Original Research
Frontiers in Ecology and Evolution ·
Volume 14 - 2026 | https://doi.org/10.3389/fevo.2026.1872137
Quantifying aboveground biomass and carbon stock in Drepanostachyum falcatum , a temperate Himalayan bamboo in India: an allometric modeling framework
- Indra Singh1*corresponding author
- Sadikul Islam2*corresponding author
- V.P. Khanduri1
- Pravin Rawat3
- C.S. Dhanai1
- Aman Dabral4
- JMS Tomar2
- Pritam Ayush5
- Abhay Kumar6
- Saraswati Prakash Sati7
- Manoj Kumar Riyal7
- Gaddam Sudharshan Reddy8
- 1Department of Silviculture and Agroforestry, VCSGUUHF, Bharsar. College of Forestry, Ranichauri, Tehri Garhwal, Uttarakhand, India
- 2ICAR – Institute of Soil and Water Conservation, Dehradun, India
- 3ICFRE – Himalayan Forest Research Institute Shimla, Himachal Pradesh, India
- 4Department of Forest Biology and Tree Improvement, VCSGUUHF, Bharsar. College of Forestry, Ranichauri, Tehri Garhwal, Uttarakhand, India
- 5Silviculture and Forest Management Division, ICFRE-FRI, Dehradun, Uttarakhand, India
- 6Department of Silviculture and Agroforestry, Faculty of Forestry, Birsa Agricultural University, Kanke, Ranchi, Jharkhand, India
- 7Department of basic and Social Sciences, VCSGUUHF, Bharsar. College of Forestry, Ranichauri, Tehri Garhwal, Uttarakhand, India
- 8Silviculture and Forest Management Division, ICFRE-IWST, Bengaluru, Karnataka, India
Abstract
Despite the growing interest in bamboo as a carbon sink, reliable aboveground carbon stock estimates for Himalayan bamboo species remain scarce, largely because species-specific allometric models have not been developed for most high-altitude taxa. To address this gap, the present study focused on Drepanostachyum falcatum (Nees) Wen—locally known as Ringal—a clump-forming sympodial bamboo native to the temperate forests of Uttarakhand, India, with the aim of developing and validating power-law allometric equations for estimating aboveground biomass (AGB) and aboveground carbon stocks (ACS). Field sampling followed a two-stage stratified design, in which 60 culms were destructively harvested across three age classes and three clump size categories, with biomass separated into culm, branch, and leaf fractions. Three model forms were constructed using culm diameter ( D ) and height ( H ) as predictors: a diameter-only model (model I), a combined diameter-squared-height model (model II), and a diameter–height model (model III). All models were evaluated against Adj- R 2 , AIC, BIC, RMSE, BIAS, and MAPE. Among the three models evaluated, model III ( D – H ) showed the strongest fit, with an Adj- R 2 of 0.93, RMSE of 0.05, and MAPE of 5.51%. The residuals showed no directional bias and were spread evenly around zero, while the observed and predicted values sat close to the 1:1 reference line—together suggesting that the model produces consistent, dependable estimates. At the individual culm level, mean AGB came out at 0.524 ± 0.018 kg, with a corresponding mean ACS of 0.262 ± 0.009 kg. When these figures were extrapolated to the stand level, the total aboveground biomass reached 23.14 t ha −1 and the carbon stocks reached 11.57 t ha −1 , with large clumps contributing the largest proportion—53.2% of the overall carbon stored. To summarize, these findings provide preliminary site-specific allometric equations and a practical field method for estimating aboveground biomass and carbon stock in D. falcatum and a baseline standing-stock estimate for the study area. These baseline values may provide an input to future carbon accounting work in temperate Himalayan bamboo stands, but the single site, single time-point design limits wider extrapolation.
Keywords
1 Introduction
Bamboo has emerged as a notable carbon sink, owing to its rapid growth, its ability to renew itself without replanting, and its capacity to capture and store a substantial amount of carbon (Scurlock et al., 2000). It is technically a grass, classified within the family Poaceae under the subfamily Bambusoideae, but it behaves more like a tree, and it grows almost everywhere—across the tropical forests of Asia, into the savannas of Africa, and into the Americas and temperate zones of the world (Cheng et al., 2023; Kuehl et al., 2013). What really sets it apart is its growth speed: a few species can shoot up nearly a meter in a single day (Getachew et al., 2021), and most stalks reach their full height within a couple of months of breaking ground (Kibwage et al., 2008). The plant covers somewhere near 35 million hectares worldwide and figures in the daily lives of more than 1.5 billion people, who turn it into houses, food, paper, and, of late, fuel (Embaye et al., 2003; Nongdam and Tikendra, 2014; INBAR, 2022). India accounts for roughly 15.47 million hectares of that total (Forest Survey of India, 2023), a figure that speaks to the plant’s economic and ecological standing and to its bearing on several sustainable development goals (SDG 1, 7, 11–13, 15, and 17; INBAR, 2019).
The Indian Himalayan Region (IHR) comprises different kinds of bamboo (~136 species), spread over diverse forest types, elevations, and climatic conditions (Forest Survey of India, 2023). Under the IHR, the temperate bamboo species Drepanostachyum falcatum (Munro) Wen (syn. Arundinaria falcata Nees) is particularly found in the Garhwal and Kumaon Himalaya of Uttarakhand at altitudes ranging from 1,200 to 3,000 m above mean sea level (amsl) (Tewari, 1992; Arya et al., 2015; Tewari et al., 2015). It is recognized locally as “Ringal” and grows in thick natural stands. It grows in dense, tufted clumps in thick natural stands. It delivers key ecosystem services (e.g., watershed regulation, slope stabilization, non-timber forest products, and soil reclamation) for nearby communities (Kaushal et al., 2020; Kumar et al., 2023). D. falcatum was selected for this study because of its significant commercial value (Saini et al., 2016) and its wide distribution in the hilly areas of Uttarakhand (Meena et al., 2021). To develop a scientific basis in quantifying the potential of bamboo in accumulating biomass and carbon stocks, reliable and practically feasible estimation is essential. However, its accurate quantification remains constrained by limited species-specific data and methodological inconsistencies (Scurlock et al., 2000; Yuen et al., 2017). The sympodial, clump-forming species D. falcatum shows high spatial variation in culm height, diameter, density, and rhizome morphology and therefore needs a species-specific allometric model to measure biomass and carbon non-destructively. However, most existing models were created for tropical monopodial bamboos or the whole bamboo group, which biases the models for high-altitude, clump-forming species.
Biomass has traditionally been quantified through destructive harvesting (Brown et al., 1989; Kaushal et al., 2022). This method is accurate for the individuals sampled but is costly and labor-consuming and destroys the plants permanently, making it impossible to monitor again and to scale to the landscape level (IPCC, 2019; Rathore et al., 2021; Bhutia et al., 2022; Megha et al., 2025). Regression-based allometric modeling alleviates these limitations, with a one-time destructive sample used to relate easily measured biometric variables (diameter, height, or both) to biomass, which can then be estimated from non-invasive field observations across entire populations (Chave et al., 2005; Mandal and Joshi, 2015; Bhutia et al., 2025). The equations offer a practical, repeatable tool for forest inventories, carbon-monitoring programs, and management planning at low additional cost (Sileshi, 2014; Nath et al., 2009; Kaushal et al., 2022).
