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Article

Combining Stand Diameter Distribution Quantified by the Weibull Function to Develop a Carbon Yield Model for Makino Bamboo (Phyllostachys makinoi Hayata)

by
Yi-Hung Liu
1 and
Tian-Ming Yen
2,*
1
The Experimental Forest Management Office, National Chung Hsing University, 145, Xingda Road, South District, Taichung City 402202, Taiwan
2
Department of Forestry, National Chung Hsing University, 145 Xingda Road, Taichung City 402202, Taiwan
*
Author to whom correspondence should be addressed.
Forests 2025, 16(3), 436; https://doi.org/10.3390/f16030436
Submission received: 31 January 2025 / Revised: 19 February 2025 / Accepted: 25 February 2025 / Published: 27 February 2025
(This article belongs to the Special Issue Ecological Research in Bamboo Forests: 2nd Edition)
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Abstract

:
Bamboo forests with high potential carbon storage have been found worldwide. Makino bamboo is critical, with a broad area of plantations distributed around Taiwan. This study established a thinning trial to monitor aboveground carbon storage (AGCS) and aimed to develop a carbon yield model for this bamboo species based on the Weibull function. Four thinning treatments, each replicated four times, were applied in this study. We collected data in 2019 after thinning and in 2021. We used the allometric function to predict the AGCS and the Weibull function to quantify the diameter distribution for each record. The culm number (N) and the parameters of the Weibull function were employed as independent variables to develop the AGCS model. The results showed that using N as a variable had an 83.6% predictive capability (Radj2 = 0.836). When adding the parameters b and c of the Weibull function to the model, the predictive capability can improve to 93.9% (Radj2 = 0.939). This confirmed that adding the parameters of the Weibull function helped promote AGCS prediction for Makino bamboo. Moreover, the advantages of this model are that it not only shows AGCS but also displays the diameter distribution.

1. Introduction

Bamboo is a vital resource worldwide because it offers numerous advantages, including rapid growth, high productivity, a short yield period, and multiple uses [1,2,3,4,5]. Bamboo forests are unique among forests because they comprise hollow culms of various ages, which result from the culms developing over various years [6,7,8,9]. As a result, bamboo forests show an uneven-aged structure, regardless of whether they are natural forests or plantations [10,11,12,13,14]. Bamboo is a crucial resource widely used by people globally. Bamboo forests cover over 36 million hectares worldwide, with approximately 65% in Asia [1,2]. Because the weather and environmental factors suit bamboo growth, over 150,000 ha of bamboo forests cover terrestrial areas with high biodiversity and productivity, providing multiple ecological services for people in Taiwan [1,7,8,15,16]. Most bamboo forests in Taiwan are monoculture plantations managed by farmers. Traditionally, culms and bamboo shoots are two main products that provide essential income for village residents [17,18,19,20,21]. They also play an important role in slowing global warming through carbon storage [15,19,21].
The development of bamboo plants occurs through asexual reproduction. New individuals sprout out from their rhizome year by year [22,23,24,25]. Therefore, selective cutting or thinning is necessary to improve productivity in managed bamboo plantations, regardless of harvesting culms or bamboo shoots [26,27]. Due to only removing old culms, most are still maintained and covered in the lands after harvesting. This pattern is friendly to the environment, and the products of bamboo culms are also regarded as non-timber forest products (NTFPs) [13,21]. In recent years, bamboo forests with high potential for carbon storage have been discovered worldwide for various species because their rapid growth results in fast accumulation of dry mass, especially in plantations [28,29,30,31]. These studies also contained some vital bamboo species in Taiwan, such as Ma bamboo (Dendrocalamus latiflorus), Makino bamboo (Phyllostachys makinoi), Moso bamboo (Phyllostachys pubescens), and Thorny bamboo (Bambusa stenostachya). Because the above bamboo species possess high economic benefits, they are also called “economic bamboo species” [15,21].
Makino bamboo is a native species with a particular ecological value and high productivity, and more than 44,000 ha of plantations are widely distributed in northern and central Taiwan [15,32]. Usually, they are planted by monoculture for financial purposes [19]. Both this species’ culms and bamboo shoots have high economic value, with the former being an excellent raw material and the latter being a delicious food [15,19]. Due to their high ecological and economic value, numerous studies have addressed this bamboo species in various aspects. The fields of analysis include cost analysis for managed plantations [33], assessing growth and biomass accumulation for the stand level [19], analyzing the stand structure of plantations [32], quantifying stand diameter distribution by the Weibull function [19], the impact of thinning on the growth and biomass accumulation [17], and assessing the ability of carbon storage of the stand level [19,21]. Since traditional management for Makino bamboo addresses economic benefits, many studies have focused on productivity and biomass accumulation. Recently, studies assessing carbon storage for this bamboo species have increased due to its high potential for carbon sequestration.
Many studies have confirmed a high correlation between carbon storage and stand structure for bamboo plantations [19]. Quantifying the stand diameter distribution helps to explain the relationships between diameter distribution and carbon storage. The Weibull probability density function is a powerful model that has effectively quantified the stand diameter distribution for various bamboo species [19]. The parameters of this model have geometric significance that can explain the different types of stand structures. Therefore, the present study addressed Makino bamboo to develop a carbon yield model based on the diameter distribution. The objectives of this study were to (1) compare aboveground carbon storage (AGCS) with thinning treatments, (2) quantify diameter distribution using the Weibull function, and (3) develop a carbon yield model based on the parameters of the Weibull function for Makino bamboo.

