Table 1. The average stand characteristics calculated from harvester STM data. The given volumes do not contain the saw log reduction.
Stand Species N
ha–1		 G
m2 ha–1		 DG
cm 		HG
m 		Logs
m3 ha–1		 Pulp
m3 ha–1		 Size
l
1 Pine 374.67 20.87 27.55 23.43 167.94 24.94 584
Spruce 14.67 0.41 22.30 18.48 2.09 1,10 245
Birch 21.33 0.43 19.63 17.81 1.35 1.72 161
2 Pine 227.27 17.26 32.39 28.94 186.10 19.93 904
Spruce 13.64 0.57 27.95 22.12 4.55 1.23 422
Birch 23.64 0.58 22.94 17.76 2.14 2.28 190
3 Pine 296.25 17.65 28.68 23.81 164.89 22.61 631
Spruce 109.38 3.42 24.61 18.66 19.07 10.47 269
Birch 90.00 2.05 23.75 20.20 10.13 7.60 201
4 Pine 234.29 22.05 37.07 30.18 246.73 22.23 1141
Spruce 668.57 31.61 30.77 26.11 314.20 71.21 573
Birch 50.00 2.64 31.79 26.46 23.06 6.32 590
5 Pine 140.00 12.12 34.50 28.17 130.53 11.75 1013
Spruce 223.13 9.23 28.72 23.82 83.67 19.30 460
Birch 51.25 3.55 35.44 27.32 34.22 5.42 776
6 Pine 251.43 18.74 32.03 27.53 198.69 20.33 863
Spruce 494.29 28.85 30.26 26.09 301.37 55.73 721
Birch 88.57 1.17 16.41 17.58 2.59 6.18 104
7 Pine 157.43 10.26 31.09 23.06 95.51 10.84 666
Spruce 225.25 5.13 24.69 19.30 30.72 15.02 199
Birch 75.74 2.02 28.37 22.36 13.40 5.26 249
Average 182.42 10.03 28.14 23.29 96.81 16.26 522
N denotes the number of stems, G is the basal area, DG is the basal area-weighted mean diameter, HG is Lorey’s height, Logs is the saw log volume, Pulp is the pulpwood volume, and Size is the average stem size of merchantable wood.
Table 2. Assortment volume (m3) estimates and the number (N) of cut trees for the clear-cut sections based on the 41 timber trade contracts and the actual harvested characteristic by tree species. The estimated number of cut trees was given by dividing the sum of the pulpwood and the saw logs for the contracts, with the average stem size given in m3. The average difference (contract – harvested) and the standard deviations between these characteristics are given in the last 3 lines.
Pine Spruce Birch
Variable Mean Std Mean Std Mean Std
Pulpwood, contracts 70.6 65.1 66.0 63.4 37.0 64.7
Pulpwood, harvested 67.3 82.1 64.9 57.1 59.4 76.6
Saw logs, contracts 138.0 137.5 158.8 191.2 4.7 8.0
Saw logs, harvested 139.8 114.9 140.0 170.0 3.3 5.5
N of cut trees, contracts 461.1 407.2 421.5 440.5 195.3 284.9
N of cut trees, harvested 668.0 780.2 707.1 683.2 503.6 604.4
Difference between contract and actual harvested characteristics
Pulpwood 3.3 55.5 1.1 32.1 –22.4 43.1
Saw logs –1.8 87.0 18.9 67.4 1.4 9.3
Number of cut trees –206.9 660.1 –285.6 404.3 –308.3 419.3
Table 3. Prediction errors in stand characteristics when the truncated Weibull distribution was solved using optimization for the modelling data set (STM based input data).
Stand Species Iterations G
m2 ha–1		 DG
cm 		HG
m 		Saw logs
m3 ha–1		 Pulpwood
m3 ha–1
1 Pine 118 2.55 0.53 –0.05 0.00 0.00
Spruce 35 –0.07 –2.14 2.93 0.01 –0.05
Birch 36 –0.07 –2.96 3.22 –0.01 –0.02
2 Pine 33 –0.97 –2.81 2.54 0.05 1.38
Spruce 39 –0.19 –1.89 4.19 0.00 0.02
Birch 58 –0.09 –0.80 2.30 0.01 0.02
3 Pine 118 0.04 0.79 –0.20 0.02 –0.68
Spruce 29 –0.35 0.01 0.96 –0.10 0.18
Birch 40 –0.35 –1.22 1.83 0.08 –0.35
4 Pine 39 –0.30 –0.59 0.39 –0.01 –0.42
Spruce 31 –2.67 –1.84 0.14 1.20 –1.35
Birch 29 –0.09 3.25 1.81 0.03 0.40
5 Pine 32 –0.45 –2.74 1.45 –0.01 0.36
Spruce 25 –2.08 –2.62 1.71 –1.06 –2.49
Birch 101 –0.19 2.28 1.76 0.00 0.00
6 Pine 32 –0.34 –1.56 –0.23 –0.09 –2.26
Spruce 34 –2.36 –1.66 0.67 0.02 0.81
Birch 36 –0.19 –1.54 1.38 0.03 –0.20
7 Pine 1000 –0.07 1.96 0.20 0.00 0.00
Spruce 37 –1.02 –1.38 0.91 0.26 –1.42
Birch 27 –0.49 0.57 3.25 0.82 –1.70
Bias   –0.46 –0.78 1.48 0.06 –0.37
Bias%   –4.63 –2.77 6.37 0.06 –2.28
St. dev   1.05 1.77 1.26 0.40 0.97
G denotes the basal area, DG is the basal area-weighted mean diameter, and HG is Lorey’s height.
1

Fig. 1. The observed (grey line) and predicted (black line) species-specific breast height diameter (dbh) distributions for the modelling data set of seven clear-cut stands.