The power-law equation is the traditional form to estimate aboveground biomass (AGB) and aboveground carbon stock (ACS) of forest vegetation, as it follows the principles of biological scaling and can capture the non-trivial relationship between structural dimensions and biomass without complex transformation (West et al., 1999; Chave et al., 2014; Paul et al., 2016; Kaushal et al., 2022). Single-variable types are based on either fifth-internode diameter (D) or culm height (H) alone, providing simplicity in the field, whereas multi-variable types incorporate structural measurements for increased dimensional complexity but at the cost of increased measurement effort (Bhutia et al., 2025). Whether that extra effort improves predictive accuracy is an empirical matter that has to be tested with species-specific data. There is little evidence for Himalayan bamboos. The available equations are mostly derived from tropical lowland genera such as Bambusa and Phyllostachys or from generalized pan-tropical frameworks (Singnar et al., 2017). When applied to a high-altitude sympodial species such as D. falcatum, which differs in culm dimensions, wood density, and clump and rhizome architecture, they provide systematic bias as allometric relationships are species and structure dependent (Sileshi, 2014; Nath et al., 2009; Kaushal et al., 2022). This necessitates models based on field data for the species of interest. Therefore, the present study is designed to develop and evaluate single- and multi-variable power-law models for aboveground biomass and carbon stock of D. falcatum based on destructive sampling in natural stand in Uttarakhand, India, as well as field-measured structural variables and to evaluate their statistical performance and field applicability. In the process, it provides preliminary, site-specific allometric equations for a temperate Himalayan bamboo, for which no species-specific models were available so far, baseline standing-stock estimates for the study area, and a methodological template that can be adapted to other montane bamboos of the Indian Himalayan Region.
2 Materials and methods
2.1 Study area
The present study was conducted in the field of the College of Forestry, Ranichauri, located in the central mountainous region of Uttarakhand, India. The geographical coordinates of the site are 30°18′41″ N and 78°24′34″ E. The study was conducted during 2021–2024. The altitude of the location extended from 1,700 to 2,200 m above mean sea level. The climate is mostly temperate in nature but has well-demarcated seasons. The temperature falls to 0°C during winter, while it rises to 30°C during summer. Frost incidents occur from November to February. The rainfall is of orographic monsoon type, ranging from 1,200 to 1,800 mm annually.
2.2 Allometric biomass and carbon stock modeling
2.2.1 Sampling strategy and data collection
In bamboo terminology, a culm is the individual jointed, woody aerial stem that arises from the rhizome and bears branches and leaves. A clump is the compact aggregate of culms of different ages produced by a single sympodial (pachymorph) rhizome system, growing together as one genetically connected, tufted unit. D. falcatum is a densely tufted, small-diameter sympodial bamboo in which many culms emerge close together to form such a clump. Field sampling was conducted during early winter from October to November 2024 using a two-stage stratified sampling design (stratification–first stage sampling (clumps)—stratification at second stage—random sampling of culms) to capture variability at both clump and culm levels (Sukhatme et al., 1984). At the initial stage, stratification of clumps was involved, while stems were randomly sampled in the second stage, thus accessing variation at both the cluster and individual stem levels. In the initial phase, all bamboo clumps within the study area were classified into three canopy size classes—small, medium, and large—based on differences in canopy width and overall structure (details specified in “Section 2.2.2”). Due to the random and irregular spatial distribution of bamboo stands within the study area, 20 clumps were proportionally sampled from a total of 60 stands, including seven small stands, six medium stands, and seven large stands.
During the second phase of sampling, culms within each selected clump were categorized into three age classes (1 year, 2 years, and more than 3 years). One culm was randomly selected from each age class, yielding three sample culms from each clump and a total of 60 culms for the study. This proportionate sampling design ensured the adequate demonstration of variability in both clump size and culm age, thus enhancing the robustness of biomass estimates. To determine the minimum required sample size (n), Cochran (1977) t-distribution-based formula was employed, with a desired margin of error of 1.5 and a significance level (α) of 0.05 (Megha et al., 2025). This approach ensures that the sample closely represents the plant population by optimizing the sample size to achieve adequate statistical power while avoiding both under- and over-sampling (Sukhatme et al., 1984). The data set ensures reasonable statistical power, as it is more than the recommended sample size (at least 30) (Mueller-Dombois and Ellenberg, 1974; Kent and Coker, 2012; Elzinga et al., 2009; Bhutia et al., 2025).
2.2.2 Morphology-based strategy for the classification of clumps and culms
The bamboo clumps were irregular and unevenly distributed within the study area. To assess the clump biomass variability distribution, initial measurement on clump height, diameter, and crown width were recorded by visually inspecting the differently sized clumps. In the field, the clumps were sorted and graded into three size classes—small, medium, and large—using crown width (canopy spread) as a visual proxy for clump size (n = 20 sampled clumps). The clumps were selected proportionally based on their relative dominance in the plantation. The clumps were divided into three size classes according to the measured crown width (canopy spread, averaged from two perpendicular diameters), namely: small (<4.5 m), medium (4.5–6.0 m), and large (>6.0 m). These thresholds were computed from the frequency distribution of crown width within the surveyed clumps. The classes differed markedly in stocking: the small clumps averaged 178 culms per clump (39 clumps ha−1), the medium clumps had 249 culms per clump (55 clumps ha−1), and the large clumps had 379 culms per clump (62 clumps ha−1), giving a total stand density of 156 clumps ha−1 (Table 1). In each selected clump, the bamboo culms were classified into three age groups, i.e., (a) 1 year, (b) 2 years, and (c) more than 2 years old. The age of the culm was determined by visual observation of the morphological features, which is a widely adopted non-destructive method for age estimation in clump-forming bamboos (Banik, 1993, 2015; Kaushal et al., 2022). The 1-year-old culms were characterized by the presence of residual sheaths at the base, light green color, and a characteristic white powdery coating on the surface; these culms bore very few branches, with only a small number of newly formed primary branches in the upper part. The second-year culms had no sheathes at all but had some remnants of white powdery sheath on the green culms, well-developed primary and secondary branches, and very little lichen cover. Culms older than 3 years showed distinct morphological changes with lichen cover of about 30%– 80%, especially around the base. The upper branches were denser, and the older branches were darker in color and showed irregular lichen growth. The diagnostic characteristics used here—culm color, sheath persistence, branching pattern, and degree of surface lichen cover—are the standard indicators for field age determination in bamboo (Banik, 1993, 2015); the same suite of traits has been used to distinguish 1-, 2-, and 3-year culms in other species (Zhan et al., 2015).
Table 1. Descriptive statistics of clump inventory data by age class.
| Parameter | Small | Medium | Large | Total |
|---|---|---|---|---|
| Crown width (m)a | <4.5 | 4.5 to 6.0 | >6.0 | – |
| Avg. culms per clump | 178.4 | 249.05 | 379.2 | – |
| Avg. culms of age 1 | 35.65 | 49.80 | 75.80 | – |
| Avg. culms of age 2 | 53.60 | 74.85 | 113.85 | – |
| Avg. culms of age 3 | 89.15 | 124.40 | 189.55 | – |
| Mean inter-clump distance | 8 m | 8 m | 8 m | – |
| Avg. clumps per hectare | 39 | 55 | 62 | 156 |
Canopy spread, averaged from two perpendicular diameters.
2.2.3 Culm height measurement
To measure the average bamboo clump height, a straight bamboo stick was prepared by joining two 6-m-long dry bamboo culms. The stick was marked at 1-m intervals for accurate measurement. Height was measured for each culm with the stick. A total of 12 culms were selected in each clump for measuring height. The height was expressed as the average for all culms. This method ensured consistent and accurate results. All measurements were recorded in meters (Kaushal et al., 2022).
2.2.4 Clump diameter measurement
The diameter of bamboo clumps was measured at the fifth internode position above ground level using a measuring tape. The particular nodal point was selected to maintain consistency across measurements and to account for natural variations in clump morphology. Measurements were taken in a cross-sectional manner, recording the widest span between opposite sides of the clump. All diameter values were documented in meters with precision to two decimal places. This measurement protocol provided reliable data for assessing clump size and growth patterns in the study. The fifth node position was chosen as it represents a stable reference point above any potential ground-level irregularities while still capturing the characteristic girth of mature clumps (Rawat et al., 2018).