2. Materials and Methods

2.1. Study Areas

The study site was located in central Taiwan, belonging to the Tai Keng region, Beitun District, Taichung City (between 120.74° and 120.76° E and 24.16° and 24.18° N), within the lower mountainous area (at an elevation of 226 m). The topography was hilly terrain, and the soil type was sandy loam. Secondary forests and bamboo forests comprised the main vegetation composition in this area [34].
The detailed location of the study site is shown in Figure 1.
Because this region is abundant in natural resources and has beautiful scenery, it was designated as a scenic area by the Taichung City Government in 1976, called the “Dakeng Scenic Area” [34]. According to the weather data of Taichung City from 1991 to 2020, the monthly temperature ranged from 17.0 °C (in January) to 28.9 °C (in July), the mean was 23.7 °C, the relative humidity was 74.5%, and the annual rainfall was 1762.8 mm [35]. This region is also rich in bamboo resources, and Makino bamboo is a critical bamboo species. Most of the Makino bamboo are plantations managed by farmers for economic benefits. In recent decades, bamboo shoot production had a higher monetary value than the culm harvest; therefore, harvesting bamboo shoots is a significant management strategy for Makino bamboo plantations [19]. To develop a growth and yield system for this bamboo species, a site of a monoculture plantation by private farmer management was selected as an experimental site (Figure 1). The farmer allowed us to conduct this research work for a long time on his plantation.

2.2. Materials

We used Figure 2 to illustrate the flowchart of this study. Figure 2 displays the detailed processes of this research, from establishing a thinning trial to achieving the study purpose. It also contains materials, thinning treatments, data collection, and analysis approaches.
In 2019, we established a trial with various thinning intensities for the Makino bamboo plantation. Sixteen 5 × 5 m sample plots were randomly installed and surveyed in March 2019. The sample size and thinning intensity referred to previous studies [19,20,25]. Before thinning, the number of culms (N), diameter at breast height (DBH), and basal area (BA) were obtained to be 43,250 ± 14,936 culms ha−1, 2.05 ± 0.19 cm, and 15.41 ± 4.23 m2 ha−1, respectively. We used the thinning ratio of the culm number based on each plot to design the thinning project. Four treatments, namely Treatments I, II, III, and IV, were designed and installed on this site, where treatments I, II, III, and IV were thinning by 75%, 50%, 25%, and 0% of culm number for each plot, respectively (hereafter also called heavy, moderate, light, and no thinning). The thinning intensity used in this study is listed in Table 1.
Except for treatment IV without thinning, the thinning intensities allowed ±5% for the other treatments. The principle of the thinning was thinning from the older culms and abnormal culms, such as those damaged by diseases or insects. In March 2019, thinning treatments were installed and performed randomly for the original 16 sample plots. Each treatment was replicated four times. The DBH was measured, and the culm age was determined for each culm within plots after thinning treatments, where the culm age was judged based on the color and status of the culms. For the detailed approaches, please refer to Yen et al. [19]. In February 2021, we surveyed these plots again and recorded newly developed culms. To monitor the dynamic of the stand after thinning, we did not harvest bamboo shoots in this period.

2.3. Data Analysis

We predicted the AGCS based on the allometric function and quantified the stand diameter distribution using the Weibull function for each plot in 2019 and 2021, respectively.
The detailed processes of the AGCS prediction for each plot were described as follows:
  • We used the allometric model to predict aboveground biomass (AGB) for individual bamboo plants based on their DBH. Because the allometric function for predicting AGB has been built for Makino bamboo in this region by Yen et al. [19], the present study directly cited this model for estimating the AGB of each bamboo plant. The model is shown as Equation (1) [19].
AGB = 0.156 × DBH2.118
where AGB is aboveground biomass and DBH is the diameter at breast height.
2.
The AGB of plots was obtained from the summation of each individual within plots. Consequently, the AGB of all plots was obtained, and we formatted the unit of AGB as Mg ha−1.
3.
The AGCS prediction was based on the AGB and percentage of carbon content (PCC), indicating that AGCS equals AGB × PCC. In a previous study, Yen et al. [19] determined the proportion biomass of foliage, branches, and culms to be 8.4, 15.7, and 75.9%, respectively, and their PCC was 40.08, 46.06, and 47.65%, respectively, for Makino bamboo. We directly cited these data to calculate the aboveground PCC, and it was: (8.4% × 40.08%) + (15.7% × 46.06%) + (75.9% × 47.65%) = 46.76%. In this study, we used AGB × 46.76% for predicting AGCS.
Meanwhile, the Weibull probability density function was employed to quantify the diameter distribution for each plot because its parameters make it easy to explain the curve of diameter distribution. The model is given in Equation (2) [36]:
f ( x ) = c b x b c − 1 exp − x b c
where x is the diameter at breast height and b and c are parameters of the Weibull function.
We obtained the AGCS (Mg ha−1), culm number (culm ha−1), and the parameters b and c of the Weibull function for each plot with two investigations (2019 and 2021). The Kolmogorov–Smirnov (K-S) test was used to examine the goodness-of-fit for the model based on a criteria of α = 0.01.
The regression model employed the culm number, the parameters b and c of the Weibull function as independent variables, and AGCS as a dependent variable to establish a carbon yield model. The model is shown as Equation (3).
Y = β0 + β1 X1 + β2 X2 + β3 X3 + ε
where Y is aboveground carbon storage; X1 is the number of culms per hectare; X2 and X3 are the parameters b and c of the Weibull function; and ε is the error.
We adopted the stepwise method to perform a regression analysis. The root mean square error (RMSE) was used to evaluate the fitness of the models for observed and predicted AGCS. The detailed formula for RMSE is given in Equation (4)
R M S E = ∑ i = 1 n Y i − Y i ^ 2 n
where Yi and Ŷi are the i observation and the predicted aboveground carbon storage by the model, respectively, and n is the total number of observations.

