# Mean Annual Wood Density Variations of Larix gmelinii (Rupr.), Quercus mongolica Fisch. ex Ledeb., and Pinus tabulaeformis Carr. at Two Different Stem Heights

^{1}

^{2}

^{*}

## Abstract

**:**

^{−3}) and Q. mongolica (0.596 g cm

^{−3}), but significantly different between P. tabulaeformis from the two different climatic regions (0.445 g cm

^{−3}in Mulan Forest and 0.521 g cm

^{−3}in Zhongtiaoshan Forest). Mean annual wood density within trees except for P. tabulaeformis from Mulan Forest was initially increasing until an intermediate cambial age, after which it decreased again to lower values. These findings showed that tree age had to be considered in assessing carbon sequestration in wood. It also could play an important role in decision making for forest management in Mulan Forest and show the benefit of the wood properties and carbon storage potential of the faster growing L. gmelinii compared to Q. mongolica. Furthermore, these findings gave an indication that intermediate old forest stands for some tree species accumulated more carbon per year within their woody biomass than young stands or old growth forests. Our results may have an impact on the planning of rotation lengths and of tree species composition for forest stands in Mulan Forest and Zhongtiaoshan Forest.

## 1. Introduction

_{2}yearly and contribute to climate change mitigation [2]. Within a forest, carbon is stored mainly in the living aboveground biomass and in the organic matter of the mineral soil [3]. The living aboveground biomass can be divided into several compartments, where the merchantable timber compartment has an additional carbon storage function when accounting for the duration of its use as wood for human use and for its substitution effect [4]. The substitution effect can be increased if the used wood fiber is reused in different products in a wood cascade chain [5].

^{−3}according to Zanne et al. [6] and 0.684 g cm

^{−3}according to Huang et al. [21]. Jiang et al. [22] found that wood density decreased gradually with increasing stem height.

^{−3}[6], 0.432 g cm

^{−3}after 15 days of air drying [17], and 0.551 g cm

^{−3}[18]. Xu [19] found that specific gravity (i.e., the density of wood divided by the density of water) of the wood is highest close to the pith and decreased until the cambial age of 10, after which it increased again towards the bark.

^{−3}and 0.660 g cm

^{−3}[6] and 0.748 g cm

^{−3}after 15 days of air drying [24].

- Averaged over both stem heights and all observed CA, $\overline{d}$ was highest for Q. mongolica and lowest for P. tabulaeformis.
- For P. tabulaeformis, $\overline{d}$ had no significant difference between the two different climatic regions.
- With increasing CA, $\overline{d}$ increased for the two coniferous tree species L. gmelinii and P. tabulaeformis.
- For Q. mongolica, we expected $\overline{d}$ to decrease with increasing CA.
- For the effect of SH, we expected to observe significantly higher $\overline{d}$ at BH compared to at UH at the same CA for Q. mongolica and significantly lower $\overline{d}$ for the coniferous tree species.

## 2. Materials and Methods

#### 2.1. Research Area

#### 2.2. Collection of Cross-Sections

#### 2.3. Density Measurement

#### 2.4. Data Processing

^{−3}, $a$ is the parameter for the slope of the linear relationship, $b$ is the parameter for the intercept at HF output of 0, and $x$ is the measured value of relative density from HF densitometry in volts.

#### 2.5. Data Analysis

## 3. Results

#### 3.1. Effect of Tree Species

^{−3}) compared to all other tree species (L. gmelinii, 0.626 g cm

^{−3}, $p<0.001$; Q. mongolica, 0.596 g cm

^{−3}, $p<0.001$; P. tabulaeformis from Zhongtiaoshan, 0.521 g cm

^{−3}, $p=0.050$). $\overline{d}$ of P. tabulaeformis from Zhongtiaoshan was also significantly lower than $\overline{d}$ of L. gmelinii ($p=0.005$), but no significant difference of $\overline{d}$ between Q. mongolica and L. gmelinii and of $\overline{d}$ between Q. mongolica and P. tabulaeformis from Zhongtiaoshan was observed (Figure 4).

#### 3.2. Effect of Stem Height

^{−3}and at UH on average 0.625 g cm

^{−3}. For P. tabulaeformis from Mulan, $\overline{d}$ at BH was on average 0.463 g cm

^{−3}and at UH on average 0.436 g cm

^{−3}.

