# Allometric Equations for Estimating Biomass and Carbon Stocks in Afforested Open Woodlands with Black Spruce and Jack Pine, in the Eastern Canadian Boreal Forest

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}), highlighting the much larger potential of jack pine for OW afforestation projects in this environment.

## 1. Introduction

^{β2}) has been widely used to describe the relationship between tree diameter at breast height (DBH) or height (H) and biomass because it is simple and yields accurate results among species and sites [8,9]. The method for adjusting this model to data has however been the subject of debates. Using Monte Carlo simulations, Xiao et al. [10] demonstrated that the error distribution determines which method performs better, with non-linear regression better characterizing data with additive, homoscedastic, normal error, and linear regression on log-transformed data better characterizing data with multiplicative, heteroscedastic, log-normal error.

^{−1}over 70 years [6,28]; this estimate varies according to the applied silvicultural approach and the choice of planted species.

## 2. Materials and Methods

#### 2.1. Study Sites

^{3}root plug volume per cavity (IPL Inc., Saint-Damien, QC, Canada). Seedlings were planted at a density of 2500 plants ha

^{−1}in summer 2000 (sites 4–11) and 2001 (sites 15–16) [31]. A description of the seven afforested OWs (sites) is provided in Table 1.

#### 2.2. Tree Sampling

^{2}plots (20 m × 20 m) in each site: one in the portion afforested with black spruce (BS) and the other in the portion afforested with jack pine (JP), for a total of 14 plots. Both natural trees (i.e., trees that were already on the sites before plantation) and planted trees were harvested and measured.

^{−3}for BS and 469 kg m

^{−3}for JP was applied to obtain the wood dry mass [38].

^{2}+ ab + b

^{2}),

#### 2.3. Fitting Performance of Existing Allometric Equations

#### 2.4. Development of Allometric Equations

_{1}× Dv

^{β2}+ Ɛ

_{1}) × β

_{2}Dv + Ɛ

_{1}and β

_{2}) (model 2):

_{1}× (Dv

^{2}H)

^{β2}+ Ɛ

_{1}) × β

_{2}(Dv

^{2}H) + Ɛ

_{1}, β

_{2}and β

_{3}) (model 3):

_{1}× Dv

^{β2}× H

^{β3}+ Ɛ

_{1}) × β

_{2}Dv × β

_{3}H + Ɛ

_{1}, β

_{2}and β

_{3}the model’s parameters, and Ɛ the error term.

^{2}and AICc for each model. It is known that the log-transformation of the data introduces a systematic bias to biomass values predicted from linear models built from log-transformed data. This bias can be corrected by applying a correction factor (CF = exp[RSE

^{2}/2]) in the back-transformation to the original arithmetic scale [39,40].

#### 2.5. Carbon Stocks Calculation in Planted Trees, Nine Years after Afforestation

^{2}plots based on the diameter and height of each planted tree. The total C in each tree was calculated as the sum of the dry mass of each tree compartment (needles, stems, branches, and roots), then multiplied by 0.5 as suggested by the Intergovernmental Panel on Climate Change (IPCC) [41]. We obtained the C stocks in the planted trees by summing the total C in all planted trees in each plot and then multiplying by a factor 25 to obtain C stocks in tons (t) per ha. The density of trees varied widely among plots (Table 1). To estimate the C sequestration potential of OW afforestation with the commonly applied planting density (2000 trees ha

^{−1}), C stock values in each plot were normalized with tree density.

## 3. Results

#### 3.1. Fitting Performance of Existing Allometric Equations

#### 3.2. Species-Specific Allometric Equations

#### 3.2.1. Black Spruce and Jack Pine Trees with H > 1.3 m

_{1}, β

_{2}and β

_{3})—yielded the lowest AICc and highest R

^{2}for all BS compartments (Table 2; Figure 3). Model 3 also yielded the best results for JP’s roots and stem biomasses but model 2 had equally low or lower AICc for branches, needles and aboveground biomasses (Table 3; Figure 3).

#### 3.2.2. Black Spruce Trees with H < 1.3 m

#### 3.2.3. Planted Jack Pine Trees

#### 3.2.4. Equations Parameters

#### 3.3. Shoot Root Ratio

#### 3.4. C Stocks in Planted Trees

^{−1}for BS and JP, respectively). There was a large variability among sites partly due to a large variation in tree density (Table 1). However, even when C stocks values were normalized with tree density the variation among sites remained high (large error bars) due to differences in growth rates, which were significantly higher at sites 9 and 11 for both species (Table 1).