3. Results

3.1. Stand Characteristics at Two Investigations

The N, MDBH, and BA were calculated based on the plot data. Table 2 shows these stand characteristics for various treatments, with two investigations.
All stand characteristics significantly differed between treatments in both 2019 and 2021. In 2019, after thinning, N and BA decreased, and MDBH increased, with thinning intensity increasing. Since this trial adopted thinning from below, MDBH increased with thinning intensity increasing, which was reasonable. The above stand characteristics also displayed the same pattern in 2021. Meanwhile, N and BA rose from 2019 to 2021 during stand development, regardless of thinning intensity. The data in Table 2 provided the background information on the stand characteristics.

3.2. AGCS with Various Treatments

According to Equation (1), the AGB of each plot with two investigations was obtained. Their AGCS was calculated from the AGB and PCC. The results of the AGCS with thinning treatments are shown in Figure 3.
The AGB and AGCS showed an identical pattern with treatment because the AGCS was derived from the AGB. We only showed the AGCS in Figure 3. In 2019, after thinning, the AGB and AGCS decreased with increasing thinning intensity. They also displayed the same pattern in 2021. However, AGCS did not significantly differ from the thinning treatment in 2021 because a higher standard deviation was displayed in each treatment (Figure 3).

3.3. Stand Diameter Distribution Quantified by the Weibull Function

We used the Weibull function to quantify the stand diameter distribution for each plot, and the parameters of the Weibull function with treatments are shown in Table 3.
In 2019, after thinning, stand diameter distribution varied with thinning treatments. We used the Weibull function to predict stand diameter distribution for each plot and obtained the parameters of this function. In 2019, parameters b and c increased with thinning intensity. The change of these two parameters followed stand development in 2021. However, their patterns were similar to 2019. All samples passed the K–S test based on a criteria of α = 0.01. To understand the fitness of the Weibull function, we used the observed data and predicted values to display for each treatment in 2019 and 2021. The results are shown in Figure 4.
We found this function matched the data, regardless of treatments. It indicated that the Weibull function effectively predicted stand diameter distribution for each thinning treatment over time.

3.4. Carbon Yield Models Based on the Parameters of the Weibull Function

We used N and the parameters b and c of the Weibull function as independent variables to develop carbon yield models. Because the stepwise approach was used for solving the regression model, the independent variables entered the model through three steps and generated three models. The results are shown in Table 4. Models I to III also indicated the order of the independent variables entering the models, which contained one to three independent variables.
We used Radj2 to assess the predictive ability of the carbon yield models. This indicator represents the models’ predictive capability or explanation ability from independent variables. It implies that a higher Radj2 has a higher predictive capability or explanation ability for the models. Model I, with only one variable, had 83.6% predictive capability (Radj2 = 0.836), indicating that N played a critical role in AGCS prediction. Adding the parameters of the Weibull function as independent variables improved Radj2. Compared to Model I, Models II (Radj2 = 0.916) and III (Radj2 = 0.939) promoted 8 and 10.3% predictive capability, respectively. This indicated that adding the parameters of the Weibull function helped improve predictive capability, regardless of only the parameter b or both the parameters b and c.
To further understand the relationship between observations and predicted AGCS, we used a scatter diagram displaying the predictive effects for each model, as shown in Figure 5.
A perceivable diagonal line implies that the observations are equal to the predicted values, which also helps in understanding the bias of the models. The bias decreased from Model I to III because the dots were closer to the 1:1 diagonal line (Figure 5). Moreover, we employed Equation (4) to calculate the RMSE value and obtained 2.833, 1.903, and 1.712 Mg ha−1 for Models I, II, and III, respectively. Model III had the lowest RMSE value, indicating this model had the highest predictive capability. From the above approaches to assess the models, this study confirmed that adding the parameters of the Weibull function improved the predictive ability.