Table 4. Parameters b and c for the optimized Weibull distribution and the Kolmogorov-Smirnov (KS) goodness-of-fit statistics, i.e., supremum S, critical KS test value and KS-quotient by Tham (1988), for each distribution in the modelling data set. The restricted distributions (KS-q > 1.0) at the 0.1 significance level are shown in bold.
Stand Species b c S KS test KS-q
1 Pine 27.65652 10.75086 0.0744 0.0516 1.4229
Spruce 22.84091 3.42576 0.1337 0.2609 0.5065
Birch 17.08886 2.04147 0.1625 0.2164 0.7519
2 Pine 33.85908 3.93423 0.0611 0.0774 0.7885
Spruce 28.18846 3.58795 0.2532 0.3160 0.7931
Birch 18.15757 2.07353 0.1396 0.2400 0.5927
3 Pine 28.54391 11.99995 0.0945 0.0562 1.5388
Spruce 21.48926 2.72832 0.0361 0.0925 0.4363
Birch 14.6169 1.48271 0.0908 0.1020 0.8490
4 Pine 36.92752 4.46618 0.0467 0.0956 0.4740
Spruce 24.96678 1.98449 0.0213 0.0566 0.8099
Birch 28.00898 4.50419 0.0729 0.2069 0.3601
5 Pine 35.85537 3.9325 0.0570 0.0818 0.5271
Spruce 25.53413 2.2826 0.0643 0.0648 0.8973
Birch 32.39969 4.36577 0.0510 0.1352 0.8471
6 Pine 32.92287 4.46401 0.0658 0.0923 0.7783
Spruce 29.96348 3.48296 0.0280 0.0658 0.3697
Birch 9.88933 1.44835 0.1242 0.1554 0.7981
7 Pine 29.8171 11.9427 0.0941 0.0686 0.9683
Spruce 13.22079 1.29523 0.0527 0.0574 0.6641
Birch 17.06155 1.52872 0.0691 0.0989 0.6441
Table 5. The difference (m3 for the clear-cut section) between the input assortment volumes from timber trade contracts and that of the output from the solved truncated Weibull distribution by tree species without saw log reduction and with the optional saw log reductions: MELA96, MELA05 and Bucking simulator (Malinen et al. 2007). The best results are shown in bold.
Reduction: Without MELA96 MELA05 Bucking simulator
Assortment: Pulpwood Saw logs Pulpwood Saw logs Pulpwood Saw logs Pulpwood Saw logs
Pine 40.11 2.6 10.85 1.19 1.2 0.12 10.14 1.15
Spruce 43.49 2.27 39.96 2.16 7.86 0.63 32.26 1.81
Birch 6.65 0.32 4.39 0.58 4.39 0.54 3.46 0.53
Total 30.27 1.53 18.51 1.31 4.48 0.43 14.78 1.11
Table 6. The average goodness-of-fit tests according to the Kolmogorov-Smirnov quotient (KS-q) by Tham (1988) and the Error Index (EI) by Reynolds et al. (1988). Tests are given by tree species and total with the given saw log reduction option. The number of rejected cases (KS-q > 1) by tree species with the used saw log reduction percentage (slr%) in addition to the total number of rejected cases. The best results are shown in bold.
Reduction Without MELA96 MELA05 Bucking simulator
Test KS-q EI KS-q EI KS-q EI KS-q EI
Pine 1.0755 0.5567 1.2637 0.6794 1.3584 0.7126 1.2687 0.6756
Spruce 1.5596 0.8457 1.5628 0.8344 1.3334 0.7500 1.5415 0.8287
Birch 1.5626 0.9844 1.4631 0.9062 1.4614 0.9080 1.4207 0.8771
Total 1.3903 0.7914 1.4226 0.8040 1.3787 0.7880 1.4034 0.7912
KS test: rejected (slr%) rejected (slr%) rejected (slr%) rejected (sl%)
Pine 12/41 (0) 18/41 (16) 20/41 (24) 19/41 (18)
Spruce 28/40 (0) 28/40 (2) 24/40 (18) 29/40 (6)
Birch 29/40 (0) 21/40 (30) 21/40 (29) 19/40 (41)
Total 69/121 67/121 65/121 67/121
2

Fig. 2. Example of the harvested dbh distributions for Scots pine in test data (solid grey line). The number of harvested trees (N) and assortment volumes for a clear-cut section of 2.3 ha for the contract/harvester data were: N 1020/930; pulpwood 130/65 m3; saw logs 280/234 m3. The Kolmogorov-Smirnov quotient for the predicted distribution was 0.7719 without saw log reduction (solid line), 1.0738 using 16% MELA96 reduction (broken line) and 1.7620 using 24% MELA05 reduction (dotted line).

3

Fig. 3. Example of the harvested dbh distributions for Norway spruce in test data (solid grey line). The number of harvested trees (N) and assortment volumes for a clear-cut section of 2.7 ha for the contract/harvester data were: N 704/1102; pulpwood 100/74 m3; saw logs 255/302 m3. The Kolmogorov-Smirnov quotient for the predicted distribution was 2.608 without saw log reduction (solid line), 1.577 using 6% Bucking simulator-reduction (broken line) and 0.6777 with 18% MELA05 reduction (dotted line).

4

Fig. 4. Example of the harvested dbh distributions for birch in test data (solid grey line). The number of harvested trees (N) and the assortment volumes for a clear-cut section of 4.6 ha for the contract/harvester data were: N 533/207; pulpwood 70/30 m3; saw logs 10/2 m3. The Kolmogorov-Smirnov quotient for the predicted distribution was 0.766 without saw log reduction (solid line), 0.657 using 30% MELA96 reduction (broken line) and 0.600 with 41% Bucking simulator-reduction (dotted line).