#### 3.3. Effect of Cambial Age

#### 3.4. Effect of Annual Radial Increment

#### 3.5. Effect of Cambial Age, Annual Radial Increment, and Stem Height

## 4. Discussion

^{−3}and 0.660 g cm

^{−3}, average wood density for L. gmelinii between 0.528 g cm

^{−3}and 0.599 g cm

^{−3}, and average wood density of P. tabulaeformis 0.360 g cm

^{−3}. However, the values of $\overline{d}$ for L. gmelinii found in this study were higher than most values from the literature [6,51], while those values of $\overline{d}$ for Q. mongolica were lower than most values from the literature [6,24]. Wassenberg et al. [52] showed for multiple tree species that, as wood density values of a single tree can vary within the stem, estimated mean values also vary based on the sampling strategy. It is therefore possible that under a different sampling strategy, mean wood density values would show higher similarity to cited values.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**Plot of model residuals against fitted values (

**a**), histogram of model residuals (

**b**), and QQ-plot of model residuals (

**c**) of the linear mixed-effects model of L. gmelinii.

**Figure A2.**Plot of model residuals against fitted values (

**a**), histogram of model residuals (

**b**), and QQ-plot of model residuals (

**c**) of the linear mixed-effects model of Q. mongolica.

**Figure A3.**Plot of model residuals against fitted values (

**a**), histogram of model residuals (

**b**), and QQ-plot of model residuals (

**c**) of the linear mixed-effects model of P. tabulaeformis from Mulan.

**Figure A4.**Plot of model residuals against fitted values (

**a**), histogram of model residuals (

**b**), and QQ-plot of model residuals (

**c**) of the linear mixed-effects model of P. tabulaeformis from Zhongtiaoshan.

## Appendix B

**Figure A5.**Plot of model residuals against fitted values (

**a**), histogram of model residuals (

**b**), and QQ-plot of model residuals (

**c**) of the linear mixed-effects model for pairwise comparisons of estimated marginal means between subsets of tree species and location.

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**Figure 1.**Map of north-east China indicating the research area of Mulan with the upper red circle and of Zhongtiaoshan with the lower red circle [38] (modified).

**Figure 2.**Exemplary relative density profile of LM4 at breast height (BH), radius towards north. (

**a**) shows the total relative density profile from 1923 to 2013, the red box indicates the last five years; (

**b**) shows the last five years of the relative density profile with the inter-year transients being highlighted with red hatching; (

**c**) shows the processed last five years of the relative density profile, where inter-year transients are removed. All data points are in relative density values as the output of high-frequency (HF) densitometry in volts.

**Figure 3.**Scatter plots of measured mean annual air-dry wood density over cambial age (CA) (top row) and over annual radial increment (ARI) (bottom row) for all subsets L. gmelinii, Q. mongolica, and P. tabulaeformis from Mulan and P. tabulaeformis from Zhongtiaoshan. Darker scatters show mean annual air-dry density values at BH and lighter scatters at upper height (UH).

**Figure 4.**Estimated marginal means of $\overline{d}$ for all subsets L. gmelinii, Q. mongolica, and P. tabulaeformis from Mulan and P. tabulaeformis from Zhongtiaoshan. Error bars display the standard errors of the estimated marginal means. Different lowercase letters indicate significant differences with p-values < 0.05, α-level for pairwise comparisons.

**Figure 5.**Effect plot of the significant effect of the predictor variable CA on $\overline{d}$. Solid lines are modeled $\overline{d}$ values, and dashed lines are the standard errors of modeled values.

**Figure 6.**Effect plots of significant interaction effects of the predictor variables SH and CA on $\overline{d}$. Solid lines are modeled $\overline{d}$ values, and dashed lines are the standard errors of modeled values.

**Figure 7.**Effect plot of the significant effect of the predictor variable ARI on $\overline{d}$. Solid lines are modeled $\overline{d}$ values, and dashed lines are the standard errors of modeled values.

**Figure 8.**Effect plots of the predictor variables stem height (SH) and CA on $\overline{d}$ for ARI of 1, 2, …, 6 mm of L. gmelinii. Solid lines are modeled $\overline{d}$ values, and dashed lines are the standard errors of modeled values.

**Figure 9.**Effect plots of the predictor variables SH and CA on $\overline{d}$ for ARI of 1, 2, and 3 mm of Q. mongolica. Solid lines are modeled $\overline{d}$ values, and dashed lines are the standard errors of modeled values.

**Figure 10.**Effect plots of the predictor variables SH and CA on $\overline{d}$ for ARI of 1, 2, …, 5 mm of P. tabulaeformis from Mulan. Solid lines are modeled $\overline{d}$ values, and dashed lines are the standard errors of modeled values.

**Figure 11.**Effect plots of the predictor variables SH and CA on $\overline{d}$ for ARI of 1, 2, …, 5 mm of P. tabulaeformis from Zhongtiaoshan. Solid lines are modeled $\overline{d}$ values, and dashed lines are the standard errors of modeled values.

**Table 1.**Sample trees with tree species, location, age at 1.3 m stem height in years, tree height in m, diameter at breast height (DBH) in cm, elevation in m, and slope exposition.