2.2.5 Measurement of number of culms per clump
For calculating the number of culms per clump, a complete enumeration was done for all clumps. It was done with the help of cross stick method by placing two straight sticks of 2 m in length horizontally across the clump for accuracy in dense clumps. All live culms (green, healthy) were counted within each clump, excluding all dead/dried culms. By this, the total numbers of culms per clump was calculated in each replication (Kaushal et al., 2022).
2.3 Estimation of aboveground biomass and carbon stocks
A total of 60 D. falcatum culms were chosen for destructive sampling, representing three age groups and three clump size classes. Biometric parameters, including the diameter of the fifth internode (D) and the total culm height (H) for each culm, were measured with a standard measuring tape before harvesting according to He et al. (2018).
AGB was destructively estimated by felling the selected culms at ground level using secateurs and separating into their component parts; AGB here is defined as the total oven-dry weight of all aboveground parts, comprising stem, branches, and leaves (Kaushal et al., 2022). In D. falcatum, the leaves are borne on lateral branches produced at the upper culm nodes rather than directly on the main axis. Thus, each harvested culm was divided into three aboveground parts: the main culm axis (stem), the lateral branches (branches), and the foliage (leaves). The fresh weight of each component was measured separately in the field immediately after harvesting with a portable electronic balance. A representative subsample of fresh weight of each component was then taken, its fresh weight recorded and oven-dried at 65°C ± 2°C to a constant weight. The dry weight of each component was obtained by multiplying the field fresh weight of that component by its subsample dry-to-fresh mass ratio, and the values were summed to calculate the total aboveground dry biomass (kg) per culm (Kaushal et al., 2022).
The aboveground carbon stock (ACS) was not modeled separately. A constant carbon fraction of 0.5 was used (FAO, 2012) so that ACS for any culm, clump, or unit area is directly obtained from the corresponding AGB as ACS = 0.5 × AGB; therefore, the AGB models and their associated uncertainty fully determine ACS. It should be mentioned that the standing aboveground carbon stock was estimated at a single point in time in the present study and the rate of sequestration was not measured, which would need repeated measurement of the same clumps over successive growing seasons. Thus, all carbon values reported here are stock (t ha−1) and not annual sequestration (t ha−1 year−1).
2.4 Allometric model framework
2.4.1 Allometric model development
Drawing on previously established allometric modeling approaches (Kaushal et al., 2022; Bhutia et al., 2025), two power-law equations were developed for the separate estimation of AGB and ACS. The power-law function was chosen due to its computational simplicity, stable convergence during nonlinear parameter estimation, and its widespread use in forest and bamboo allometric studies (Chave et al., 2005; Kaushal et al., 2022).
The models were specified as:
(1) Model I: z(k)=a×Db+γ
(2) Model II: z(k)=a×(D2H)b+γ
(3) Model II: z(k)=a×Db×Hc+γ
Here z denotes aboveground biomass (AGB, kg plant−1) or aboveground biomass (ACS, kg plant−1), where k refers to culm, leaves, and branches. Parameter a is a scaling constant, b and c are shape coefficients, and γ represents the random error term. The error was assumed to follow a normal distribution with a mean of zero and non-constant variance, reflecting the heteroscedastic nature typically observed in biomass data. Biomass data typically show heteroscedasticity, where the variability of residuals increases with plant size. To handle this issue, a nonlinear regression approach based on weighted maximum likelihood (WML) was used, incorporating a suitable variance function (Kaushal et al., 2022; Bhutia et al., 2025). Nonlinear models were fitted using weighted least squares with the gnls() function of the nlme package (Pinheiro et al., 2024). Since the residual variance of biomass increases with plant size (heteroscedasticity), we used a power-of-the-covariate variance function, varPower(form = ~D), which models the residual standard deviation proportional to |D|^δ, where δ is the variance exponent that was estimated jointly with the model parameters. The residuals were assumed to be independent (no autocorrelation or correlation structure was specified), with the only departure from ordinary error assumptions being the modeled non-constant variance. Model I for AGB was fitted as gnls(AGB ~ a * D^b, start = c(a = 0.5, b = 2), weights = varPower(form = ~ D)), while models II and III used the same syntax but with their respective mean functions (Equations 1–3). Choice of variance function was made by AIC comparison of constant-variance, varPower, and varExp fits in conjunction with plots of standardized residuals versus fitted values; varPower gave the lowest AIC and the most homogenous standardized residuals and was retained for all models.
2.4.2 Model fitting, validation, and uncertainty analysis
Goodness-of-fit and predictive-performance statistics were used to evaluate the allometric models. Model selection was based mainly on the Akaike Information Criterion (AIC) which corrects for model complexity (Akaike, 1973) and the Bayesian Information Criterion (BIC) which penalizes complexity more strongly and is therefore more conservative and more likely to select more parsimonious models (Schwarz, 1978). The adjusted coefficient of determination (Adj-R2) was also calculated as a descriptive measure of the proportion of variation of the aboveground biomass (AGB) or aboveground carbon stock (ACS) explained by the fitted model. However, because the coefficient of determination is not entirely suitable for nonlinear and weighted regression models, Adj.-R<sup>2</sup> was provided only as a supplementary descriptive statistic and was not used as a primary criterion for model selection. Thus, competing models were ranked primarily by smaller (more negative) AIC and BIC values, and when models performed similarly, the model with the fewest parameters was chosen to avoid over-parameterization (parsimony; Burnham and Anderson, 2002).
The stability of predictions of the developed allometric equations was assessed using a Monte Carlo cross-validation approach (Stone, 1974). At each iteration, the 60 observations were randomly split into a training set (80%, n = 48) and a validation set (20%, n = 12); the model was refitted on the training set and used to predict the held-out validation set, and each fitting and validation criterion was recorded. To make this procedure reproducible, we set the random-number generator seed (set.seed(1000)) before resampling. This procedure was repeated independently 100 times. The average bias (ABias, %), average RMSE (ARMSE, kg plant−1), and average MAPE (AMAPE, %) of model prediction accuracy were estimated on the basis of all iterations (Kaushal et al., 2022; Megha et al., 2025; Bhutia et al., 2025). The fitting and validation criteria are presented as mean ± standard deviation over the 100 runs. Equations with stable parameter estimates and low prediction errors were deemed reliable and fit for broader application (Bhutia et al., 2025).
Diagnostic plots were used to further validate the predictive performance of the developed allometric models to identify potential over- or underestimation. The first diagnostic plot was predicted versus observed values with a 1:1 reference line. The closer the predicted values were to the 1:1 line, the better the model had predictive accuracy. The second diagnostic plot assessed the relationship between weighted residuals and fitted values to detect any pattern of systematic error. Residuals following a positive or negative trend represent over- or under-estimation, respectively, while residuals scattered randomly around zero represent unbiased and reliable predictions with little systematic error.
In addition, the underlying assumptions of the regression models were checked by formal statistical tests. Shapiro–Wilk test (Shapiro and Wilk, 1965) was used to test for normality of the residuals, and Breusch–Pagan test (Breusch and Pagan, 1979) was used to test for homogeneity of variance. Both tests were applied to the variance-standardized residuals. For all models, the assumption of homogeneity of variance was met (Breusch–Pagan, p > 0.05), confirming that the varPower variance function adequately described the size-dependent error. The residuals were approximately normal with minor departures for the AGB, leaf, and ACS models (Shapiro–Wilk, p = 0.01–0.02) common at small sample sizes that do not materially affect the weighted maximum-likelihood estimates.
Parameter uncertainty was expressed as the mean ± standard error of each estimated coefficient across 100 iterations. Prediction uncertainty was also quantified by computing 95% prediction intervals for individual observations from the fitted mean response and the modeled residual variance (Montgomery et al., 2021). Calibration of these intervals was verified on the validation folds as the empirical coverage, the proportion of held-out observations that fall within their 95% prediction interval, with values close to the nominal 0.95 indicating well-calibrated prediction uncertainty.