4. Discussion

Bamboo plantations have a high carbon storage potential due to their generational pattern and harvesting or management approach. Understanding the mechanisms of development of bamboo plantations helps assess their AGCS ability. Bamboo plantations consist of individuals of various age classes, which display an uneven-aged structure [7,15,27]. Such a structure results from their development pattern and management approach [15,27,37,38]. Bamboo plants’ development is based on asexual reproduction by rhizome, and new individuals sprout out year by year. Therefore, harvesting or thinning old culms (usually over 4–5 years old) is necessary because it helps increase growth space for new culms and maintain vitality for the entire stands [7,15,19]. The products of bamboo forests are culms and bamboo shoots. Therefore, the key factors that affect the carbon stocking of bamboo plantations are the yield of the quantity of bamboo shoots and culms. If farmers harvest a significant number of bamboo shoots and only keep a few for further developing culms, bamboo plantations might show lower stockings [15,19].
On the other hand, bamboo plantations also display lower stockings when they harvest more old culms. The present study did not harvest bamboo shoots to control this trial and only used various thinning intensities to deal with the prosecution. However, the AGCS decreased with increasing thinning intensity in 2021, but did not significantly differ with thinning treatments because a higher standard deviation was displayed in each treatment.
Because bamboo plants possess hollow structures in culms, their volume is not easy to measure. Therefore, carbon storage is usually predicted through biomass, not volume [7,15,19]. An allometric equation is a power tool for predicting biomass or carbon storage, and numerous studies have proposed using it for predicting bamboo plants [7,15,27,39,40,41]. Therefore, the allometric model has been widely developed for predicting biomass and carbon storage in bamboo forests with various species [15,19,22,27]. The allometric model may target a certain bamboo species or a combination of multiple bamboo species [15,17,19]. Usually, the model developed for a specific bamboo species has a higher predictive ability than for across bamboo species.
Meanwhile, developing an allometric model is usually based on DBH and culm height (H) as independent variables. Commonly, using DBH alone (AGB = a × DBHb) and both DBH and H (AGB = a × DBHb × Hc) are the two main types of allometric models, which vary with bamboo species. The correlation between DBH and H determines whether to use one or two independent variables for various bamboo species. If there is a high correlation between DBH and H, using DBH as an independent variable for predicting AGB is sufficient, such as Makino bamboo and Moso bamboo [15,19]. On the contrary, when the relationship between DBH and H is not so strong, using both DBH and H can improve the predictive ability for AGB, such as Thorny bamboo [15]. Since Makino bamboo is a critical bamboo in Taiwan, the allometric model has been developed in a previous study. The present study cites it and PCC to predict an AGCS that is reliable.
Since bamboo plantations usually display pure stands, the diameter distribution is a vital characteristic that describes the stand structure of bamboo plantations [19]. The Weibull function is a power model used to quantify the diameter distribution of forests. Bailey and Dell [36] confirmed its suitability for timber forests compared to the beta, gamma, and other distributions. This model has been widely employed for quantifying the diameter distributions of various forest types, including natural forests, timber plantations, and bamboo forests [19,42]. Usually, the goodness-of-fit for examining the Weibull distribution was proposed by the K–S test. Our study confirms that the Weibull model is suitable for quantifying the diameter distribution with various thinning treatments of Makino bamboo based on the K-S test. We recommend the Weibull function to quantify the diameter distribution for bamboo plantations. Moreover, its superiority includes parameters with various geometrical meanings that help explain multiple distributions, where b and c indicate the scale and shape of the curves, respectively [19,36,42]. The Weibull distribution covers broad distribution types, including the positively skewed, normal, and negatively skewed distributions when the range of parameter c: 1 < c < 3.6, c = 3.6, and c >  3.6, respectively. The parameters can explain the curve’s shape and can also be used to predict forest stockings [42].
Stand diameter distribution changes over time following thinning treatments, which has biological and ecological meanings for bamboo plantations. However, the present study only addressed quantifying the diameter distribution and did not further analyze the biological and ecological meanings of stand diameter distribution over time. This was our study limitation.
Stand density is a key factor affecting forests’ growth and yield, where the number per ha is commonly used to present the stand density of bamboo forests [19,21]. It is also an indispensable element for showing the stand diameter distribution. Therefore, this variable and the parameters of the Weibull function were used to develop the AGCS yield model. As expected, N was a significant variable, with 83.6% predictive ability. We inferred this might result from the fact that the size of the culms has only a slight difference within bamboo plantations; therefore, there is a high correction between N and AGCS. Our findings demonstrate that adding the parameters b and c of the Weibull function enhanced predictive accuracy by over 10%. We inferred that the parameters b and c reflect thinning-induced structural changes, and adding the parameters helps improve the predictive ability of the model. This indicated that the Weibull function not only effectively quantified the stand diameter distribution, but also promoted the predictive ability of the AGCS yield model.
Traditionally, farmers address the economic benefits of Makino bamboo plantation management. Currently, they favor harvesting bamboo shoots as their primary product because bamboo shoots have higher economic benefits than culms. As a result, harvesting bamboo shoots is the primary management type for Makino bamboo plantations. Numerous researchers have confirmed that the plantations of this bamboo species have a high potential for carbon storage because of their high productivity [17,18,19,21]. Planting bamboo plantations is also regarded as a nature-based solution for global warming. Liu and Yen [21] analyzed 12 records from the publication data concerning the biomass and carbon storage of Makino bamboo plantations. The AGCS ranged from 6.84 to 95.3 Mg ha−1 (22.22 ± 24.66 Mg ha−1), indicating a large diversity of AGCS in Makino plantations. This might result from various management patterns. In our study, AGCS ranged from 7.32 to 24.43 Mg ha−1, and it decreased with thinning intensity increasing. These values also fall within the range of previous studies.

