# Sawlog Recovery in Birch, Black Alder, and Aspen Stands of Hemiboreal Forests in Latvia

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- Δ
_{Sawlogs}—the difference in yield (per cent point); - Sawlogs
_{theor}—theoretical sawlog recovery (%); - Sawlogs
_{actual}—actual sawlog recovery (%).

^{3}. This study used data from 4745 forest elements from 3543 final fellings: 3042 for birch, 684 for black alder, and 1019 for aspen.

- x—diameter class;
- α, β, and γ—function parameters.

- D
_{g}—mean quadratic diameter of the forest element (cm); - G—basal area of the forest element (m
^{2}ha^{−1}); - α, β, γ—parameters of the Weibull function;
- ρ—empirical coefficient, which is 2.0 for birch and black alder and 3.0 for aspen.

- H—tree height (m);
- D—tree diameter (cm);
- H
_{g}—height for the tree with the mean quadratic diameter of the forest element (m); - D
_{g}—mean quadratic diameter of the forest element (cm); - a
_{1}, a_{2}—species-specific empirical coefficients. For birch: a_{1}= 0.1925, a_{2}= 2.8489; for black alder: a_{1}= 0.1442, a_{2}= 2.8137; and for aspen: a_{1}= 0.1036, a_{2}= 3.6036.

- v—volume of a log without bark (m
^{3}); - D—the measured diameter at centre of the diameter class (cm);
- H—height of the tree measured directly or found by smoothing the field data according to diameter class (m);
- h—the distance from the butt end to a freely selected cut (0 < h < H) (m);
- d—the actual diameter of the tree trunk with bark at height h (cm);
- P
_{6}(x)—the sixth-power polynomial describing the statistical average tree trunk form:$${P}_{6}\left(x\right)={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+\dots +{a}_{6}{x}^{6};$$ - x—relative height (x = h/H, 0 < x < 1);
- Q
_{4}(x)—double thickness of bark in per cent of the diameter of the tree trunk with bark as the fourth-power polynomial:$${Q}_{4}\left(x\right)={b}_{0}+{b}_{1}x+{b}_{2}{x}^{2}+{b}_{3}{x}^{3}+4{x}^{4}$$_{0}, b_{1}, b_{2}, b_{3}, b_{4}—coefficients of the fourth-power polynomial (Table 2).

_{Sawlogs}for sawlog recovery without a more detailed breakdown since harvester data were available at such a level. In addition, sawlog recovery was expressed as a percentage of the total merchantable volume to make fellings with different harvested volumes comparable.

## 3. Results

^{3}for the latter (Table 4). Our results show that the difference in yield of sawlogs is not the same for all soil types, and it also varies depending on the average age and average diameter of the forest element.

_{Sawlogs}tended to be the lowest on drained peat soil, followed by drained mineral soil and wet mineral soil compared with dry mineral soil (Table 6). For birch age classes up to 30 years, and for aspen and black alder up to 20 years, the theoretical sawlog recovery is on average smaller than the actual, but for higher age classes, it is higher. For birch in the diameter classes up to 16 cm, and for aspen and black alder up to 14 cm, the theoretical recovery is on average smaller than the actual outcome but overestimated in higher diameter classes (Figure 1). Moreover, for both age and diameter, this relationship is non-linear. Consequently, the analysis includes the logarithmic values of those inventory parameters.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Changes in assortments of sawlogs depending on soil type, mean age, and diameter of the forest element. Soil types: A—dry mineral soil, B—wet mineral soil, C—peat soil, D—drained mineral soil, E—drained peat soil. Age decade is the mean age group of the forest element (1—1–10 age, 2—11–20 age, …15—141–150 age). DBH is the mean diameter of the forest element at a height of 1.3 m, rounded into 1 cm groups.

**Table 1.**Characteristics of data by species. The number of observations is provided for categorical variables; the range and mean ± standard deviation (SD) is provided for continuous variables.

