Table 1. General characteristics of the study stands. Volumes of trees are calculated from the harvester data.
No Area
ha 		Site type Volumes Latitude Longitude Municipality
Pine m3/ha Spruce m3/ha Birch m3/ha Total m3/ha
1 1.7 VT 194 3.2 2.9 200 61.2149 25.0953 Hämeenlinna
2 1.1 VT 206 5.8 4.5 216 61.2061 25.0981 Hämeenlinna
3 1.6 OMT 188 30 18 236 61.1976 25.1361 Hämeenlinna
4 0.7 MT 268 388 30 686 61.1822 25.1523 Hämeenlinna
5 1.6 MT/VT 142 104 40 286 61.2043 25.0651 Hämeenlinna
6 0.7 MT 218 359 9.5 586 60.9049 25.6822 Orimattila
7 2.0 VT 106 47 19 172 60.7142 25.8791 Myrskylä
Table 2. The average ground-truth stand characteristics calculated from harvester data (Cut trees).
Cut trees N, ha–1 G, m2ha–1 DG, cm HG, m V, m3ha–1 Log, m3ha–1 Pulp, m3ha–1
pine 240.2 17 31.9 26.4 188.8 149.8 38.4
spruce 249.8 11.3 27 22.1 133.7 113.6 18.8
broadleaves 57.2 1.8 25.5 21.4 17.7 6.2 11.3
Total 547.3 30.1 30.3 25.3 340.4 269.7 68.5
N denotes number of stems, G basal area, DG basal area-weighted mean diameter, HG Lorey’s height, V total volume, Log log wood volume and Pulp pulp wood volume.
Table 3. The descriptive statistics of 8763 trees from 364 sample plots of 16 × 16 m used for ABA modelling around the Hämeenlinna test site (e.g. Yu et al. 2015).
  minimum maximum mean Standard deviation
N, ha–1 195 3242 940 596
G, m2ha–1 3.7 57.3 26.8 9.2
DG, cm 10.4 53.0 25.7 7.9
HG, m 7.6 33.2 21.0 4.5
V, m3ha–1 21.3 786.1 270.1 123.8
Tree dbh, cm 5.0 71.9 16.6 9.4
N denotes number of stems, G basal area, DG basal area-weighted mean diameter, HG Lorey’s height, V total volume.
Table 4. Absolute and relative bias in stand characteristics by the optional methods. The best methods by tree species and stand totals are highlighted in bold and the worst are shown in italics.
  N,ha–1 G, m2ha–1 DG, cm HG, m Bias% N, % G, % DG, % HG, %
ABA grid
pine –51.62 –1.64 –1.68 1.97   –21.5 –9.6 –5.3 7.5
spruce 28.51 4.12 4.82 3.32   11.4 36.4 17.8 15.0
broadleaves –43.94 0.01 5.65 1.94   –76.8 0.8 22.2 9.1
Total –67.05 2.49 0.64 2.03   –12.3 8.3 2.1 8.0
ABA stand
pine –52.97 –1.61 –1.19 2.46   –22.1 –9.5 –3.7 9.3
spruce –50.80 3.91 9.93 7.05   –20.3 34.5 36.7 31.9
broadleaves –77.17 –0.50 8.18 3.49   –134.9 –27.9 32.1 16.4
Total –180.94 1.80 3.02 3.27   –33.1 6.0 10.0 12.9
Trestima 5
pine –25.27 0.79 0.37 2.76   –10.5 4.6 1.2 10.4
spruce 29.74 1.53 8.71 8.28   11.9 13.6 32.2 37.5
broadleaves –45.41 –0.23 9.22 9.38   –79.4 –13.0 36.2 43.9
Total –40.95 2.10 1.43 3.07   –7.5 7.0 4.7 12.1
Trestima 10
pine –35.60 0.25 0.34 4.04   –14.8 1.5 1.1 15.3
spruce 40.95 2.17 4.48 4.73   16.4 19.1 16.6 21.4
broadleaves 4.78 0.29 10.52 8.33   8.4 16.5 41.3 39.0
Total 10.13 2.71 0.84 3.16   1.9 9.0 2.8 12.5
EMO
pine 44.37 0.86 –1.80 1.83   18.5 5.1 –5.6 6.9
spruce 160.09 6.03 6.64 7.92   64.1 53.3 24.6 35.9
broadleaves 46.66 1.17 7.41 9.25   81.5 65.7 29.1 43.3
Total 251.12 8.06 –2.60 1.50   45.9 26.8 –8.6 5.9
N denotes number of stems, G basal area, DG basal area-weighted mean diameter, HG Lorey’s height.
Table 5. Absolute and relative RMSE in stand characteristics by methods. The best methods by tree species and stand totals are highlighted in bold and the worst are shown in italics.
  N, ha–1 G, m2ha–1 DG, cm HG, m RMSE% N, % G, % DG, % HG, %
ABA grid
pine 145.6 7.5 7.1 2.5   60.6 44.0 22.4 9.6
spruce 182.1 10.9 6.2 4.4   72.9 96.4 23.0 19.9
broadleaves 73.5 1.3 10.4 6.5   128.5 70.3 40.8 30.4
Total 193.5 7.8 3.2 2.3   35.4 26.0 10.6 9.3
ABA stand
pine 150.0 7.9 6.6 3.5   62.5 46.3 20.7 13.2
spruce 204.8 10.6 11.7 8.7   82.0 94.0 43.2 39.4
broadleaves 105.1 1.5 11.6 8.9   183.7 83.7 45.7 41.9
Total 315.6 7.6 5.0 4.6   57.7 25.1 16.4 18.3
Trestima 5
pine 129.1 6.6 4.6 4.2   53.7 38.7 14.6 15.9
spruce 93.8 5.7 15.6 12.4   37.5 50.6 57.6 56.4