## 4. Discussion

#### 4.1. Comparison with Existing Equations

#### 4.2. Equations Selection

^{2}values often lower by < 0.02. Adding the H variable to the model also had a small impact on C stock estimates at the stand level, although model 1 tended to slightly overestimate JP C sequestration (Figure 7). This result agrees with other studies that held diameter as the most important variable for estimating biomass, even when used alone, because H measurements only marginally improve estimates in most cases [13,16,42,55,56].

#### 4.3. Root:Shoot Ratio (RSr)

^{−1}) and that proposed in the IPCC Guidelines for National Greenhouse Gas Inventories [58]. Mokany et al. [57] found that in forests with an AGBM > 75 tons ha

^{−1}, the ratio was 0.23, a value closer to the one obtained in the present study and to the value of 0.22 used in the budget model of the Canadian Forest Sector [59]. A recent study also found RSr in the hemiboreal forest zone to vary between 0.20 and 0.25 for pine and between 0.21 and 0.30 for spruce [55].

^{−1}) boreal stands studied by Mokany et al. [57], who observed RSr values of 0.22 to 0.96. Coniferous trees with DBH values < 10–15 cm generally have a lower RSr [55]. Of the 32 natural trees analyzed for RSr, only 10% had a DBH > 15 cm, and 68% had a DBH < 10 cm, possibly explaining why the planted trees had a lower RSr in our study, and why planted trees had a lower RSr than natural trees. Even if root biomass was underestimated in this study, our obtained RSr values are very similar to previous studies, and the estimates are conservative, which is expected for reliable C balance accounting. Additionally, the fine-root biomass can be assessed via the organic and mineral soil compartments in the perspective of establishing a complete C balance for the OWs.

#### 4.4. Estimates of Total Biomass

^{−1}) and a large range in tree H for both species. However, the large variability remained even when tree density was normalized (from 0.06–2.4 t·C ha

^{−1}for JP and 0.008–0.66 t·C ha

^{−1}for BS) (Figure 7). Tree height was much higher at both sites located in the Chibougamau region (sites 9 and 11), which resulted in much higher biomass values than at the other sites. Growth rates has been shown to differ between OWs [65] partly due to differences in humus depth, whereas the adjacent closed-crown stands have a more constant humus depth. In contrast, OW mineral soil layers likely contain similar available nutrient pools than in nearby closed-crown forests [66].

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Average biomass allocation to stems, branches, and needles for black spruce (n = 96) and jack pine (n = 50) trees (height >1.3 m) sampled in open woodlands of Quebec (measured) vs. predicted allocation by using the allometric equations developed by Lambert et al. (2005).

**Figure 3.**Roots (

**a**,

**b**)

**,**stem (

**c**,

**d**), branches (

**e**,

**f**), needles (

**g**,

**h**) and aboveground biomasses (

**i**,

**j**) (AGBM) predicted by the three models vs. measured values for black spruce (n = 96) and jack pine (n = 50) trees (height > 1.3 m) sampled in boreal open woodlands of Quebec.

**Figure 4.**Roots (

**a**), stem (

**b**), branches (

**c**), needles (

**d**) and aboveground biomasses (

**e**) (AGBM) predicted by the three models vs. measured values for black spruce (n = 21) trees (height < 1.3 m) sampled in boreal open woodlands of Quebec.

**Figure 5.**Roots (

**a**), stem (

**b**), branches (

**c**), needles (

**d**) and aboveground biomasses (

**e**) (AGBM) predicted by the three models vs. measured values for planted Jack pine (n = 21) trees sampled in boreal open woodlands of Quebec.

**Figure 6.**Relationships between shoot mass and root mass of black spruce (red circles) and jack pine (green circles) for (

**a**) planted and (

**b**) natural trees. *** indicates p < 0.001.

**Figure 7.**Estimates of carbon stocks (t C·ha

^{−1}) for each tree compartment (stems, needles, branches, roots), aboveground biomass (AGBM), and total tree biomass in OWs planted with black spruce (BS) and jack pine (JP) at a density of 2000 Table 1. Each value is the mean ± SD of seven sites (Figure 1).

**Table 1.**Characteristics of the sampled afforested open woodlands (OW), planted with black spruce (BS) and jack pine (JP) trees. For natural (i.e., not planted) trees, only with DBH over 9 cm were included. All values represent mean (± SE).