Stand Element Characteristics | Description | Classes/Parameter | Birch | Black Alder | Aspen |
---|---|---|---|---|---|

Age, years | Average age of trees belonging to one forest element | Range | 10–141 | 10–134 | 10–144 |

Mean ± SD | 69.4 ± 26.5 | 69.2 ± 23.7 | 71.6 ± 20.9 | ||

Height, m | Average height of trees belonging to one forest element | Range | 8–36 | 8–35 | 8–35 |

Mean ± SD | 23.9 ± 5.5 | 22.8 ± 4.7 | 27.8 ± 4.8 | ||

DBH, cm | Average DBH of trees belonging to one forest element | Range | 8–49 | 8–42 | 8–60 |

Mean ± SD | 25.1 ± 7.3 | 25 ± 5.7 | 33.9 ± 8.4 | ||

Volume, m^{3} | The volume of assortments prepared in the felling | Range | 30–1015 | 30–753 | 30–1567 |

Mean ± SD | 145 ± 110 | 116 ± 91 | 195 ± 200 | ||

Area, ha | Felling area | Range | 0.5–5.0 | 0.5–5.0 | 0.5–5.0 |

Mean ± SD | 1.7 ± 0.9 | 1.7 ± 0.7 | 1.9 ± 1.0 | ||

Site type | Site type groups, based on the depth of the peat layer and moisture regime | Dry mineral soil, number of fellings | 1229 | 158 | 555 |

Wet mineral soil, number of fellings | 369 | 109 | 119 | ||

Peat soil, number of fellings | 137 | 40 | 22 | ||

Drained mineral soil, number of fellings | 816 | 194 | 252 | ||

Drained peat soil, number of fellings | 491 | 183 | 71 |

**Table 2.**Coefficients of the sixth-power polynomial P

_{6}(x) and the fourth-power polynomial Q

_{4}(x) according to Ozolins (2002).

Coefficient | Birch | Black Alder | Aspen |
---|---|---|---|

a_{0} | 120.567 | 120.224 | 110.428 |

a_{1} | −312.074 | −310.985 | −143.288 |

a_{2} | 1388.288 | 1450.125 | 530.481 |

a_{3} | −3725.819 | −4238.703 | −1643.3 |

a_{4} | 5197.005 | 6644.011 | 2606.605 |

a_{5} | −3788.858 | −5408.312 | −2212.94 |

a_{6} | 1120.891 | 1743.64 | 752.018 |

b_{0} | 9.61 | 8.34 | 7.57 |

b_{1} | −39.92 | 0.93 | −17.99 |

b_{2} | 117.49 | 20.45 | 43.35 |

b_{3} | −134.22 | −62.45 | −37.07 |

b_{4} | 55.73 | 55 | 14.24 |

Type of Assortment | Species | Assortment Length, m | Minimum Diameter of the Assortment, cm |
---|---|---|---|

Thick sawlogs | Birch | 2.8 | 18.0 |

Black alder | 2.5 | 24.0 | |

Aspen | 2.5 | 24.0 | |

Thin sawlogs | Birch | 2.4 | 12.0 |

Black alder | 2.4 | 12.0 | |

Aspen | 2.4 | 12.0 |

**Table 4.**Mean values with standard error (SE) for the actual and modelled theoretical sawlog volume.

Species | Actual Volume, m^{3} | Theoretical Volume, m^{3} | ||
---|---|---|---|---|

Mean | SE | Mean | SE | |

Birch | 50.09 | 0.62 | 69.21 | 0.81 |

Black Alder | 31.37 | 1.26 | 58.02 | 1.88 |

Aspen | 29.43 | 0.96 | 92.37 | 2.49 |

**Table 5.**Test of linear model effects on Δ

_{Sawlogs}(theoretical sawlog recovery (%)—actual sawlog recovery (%)).

Species | Wald Chi-Square | df | Sig. | |
---|---|---|---|---|

Birch | Intercept | 3749.430 | 1 | <0.001 |

Soil Type | 113.935 | 4 | <0.001 | |

ln(Age) | 345.079 | 1 | <0.001 | |

ln(DBH) | 227.568 | 1 | <0.001 | |

Black Alder | Intercept | 592.336 | 1 | <0.001 |

Soil Type | 7.174 | 4 | 0.127 | |

ln(Age) | 6.424 | 1 | 0.011 | |

ln(DBH) | 162.596 | 1 | <0.001 | |

Aspen | Intercept | 1123.854 | 1 | <0.001 |

Soil Type | 5.385 | 4 | 0.250 | |

ln(Age) | 139.033 | 1 | <0.001 | |

ln(DBH) | 79.407 | 1 | <0.001 |

**Table 6.**Linear model parameter estimates. Dependent variable Δ

_{Sawlogs}(theoretical sawlog recovery (%)—actual sawlog recovery (%)).

