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Figure 16.
Average model residuals for different models for calculating assortment volumes by tree species_
| Tree species | Assortment | Average model residuals, % | |
|---|---|---|---|
| old model | new model | ||
| Scots pine | saw log | 6.74 | −0.01 |
| firewood | −1.33 | −0.82 | |
| Norway spruce | saw log | 7.78 | 2.40 |
| firewood | −3.67 | −2.55 | |
| Birch species | saw log | 11.83 | 1.23 |
| firewood | 2.21 | −0.16 | |
| European aspen | saw log | 0.75 | 0.42 |
| firewood | 22.48 | −2.34 | |
| Black alder | saw log | −17.98 | −7.84 |
| Grey alder | saw log | −33.45 | −2.99 |
Saw log proportion reduction_
| Tree species | Age used in the Estonian model | Malinen et al. 2007 | Estonian model (Figure 3) | ||
|---|---|---|---|---|---|
| MELA-96 | MELA-05 | Bucking simulation | |||
| Pine | 60–100 | 16.04 | 24.25 | 18.17 | 9–28% |
| Spruce | 60–80 | 2.35 | 17.79 | 6.38 | 10–29% |
| Birch | 50–70 | 30.27 | 29.35 | 41.46 | 38–64% |
Site index classes and site index H100 relationship_
| Site index H100, m | Site index class | Site index class in calculations |
|---|---|---|
| < 11.5 | 5A | 6 |
| 11.5…15.5 | 5 | 5 |
| 15.5…19.5 | 4 | 4 |
| 19.5…23.5 | 3 | 3 |
| 23.5…27.5 | 2 | 2 |
| 27.5…31.5 | 1 | 1 |
| > 31.5 | 1A | 0 |
j_fsmu-2023-0013_tab_008
| Relative diameter of a tree in relation to the diameter of a stand element | Number of trees, per mille |
|---|---|
| 0.4 | 11 |
| 0.5 | 34 |
| 0.6 | 59 |
| 0.7 | 96 |
| 0.8 | 131 |
| 0.9 | 154 |
| 1.0 | 154 |
| 1.1 | 132 |
| 1.2 | 96 |
| 1.3 | 64 |
| 1.4 | 35 |
| 1.5 | 18 |
| 1.6 | 10 |
| 1.7 | 4 |
| 1.8 | 2 |
General data on felled elements included in the analysis_ Site index class and site index H100 relationship are described in Table 2_
| Tree species | No. of elements | Age, years | Site index class | ||
|---|---|---|---|---|---|
| minimum | maximum | maximum | minimum | ||
| Scots pine (Pinus sylvestris L.) | 14,013 | 21 | 219 | 1A | 5A |
| Norway spruce (Picea abies (L.) H. Karst.) | 3,045 | 16 | 177 | 1A | 5 |
| Silver and downy birch (Betula pendula Roth, Betula pubescens Ehrh.) | 7,145 | 22 | 153 | 1A | 5 |
| European aspen (Populus tremula L.) | 1,862 | 23 | 140 | 1A | 3 |
| Black alder (Alnus glutinosa (L.) Gaertn.) | 679 | 37 | 138 | 1A | 4 |
| Grey alder (Alnus incana (L.) Moench) | 770 | 18 | 75 | 1A | 4 |
| Total | 27,514 | 16 | 219 | 1A | 5A |
Parameters of timber assortments (roundwood) used in the analysis_
| Tree species | Assortment | Top diameter, cm | Length, m | ||
|---|---|---|---|---|---|
| minimum | step | Maximum | |||
| Scots pine | Log | 28–… | 3.1 | 0.3 | 6.1 |
| Log | 23–28 | 3.1 | 0.3 | 6.1 | |
| Log | 18–23 | 3.1 | 0.3 | 6.1 | |
| Log | 13–18 | 3.1 | 0.3 | 6.1 | |
| Log | 10–13 | 3.1 | 0.3 | 6.1 | |
| Pulpwood | 5 | 3.0 | 3.0 | ||
| Firewood | 3 | 3.0 | 3.0 | ||
| Norway spruce | Log | 25–… | 3.1 | 0.3 | 6.1 |
| Log | 18–25 | 3.1 | 0.3 | 6.1 | |
| Log | 13–18 | 3.1 | 0.3 | 6.1 | |
| Log | 10–13 | 3.1 | 0.3 | 6.1 | |
| Pulpwood | 5 | 3.0 | 3.0 | ||
| Firewood | 3 | 3.0 | 3.0 | ||
| Silver and downy birch | Log | 14–… | 3.1 | 0.3 | 6.1 |
| Pulpwood | 5 | 3.0 | 3.0 | ||
| Firewood | 3 | 3.0 | 3.0 | ||
| European aspen | Log | 14–… | 3.1 | 0.3 | 6.1 |
| Pulpwood | 5 | 3.0 | 3.0 | ||
| Firewood | 3 | 3.0 | 3.0 | ||
| Black alder | Log | 18–… | 3.1 | 0.3 | 6.1 |