5. Conclusions

This study aimed to develop an AGCS model for Makino bamboo based on the diameter distribution. We predicted the AGCS and employed the N and the parameters of the Weibull function. The following conclusions were obtained:
  • During the thinning treatments from 2019 to 2021, treatment IV had higher AGCS in 2021. The trend of AGCS increased with decreasing thinning intensities but did not significantly differ by the statistical levels.
  • The stand diameter distribution of various treatments matched the curve predicted by the Weibull function, and all samples passed the K-S test, regardless of thinning intensities. This model can effectively describe Makino bamboo with various thinning treatments over time.
  • We developed the AGCS model based on N and the parameters b and c of the Weibull function. The N was a significant variable, with 83.6% predictive ability for the AGCS model.
  • Adding the parameters of the Weibull function enhanced predictive accuracy by over 10%. This model not only shows AGCS but also displays the diameter distribution. Therefore, we recommended combining the carbon yield model with the Weibull distribution for Makino bamboo.

Author Contributions

Conceptualization, T.-M.Y. and Y.-H.L.; methodology, T.-M.Y. and Y.-H.L.; software, Y.-H.L.; validation, T.-M.Y. and Y.-H.L.; formal analysis, T.-M.Y. and Y.-H.L.; investigation, Y.-H.L.; resources, T.-M.Y. and Y.-H.L.; data curation, T.-M.Y. and Y.-H.L.; writing—original draft preparation, T.-M.Y. and Y.-H.L.; writing—review and editing, T.-M.Y.; visualization, T.-M.Y. and Y.-H.L.; supervision, T.-M.Y.; project administration, T.-M.Y. and Y.-H.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Data is contained within the article.