Species | Variable | Estimate | Standard Error | 95% Wald Confidence Interval | Sig. | |
---|---|---|---|---|---|---|

Lower | Upper | |||||

Birch | Intercept | −174.119 | 2.8368 | −179.679 | −168.559 | <0.001 |

DrainedPeatSoil | 8.238 | 0.9136 | 6.447 | 10.028 | <0.001 | |

DrainedMineralSoil | 6.161 | 0.7700 | 4.652 | 7.670 | <0.001 | |

PeatSoil | 4.571 | 1.5711 | 1.492 | 7.650 | 0.004 | |

WetMineralSoil | 6.062 | 1.0179 | 4.067 | 8.057 | <0.001 | |

DryMineralSoil | - | - | - | - | - | |

ln(Age) | 24.237 | 1.3047 | 21.680 | 26.794 | <0.001 | |

ln(DBH) | 29.791 | 1.9748 | 25.920 | 33.661 | <0.001 | |

Black Alder | Intercept | −195.027 | 8.2000 | −211.098 | −178.955 | <0.001 |

DrainedPeatSoil | 4.714 | 1.8675 | 1.054 | 8.374 | 0.012 | |

DrainedMineralSoil | 2.186 | 1.8406 | −1.422 | 5.793 | 0.235 | |

PeatSoil | 2.062 | 3.0761 | −3.967 | 8.091 | 0.503 | |

WetMineralSoil | 0.861 | 2.1506 | −3.354 | 5.076 | 0.689 | |

DryMineralSoil | - | - | - | - | - | |

ln(Age) | 6.804 | 2.6847 | 1.543 | 12.066 | 0.011 | |

ln(DBH) | 63.606 | 4.9882 | 53.829 | 73.383 | <0.001 | |

Aspen | Intercept | −160.370 | 4.7425 | −169.665 | −151.075 | <0.001 |

DrainedPeatSoil | −3.540 | 1.8369 | −7.141 | 0.060 | 0.054 | |

DrainedMineralSoil | −1.145 | 1.1144 | −3.329 | 1.040 | 0.304 | |

PeatSoil | −4.020 | 3.1718 | −10.236 | 2.197 | 0.205 | |

WetMineralSoil | −0.398 | 1.4762 | −3.292 | 2.495 | 0.787 | |

DryMineralSoil | - | - | - | - | - | |

ln(Age) | 29.344 | 2.4887 | 24.467 | 34.222 | <0.001 | |

ln(DBH) | 28.382 | 3.1851 | 22.140 | 34.625 | <0.001 |

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## Share and Cite

**MDPI and ACS Style**

Donis, J.; Šņepsts, G.; Zeltiņš, P.; Jansons, J.; Zālītis, P.; Jansons, Ā.
Sawlog Recovery in Birch, Black Alder, and Aspen Stands of Hemiboreal Forests in Latvia. *Forests* **2024**, *15*, 326.
https://doi.org/10.3390/f15020326

**AMA Style**

Donis J, Šņepsts G, Zeltiņš P, Jansons J, Zālītis P, Jansons Ā.
Sawlog Recovery in Birch, Black Alder, and Aspen Stands of Hemiboreal Forests in Latvia. *Forests*. 2024; 15(2):326.
https://doi.org/10.3390/f15020326

**Chicago/Turabian Style**

Donis, Jānis, Guntars Šņepsts, Pauls Zeltiņš, Jurģis Jansons, Pēteris Zālītis, and Āris Jansons.
2024. "Sawlog Recovery in Birch, Black Alder, and Aspen Stands of Hemiboreal Forests in Latvia" *Forests* 15, no. 2: 326.
https://doi.org/10.3390/f15020326