2.5 Assessment of height–diameter relationship
The height–diameter relationship in D. falcatum was explored through allometric modeling, recognizing that culm height and culm diameter are among the most dynamic growth parameters in bamboo. Since both variables undergo rapid change during culm development, a combined allometric model incorporating both parameters some time provide good results, but height measurement is difficult for standing culm, so applying the H–D relationship will provide a proxy H. Results of the best D allometric form applied to culm height (Kaushal et al., 2022).
2.6 Allometry-based estimation of AGB and ACS
The developed allometric equations were used to estimate aboveground biomass (AGB) and aboveground carbon storage (ACS) of D. falcatum at three hierarchical levels: culm, clump, and stand. Field observations from clumps classified into small, medium, and large categories were used as input for the estimation.
2.6.1 Culm-level estimation
AGB at the culm level was estimated using field-measured diameter and height values in the selected best-fit allometric model. Carbon storage was calculated by applying a conversion factor of 0.5 to the estimated biomass, following commonly accepted bamboo carbon estimation practices. Summary statistics, including mean, standard deviation (SD), and standard error (SE), were computed to describe the distribution of AGB and ACS across sampled culms.
2.6.2 Clump-level estimation
Clump-level AGB was calculated by multiplying the average culm biomass by the number of culms present in each clump for the respective size categories. The same approach was used to estimate clump-level ACS. Variation in culm density among small, medium, and large clumps allowed for a size-based assessment of biomass and carbon, reflecting the structural differences within the population.
2.6.3 Area-level estimation (per hectare basis)
At stand level, estimates of biomass and carbon stocks were calculated per hectare by scaling the clump level estimates by the density of clumps measured in the study area. The density of clumps in each size class was obtained by field enumeration, with 39, 55, and 62 clumps ha-1 for small, medium, and large clumps, respectively, for a total of 156 clumps ha-1 (Table 1); the corresponding mean inter-clump distance of 8 m is therefore a consequence of the measured density rather than an assumed uniform spacing. Stand-level AGB was calculated as the sum of the mean clump-level biomass of each size class multiplied by its density, and aboveground carbon stock was calculated as ACS = 0.5 × AGB. To quantify uncertainty, the standard error of the mean culm-level biomass was propagated through this scaling to give 95% confidence intervals for the per-hectare AGB and ACS. Final estimates are given in both kg ha-1 and t ha-1.
2.7 Statistical analysis
All analyses were done in RStudio (R version 4.2.1) with the packages nlme, agricolae, and ggplot2. Descriptive statistics of the mean, standard deviation, and range (minimum and maximum) were calculated for each of the recorded biometric variables. Prior to model fitting, relationships between the candidate predictor variables (fifth-internode diameter, D, and culm height, H) and the response variables, aboveground biomass (AGB) and its stem, branch, and leaf components, were explored using Pearson correlation analysis. The mean values of aboveground components were compared using analysis of variance, followed by Duncan’s multiple range test (DMRT; Duncan, 1955) using the agricolae package (de Mendiburu, 2023). All tests were two-sided, and a level of significance of p < 0.05 was used.
Species-specific allometric equations were then developed separately for total AGB and for each biomass component (stem, branch, and leaf). We fitted three candidate power-law forms for each response variable: (i) a diameter-only model (model I, Y = aDb), (ii) a compound-variable model based on D2H (model II, Y = a(D2H)b), and (iii) a combined diameter–height model using D and H as separate predictors (model III). The variance of the residuals of biomass increased with plant size (heteroscedasticity), and therefore models were fitted by weighted nonlinear regression using the gnls routine of the nlme package rather than ordinary least squares. The non-constant error variance was explicitly modeled using a power-of-the-covariate variance function [varPower (form = ~D); estimated variance exponent δ = 1.67], allowing the residual standard deviation to vary with the predictor. The variance function was selected by comparing constant variance, varPower, and varExp fits on AIC and by plotting standardized-residuals against fitted values.
Table 2 for total AGB and Table 3 for stem, branch, and leaf components report the estimated parameters (a, b and, for model III, c) with their standard errors and 95% confidence intervals for each fitted model. The model was assessed not on a single statistic but on a suite of metrics: Adj-R2, Akaike information criterion (AIC), and Bayesian information criterion (BIC) for fit and parsimony, and root mean square error (RMSE), mean bias, and mean absolute percentage error (MAPE) for predictive accuracy. Adj-R2 is not a fully appropriate measure of goodness-of-fit for nonlinear, weighted models, and thus model selection was based primarily on AIC, BIC, and out-of-sample prediction error, with Adj-R2 reported only as a supplementary descriptor.
Table 2. Estimated parameters and validation metrics of the allometric aboveground biomass (AGB, kg plant-1) models for Drepanostachyum falcatum based on 100-iteration Monte Carlo cross-validation (80% training/20% validation; seed = 1,000).
| Model (parameter estimate, 95% CI) | Fitting criteria | Validation criteria | Remarks | |||||
|---|---|---|---|---|---|---|---|---|
| Adj-R2 | AIC | BIC | Bias | RMSE (kg plant−1) | MAPE | 95% PI coverage | ||
| AGB = 0.357. D0.542a = 0.357 (0.348, 0.365)b = 0.542 (0.479, 0.604) | 0.52 ± 0.16 | -120.4 ± 16.4 | -107.30 ± 16.4 | 6.66 ± 4.71 | 0.15 ± 0.041 | 10.50 ± 3.67 | 0.865 | Good |
| AGB = 0.274. (D2·H)0.216a = 0.274 (0.263, 0.285)b = 0.216 (0.199, 0.242) | 0.63 ± 0.07 | -129.8 ± 14.5 | -116.70 ± 14.5 | 5.32 ± 3.87 | 0.13 ± 0.039 | 9.22 ± 2.82 | 0.882 | Better |
| AGB = 0.046. D−0.469 · H1.682*a = 0.046 (0.032, 0.059)b = −0.469 (−0.614, −0.324)c = 1.682 (1.351, 2.013) | 0.93 | -177.02 | -156.44 | 1.89 | 0.05 | 5.51 | 0.928 | Best |
| Reference value/desired direction (Kaushal et al., 2022; Bhutia et al., 2025) | Higher (max 1) | Absolute Lower | Absolute lower | Lower (min 0) | Lower (min 0) | Lower (min 0) | ≈ 0.95 |
95% PI coverage = proportion of held-out observations falling within the model-based 95% prediction interval (varPower residual variance σ2 D2δ); a value close to 0.95 suggests well-calibrated prediction uncertainty. Residual diagnostics (normalized residuals of the full-dataset fit, n = 60; α = 0.05): Shapiro–Wilk W = 0.954, p = 0.024; Breusch–Pagan LM = 0.45, p = 0.50 for the chosen D–H model. Homogeneity of variance was confirmed and varPower accounted for the size-dependent error. The small deviation from normality is common at small n and does not influence the weighted maximum-likelihood estimates.
“*” denotes the best-performing model. AIC and BIC are absolute values that can only be used to compare relatively. Lower (more negative) is better.
Fitting and validation criteria are reported as mean ± standard deviation over the iterations. Parameter estimates and 95% confidence intervals are from the weighted (varPower) generalized least-squares fit to the full dataset (n = 60).
