Comparison of Allometric Equation and Destructive Measurement of Carbon Storage of Naturally Regenerated Understory in a Pinus rigida Plantation in South Korea

The forest understory plays an important role in the carbon and nutrient cycling and forest stability, but cost-efficient quantification of its biomass remains challenging. Most of the existing biomass allometric equations have been developed and designed only for mature forest trees (i.e., Diameter at breast height (DBH) ≥ 10 cm), and those for trees with DBH less than 10 cm are not readily available. In this study, we compared the biomass by plant component (i.e., foliage, branch, and stem) measured by a destructive method with those estimated by the existing biomass allometric equations for understory trees with DBH less than 10 cm in a Pinus rigida plantation. We also developed an allometric biomass equation for the identified understory tree species, namely, Quercus variabilis, Quercus acutissima, Quercus mongolica, Quercus serrata, and Carpinus laxiflora. The estimated biomass using allometric equations for foliage, branch, and stem was lower than the values obtained using the destructive method by 64%, 41%, and 18%, respectively. The biomass allometric equations developed in this study showed high coefficients of determination (mean R2 = 0.970) but varied depending on species and tree part (range: 0.824–0.984 for foliage, 0.825–0.952 for branch, and 0.884–0.999 for the stem, respectively). The computed biomass of the understory vegetation was 22.9 Mg ha−1, representing 12.0% of the total biomass of the P. rigida plantation. The present study demonstrates that understory trees with DBH less than 10 cm account for a considerable portion of carbon stock in forest ecosystems, and therefore suggests that more biomass allometric equations should be optimized for small-DBH trees to improve forest carbon stock estimation.


Introduction
Increasing the use of fossil fuels and changes in land use worldwide are mostly responsible for global warming [1,2]. Forests have long been recognized as a major reservoir of global carbon, which plays a very crucial role in the mitigation of climate change [3][4][5]. In response, many countries have been developing methods for accurate national forest carbon stock estimations to help define management options for the changing global carbon cycle [6][7][8][9]. Thus, a comprehensive and accurate estimation of carbon stocks in different vegetation types is deemed important for a better understanding of both local and global carbon budgets.
Forest biomass can be estimated by either direct or indirect methods. The former is considered the most accurate method but requires destructive sampling because it involves whole-tree cutting which is complicated, labor-intensive, and time-consuming [10,11]. Indirect estimations of biomass using satellite data, aerial imagery, and numerical altitude models for large forest areas have recently dominant understory tree species, and (3) to develop allometric equations for estimating the biomass of regenerating trees of five important understory tree species in Pinus plantations. This study will demonstrate the important contribution of the understory vegetation biomass in the overall or total carbon storage in a Pinus plantation.

Study Site
This study was conducted in a 5.9 ha Pinus rigida plantation located in the premises of the Forest Technology and Management Research Center, National Institute of Forest Science in Pocheon, Gyeonggi-do (37.76° N, 127.10° E), located in northeastern Seoul in a 27 km distance ( Figure 1). P. rigida used to be a main species in artificial plantation in Korea, composing 26.0% of plantation [34]. In 2015, the mean temperature and total precipitation were 12.8 °C and 988 mm, respectively [35]. This P. rigida plantation was established in 1967 on a northwestern slope at 164 m altitude [36]. The stand structural parameters of the canopy tree species P. rigida are as follows: stand density = 717 trees ha⁻ 1 , mean tree height = 21.5 m, mean DBH = 24.2 cm, and mean basal area = 34.9 m 2 ha⁻ 1 . Soil in 0-10 cm depth were sampled to analyze and soil characteristics of the research area are shown in Table 1.

Estimation of Understory Aboveground Biomass Using a Destructive Method
In this study site, four plots (16 × 16 m) were established randomly in August 2015. Average steepness of the slope of the research sites were 16 • . To measure the understory vegetation biomass within a quadrat using the destructive method, we cut all plants with a diameter larger than 1 cm at the 1 cm height from the ground using a hand saw. Afterward, we measured the tree height and diameter at 10 cm height from the cut edge using a diameter tape (Table 2) and measured the fresh weights by component (foliage, branch, and stem). DBHs for trees < 2 cm at 1.3 m in height were estimated by the DBH = aD s b equation, where D means diameter at 10 cm in height above the ground, which was developed by the Korea Forest Services (KFS) in this region [37]. A total of 123 trees belonging to 16 species were used in this study. Lastly, samples of each species by tree part were transferred to the laboratory and oven-dried for 72 h at 65 • C. The ratio of dry weight to fresh weight of the cut trees was 0.375, 0.584, and 0.670 for foliage, branch, and stem, respectively (Supplementary Table S1).