| small log | 14–18 | 3.1 | 0.3 | 6.1 | |
| Firewood | 3 | 3.0 | 3.0 | ||
| Grey alder | Log | 18–… | 3.1 | 0.3 | 6.1 |
| small log | 14–18 | 3.1 | 0.3 | 6.1 | |
| Firewood | 3 | 3.0 | 3.0 | ||
Equation parameters obtained by comparing roundwood assortment volumes_
| Tree species | Assortment | a | b | c | d | f | i | R2 | p-value |
|---|---|---|---|---|---|---|---|---|---|
| Scots pine | Log volume reduction | −0.4560 | −6.7947 | −46.8016 | 99 | 100 | 1 | 0.0356 | < 0.0001 |
| Firewood increase | 2.7817 | 1.0015 | 267.0156 | 99 | 100 | 1 | 0.0233 | < 0.0001 | |
| Norway spruce | Log volume reduction | 0.2145 | 6.7871 | −0.0656 | 1 | 20 | 1.1 | 0.0158 | < 0.0001 |
| Firewood increase | −3.1086 | 17.2571 | −91.9444 | 49 | 50 | 0.1 | 0.0195 | < 0.0001 | |
| Silver and downy birch | Log volume reduction | 1.0622 | 9.1595 | 0.3487 | 10 | 50 | 1 | 0.0945 | < 0.0001 |
| Firewood increase | 0.1733 | 3.2363 | 0.0063 | 0,1 | 1 | 1 | 0.0052 | < 0.0001 | |
| Veneer log | −3.6396 | 10.4272 | −2.6481 | 10 | 20 | 0.1 | 0.1445 | < 0.0001 | |
| European aspen | Log volume reduction | 1.0522 | 12.6587 | 15.8415 | 49 | 50 | 1 | 0.1991 | < 0.0001 |
| Firewood increase | −1.0607 | 28.4761 | −0.0969 | 0.1 | 0.2 | 0.1 | 0.0381 | < 0.0001 | |
| Black alder | Log volume reduction | 0.6106 | 22.1975 | −0.0837 | 1 | 2 | 1 | 0.0789 | < 0.0001 |
| Grey alder | Log volume reduction | −6.106 | 12.485 | −61.485 | 90 | 100 | 1 | 0.0353 | 0.0257 |
The parameter n of the volume change Equation 3 and the parameters of the Equation for calculating its coefficients a, b and c (Equation 5)_
| Tree species | Formula | Constant | Equation coefficients | |||
|---|---|---|---|---|---|---|
| k | l | m | n | |||
| Scots pine | log volume reduction | a | −2.259 | 0.24693 | −0.01345 | 3 |
| b | 11.35752 | −2.10076 | 0.1712 | |||
| c | 894.235 | −304.766 | 28.869 | |||
| firewood increase | a | −3.3503 | 0.0159 | −0.0013 | 2 | |
| b | 1.5375 | −0.0271 | 0.0022 | |||
| c | 1.5328 | −0.0261 | 0.0021 | |||
| Norway spruce | log volume reduction | a | −0.89371 | −0.13886 | 0.01049 | 4 |
| b | 29.4603 | 4.36432 | −0.33114 | |||
| c | −366800 | −228124 | −4093 | |||
| firewood increase | a | −1.66542 | −0.06081 | 0.0012 | 4 | |
| b | 29.59224 | 0.27817 | 0.09189 | |||
| c | −115756 | −24063 | 89.533 | |||
| Silver and downy birch | log volume reduction | a | −0.39607 | 0.06595 | −0.0032 | 5 |
| b | 28.784 | −1.088 | 0.042 | |||
| c | 3829316 | 885112 | 80082 | |||
| firewood increase | a | −1.67591 | 0.01012 | −0.00097 | 4 | |
| b | 25.21899 | −0.21777 | 0.02076 | |||
| c | −211985 | 7782.9 | −749.88 | |||
| veneer block recovery | a | −2.7282 | −0.2457 | −0.0683 | 4 | |
| b | 30.281 | 12.921 | −1.639 | |||
| ln(-c) | 12.655 | 0.8226 | 0.2254 | |||
| European aspen | log volume reduction | a | 0.09015 | 0.01429 | −0.00061 | 4 |
| b | 27.49482 | −0.06593 | −0.01049 | |||
| c | −150369 | 7285 | −387 | |||
| firewood increase | a | −1.34789 | −0.01386 | 0.0011 | 5 | |
| b | 46.31225 | 0.04688 | −0.00447 | |||
| c | 10507971 | 920148 | −82200 | |||
| Black alder | firewood increase | a | 0.1209 | −0.09111 | 0.01198 | 10 |
| b | 73.66109 | −4.70172 | 0.78866 | |||
| c | −2.703·1015 | −5.258·1015 | 6.974·1014 | |||
| Grey alder | firewood increase | a | −0.82187 | −0.30129 | 0.00434 | 7 |
| b | 58.03680 | −0.13325 | 5.87003 | |||
| c | 3.048·1011 | −2.887·1011 | 4.242·1012 | |||