätalo (2002). See Materials and Methods for detailed definitions. The study area is located in boreal forest in eastern Finland and it is dominated by Scots pine.

Table 7. Root mean squared error (RMSE%) and BIAS% values for the model of Mehtätalo (2002) when estimating the factual sawlog volume with different sets of Scots pines. Subset 1 = pines with factual sawlog volume > 0. Subset 2 = pines with factual sawlog volume > 0, but not flawless. Subset 3 = flawless pines. Subset 4 = all defective pines. The main characteristics of the relative sawlog reduction (%) at the tree-level for both observed and modelled values with different sets of pines are also shown. The study area is located in boreal forest in eastern Finland.
RMSE% BIAS% MinSR MaxSR MeanSR SdSR
Observed - - 0 100 39.8 36.9
All pines (n = 1235) 73.6 –18.0 15.4 63.1 32.4 10.4
Subset 1 (n = 971) 38.8 1.3 15.4 58.5 31.2 10.0
Subset 2 (n = 625) 43.7 –15.3 15.4 58.5 30.1 9.6
Subset 3 (n = 346) 30.4 27.8 16.1 58.2 33.3 10.2
Subset 4 (n = 889) 96.9 –46.7 15.4 63.1 32.1 10.5
Sd = standard deviation, SR = sawlog reduction (%).