Understory Vegetation Biomass Estimation Using Existing Allometric Equations
The DBH and height were measured to estimate the biomass of the canopy tree species P. rigida. We estimated the understory vegetation biomass by species and tree part using existing biomass allometric equations developed for P. rigida, Q. variabilis, Q. acutissima, Q. mongolica, Q. serrata, and C. laxiflora from the Korea Forest Service [37]. For the species that have no existing allometric equations, we applied the most suitable allometric equation taking into account the species-specific developmental curve. The allometric biomass equation of Q. serrata was used for Fraxinus rhynchophylla, Prunus sargentii, and C. laxiflora, for the remaining species (Table 3). Table 3. The coefficients for allometric equations of each part of the species [37]. Y = aD b H c was used for allometric equations, where D is DBH, H is tree height, and Y is dry weight. The coefficients for allometric equations were developed for over 6 cm of DBH trees.

Development and Statistical Analysis of Biomass Allometric Equations for the Main Understory Tree Species
We used the data obtained using the destructive method for developing the biomass allometric equations for the aboveground components of the five major understory tree species (Q. variabilis, Q. acutissima, Q. mongolica, Q. serrata, and C. laxiflora). The allometric equations for estimating the total aboveground biomass and the component-specific biomass were derived using the linear regression equation (log Y = a + b log D + c log H) with DBH (D) and height (H) as the independent variables and the dry weight of each component (Y) as the dependent variable. The regression equations were then derived and were considered for statistical significance at α = 0.05. Lastly, the coefficients of determination (R 2 ) were calculated. All analyses were performed using SPSS 24.0 (SPSS, Inc., Chicago, IL, USA) statistical software packge.

Biomass Analysis by Species
The biomass of each tree part estimated with the regression equation (hereinafter the "estimated value") was generally lower than the values obtained using the destructive method (hereinafter the "measured value"). However, variations across species and tree parts were observed ( Figure 2). The measured values of the foliage and branch biomass of Q. variabilis varied significantly by DBH, such that the stem biomass increased exponentially as the DBH increased (Figure 2a). In the case of branch of Q. acutissima, the measured value was less than the estimated value in the DBH range of 5.5-5.9 cm (Figure 2b). Foliage and branch biomass of Q. mongolica was underestimated, but stem biomass was estimated close to the measured value (Figure 2c). In Q. serrata, the difference between the measured and estimated values of aboveground biomass (foliage, branch, and stem) tended to increase with the increase in the DBH (Figure 2d). Lastly, the estimated value of foliage biomass in the case of C. laxiflora was remarkably lower than the measured value (Figure 2e). that the stem biomass increased exponentially as the DBH increased (Figure 2a). In the case of branch of Q. acutissima, the measured value was less than the estimated value in the DBH range of 5.5-5.9 cm (Figure 2b). Foliage and branch biomass of Q. mongolica was underestimated, but stem biomass was estimated close to the measured value (Figure 2c). In Q. serrata, the difference between the measured and estimated values of aboveground biomass (foliage, branch, and stem) tended to increase with the increase in the DBH (Figure 2d). Lastly, the estimated value of foliage biomass in the case of C. laxiflora was remarkably lower than the measured value (Figure 2e).

Biomass Analysis by Plot
Generally, the biomass estimated with allometric equations were lower than the measured values in all plots (Figure 3), with the mean estimated values for foliage, branch, and stem lower than the mean measured values by 64%, 41%, and 18%, respectively. Specifically, the estimated values for foliage and branch were lower than the measured values in all plots by 50%-72% and 13%-54%, respectively. In the case of the stem, however, whereas the estimated value was lower in plots 2 and

Biomass Analysis by Plot
Generally, the biomass estimated with allometric equations were lower than the measured values in all plots (Figure 3), with the mean estimated values for foliage, branch, and stem lower than the mean measured values by 64%, 41%, and 18%, respectively. Specifically, the estimated values for foliage and branch were lower than the measured values in all plots by 50%-72% and 13%-54%, respectively. In the case of the stem, however, whereas the estimated value was lower in plots 2 and 4 by 58% and 34% respectively, it was 33% higher in plot 5.
The estimated mean total biomass of P. rigida was 167.6 Mg ha −1 . The measured and estimated mean total values of understory vegetation were 22.9 and 15.9 Mg ha −1 respectively (Figure 3), accounting for 12.0% and 8.6% of the total biomass of the P. rigida plantation.

Species-Specific Biomass Allometric Equations
In the biomass allometric equations derived for the five understory tree species based on the DBH and height, the constants a, b, and c varied depending on species and tree part (Table 3; Figure 2). The biomass allometric equations showed high explanatory power in all the aboveground components of all five species (mean R 2 = 0.970). The range of R 2 values of the allometric equations for the foliage, branch, and stem biomass estimations in the five species were 0.824-0.984, 0.825-0.952, and 0.884-0.999, respectively. Almost all of the constants and coefficients of the allometric equations by species and tree part were statistically significant (Table 4). Table 4. Regressions coefficients, their probabilities, and determination coefficients of tree component dry mass (kg) on diameter (cm) at breast height (DBH), height (m) and equation (eq) for 5 species of understory vegetation in the Pinus rigida plantation. Equations follow the form: log Y = a + b log D + c log H, where D is stem DBH, H is tree height and Y is component dry mass. "n" means the number of trees of each species that were destructively sampled in this study.