broadleaves 156.2 1.9 17.0 14.2   273.0 108.0 66.8 66.4
Total 240.3 9.3 4.0 4.2   43.9 30.9 13.2 16.5
Trestima 10
pine 128.7 5.4 2.6 4.7   53.6 31.5 8.2 17.6
spruce 81.5 4.7 10.8 8.2   32.6 41.7 39.9 37.2
broadleaves 52.7 1.2 15.9 12.4   92.2 67.2 62.6 57.9
Total 187.0 9.4 2.5 3.7   34.2 31.3 8.2 14.6
EMO
pine 60.7 2.7 2.6 2.2   25.3 16.2 8.0 8.3
spruce 230.8 10.1 15.7 12.3   92.4 88.9 58.1 55.6
broadleaves 57.0 1.7 18.7 14.9   99.6 96.2 73.5 69.9
Total 317.4 12.1 3.4 1.9   58.0 40.3 11.1 7.6
N denotes number of stems, G basal area, DG basal area-weighted mean diameter, HG Lorey’s height.
Table 6. Absolute and relative bias in volume characteristics by methods. The best methods by tree species and stand totals are highlighted in bold and the worst are shown in italics.
  Volume, m3ha–1 Logs, m3ha–1 Pulp, m3ha–1 Bias% Volume Logs Pulp
ABA grid
pine –10.33 –1.62 –9.01   –5.5 –1.1 –22.2
spruce 54.83 51.98 3.56   41.0 45.7 15.8
broadleaves 1.58 1.49 0.17   8.9 23.9 2.4
Total 46.13 51.87 –5.26   13.6 19.2 –7.7
ABA stand
pine –5.09 3.23 –8.15   –2.7 2.2 –21.3
spruce 60.11 63.64 –2.74   44.9 56.0 –14.5
broadleaves 0.29 1.94 –1.35   1.7 31.2 –11.9
Total 55.36 68.85 –12.22   16.3 25.5 –17.8
Trestima 5
pine 23.10 21.87 –1.70   12.2 14.6 –4.4
spruce 38.48 35.51 1.35   28.7 31.2 7.2
broadleaves 1.59 0.30 2.26   9.0 4.7 20.0
Total 59.66 57.70 1.94   17.5 21.4 2.8
Trestima10
pine 19.86 21.82 –1.82   10.5 14.6 –4.8
spruce 30.32 28.29 1.84   22.7 24.9 9.7
broadleaves 7.00 2.78 4.21   39.6 44.6 37.2
Total 57.22 52.91 4.24   16.8 19.6 6.2
EMO
pine 14.42 8.73 5.53   7.6 5.8 14.4
spruce 80.34 67.70 11.69   60.0 59.6 62.1
broadleaves 12.21 3.33 8.76   69.0 53.4 77.4
Total 107.01 79.78 26.00   31.4 29.6 37.9
Table 7. Absolute and relative RMSE in volume characteristics by methods. The best methods by tree species or stand totals are highlighted in bold and the worst are shown in italics.
  Volume, m3ha–1 Logs, m3ha–1 Pulp, m3ha–1 RMSE% Volume Logs Pulp
ABA grid
pine 77.7 60.0 20.3   41.1 40.1 52.8
spruce 140.0 125.5 14.4   104.6 110.4 76.3
broadleaves 14.1 6.6 7.8   80.0 105.6 69.4
Total 111.3 106.1 11.9   32.7 39.3 17.3
ABA stand
pine 77.3 60.4 20.5   40.9 40.3 53.5
spruce 141.7 130.4 15.9   105.9 114.8 84.4
broadleaves 14.2 7.3 7.6   80.2 117.0 67.0
Total 115.2 111.6 20.7   33.8 41.4 30.3
Trestima 5
pine 79.0 66.0 20.8   41.9 44.0 54.3
spruce 85.1 79.9 7.6   63.6 70.3 40.5
broadleaves 14.9 7.5 10.2   84.1 120.7 89.8
Total 146.9 126.9 26.9   43.2 47.1 39.3
Trestima10
pine 65.3 51.8 18.9   34.6 34.5 49.3
spruce 67.1 61.6 6.7   50.1 54.2 35.4
broadleaves 12.9 4.4 8.7   73.0 71.1 77.3
Total 129.2 109.6 25.0   38.0 40.6 36.5
EMO
pine 34.4 27.0 8.2   18.2 18.0 21.3
spruce 138.3 119.6 17.8   103.3 105.2 94.7
broadleaves 18.5 6.7 12.0   104.4 108.2 106.4
Total 166.0 133.2 33.4   48.8 49.4 48.8
Table 8. Goodness of fit tests using Kolmogorov-Smirnov (KS-quotient, Tham 1998) and Error-Index (Reynolds et al. 1988). The smaller the value, the better the fit is. KS-quotient < 1 means passed case. The best test values by stands are highlighted in bold and the worst in italics.
Stand   ABA grid ABA stand Trestima 5 Trestima 10 EMO
1 KS-quotient 1.541 1.341 1.229 1.070 0.695
Error-Index 0.575 0.767 0.616 0.536 0.553
2 KS-quotient 0.744 1.021 2.242 1.226 0.384
Error-Index 0.494 0.809 0.783 0.646 0.393
3 KS-quotient 1.629 1.340 1.774 0.833 0.424
Error-Index 0.467 0.622 0.783 0.499 0.570
4 KS-quotient 0.577 0.796 1.132 0.558 0.678
Error-Index 0.609 0.505 0.618 0.313 0.446
5 KS-quotient 0.859 1.182 1.258 0.618 0.599
Error-Index 0.486 0.669 0.745 0.443 0.394
6 KS-quotient 0.574 0.793 0.608 0.566 0.591
Error-Index 0.477 0.499 0.419 0.328 0.624
7 KS-quotient 0.829 1.005 1.028 0.973 1.045
Error-Index 0.372 0.514 0.803 0.567 0.992
1