Table 3. Parameter estimates and fitting/validation metrics for component-wise biomass of Drepanostachyum falcatum (kg plant-1) calculated from the diameter–height (D–H) allometric model AGB = a.Db.Hc.
| Fitted model (parameter estimate, 95% CI) | Fitting criteria | Validation criteria | |||||
|---|---|---|---|---|---|---|---|
| Adj-R2 | AIC | BIC | Bias (%) | RMSE (kg plant−1) | MAPE (%) | 95% PI coverage | |
| SB = 0.027 · D−0.005 · H5.24a = 0.027 (0.016, 0.037)b = −0.005 (-0.0038, -0.006)c = 5.24(4.898, 5.581) | 0.93 ± 0.02 | -194.2 ± 5.5 | -173.6 ± 2.41 | −0.39 ± 2.41 | 0.034 ± 0.009 | 5.96 ± 1.23 | 0.921 |
| BB = 0.005 · D−0.71 · H1.91a = 0.005 (0.001, 0.011)b = −0.71 (-0.807, -0.621)c = 1.910 (1.831, 1.99) | 0.94 ± 0.01 | -373.79 ± 4.2 | -353.21 ± 4.2 | 0.14 ± 2.14 | 0.005 ± 0.001 | 5.62 ± 0.99 | 0.908 |
| LB = 0.0096 · D−0.374 · H1.314a = 0.0096 (0.009, 0.011)b = −0.374 (-0.423, -0.322)c = 1.314 (1.212, 1.411) | 0.91 ± 0.08 | -396.23 ± 11.0 | -375.65 ± 11.0 | 0.25 ± 2.22 | 0.005 ± 0.002 | 4.57 ± 1.01 | 0.918 |
Residual diagnostics (normalized residuals of the full-dataset fit, n = 60; α = 0.05)—Shapiro–Wilk/Breusch–Pagan: stem W = 0.967, p = 0.107/LM = 0.21, p = 0.65; branches W = 0.968, p = 0.123/LM = 0.004, p = 0.95; leaves W = 0.945, p = 0.010/LM = 0.003, p = 0.95; ACS W = 0.953, p = 0.023/LM = 0.17, p = 0.68. Homogenous variance across all components (Breusch–Pagan p ≥0.65); residuals approximated normality with a minor departure for leaves.
SB, stem biomass; BB, branches biomass; LB, leaves biomass.
Values are mean ± SD over 100 cross-validation iterations (seed = 1,000), parameters (95% CI) are from the full-data weighted GLS fit (n = 60).
The predictive performance was verified by means of Monte Carlo cross-validation. The dataset was randomly split into a training set (80%, n = 48) and a validation set (20%, n = 12) in each of 100 iterations. The model was refitted on the training set and used to predict the withheld observations, and RMSE and bias were recorded for each iteration. The random-number seed was fixed (set.seed(1000)) for reproducibility, and the validation metrics are reported as mean ± standard deviation over 100 iterations. The regression assumptions for the selected models were verified by visual inspection of normal Q–Q plots (confirmed by Shapiro–Wilk test) for normality and standardized-residual-versus-fitted plots for homoscedasticity. Aboveground carbon stock (ACS) was not modeled separately. ACS was derived directly from predicted AGB using a constant carbon fraction of 0.5 (ACS = 0.5 × AGB), and therefore the AGB model and its associated uncertainty completely controls ACS.
3 Results
3.1 Descriptive analysis
Among 60 sampled plants, the fresh weight, biomass (or dry weight), and carbon stocks of the aboveground components, including culm, branches, and leaves of D. falcatum, varied significantly with a distinct pattern (p < 0.05) (Table 4). The aboveground fresh weight (AFW) ranged from 1.16 to 4.05 kg, with a mean of 2.67 ± 0.07 kg, and the aboveground biomass (AGB) varied from 0.31 to 0.94 kg, with a mean of 0.53 ± 0.02 kg, whereas the average aboveground carbon stocks (ACS) were 0.27 ± 0.01 kg, which extended between 0.16 and 0.47 kg.
Table 4. Descriptive statistics of the aboveground biometric characteristics of D. falcatum.
| Biomass and carbon metrics | Parameters | Mean ± SE | Minimum | Maximum |
|---|---|---|---|---|
| Fresh weight (kg) | Stem/culm | 1.86 ± 0.06b | 0.70 | 2.60 |
| Leaves | 0.72 ± 0.03c | 0.40 | 1.31 | |
| Branches | 0.09 ± 0.00d | 0.06 | 0.14 | |
| Aboveground | 2.67 ± 0.07a | 1.16 | 4.05 | |
| Dry weight (biomass, kg) | Stem | 0.40 ± 0.02b | 0.22 | 0.72 |
| Leaves | 0.06 ± 0.00c | 0.04 | 0.10 | |
| Branches | 0.07 ± 0.00c | 0.04 | 0.12 | |
| Aboveground | 0.53 ± 0.02a | 0.31 | 0.94 | |
| Carbon stock (kg) | Aboveground | 0.27 ± 0.01 | 0.16 | 0.47 |
Different symbols suggest significant difference (p = 0.05); sample size of culms/stands = 60.
The culm was the highest contributor to aboveground fresh weight (1.86 ± 0.06 kg), followed by leaves (0.72 ± 0.03 kg) and branches (0.09 ± 0.00 kg). A similar pattern was observed for dry biomass, where the culm again contributed the most (0.40 ± 0.02 kg), whereas branches (0.07 ± 0.00 kg) and leaves (0.06 ± 0.00 kg) contributed much less. Overall, the results highlight that the culm accumulates the majority of biomass and carbon, whereas leaves and branches contribute relatively smaller portions (Table 4).
The results of the average number of culms per clump (Cu/Cl), clump density per hectare, along with size–age distribution, are depicted in Table 1. It was found that Cu/Cl increased with clump size, ranging from 178.4 (in small clumps), followed by medium clumps (249.05), and large clumps (379.2). Within each size class, Cu/Cl estimated in three age classes (year 1, 2, and 3), revealed an increasing trend, with an increase in age from year 1 to 3. In small clumps, the Cu/Cl count ranged from 35.65 to 89.15, while in medium clumps it varied from 49.80 to 124.40, and in large clumps it was highest, extending from 75.80 to 189.55. This Cu/Cl count pattern clearly marked a structured age configuration within clumps, where older age classes consistently outnumbered the younger ones regardless of clump size. Clump density was calculated in the field as 156 ha-1 for small (39), medium (55), and large (62) clumps; this density corresponds to an average distance between clumps of approximately 8 m (Table 1).
3.2 Allometric model framework
3.2.1 Allometric model development—AGB
Three models were developed for aboveground biomass (AGB) using a single variable: diameter (D), single compound variable of D and height (H), i.e., D2H and two variables D and H (D–H). The results of model parameter estimates, fitting accuracy, and validation are detailed in Table 2. The allometric model AGB^=0.357×D0.542 (model I) revealed moderate goodness of fit (adjusted R2 0.52), whereas 0.63 was found for AG^B=0.274×(D2H)0.216 (model II) and the highest at 0.93 was estimated for AG^B=0.046×D-0.469×H1.682. The pattern of findings of Adj-R2 was complemented by both AIC and BIC values of the models that range from -177.02 to -120.4 and -156.44 to -107.30. The results of the validation revealed that model III is best with the smallest errors (bias = 1.89, RMSE = 0.05, MAPE = 5.51%), followed by model II (bias = 5.32, RMSE = 0.13, MAPE = 9.22%) and model I (bias = 6.66, RMSE = 0.15, MAPE = 10.50%). Model III’s 95% prediction-interval coverage had the smallest deviation from the nominal 0.95 at 0.928, showing well-calibrated prediction uncertainty. This indicates that incorporation of H significantly improves prediction accuracy, and the further addition of one more model parameter (c) further provides flexibility in the fitting. The performances of the models—D, D2H, and D–H—for estimating AGB are visualized in Figure 1, which presents, for each model, the fitted allometric curve (column a), observed versus predicted AGB (column b), residuals versus predicted AGB (column c), and the normal Q–Q plot (column d). For the chosen D–H model, variance was homogeneous (Breusch–Pagan LM = 0.45, p = 0.50), indicating that varPower function accounted for the size-dependent error; the standardized residuals were approximately normal (Shapiro–Wilk W = 0.954, p = 0.024), the slight departure being typical at this sample size and not affecting the weighted maximum-likelihood estimates.