Sites | Plantation Density (Stems ha^{−1}) | Planted Tree Mean Height (m) | Natural Tree Density (Stems ha^{−1}) | Dominant Tree Mean Height (m) | Dominant Tree Age (Years) | ||
---|---|---|---|---|---|---|---|

BS | JP | BS | JP | ||||

4 | 925 | 475 | 0.41 ± 0.12 | 1.18 ± 0.56 | 113 | 8.78 ± 0.87 | 54 |

5 | 275 | 850 | 0.54 ± 0.14 | 1.69 ± 0.67 | 138 | 10.56 ± 1.41 | 67 |

6 | 625 | 700 | 0.51 ± 0.12 | 1.31 ± 0.54 | 200 | 8.94 ± 1.83 | 59 |

9 | 2350 | 1925 | 0.99 ± 0.40 | 2.85 ± 0.65 | 0 | 5.92 ± 0.47 | 32 |

11 | 2175 | 2125 | 0.74 ± 0.29 | 2.3 ± 0.98 | 275 | 8.32 ± 0.95 | 58 |

15 | 1500 | 1650 | 0.41 ± 0.14 | 1.37 ± 0.49 | 500 | 10.81 ± 0.30 | 60 |

16 | 1875 | 2000 | 0.58 ± 0.18 | 1.54 ± 0.47 | 113 | 11.2 ± 2.20 | 62 |

**Table 2.**Comparison of fitting performances (R

^{2}and AICc) of the three models for needles, branches, stem, roots and aboveground biomass (AGBM) in black spruce (n = 96) trees with height > 1.3 m. R

^{2}and AICc values of the best model are shown in bold for each compartment.

Model 1 | Model 2 | Model 3 | ||||
---|---|---|---|---|---|---|

R^{2} | AICc | R^{2} | AICc | R^{2} | AICc | |

roots | 0.88 | 58 | 0.89 | 52 | 0.91 | 50 |

stem | 0.94 | 120 | 0.96 | 84 | 0.97 | 40 |

branches | 0.79 | 222 | 0.81 | 216 | 0.81 | 215 |

needles | 0.74 | 226 | 0.75 | 221 | 0.76 | 219 |

AGBM | 0.86 | 174 | 0.88 | 161 | 0.89 | 152 |

**Table 3.**Comparison of fitting performances (R

^{2}and AICc) of the three models for needles, branches, stem, roots and aboveground biomass (AGBM) in Jack pine (n = 50) trees with height > 1.3 m. R

^{2}and AICc values of the best model are shown in bold for each compartment.

Model 1 | Model 2 | Model 3 | ||||
---|---|---|---|---|---|---|

R^{2} | AICc | R^{2} | AICc | R^{2} | AICc | |

roots | 0.92 | 54 | 0.93 | 48 | 0.94 | 46 |

stem | 0.97 | 47 | 0.98 | 32 | 0.98 | 25 |

branches | 0.95 | 76 | 0.96 | 74 | 0.96 | 76 |

needles | 0.94 | 55 | 0.94 | 55 | 0.94 | 57 |

AGBM | 0.96 | 49 | 0.97 | 41 | 0.97 | 42 |

**Table 4.**Comparison of fitting performances (R

^{2}and AICc) of the three models for needles, branches, stem, roots and aboveground biomass (AGBM) in black spruce (n = 21) trees with height < 1.3 m. R

^{2}and AICc values of the best model are shown in bold for each compartment.

Model 1 | Model 2 | Model 3 | ||||
---|---|---|---|---|---|---|

R^{2} | AICc | R^{2} | AICc | R^{2} | AICc | |

roots | 0.91 | −130 | 0.90 | −127 | 0.92 | −129 |

stem | 0.95 | −143 | 0.95 | −145 | 0.95 | −142 |

branches | 0.94 | −103 | 0.94 | −105 | 0.94 | −102 |

needles | 0.87 | −135 | 0.90 | −140 | 0.91 | −140 |

AGBM | 0.93 | −78 | 0.94 | −81 | 0.94 | −78 |

**Table 5.**Comparison of fitting performances (R

^{2}and AICc) of the three models for needles, branches, stem, roots and aboveground biomass (AGBM) in planted Jack pine (n = 28) trees. R

^{2}and AICc values of the best model are shown in bold for each compartment.