Acknowledgments

We thank the farmer who provided the bamboo forest materials for the experiments.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Lobovikov, M.; Paudel, S.; Piazza, M.; Ren, H.; Wu, J. World Bamboo Resources: A Thematic Study Prepared in the Framework of the Global Forest Resources Assessment 2005; Food and Agriculture Organization of the United Nations (FAO): Rome, Italy, 2007. [Google Scholar]
  2. International Network for Bamboo and Rattan. International Trade of Bamboo and Rattan 2012; International Network for Bamboo and Rattan: Beijing, China, 2014; Available online: https://www.inbar.int/resources/inbar_publications/international-trade-of-bamboo-and-rattan-2012/ (accessed on 25 March 2024).
  3. Shanmughavel, P.; Francis, K. Above ground biomass production and nutrient distribution growing bamboo (Bambusa bambos (L.) Voss). Biomass Bioenerg. 1996, 10, 383–391. [Google Scholar] [CrossRef]
  4. Scurlock, J.M.O.; Dayton, D.C.; Hames, B. Bamboo: An overlooked biomass resource? Biomass Bioenerg. 2000, 19, 229–244. [Google Scholar] [CrossRef]
  5. Shanmughavel, P.; Peddappaiah, R.S.; Muthukumar, T. Biomass production in an age series of Bambusa bambos plantations. Biomass Bioenerg. 2001, 20, 113–117. [Google Scholar] [CrossRef]
  6. Liese, W.; Kumar, S. Bamboo Preservation Compendium; Technical report 22; International Network Bamboo and Rattan, INBAR: Beijing, China, 2003. [Google Scholar]
  7. Lu, C.-M. Cultivation and Management of Bamboo Forests; Taiwan Forestry Research Institute: Taipei, Taiwan, 2001; pp. 1–204. [Google Scholar]
  8. Lin, Y.-J. Review, current status, and prospects of the bamboo industry in Taiwan. Taiwan J. For. Sci. 2011, 26, 99–111. [Google Scholar]
  9. Silva, M.F.; Menis-Henrique, M.E.; Felisberto, M.H.; Goldbeck, R.; Clerici, M.T. Bamboo as an eco-friendly material for food and biotechnology industries. Curr. Opin. Food Sci. 2020, 33, 124–130. [Google Scholar] [CrossRef]
  10. Xu, L.; Fang, H.; Deng, X.; Ying, J.; Lv, W.; Shi, Y.; Zhou, G.; Zhou, Y. Biochar application increased ecosystem carbon sequestration capacity in a Moso bamboo forest. For. Ecol. Manag. 2020, 475, 118447. [Google Scholar] [CrossRef]
  11. Patel, B.; Patel, A.; Syed, B.A.; Gami, B.; Patel, P. Assessing economic feasibility of bio-energy feedstock cultivation on marginal lands. Biomass Bioenerg. 2021, 154, 106273. [Google Scholar] [CrossRef]
  12. Ouyang, M.; Yang, C.; Tian, D.; Pan, J.; Chen, G.; Su, H.; Yan, Z.; Ji, C.; Tang, Z.; Fang, J. A field-based estimation of moso bamboo forest biomass in China. For. Ecol. Manag. 2022, 505, 119885. [Google Scholar] [CrossRef]
  13. Jeffery, I.E.; Akinyemi, O.O.; Adedoyin, A.A.; Matthew, U.F. Potentials of bamboo and its ecological benefits in Nigeria. Adv. Bamboo Sci. 2023, 4, 100032. [Google Scholar]
  14. Kharlyngdoh, E.; Barik, S.K. Evaluating bioeconomic potential of Phyllostachys mannii Gamble, a monopodial bamboo and Chimonocalamus griffithianus (Munro) Hsueh & T.P. Yi, a sympodial bamboo from north-eastern India. Biomass Bioenerg. 2024, 182, 107076. [Google Scholar]
  15. Li, L.E.; Yen, T.M.; Lin, Y.J. A generalized allometric model for predicting aboveground biomass across various bamboo species. Biomass Bioenerg. 2024, 184, 107215. [Google Scholar] [CrossRef]
  16. Alamerew, A.N.; Kozak, R.; Shrestha, A.K.; Zhu, Z.; Wang, G. A way for livelihood improvement: Systematic review on bamboo forest research. Trees For. People 2024, 16, 100571. [Google Scholar] [CrossRef]
  17. Chen, T.H.; Chung, H.Y.; Wang, D.H.; Lin, S.H. Growth and biomass of makino bamboo in Shinmen reservoir watershed area. Q. J. Chin. For. 2009, 42, 519–527, (In Chinese with English Summary). [Google Scholar]
  18. Chung, H.Y.; Liu, C.P.; Chen, T.H. Effects of thinning on the growths and biomass of Makino Bamboos in Lienhuachih. Q. J. Chin. For. 2010, 43, 223–231, (In Chinese with English Summary). [Google Scholar]
  19. Yen, T.-M.; Ji, Y.-J.; Lee, J.-S. Estimating biomass production and carbon storage for a fast-growing makino bamboo (Phyllostachys makinoi) plant based on the diameter distribution model. For. Ecol. Manag. 2010, 260, 339–344. [Google Scholar] [CrossRef]
  20. Chen, T.-H.; Wang, D.-H.; Chung, H.-Y. Effects of management strategy on growth and shoot products in Dendrocalamus latiflorus. Q. J. For. Res. 2012, 34, 297–304. [Google Scholar]
  21. Liu, Y.-H.; Yen, T.-M. Assessing aboveground carbon storage capacity in bamboo plantations with various species related to its affecting factors across Taiwan. For. Ecol. Manag. 2021, 481, 118745. [Google Scholar] [CrossRef]
  22. Nath, A.J.; Das, G.; Das, A.K. Above ground standing biomass and carbon storage in village bamboos in North East India. Biomass Bioenergy 2009, 33, 1188–1196. [Google Scholar] [CrossRef]
  23. Chen, X.; Zhang, X.; Zhang, Y.; Booth, T.; He, X. Changes of carbon stocks in bamboo stands in China during 100 years. For. Ecol. Manag. 2009, 258, 1489–1496. [Google Scholar] [CrossRef]