![Evaluation of the three candidate allometric models for aboveground biomass (AGB, kg plant<sup>−1</sup>) of *Drepanostachyum falcatum*. Rows correspond to model I [AGB = a·*D*b; **(a–d)**], model II [AGB = a·(*D*<sup>2</sup>*H*) b; **(e–h)**], and model III [AGB = a·*D*<sup>b</sup>·*H*<sup>c</sup>, best*; **(i–l)**]. We fitted the models to the full dataset (*n* = 60) using weighted maximum-likelihood regression with a power-of-diameter variance function (varPower; residual variance ∝ D<sup>2δ</sup>). The panels for each model show the fitted curve with observed data and 95% confidence and 95% prediction bands, observed versus predicted values with the 1:1 line, standardized residuals versus predicted values with the 2 SD band, and a normal quantile–quantile plot of the standardized residuals with the Shapiro–Wilk statistic. Diameter (*D*), cm; height (*H*), m.](https://www.frontiersin.org/files/Articles/1872137/xml-images/fevo-14-1872137-g001.webp)
3.2.2 Allometric model development of aboveground components
With the selected diameter–height form (model III), separate equations were developed for the stem, branch, and leaf biomass components (Table 3). All component models had good fits for the data (Adj.-R2 range 0.91–0.94, low information criteria; Table 3). They predicted accurately with negligible bias on the validation data: ARMSE ranged from 0.005 kg plant−1 (branches and leaves) to 0.034 kg plant−1 (stem), AMAPE ranged from 4.57% (leaves) to 5.96% (stem), and ABias was within ±0.4% for each component. Prediction-interval coverage was near nominal for all components (0.908–0.921). Figure 2 summarizes the point estimates and 95% confidence intervals of the fitted parameters (scaling coefficient a, diameter exponent b, and height exponent c) for the AGB and component models (values as reported in Tables 2, 3), and the intervals for most of the parameters did not cross the zero reference line, suggesting that the estimated coefficients were well constrained.

Full-dataset fits were subjected to residual diagnostics, which indicated that model assumptions were appropriately met for all components (Table 3). Homogeneity of variance was confirmed for all models (Breusch–Pagan p ≥ 0.65: stem LM = 0.21; branches LM = 0.004; leaves LM = 0.003; ACS LM = 0.17), and standardized residuals were approximately normally distributed (Shapiro–Wilk: stem W = 0.967, p = 0.107; branches W = 0.968, p = 0.123; leaves W = 0.945, p = 0.010; ACS W = 0.953, p = 0.023); only slight deviations were detected for leaves. Overall, the results reflected the highest model fitting accuracy for stem biomass, followed by a slightly lower accuracy for branches and leaves, while still providing dependable estimates. The performances of the best-suited model D–H are depicted in Figure 3A for SB, in Figure 3B for BB, and in Figure 3C for LB.

3.2.3 ACS estimation
The aboveground carbon stock (ACS) was not fitted with a separate allometric equation; it was instead obtained directly from the predicted AGB by applying a carbon fraction of 0.5 (ACS = 0.5 × AGB). Substituting the best-fitting diameter–height model gives ACS = 0.023 × D^(−0.469) × H^(1.682). Because ACS is a fixed proportion of AGB, its relative fitting and validation performance is identical to that of the AGB model (Adj.-R2 = 0.93; MAPE = 5.51%; 95% prediction-interval coverage = 0.928; Table 2), while the absolute error terms (RMSE and bias in kilogram) are exactly halved. The derived estimates were consistent with the descriptive mean carbon stock of 0.27 ± 0.01 kg per culm (range 0.16–0.47 kg; Table 4), and the residual diagnostics of the ACS predictions were satisfactory (Shapiro–Wilk W = 0.953, p = 0.023; Breusch–Pagan LM = 0.17, p = 0.68; Table 3), confirming that the AGB-based carbon estimates are well calibrated.
3.2.4 Allometric development of height–diameter relationship
The best-suited allometric height model, H (m) = 2.598 × D1.032, for developing a relationship between height and diameter of culm is depicted in Figure 4. Figure 4 reveals that the model is reliable enough to predict height using the diameter of the culm. The observed and predicted values, which were lying near the 1:1 reference line, suggest goodness of fit. The residuals are randomly scattered around zero, ranging from -1.0 to +1.1 m, while the majority lies between -0.5 and +0.5 m (Figure 4). The model captures the general trend effectively within the entire data range, 2.8 to 8.3 m, so it can be considered for H prediction.

3.3 Model-based AGB and ACS estimation
3.3.1 Culm-level estimates
The summary of average culm-level estimates of AGB and ACS by the best-suited D–H models is presented in Table 5. The predicted average AGB was 0.524 ± 0.0179 kg per culm, while the corresponding ACS was 0.262 ± 0.0090 kg per culm. Here relatively low standard error values reflect the reliability of the means.
Table 5. Average culm-level AGB and ACS estimates for D. falcatum.
| Parameter | Mean | SD | SE |
|---|---|---|---|
| Culm AGB (kg/culm) | 0.524 | 0.139 | 0.0179 |
| Culm ACS (kg/culm) | 0.262 | 0.069 | 0.0090 |
3.3.2 Clump-level estimates
The model-based culm level AGB and ACS estimates were scaled up to clump level by multiplying culm-level AGB with the corresponding number of culms. The results revealed that clump-level AGB was 93.48 kg per clump for small clumps, whereas it was 130.50 kg per clump for medium clumps and 198.70 kg per clump for large clumps, respectively. Overall, mean AGB was 140.90 kg per clump. The mean ACS value was 70.45 kg, distributed among small (46.74 kg), medium (65.25 kg), and large size (99.35 kg) (Table 6).
Table 6. Clump-level AGB and ACS estimates by size class.
| Clump size | Avg. AGB (kg/clump) | Avg. ACS (kg/clump) |
|---|---|---|
| Small | 93.48 | 46.74 |
| Medium | 130.50 | 65.25 |
| Large | 198.70 | 99.35 |
| Average | 140.90 | 70.45 |
3.3.3 Area-level estimates (per-hectare basis)
The estimated clump densities for the small, medium, and large size classes were 39, 55, and 62 clumps ha-1, respectively, with an overall stand density of 156 clumps ha-1 and a mean inter-clump spacing of ~8 m (Table 1). Scaling clump level AGB using these class-specific densities produced small clumps with 3,645.78 kg ha−1, medium clumps with 7,177.62 kg ha−1, and large clumps with 12,319.45 kg ha−1. Across classes, the total aboveground biomass was 23,142.85 kg ha−1 (23.14 t ha−1; 95% CI ≈ 21.6–24.7), and the total aboveground carbon stock was 11,571.43 kg ha−1 (11.57 t ha−1; 95% CI ≈ 10.8–12.4) (Table 7).
Table 7. Area-level AGB and ACS estimates per hectare by clump size class.
| Clump size | Clumps/ha | AGB (kg/ha) | ACS (kg/ha) |
|---|---|---|---|
| Small | 39 | 3,645.78 | 1,822.89 |
| Medium | 55 | 7,177.62 | 3,588.81 |
| Large | 62 | 12,319.45 | 6,159.73 |
| Total | 156 | 23,142.85 | 11,571.43 |
| Total (t/ha) | 23.14 | 11.57 |
4 Discussion
4.1 Descriptive analysis
Accurate, non-destructive biomass estimation is crucial for bamboo carbon accounting since it is rarely possible to fell and weigh entire clumps at scale (Kaushal et al., 2022). All values discussed below are aboveground carbon stock at a single point in time, not sequestration rates which would require repeated measurements of the same clumps over successive growing seasons. Descriptive analysis and post-hoc tests (DMRT) showed that the stems, branches, and leaves of D. falcatum differed significantly (p < 0.05) in fresh weight, dry biomass, and carbon stock (Table 4), which is due to the allocation based on culm age, stand density, and local growing conditions (Kaushal et al., 2022). The stem was the main component representing the highest proportion of aboveground fresh weight (2.67 ± 0.07 kg total), dry biomass (stem 0.40 ± 0.02 kg of the 0.53 ± 0.02 kg aboveground total), and carbon (0.27 ± 0.01 kg), identifying it as the primary storage pool. This culm-dominant allocation is consistent with an erect, self-supporting growth form: similar culm fractions have been reported for other upright bamboos, at 73%–78% in Phyllostachys makinoi (Yen et al., 2010) and 69.6%–78.7% across seven Himalayan species (Kaushal et al., 2022). Allocation in bamboo therefore is a function of growth habit and architecture rather than size per se, and a stem-dominant pattern suggests that the majority of fixed carbon is in the longer-lived structural fraction. Similarly, Devi and Singh (2021) also reported culm-dominated storage in Bambusa tulda and Dendrocalamus longispathus in northeast India, which reinforces the culm as the main aboveground carbon pool in bamboo systems.