Fig. 1. Example of the breast height diameter (dbh) distributions for stand no. 1. EMO provided the best fit for total dbh distribution (all species together) according to Kolmogorov-Smirnov (KS) and Trestima 10 according to Error-Index (EI) goodness-of-fit tests.

2

Fig. 2. Example of the breast height diameter (dbh) distributions for stand no. 5. ABA grid, Trestima 10 and EMO methods passed the Kolmogorov-Smirnov goodness-of-fit test while EMO had the best test values. Trestima 5 resulted in a too peaked dbh distribution.

3

Fig. 3. Example of the breast height diameter (dbh) distributions for stand no. 7. ABA stand and ABA grid methods performed the best and second best according to Kolmogorov-Smirnov (KS) but according to Error-Index (EI), the ABA grid was slightly better. Trestima 5 and EMO did not pass the KS test and they provided the highest EI values.

4

Fig. 4. Example of the breast height diameter (dbh) distributions for stand no. 6. Trestima 10 fitted the best according to Kolmogorov-Smirnov (KS) and Error-Index (EI) goodness-of-fit tests. The second best EI and KS test values were found using Trestima 5 and EMO, respectively. All the predicted dbh distributions passed the KS test.

Table 9. Ranking the methods by the number of the best and the number of the worst cases among analysed criteria: Bias and RMSE for number of stems, basal area, basal area-weighted mean diameter, Lorey’s height, total volume, log and pulp wood volume by tree species and stand totals, as well as Kolmogorov-Smirnov (KS) and Error-Index (EI) tests. (Total of 70 criterion). The best performed method by each criteria is highlighted in bold.
Rank Best Worst
Criteria ABA grid ABA stand Trestima 5 Trestima 10 EMO ABA grid ABA stand Trestima 5 Trestima 10 EMO
Bias 9 3 7 7 2 2 4 4 2 15
RMSE 8 1 0 11 8 2 5 8 1 12
KS 1 0 0 2 4 1 1 5 0 0
EI 2 0 0 3 2 0 2 3 0 2
Total 20 4 7 23 16 5 12 20 3 30