  24. Huang, Y.; Hou, Y.; Ren, J.; Yang, J.; Wen, Y. How to promote sustainable bamboo forest management: An empirical study from small-scale farmers in China. Forests 2024, 15, 12. [Google Scholar] [CrossRef]
  25. Wang, J.; Chen, T.H.; Chen, S.Y.; Chung, H.Y.; Liu, E.U.; Li, T.I.; Liu, C.P. Estimating aboveground biomass and carbon sequestration of moso bamboo grown under selection cutting after two years. Q. J. For. Res. 2010, 32, 35–43, (In Chinese with English Summary). [Google Scholar]
  26. Zhang, Y.; Feng, Y.; Fan, S.; Zhang, M.; Zhang, X.; Zhou, X.; Guan, F. Effects of different harvesting methods on aboveground nutrient pools of moso bamboo (Phyllostachys edulis) forest in China. Forests 2022, 13, 2138. [Google Scholar] [CrossRef]
  27. Yen, T.-M.; Sun, P.-K.; Li, L.-E. Predicting aboveground biomass and carbon storage for ma bamboo (Dendrocalamus latiflorus Munro) plantations. Forests 2023, 14, 854. [Google Scholar] [CrossRef]
  28. Inoue, A.; Koshikawa, K.; Sato, M.; Shima, H. Allometric equations for predicting the aboveground biomass of square bamboo. Chimonobambusa Quadrangularis. J. For. Res. 2019, 24, 376–381. [Google Scholar] [CrossRef]
  29. Abebe, S.; Gebeyehu, G.; Teketay, D.; Long, T.-T.; Jayaraman, D. Allometric models for estimating biomass storage and carbon stock potential of Oldeania alpina (K. Schum.) Stapleton forests of south-western Ethiopia. Adv. Bamboo Sci. 2023, 2, 100008. [Google Scholar] [CrossRef]
  30. Jember, A.-A.; Taye, M.-A.; Gebeyehu, G.; Mulu, G.; Long, T.-T.; Jayaraman, D.; Abebe, S. Carbon stock potential of highland bamboo plantations in northwestern Ethiopia. Carbon Balanc. Manag. 2023, 18, 3. [Google Scholar] [CrossRef]
  31. Pan, C.; Zhou, G.; Shrestha, A.-K.; Chen, J.; Kozak, R.; Li, N.; Li, J.; He, Y.; Sheng, C.; Wang, G. Bamboo as a nature-based solution (NbS) for climate change mitigation: Biomass, products, and carbon credits. Climate 2023, 11, 175. [Google Scholar] [CrossRef]
  32. Lu, C.-M.; Chen, T.-H. The structure and biomass of makino bamboo (Phyllostachys makinoi) stand—An example from Tun-Tou Area. Bull. Taiwan Forest Res. Inst. 1992, 7, 1–13, (In Chinese with English Summary). [Google Scholar]
  33. Lee, J.-S.; Hsu, H.-C. The cost analysis of management of makino bamboo in Chu-Sun area (I). Q. J. Chin. For. 1983, 16, 403–410, (In Chinese with English Summary). [Google Scholar]
  34. Urban Development Bureau, Taichung City Government 2014. Available online: https://www.ud.taichung.gov.tw/ (accessed on 25 March 2024).
  35. Taiwan Central Weather Bureau. Available online: https://www.cwa.gov.tw/eng/ (accessed on 3 May 2022).
  36. Bailey, R.; Dell, T. Quantifying diameter distributions with the Weibull function. For. Sci. 1973, 19, 97–104. [Google Scholar]
  37. Kao, Y.-P. Comparative study on the dry matter productions of Dendrocalamus giganteus and D. asper. Bull. Taiwan Forest Res. Inst. 1991, 6, 249–282, (In Chinese with English Summary). [Google Scholar]
  38. Kao, Y.-P.; Chang, T.-Y. The growth and biomass production of Dendrocalamus asper Plantation. Bull. Taiwan Forest Res. Inst. 1989, 4, 31–41, (In Chinese with English Summary). [Google Scholar]
  39. García, J.-C.-C.; Arango, A.-M.-A.; Trinh, L. The potential of bamboo forests as a carbon sink and allometric equations for estimating their aboveground biomass. Environ. Dev. Sustain. 2023, 26, 1–29. [Google Scholar]
  40. Liu, S.-C.; Kao, Y.-P. Generalized biomass equations for moso bamboo and plantations. Bull. Taiwan For. Res. Inst. 1998, 3, 393–406. [Google Scholar]
  41. Da Silva, J.-K.-L.; Garcia, J.-G.-M.; Barbosa, L.-A. Allometric scaling laws of metabolism. Phys. Life Rev. 2006, 3, 229–261. [Google Scholar] [CrossRef]
  42. Lee, J.-S.; Chen, C.-T. Study on the stand structure and composition of species in natural forests of Cho-Kou watershed. Annu. Taiwan Mus. 1991, 34, 11–32, (In Chinese with English Summary). [Google Scholar]
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Figure 1. Location of this study.
Figure 1. Location of this study.
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Figure 2. The flowchart of this study.
Figure 2. The flowchart of this study.
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Figure 3. The aboveground carbon storage (AGCS) with treatments, where the length of the trend lines above the bars indicates the standard deviation. Analysis of variance was used to examine each stand characteristic with treatments. The same letter indicates not significantly different at p = 0.05 by the least significance difference method.
Figure 3. The aboveground carbon storage (AGCS) with treatments, where the length of the trend lines above the bars indicates the standard deviation. Analysis of variance was used to examine each stand characteristic with treatments. The same letter indicates not significantly different at p = 0.05 by the least significance difference method.
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Figure 4. The observed data and predicted values by the Weibull function for treatments in 2019 and 2021.