Table 1 shows the average number of culms per clump (Cu/Cl), clump density per hectare, and size–age distribution. Cu/Cl increased with clump size from 178 (small) to 249 (medium) to 379 (large). In a sympodial bamboo, this increase with clump size is because the rhizome system and clump architecture expand over time, supporting ever greater numbers of culms: the axillary buds on the rhizome give rise to new shoots, and as the clump ages the growing rhizome network creates an increasing number of bud sites, raising the number of culms recruited each year (Banik, 2015). Within each size class, Cu/Cl showed a consistent increase with age, from 36 (year 1) to 89 (year 3) in small, 50 to 124 in medium, and 76 to 190 in large clumps. This reflects the additive nature of culm recruitment, with fresh culms being added during each shooting season without the complete removal of earlier cohorts. Similar trends were reported by Nath et al. (2009) in Bambusa tulda and Dendrocalamus longispathus in northeastern India. Banik (1995) gave a fundamental insight on the growth and productivity of bamboo. However, a small rhizome system can only support a limited number of culms, and a well-developed rhizome network provides a larger source of stored carbohydrate and more bud sites for greater culm emergence (Nath et al., 2009). The relatively high Cu/Cl recorded here (up to 379 in large clumps) is higher than values typical of managed plantations and is consistent with the under-harvested condition of the stand where culms have accumulated over several annual cohorts (Table 1).
4.2 Allometric model framework
4.2.1 Allometric model development—AGB
The primary objective of this study was to develop and validate allometric models for the non-destructive estimation of AGB and ACS of D. falcatum of the Uttarakhand hills so as to strike a balance between accuracy and field feasibility. We fitted three power-form models following Megha et al. (2025) and Kaushal et al. (2022). Model I was based on diameter (D) alone, model II was based on a compound variable (D2H, calculated as the product of diameter squared and height, H), and model III was based on D and H as separate predictors. Table 2 shows the parameter estimates, goodness of fit, and validation. Adding height increased the prediction accuracy considerably. Model I (AGB = 0.357 × D0.542) was fitted only moderately well (adjusted R2 = 0.52). Model II increased this to 0.63, and model III gave the highest adjusted R2 of 0.93.
Additional criteria were used to test whether the added complexity of models II and III resulted in a genuine improvement in fit: AIC and BIC. Both were in agreement with the Adj-R2 that gave the lowest values for model III (AIC = −177.02, BIC = −156.44). All three models were negative for both AIC (−177.02 to −120.4) and BIC (−156.44 to −107.30), indicating a high fitting accuracy. Given the penalty for added parameters, the agreement between AIC and BIC indicates that the improvement in model III is genuine and not an artefact of overfitting (Bhutia et al., 2025). The validation showed that model III was the best with the least errors (bias = 1.89, RMSE = 0.05, MAPE = 5.51%), followed by model II and model I (Table 2; Figure 1), which is in line with the findings of previous studies (Kaushal et al., 2022; Yen and Lee, 2011). Model III estimates three parameters from 60 observations, with a data-to-parameters ratio of about 20:1. Together with the fact that AIC and BIC, both of which penalize the added parameters, independently selected this model and that its out-of-sample validation error (RMSE = 0.05 kg plant−1) is close to its in-sample fitting error, this indicates that the improved fit is not an artefact of overfitting. This result has an ecological interpretation: diameter is the best single predictor of biomass in bamboo, but diameter alone cannot account for differences in vertical growth, and the combination of height plus a third parameter allows model III to account for the slender, tall culms of D. falcatum. Similarly, previous authors have reported better prediction of biomass in bamboo when the height is included (Devi et al., 2023; Yen and Lee, 2011; Kaushal et al., 2022). Model III (D–H) is recommended in general, while model I is still usable where height data are not available.
4.2.2 Allometric model development of aboveground components
The three major aboveground components—stem, branches, and leaves—were modeled independently. Model III continued to perform well at the component level (Table 3). All three components were modeled well, with Adj-R2 ranging from 0.91 (leaf biomass) to 0.94 (branch biomass) and 0.93 (stem biomass). The highest fitting accuracy was thus obtained for branch and stem biomass, with leaf biomass being marginally lower but still providing reliable estimates. The best-fit component models are presented in Figure 3A (stem), Figure 3B (branch), and Figure 3C (leaf), which were consistent with prior studies on bamboo (Yuen et al., 2017; Kaushal et al., 2022). This lower performance for leaves is to be expected due to their greater spatial variability and rapid turnover, which introduced further uncertainty to estimation. Across the AGB and component models, the fitted scaling coefficients and exponents were generally well constrained, with 95% confidence intervals that mostly excluded zero (Figure 2; Tables 2, 3), confirming that the estimated parameters were statistically robust rather than artefacts of overfitting.
4.2.3 ACS estimation
The aboveground carbon stock was not modeled using separate allometric equations. ACS is directly derived from predicted AGB as ACS = 0.5 × AGB after applying a constant carbon fraction of 0.5; thus, all of the allometric behavior and uncertainty of ACS are completely determined by the AGB models. Therefore, carbon stock estimates are proportional to AGB (Nath et al., 2009; Yuen et al., 2017). This method of deriving ACS obviates the need to fit independent equations for carbon, which introduces additional propagated error, and provides a single, transparent conversion to users.
4.2.4 Allometric development of height–diameter relationship
The best-performing biomass models are based on height as an input, which cannot be applied where H is not available. A height–diameter relationship was therefore developed since D is the most commonly measured biometric variable and is strongly related to H in bamboo (Kaushal et al., 2022). The fitted equation H = 2.598 × D1.032 was highly accurate (Figure 4) and reliably predicted culm height over the observed range of 2.8 to 8.3 m. The model captured the general trend well and provided a practical means of generating synthetic H values from measured D.
4.3 Model-based AGB and ACS estimation
4.3.1 Culm-level estimates
At the culm level, the selected D–H model predicted a mean aboveground biomass of 0.524 ± 0.0179 kg per culm and a corresponding carbon stock of 0.262 ± 0.0090 kg per culm (Table 5). The low standard errors indicate that these per-culm means are reliable and provide a robust basis for scaling biomass and carbon to the clump and stand levels. These modest per-culm values reflect the slender, thin-walled architecture of D. falcatum and constitute the fundamental unit from which the clump- and area-level estimates discussed below were derived.
4.3.2 Estimates of clump level
Clump estimates were extrapolated from culm-level estimates by multiplying by the number of culms per clump (Table 6). The mean AGB at clump level was 140.90 kg, ranging from 93.48 kg (small) to 130.50 kg (medium) to 198.70 kg (large). The near-doubling of AGB between small and large clumps underscores the importance of clump size for reliable estimation; similar patterns, where biomass accumulation is strongly influenced by culm density and maturity, have been identified in bamboo ecosystems (Nath et al., 2009; Yuen et al., 2017; Kaushal et al., 2022). Reliable estimates of AGB and ACS require size-stratified field sampling because pooling size classes would bias stand-level estimates (Table 6).