Species-Specific Biomass Allometric Equations
In the biomass allometric equations derived for the five understory tree species based on the DBH and height, the constants a, b, and c varied depending on species and tree part (Table 3; Figure 2). The biomass allometric equations showed high explanatory power in all the aboveground components of all five species (mean R 2 = 0.970). The range of R 2 values of the allometric equations for the foliage, branch, and stem biomass estimations in the five species were 0.824-0.984, 0.825-0.952, and 0.884-0.999, respectively. Almost all of the constants and coefficients of the allometric equations by species and tree part were statistically significant (Table 4). Table 4. Regressions coefficients, their probabilities, and determination coefficients of tree component dry mass (kg) on diameter (cm) at breast height (DBH), height (m) and equation (eq) for 5 species of understory vegetation in the Pinus rigida plantation. Equations follow the form: log Y = a + b log D + c log H, where D is stem DBH, H is tree height and Y is component dry mass. "n" means the number of trees of each species that were destructively sampled in this study.

Species
Tree

Discussion
In this study, we stated that the DBH-dependent biomass variations make the existing biomass allometric equations developed for large-DBH trees inappropriate to apply for trees with smaller DBH values (e.g., understory tree regeneration) for biomass estimation. One possible reason is the inevitable inaccuracy/error in estimating foliage and branch biomass due to differences in growth rates among tree species [20]. For example, in a study measuring the DBH-dependent biomass of the aboveground components in a forest plantation, foliage and branch biomass decreased and stem biomass increased with the increase in the DBH [38]. This is because understory vegetation biomass growth is influenced by the structural characteristics of a forest stand [39,40]. At an early developmental stage, canopy biomass increases rapidly because of fast foliage growth to enhance photosynthesis. Once the canopy closure is reached, however, the proportion of stem biomass increases [16,20].
Across understory trees investigated, there were up to five-fold differences in the total aboveground biomass between the estimated and measured values, mostly in the foliage biomass. The scope of difference was similar to that resulting from the comparison between the measured values and the values estimated with the regression equations developed for sugar maple, yellow birch, and American beech [10,22]. Aboveground forest tree biomass distribution by component varies increasingly as the stand age and DBH increase [19] on account of the increasing deviation in the foliage and branch biomass distribution in understory vegetation. This may be attributed to the differences in light availability within a forest stand depending on the degree of canopy closure [22,28,39].
The measured total aboveground biomass of the understory vegetation accounted for~12.0% of the total aboveground biomass of the P. rigida plantation. This is a much higher value compared to the values (3%-5%) reported in previous works [23,41]. This is probably because such studies were conducted in forest stands with greater stand age and canopy coverage. Stand density and age of the canopy trees play an important role in understory vegetation [16], and light-use efficiency has a great effect on the diversity of understory vegetation species [42]. This suggests the importance of some silvicultural approaches (e.g., operational thinning) to enhance the biomass growth of both overstory and understory vegetation in traditionally managed overly dense pine plantations. The explanatory power of biomass allometric equations is generally known to be highest for foliage, followed by branch and stem [11,16,17]. The results of our study are not consistent with those of a study on biomass allometric equations for nine tree species at sapling stage (DBH ≤ 8 cm) in temperate mixed deciduous forests, in which foliage and stem showed the lowest (0.750) and highest (0.954) coefficients of determination [17]. From these inconsistent findings, it can be inferred that species-specific growth characteristics, site-specific environmental characteristics, and forest stand characteristics have diverse and significant effects on biomass distribution by tree part. These three factors may further complicate the accurate biomass estimation for different aboveground components, especially foliage and branch.
Growth characteristics of understory vegetation biomass can vary greatly depending on the dominant species and site environments [21,39]. Therefore, care should be taken when applying the biomass allometric equations derived in this study to plantations with different dominant species, natural forests, and trees with higher DBH values.

Conclusions
The results demonstrate that the use of existing allometric equations for biomass estimation of understory vegetation tends to underestimate biomass compared to the actual biomass. Our findings should provide a better understanding of the distribution and circulation patterns of carbon stocks in temperate forests by including the carbon stock of understory vegetation, which accounts for a considerable portion of total forest biomass. Further, the study can help future carbon stock assessment efforts to uplift the value of forest ecosystem services of a forest plantation, particularly P. rigida plantations with similar forest site conditions as described in this study. Nevertheless, further studies on biomass estimations of understory vegetation in P. rigida plantations and other forest types with a validation test procedure will completely shed light on the biomass contained within the understory stratum of the plantation.
Supplementary Materials: The following are available online at http://www.mdpi.com/1999-4907/11/4/425/s1, Table S1: Dry-to-fresh weight ratio of each species measured for biomass calculation in the Pinus rigida plantation. Parentheses denote standard errors. 'na' means not available because of one sample only.