Figure 4. The observed data and predicted values by the Weibull function for treatments in 2019 and 2021.
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Figure 5. Relationships between observed aboveground carbon storage (AGCS) and predicted AGCS with a perceivable diagonal line (1:1 for X and Y) by the scatter diagram for three models, where (a) Model I: ABCS = 4.947 + 3.030 × 10−4 N, (b) Model II: ABCS = −29.092 + 3.859 × 10−4 N + 12.486 Parameter b, (c) Model III: ABCS = −35.411 + 3.712 × 10−4 N + 16.984 Parameter b − 0.962 Parameter c.
Figure 5. Relationships between observed aboveground carbon storage (AGCS) and predicted AGCS with a perceivable diagonal line (1:1 for X and Y) by the scatter diagram for three models, where (a) Model I: ABCS = 4.947 + 3.030 × 10−4 N, (b) Model II: ABCS = −29.092 + 3.859 × 10−4 N + 12.486 Parameter b, (c) Model III: ABCS = −35.411 + 3.712 × 10−4 N + 16.984 Parameter b − 0.962 Parameter c.
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Table 1. The various thinning treatments used in this study.
Table 1. The various thinning treatments used in this study.
TreatmentThinning IntensityPerformance
IHeavy thinningThinning 75 ± 5% of the culm number and the others retained.
IIModerate thinningThinning 50 ± 5% of the culm number and the others retained.
IIILight thinningThinning 25 ± 5% of the culm number and the others retained.
IVNo thinningWithout thinning and all culms retained.
Table 2. The culms number (N), mean diameter at breast height (MDBH), and basal area (BA) for various thinning treatments in 2019 and 2021. Analysis of variance was used to examine each stand characteristic with treatments.
Table 2. The culms number (N), mean diameter at breast height (MDBH), and basal area (BA) for various thinning treatments in 2019 and 2021. Analysis of variance was used to examine each stand characteristic with treatments.
YearTreatmentN (culms ha−1)MDBH (cm)BA (m2 ha−1)
2019Ⅰ11,500 ± 1438 c*2.71 ± 0.15 a6.82 ± 4.64 c
Ⅱ22,900 ± 1149 bc2.50 ± 0.09 a11.77 ± 1.34 b
Ⅲ31,500 ± 2600 b2.23 ± 0.18 b13.49 ± 2.34 ab
Ⅳ49,200 ± 19,713 a1.95 ± 0.16 c16.10 ± 4.64 a
F-value (p-value)9.029 (0.000)10.579 (0.001)10.133 (0.001)
2021Ⅰ29,000 ± 8116 b2.39 ± 0.14 a13.67 ± 3.27 b
Ⅱ41,300 ± 4530 b2.40 ± 0.08 a19.82 ± 1.98 b
Ⅲ53,500 ± 13,808 ab2.25 ± 0.19 a23.70 ± 7.70 ab
Ⅳ80,900 ± 35,743 a2.00 ± 0.14 b27.73 ± 10.76 a
F-value (p-value)6.715 (0.007)4.214 (0.030)5.071 (0.017)
* Mean ± standard deviation and means marked with the same letter indicate not significantly different at p = 0.05 by the least significance difference method.
Table 3. The parameters of the Weibull function for various thinning treatments in 2019 and 2021.
Table 3. The parameters of the Weibull function for various thinning treatments in 2019 and 2021.
YearTreatmentSample PlotsParametersKolmogorov-Smirnov TestPass Test Samples
bcDnDα = 0.01
2019Ⅰ42.79 ± 0.148.50 ± 1.800.1038 ± 0.01430.1355 ± 0.02994
II42.65 ± 0.115.34 ± 0.870.0983 ± 0.02030.1455 ± 0.03024
III42.40 ± 0.173.79 ± 1.380.0943 ± 0.01300.1298 ± 0.03584
IV42.17 ± 0.202.88 ± 0.300.0810± 0.01480.0941± 0.01704
2021Ⅰ42.58 ± 0.165.20 ± 0.770.0810 ± 0.00890.1027 ± 0.00714
II42.59 ± 0.104.49 ± 0.570.0743 ± 0.00840.1060 ± 0.01774
III42.45 ± 0.203.58 ± 0.920.0815 ± 0.01110.0984 ± 0.01694
IV42.22 ± 0.133.26 ± 0.450.0984 ± 0.01690.0701 ± 0.01054
Table 4. The regression coefficients and Radj2 of regression models for predicting aboveground carbon storage by culm number (N) and the parameters of the Weibull function.
Table 4. The regression coefficients and Radj2 of regression models for predicting aboveground carbon storage by culm number (N) and the parameters of the Weibull function.
Model Regression Model AGCS = β0 + β1 X1 + β2 X2 + β3 X3Radj2
Independent VariablesRegression Coefficients
X1X2X3β0β1β2β3
IN––4.9473.030 × 10−4––0.836
IINParameter b–−29.2923.859 × 10−412.486–0.916
IIINParameter bParameter c−35.4113.712 × 10−416.984−0.9620.939
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Liu, Y.-H.; Yen, T.-M. Combining Stand Diameter Distribution Quantified by the Weibull Function to Develop a Carbon Yield Model for Makino Bamboo (Phyllostachys makinoi Hayata). Forests 2025, 16, 436. https://doi.org/10.3390/f16030436

AMA Style

Liu Y-H, Yen T-M. Combining Stand Diameter Distribution Quantified by the Weibull Function to Develop a Carbon Yield Model for Makino Bamboo (Phyllostachys makinoi Hayata). Forests. 2025; 16(3):436. https://doi.org/10.3390/f16030436

Chicago/Turabian Style

Liu, Yi-Hung, and Tian-Ming Yen. 2025. "Combining Stand Diameter Distribution Quantified by the Weibull Function to Develop a Carbon Yield Model for Makino Bamboo (Phyllostachys makinoi Hayata)" Forests 16, no. 3: 436. https://doi.org/10.3390/f16030436

APA Style

Liu, Y.-H., & Yen, T.-M. (2025). Combining Stand Diameter Distribution Quantified by the Weibull Function to Develop a Carbon Yield Model for Makino Bamboo (Phyllostachys makinoi Hayata). Forests, 16(3), 436. https://doi.org/10.3390/f16030436

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