4.3.3 Area-level estimates (per-hectare basis)
Clump-level AGB was scaled to the hectare with a measured density of 156 clumps ha-1 (39 small + 55 medium + 62 large; mean inter-clump spacing ~8 m; Table 1). Stand-level AGB was 23,142.85 kg ha-1 (23.14 t ha-1) and ACS was 11,571.43 kg ha-1 (11.57 t ha-1) with small, medium, and large clumps contributing 3,645.78, 7,177.62, and 12,319.45 kg ha-1, respectively (Table 7). The contribution was not equal as large clumps contributed 53.2%, medium 31.0%, and small 15.8%, indicating a strong influence of clump size, culm density, and maturity on stand-level accumulation (Nath et al., 2009).
These values are small compared to most Indian bamboos. Nath et al. (2009) recorded 121.51 t ha-1 AGB (61.05 t ha-1 carbon) for village bamboos of Barak Valley, and Devi and Singh (2021) found 73.6–150 t ha-1 AGB in Bambusa tulda and Dendrocalamus longispathus. Kaushal et al. (2022) found AGB up to 212.6 t ha−1 in the thick-culmed B. balcooa, with a mean annual range from 11.87 t ha−1 (D. stocksii) to 30.37 t ha−1 (B. balcooa), where the present estimate lies at the lower end; the closest analogues are thin-walled bamboos, for which Singnar et al. (2017) reported carbon densities of only 21–23 Mg ha−1. This placement follows directly from culm structure: with an average culm diameter of 1.86 cm (maximum 2.60 cm), well under the 4–10 cm of Bambusa and Dendrocalamus, D. falcatum has low per-culm mass, so its modest stand biomass is a consequence of narrow culms and not of sparse stocking (culm density, in fact, is high (up to 379 culms clump-1; 156 clumps ha-1). Thus, dense clonal packing compensates for thin culms, a density–mass trade-off among bamboo growth forms. This architecture also contains an altitudinal signal. D. falcatum is a temperate species of 1,200–3,000 m that has shorter, cooler growing seasons than tropical lowland bamboos, limiting culm size and biomass, but its dense clumping and extensive rhizome network make it useful for slope stabilization and soil binding (Kaushal et al., 2020; Kumar et al., 2023). Therefore, the stock reported here should be taken as a near-maximal standing value for an under-harvested stand and provides the first species-specific, field-based biomass and carbon baseline for D. falcatum, supporting the importance of scale-specific, size-stratified approaches when quantifying carbon in structurally heterogeneous bamboo ecosystems.
4.3.4 Limitations
These equations were calibrated from 60 culms in 20 clumps in one temperate Himalayan location and thus are site-specific models. The model accuracy outside the calibration range of stem diameter and height and within similar temperate Himalayan climatic and edaphic conditions is unknown. Ecological variability across altitude, aspect, soil, and stand density could not be accommodated by the present design. We therefore recommend that these models be used only under comparable conditions and externally validated with independent data from other sites and altitudinal belts before wider use.
There is some possibility of misclassification between adjacent age classes as age was assigned visually by a single trained observer. To mitigate this possibility, several morphological indicators were combined rather than relying on any one. However, direct age validation (i.e., tagged-cohort tracking) was not within the scope of this study but is recommended as future work.
Stand-level values were upscaled from 20 clumps using class-mean densities. Natural bamboo stands are spatially clumped, not evenly distributed, and because we did not measure variation in clump density or biomass within classes, the confidence intervals that we present are based solely on the measurement uncertainty of mean biomass at the culm level and are likely to underestimate the true uncertainty of extrapolation to the landscape scale beyond the surveyed area.
Aboveground carbon stock was not directly measured, but it was estimated using a standard carbon fraction of 0.5. Carbon concentration varies between bamboo species and tissues. The reported carbon stocks should be treated as rough estimates, and there is additional unquantified uncertainty besides the biomass models.
5 Conclusion
In this study, the species-specific allometric model was developed and validated for estimating aboveground biomass and carbon stock (ACS) in D. falcatum in the temperate region of north-western Himalaya, Uttarakhand, India. This study thoroughly integrated field sampling using a two-stage stratified sampling design, destructive biomass estimation, and statistical modeling to establish a precise and practical approach for assessing biomass and carbon at different levels (culm, clump, and per-hectare level). The results confirmed that the bamboo is a highly productive resource, holding significant potential for biomass and carbon storage. The analysis of biomass among the various components of bamboo such as culms, leaves, and branches revealed significant differences. The culms contributed the highest share of total aboveground biomass, while the leaves and branches contributed smaller shares. Among the models tested, the diameter and height (D–H) model exhibited the highest performance in estimating biomass and carbon stocks, with high prediction accuracy and low error across a wide range of culm sizes. The close match between measured and estimated values suggests that the model captures the growth pattern of the species well. The component-wise models for stems, branches, leaves, and total aboveground carbon stocks demonstrated robust predictive capacity, validating the utility of the developed model for biomass estimation. Since these models utilize easily measurable variables such as diameter and height, they are highly practical for field applications without the need of destructive sampling. Height–diameter relationship was also developed in case height data were not available. Overall, this study has addressed the significance of developing the species-specific models for sympodial species in the temperate region of Uttarakhand. The developed model offers a reliable method for estimating aboveground biomass and aboveground carbon stocks, which could support sustainable management, carbon storage, and climate change mitigation efforts. Furthermore, these models were developed from a limited data set covering the Himalayan region with a temperate climate, which limits its application to comparable site circumstances. It should be noted that the climate change mitigation and REDD+ relevance discussed in this study are inferred from the estimated aboveground biomass and carbon stocks rather than from direct measurements of carbon sequestration rates, carbon fluxes, or greenhouse gas exchange. These species-specific stock estimates are a necessary input to broader carbon accounting and REDD+/NDC reporting, but the present local, single-time-point dataset is only a preliminary building block; scaling to policy-relevant conclusions would require multi-site sampling and temporal remeasurement.
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Footnotes
Edited by: Syam Viswanath, Indian Council of Forestry Research and Education (ICFRE), India
Reviewed by: D. Balasubramanian, Arunachal University of Studies, India
Rupali Singh, Forest Research Institute (ICFRE), India
Jeet Ram, Kumaun University, India
Statements
- Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The reviewer RS declared a shared affiliation with the authors PR, PA, GR to the handling editor at the time of review.
- Funding
The author(s) declared that financial support was not received for this work and/or its publication.
- Data availability
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
- Author contributions
IS: Conceptualization, Data curation, Formal analysis, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing. SI: Conceptualization, Data curation, Formal analysis, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing. VK: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing. PR: Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. CD: Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. AD: Conceptualization, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. JT: Methodology, Visualization, Writing – original draft, Writing – review & editing. PA: Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. AK: Methodology, Visualization, Writing – original draft, Writing – review & editing, Validation. SS: Methodology, Validation, Writing – original draft, Writing – review & editing. MR: Methodology, Visualization, Writing – original draft, Writing – review & editing. GR: Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing.
- Acknowledgements
We express our gratitude to the College of Forestry, Ranichauri, and the Dean and Chairmen of the PhD advisory committee for granting permission to conduct the study and for extending the necessary support throughout the study.
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Citation
Singh, I., et al. (2026). Quantifying aboveground biomass and carbon stock in Drepanostachyum falcatum , a temperate Himalayan bamboo in India: an allometric modeling framework. Frontiers in Ecology and Evolution, Volume 14. https://doi.org/
- Received
- Accepted
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- Volume
- 14 - 2026
Copyright
Copyright © 2026 Singh, Islam, Khanduri, Rawat, Dhanai, Dabral, Tomar, Ayush, Kumar, Sati, Riyal and Reddy.
License: https://creativecommons.org/licenses/by/4.0/
*Correspondence: Indra Singh; Sadikul Islam
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