Validation of saw log and technological wood assortment recovery and reduction predictions based on cut-to-length harvester data

Allar Padari; Ahto Kangur

doi:10.2478/fsmu-2023-0013

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Validation of saw log and technological wood assortment recovery and reduction predictions based on cut-to-length harvester data

Forestry Studies

Volume 79 (2023): Issue 1 (December 2023)

By: Allar Padari and Ahto Kangur

Open Access

|Apr 2024

Figures & Tables

Proportion of damaged trees depending on tree species and age.

Table 1.

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
Tree species	No. of elements	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

Table 2.

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

Table 3.

Parameters of timber assortments (roundwood) used in the analysis.

Tree species	Assortment	Top diameter, cm	Length, m
Tree species	Assortment	Top diameter, cm	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
Silver and downy birch	Pulpwood	5	3.0		3.0
Firewood	3	3.0		3.0
European aspen	Log	14–…	3.1	0.3	6.1
European aspen	Pulpwood	5	3.0		3.0
Firewood	3	3.0		3.0
Black alder	Log	18–…	3.1	0.3	6.1
Black alder	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
Grey alder	small log	14–18	3.1	0.3	6.1
Firewood	3	3.0		3.0

Table 4.

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
Scots pine	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
Norway spruce	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
European aspen	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

[i] Note. a, b, c, d, f and i are constants of Equations 1 and 2.

Table 5.

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
Tree species	Formula	Constant	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

Log volume reduction (A, C, E and G) and firewood volume increase (B, D, F and H) depending on stand age and site index class (A, B – Scots pine; C, D – Norway spruce; E, F – Birch spp.; G, H – European aspen).

Birch veneer log recovery depending on site index class and stand element age.

Black alder (left) and grey alder (right) firewood increase, and log volume reduction proportion depending on site index class and stand element age.

Distribution of Scots pine assortments calculated by diameter classes according to actual data, the old model and new model.

Distribution of Norway spruce assortments calculated by diameter classes according to actual data, the old model and new model.

Distribution of birch species (silver and downy birch) assortments calculated by diameter classes according to actual data, the old model and new model.

Distribution of European aspen assortments calculated by diameter classes according to actual data, the old model and new model.

Distribution of black alder assortments calculated by diameter classes according to actual data, the old model and new model.

Distribution of grey alder assortments calculated by diameter classes according to actual data, the old model and new model.

Old and new model prediction comparison residuals for volumes of Scots pine and Norway spruce assortments.

Old and new model prediction comparison residuals for volumes of silver and downy birch, and European aspen assortments.

Old and new model prediction comparison residuals for volumes of black and grey alder assortments.

Average model residuals by tree species.

Table 6.

Average model residuals for different models for calculating assortment volumes by tree species.

Tree species	Assortment	Average model residuals, %
Tree species	Assortment	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 proportions of the total volume of all roundwood assortments by tree species and sources.

Table 7.

Saw log proportion reduction.

Tree species	Age used in the Estonian model	Malinen et al. 2007			Estonian model (Figure 3)
Tree species	Age used in the Estonian model	MELA-96	MELA-05	Bucking simulation	Estonian model (Figure 3)
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%

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

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DOI: https://doi.org/10.2478/fsmu-2023-0013 | Journal eISSN: 1736-8723 | Journal ISSN: 1406-9954

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Language: English, Estonian

Page range: 66 - 89

Published on: Apr 13, 2024

Published by: Estonian University of Life Sciences

In partnership with: Paradigm Publishing Services

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© 2024 Allar Padari, Ahto Kangur, published by Estonian University of Life Sciences
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 79 (2023): Issue 1 (December 2023)

Validation of saw log and technological wood assortment recovery and reduction predictions based on cut-to-length harvester data

Figures & Tables

Figure 1.

Figure 2.

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Table 6.

Figure 16.

Table 7.

Paradigm

My account

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

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

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