Model 1 | Model 2 | Model 3 | ||||
---|---|---|---|---|---|---|

R^{2} | AICc | R^{2} | AICc | R^{2} | AICc | |

roots | 0.92 | 8.6 | 0.93 | 7.5 | 0.93 | 9.5 |

stem | 0.94 | −6.8 | 0.97 | −24.5 | 0.97 | −24.5 |

branches | 0.92 | 12.9 | 0.93 | 8.7 | 0.93 | 11.4 |

needles | 0.88 | 11.7 | 0.88 | 10.7 | 0.88 | 13.1 |

AGBM | 0.95 | −8.7 | 0.96 | −18.4 | 0.96 | −15.7 |

**Table 6.**Selected equations for each tree compartment for black spruce and Jack pine trees with H > 1.3 m (n = 96 and 50, respectively), black spruce trees with H < 1.3 m (n = 21) and planted Jack pine trees (n = 28).

Black Spruce (H > 1.3 m) | Jack Pine (H > 1.3 m) | Black Spruce (H < 1.3 m) | Jack Pine (Planted) | |
---|---|---|---|---|

roots | 0.135 × DBH^{0.38} × H^{1.55} × 1.13 | 0.018 × DBH^{0.81} × H^{1.99} × 1.09 | 0.006 × DHS^{4.23} | 0.006 × (DHS^{2} × H)^{0.97} × 1.03 |

stem | 0.104 × DBH^{0.47} × H^{1.88} × 1.04 | 0.045 × DBH^{0.82} × H^{1.94} × 1.04 | 0.015 × (DHS^{2} × H)^{1.28} | 0.019 × (DHS^{2} × H)^{0.89} × 1.01 |

branches | 0.225 × DBH^{0.63} × H^{1.23} × 1.30 | 0.030 × (DBH^{2} × H)^{0.84} × 1.12 | 0.042 × (DHS^{2} × H)^{1.19} | 0.005 × (DHS^{2} × H)^{1.03} × 1.03 |

needles | 0.278 × DBH^{0.42} × H^{1.31} × 1.31 | 0.092 × (DBH^{2} × H)^{0.60} × 1.08 | 0.043 × DHS^{0.63} × H^{2.06} | 0.020 × (DHS^{2} × H)^{0.79} × 1.04 |

AGBM | 0.593 × DBH^{0.46} × H^{1.52} × 1.15 | 0.193 × (DBH^{2} × H)^{0.75} × 1.06 | 0.085 × (DHS^{2} × H)^{1.12} | 0.042 × (DHS^{2} × H)^{0.88} × 1.01 |

**Table 7.**The root:shoot ratio (RSr) of planted (n = 28 for BS and JP) and natural (n = 24 for BS and 8 for JP) trees and their minimum and maximum values. Results presented as mean ± SE.

Planted Trees | Natural Trees | |||||||
---|---|---|---|---|---|---|---|---|

Species | RSr | SE | Min. | Max. | RSr | SE | Min. | Max. |

BS | 0.20 | 0.06 | 0.09 | 0.33 | 0.24 | 0.08 | 0.08 | 0.44 |

JP | 0.21 | 0.06 | 0.13 | 0.41 | 0.26 | 0.06 | 0.17 | 0.37 |

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**MDPI and ACS Style**

Fradette, O.; Marty, C.; Tremblay, P.; Lord, D.; Boucher, J.-F. Allometric Equations for Estimating Biomass and Carbon Stocks in Afforested Open Woodlands with Black Spruce and Jack Pine, in the Eastern Canadian Boreal Forest. *Forests* **2021**, *12*, 59.
https://doi.org/10.3390/f12010059

**AMA Style**

Fradette O, Marty C, Tremblay P, Lord D, Boucher J-F. Allometric Equations for Estimating Biomass and Carbon Stocks in Afforested Open Woodlands with Black Spruce and Jack Pine, in the Eastern Canadian Boreal Forest. *Forests*. 2021; 12(1):59.
https://doi.org/10.3390/f12010059

**Chicago/Turabian Style**

Fradette, Olivier, Charles Marty, Pascal Tremblay, Daniel Lord, and Jean-François Boucher. 2021. "Allometric Equations for Estimating Biomass and Carbon Stocks in Afforested Open Woodlands with Black Spruce and Jack Pine, in the Eastern Canadian Boreal Forest" *Forests* 12, no. 1: 59.
https://doi.org/10.3390/f12010059