Tree No. | Species Location | Age at 1.3 m Stem Height (y) | Tree Height (m) | DBH (cm) | Elevation (m) | Exposition |
---|---|---|---|---|---|---|

LM1 | L. gmelinii Mulan | 80 | 27.00 | 53.0 | 1450 | NW |

LM2 | 79 | 27.16 | 58.0 | 1430 | NW | |

LM3 | 80 | 27.64 | 48.8 | 1430 | NW | |

LM4 | 94 | 25.65 | 52.4 | 1293 | NE | |

LM5 | 93 | 25.30 | 52.7 | 1338 | E | |

QM1 | Q. mongolica Mulan | 55 | 11.75 | 27.5 | 1352 | NA |

QM2 | 66 | 15.30 | 28.6 | 1130 | W | |

QM3 | 66 | 15.42 | 28.6 | 1352 | S | |

QM4 | 66 | 14.06 | 29.2 | 1347 | S | |

QM5 | 70 | 13.65 | 28.2 | 1185 | N | |

PM1 | P. tabulaeformis Mulan | 67 | 19.85 | 42.8 | 1162 | NW |

PM2 | 70 | 24.60 | 41.5 | 954 | NE | |

PM3 | 101 | 25.80 | 50.6 | 961 | NE | |

PM4 | 98 | 24.70 | 42.2 | 1020 | NW | |

PM5 | 100 | 23.74 | 46.8 | 1013 | NW | |

PZ1 | P. tabulaeformis Zhongtiaoshan | 71 | 11.98 | 21.2 | 1223 | NW |

PZ2 | 87 | 15.40 | 34.5 | 1190 | NE | |

PZ3 | 75 | 16.14 | 41.4 | 1614 | NW | |

PZ4 | 72 | 16.50 | 63.0 | 1211 | NW | |

PZ5 | 55 | 17.90 | 34.5 | 1578 | N |

**Table 2.**ANOVA table of the linear mixed-effects models for subsets of species and location. p-values < 0.05 α-level are highlighted in bold type.

Fixed-Effect(s) | Subset | F-Value | p-Value | Subset | F-Value | p-Value |
---|---|---|---|---|---|---|

$CA$ | L. gmelinii | 29.69 | <0.001 | P. tabulaeformis Mulan | 19.39 | <0.001 |

$ARI$ | 11.14 | <0.001 | 56.26 | <0.001 | ||

$SH$ | 87.36 | <0.001 | 26.17 | <0.001 | ||

$CA\times ARI$ | 6.35 | 0.002 | 17.80 | <0.001 | ||

$CA\times SH$ | 16.28 | <0.001 | 7.56 | 0.006 | ||

$ARI\times SH$ | 34.29 | <0.001 | 20.52 | <0.001 | ||

$CA\times ARI\times SH$ | 14.25 | <0.001 | 5.95 | 0.015 | ||

$CA$ | Q. mongolica | 12.38 | <0.001 | P. tabulaeformis Zhongtiaoshan | 4.50 | 0.012 |

$ARI$ | 12.08 | <0.001 | 0.61 | 0.436 | ||

$SH$ | 0.22 | 0.642 | 0.40 | 0.529 | ||

$CA\times ARI$ | 7.71 | <0.001 | 10.62 | <0.001 | ||

$CA\times SH$ | 1.96 | 0.142 | 4.59 | 0.011 | ||

$ARI\times SH$ | 0.02 | 0.978 | 0.49 | 0.482 | ||

$CA\times ARI\times SH$ | 3.26 | 0.012 | 3.05 | 0.048 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sprengel, L.; Cheng, Z.; Hipler, S.-M.; Wu, S.; Spiecker, H.
Mean Annual Wood Density Variations of *Larix gmelinii* (Rupr.), *Quercus mongolica* Fisch. ex Ledeb., and *Pinus tabulaeformis* Carr. at Two Different Stem Heights. *Forests* **2020**, *11*, 394.
https://doi.org/10.3390/f11040394

**AMA Style**

Sprengel L, Cheng Z, Hipler S-M, Wu S, Spiecker H.
Mean Annual Wood Density Variations of *Larix gmelinii* (Rupr.), *Quercus mongolica* Fisch. ex Ledeb., and *Pinus tabulaeformis* Carr. at Two Different Stem Heights. *Forests*. 2020; 11(4):394.
https://doi.org/10.3390/f11040394

**Chicago/Turabian Style**

Sprengel, Lars, Zhongqian Cheng, Sandra-Maria Hipler, Shuirong Wu, and Heinrich Spiecker.
2020. "Mean Annual Wood Density Variations of *Larix gmelinii* (Rupr.), *Quercus mongolica* Fisch. ex Ledeb., and *Pinus tabulaeformis* Carr. at Two Different Stem Heights" *Forests* 11, no. 4: 394.
https://doi.org/10.3390/f11040394