Figure 1.
Figure 2.
Materials_
| Case | Materials | Statistical characteristics |
|---|---|---|
| Case 1 (Bilous et al., 2021) | 105 Scots pine trees from the Polissya climate zone (Ukraine) | Linear regression dependence of the mid-log taper on the midpoint diameter of the sawlog |
| Case 2 (Bilous et al., 2021) | 149 common oak trees from the Forest-Steppe climate zone (Ukraine) | The same |
| Case 3 (Chiorescu & Grönlund, 2001) | 625 Scots pine sawlogs (the Swedish Pine Stem Bank) | Numerical characteristics of the dimensions and sawlogs’ taper (average, standard deviation, and skewness) |
| Case 4 (Chiorescu et al., 2003) | 3000 sawlogs (a mix of Scots pine and Norway spruce) from southern Sweden | The same |
| Case 5 (Chiorescu & Grönlund, 2004a) | 773 Scots pine sawlogs from northern Sweden | The same |
| Case 6 (Chiorescu & Grönlund, 2004) | 506 Scots pine sawlogs from southern Sweden | The same |
| Case 7 (Chiorescu & Grönlund, 2004b) | 2665 Norway spruce sawlogs from southern Sweden | The same |
| Case 8 (Pyörälä et al., 2019) | 42 Scots pine middle sawlogs from southern Finland | Numerical characteristics of the dimensions and taper of sawlogs (mean, standard deviation) |
| Case 9 (Pyörälä et al., 2019) | 52 Scots pine butt sawlogs from southern Finland | The same |
Probability value that a sawlog has a taper less than its estimate and the first and third quartiles of the taper distribution_
| Case | Q | s0.25 | s0.75 |
|---|---|---|---|
| Case 3 | 25% | 6.6 mm·m−1 (100% ST) | 11.8 mm·m−1 (179% ST) |
| Case 4 | 35% | 6.5 mm·m−1 (86% ST) | 11.5 mm·m−1 (150% ST) |
| Case 5 | 20% | 7.9 mm·m−1 (112% ST) | 14.1 mm·m−1 (200% ST) |
| Case 6 | 31% | 6.2 mm·m−1 (90% SM) | 11.8 mm·m−1 (170% SM |
| Case 7 | 36% | 6.5 mm·m−1 (85% SM) | 11.5 mm·m−1 (150% SM) |
| Case 8 | 34% | 6,3 mm·m−1 (94% S23) | 8.4 mm·m−1 (126% S23) |
| Case 9 | 27% | 6,4 mm·m−1 (98% S23) | 9.6 mm·m−1 (146% S23) |
Parameters of the approximation of the distribution of the sawlogs’ taper by the metalog distribution and numerical characteristics of the distribution_
| Case | α1 | α2 | α3 | α4 | m (mm·m−1) | σ (mm·m−1) | S |
|---|---|---|---|---|---|---|---|
| Case 3 | 9.16 | 0.044 | 0.0360 | 10.129 | 9.18 | 3.00 | 1.07 |
| Case 4 | 8.99 | 2.139 | 0.0151 | 0.438 | 9.00 | 4.00 | 0.70 |
| Case 5 | 10.99 | 2.636 | 0.0103 | 0.792 | 11.00 | 5.00 | 0.73 |
| Case 6 | 8.99 | 2.408 | 0.0171 | 0.480 | 9.00 | 4.50 | 1.00 |
| Case 7 | 8.99 | 2.084 | 0.0133 | 0.795 | 9.00 | 4.00 | 0.60 |
Parameters of the approximation of the distribution of the sawlogs’ taper by a normal distribution_
| Case | m (mm·m−1) | σ (mm·m−1) |
|---|---|---|
| Case 8 | 7.3 | 1.6 |
| Case 9 | 8.0 | 2.4 |
Average dimensions of sawlogs and estimates of their tapers_
| Case | Type of taper | Taper (mm·m−1) | Taper estimate (mm·m−1) | The relative error of the taper estimate |
|---|---|---|---|---|
| Case 1 | Mid-log taper (inside the bark) | 8.5* | 7.3 | -14% |
| Case 2 | Mid-log taper (inside the bark) | 12.0* | 10.1 | -15% |
| Case 3 | Total taper | 9.18** | 6.6 | -28% |
| Case 4 | Total taper (inside the bark) | g** | 7.6 | -15% |
| Case 5 | Total taper (inside the bark) | 11** | 7.0 | -36% |
| Case 6 | Mid-log taper (inside the bark) | g** | 6.9 | -23% |
| Case 7 | Mid-log taper (inside the bark) | g** | 7.7 | -15% |
| Case 8 | Taper at 2/3 of the length (over the bark) | 7.3** | 6.5 | -9% |
| Case 9 | Taper at 2/3 of the length (over the bark) | 8.0** | 6.7 | -18% |