An Allometric Model Based Approach For Estimating Biomass In Seven Indian Bamboo Species In Western Himalayan Foothills, India

doi:10.21203/rs.3.rs-1106649/v1

The rapid growth rate, high biomass production, and annual harvesting, makes bamboo as suitable species for commercial production. Allometric equations for many broadleaf and conifer tree species are available. However, knowledge on biomass production and allometric equations of bamboos are limited. This study aims at developing species specific allometric models for predicting biomass and synthetic height values as a proxy variable for seven bamboo species in Himalayan foothills. Two power form based allometric models were used to predict above ground and culm biomass using Diameter at breast height (D) alone and D in combination with culm height (H) as independent variable. This study also extended to establishing H-D allometric model that can be used to generate synthetic H values as proxy to missing H. In the seven bamboo species studied, among three major biomass component (culm, branch and foliage), culm is the most important component with highest share (69.56 to 78.71%).Distribution of percentage (%) share of culm, branch and foliage to above ground fresh weight varies significantly between different bamboo species. D. hamiltonii has highest productivity for above ground biomass components. Ratio of dry to fresh weight of seven bamboo species was estimated for culm, branch, foliage and above ground biomass to convert fresh weight to dry weight.

Plant Physiology and Morphology

Forestry

Bamboo

Biomass

Diameter

Height

Monte Carlo cross-validation

power function

Synthetic bamboo height

Bamboos are a group of perennial plants belonging to Poaceae family and subfamily Bambusoideae. A total of 1642 bamboo species occupy a wide ecological regime across the globe, mostly in tropical and sub-tropical regions¹. The rapid growth rate, high biomass production, and annual harvesting, makes bamboo as suitable species for commercial production. Being an annual yielding crop with a wide range of product possibilities such as construction materials, woven products, pulp and paper, food, feed and fodder, scaffolding, bio-energy, engineered products, lifestyle products, medicine among others, offers itself to contribute to poverty reduction, job creation and green economy development. Moreover, bamboo has proven wide range of ecosystem services especially soil erosion control, water recharge, slope stabilisation, climate change, wildlife habitat and biodiversity conservation. Overall, bamboo contributes in achieving a number of United Nations 2030 Agenda Sustainable Development Goals – particularly, SDG1, SDG7, SDG 11, SDG 12, SDG 13, SDG 15, and SDG 17².

Worldwide, bamboo grows over in 35 million ha area and covers 3.2 percent of the forest areas of their host countries, or about 1 percent of the global forest area^3,4. In India, bamboo grows naturally throughout the country except in Kashmir region. India is one of the richest countries of the world in terms of bamboo genetic resources with 125 bamboo species belonging to 23 genera. In term of coverage, India has largest bamboo cover, the bamboo area in the country is 15.68 million hectare which provides livelihood to about 2 million traditional artisans through harvesting, processing, value addition and selling bamboo products⁵. The demand of bamboo is estimated to be 26.69 million tonnes as against supply of 13.47 million tonnes in the country⁶. Recognizing the importance of bamboo, Government of India (GOI) allocated an outlay of Rs.12.90 billion ($177.6 million) for promoting bamboo sector and has set a target to bring about 0.1 million ha area under bamboo plantations in forests, degraded lands and farmlands for generating livelihood opportunities and meeting the industrial demand⁷.

Bamboo cuts across various sector: agriculture, forestry, manufacturing, construction, and energy. Particularly, agriculture, forestry and land use contributes to about one-fifth of the GHG emissions. India has set its target to cut its carbon emissions to net zero by 2070 at the United Nations Climate Change Conference (COP26) climate crisis summit 2021 organized in Glasgow, UK for which monitoring and measurement of tree biomass assumes a greater importance. Assessment of biomass is helpful in timber extraction, tracking changes in the carbon stocks and quantifying the amount of carbon dioxide which can be sequestered from the atmosphere. Destructive methods and indirect methods (biomass equations) are generally used for estimating tree biomass. Use of biomass equations is cost effective and less time consuming and is recognized by United Nation as a common framework and good practice guidance for carbon reporting in the implementation of the emerging carbon credit market mechanism⁸. Biomass equation predicts biomass based on easily correlated measured variables like diameter at breast height and tree height^9–10. However, in bamboos biomass estimation becomes more complicated due to presence of different aged and multiple culms. In bamboos, so far, occular methods are being used for assessing biomass by the traders and farmers which require long field experience and suffer from high degree of inaccuracy and therefore results in huge losses to the farmers, foresters, industries and other bamboo growers. Therefore, there is an urgent need to develop site specific predictive models/ equations for estimating biomass in bamboos. Of various non linear models, allometric models have been found to be most efficient forestimating biomass because of numerous computational advantages like, high convergence of model parameters compared to most of the other non-linear models, best goodness of fit and the low statistical errors^11–14.

In literature, allometric equations are available for broadleaf and conifer tree species. However, knowledge on biomass production in bamboos is limited. Most of allometric equations for bamboo are available for Phyllostachys species in China^15–18. In India, despite of large area under bamboo, allometric equations are available for few species viz., Bambusa cacharensis, Bambusa balcooa, Bambusa tulda, Bambusa vulgaris, Dendrocalamus hamiltonii, Dendrocalamus longispathus, Melocanna baccifera, Schizostachyum dullooa and Pseudostachyum polymorphum in north east India^19–20; D. strictus in north India^21–22; Bambusa bambos in eastern India²³ and South India²⁴. In north India, not much work has been attempted on biomass estimation in bamboos. The present study was therefore undertaken in seven commercial important bamboo species with the objectives: (1) to build species specific allometric models for aboveground biomass and culm biomass using diameter (D), height (H), D²H (2) to predict synthetic height values as a proxy variable using diameter for biomass estimation.

2.1 Study area

The study was carried out to develop allometric models for predicting biomass in seven commercial important bamboo species viz., Bambusa balcooa, Bambusa bambos, Bambusa vulgaris, Bambusa nutans, Dendrocalamus hamiltonii, Dendrocalamus stocksii and Dendrocalamus strictus in the western Himalayan foothills from 2017-2020. All the selected bamboo species are of commercial importance and on priority list of National Bamboo Mission, Government of India and International Bamboo and Rattan Organization (INBAR). Two sites located at distance of 275 Km were selected for collecting the data of seven different bamboo species (Figure 1). The details of the study sites are given in Table 1. The planting material for Site 1 was collected from nursery of Uttarakhand Bamboo and Fiber Development Board, Dehradun, India. The planting material for Site 2 was collected from different bamboo nurseries from different parts of the country. The formal identification of the planting material was done based on morphological features described by Seethalakshmi and Kumar (1998).

Table 1

Details of the study sites
Parameters	Site1	Site 2
Location	Research farm, ICAR-Indian Institute of Soil and Water Conservation, Dhulkot and Selaqui	Agroforestry Research Centre, G.B. Pant University of Agriculture and Technology, Pantnagar
District/state/country	Dehradun, Uttarakhand, India	U.S. Nagar, Uttarakhand, India
Coordinates	30"20'59"N latitude, 77"53'05"E longitude	29°1′ 17″ N latitude and 79°29′ 14″ E longitude
Altitude	548 m	243.8
Soil type	Inceptisols	Mollisols
Climate	Sub-humid and subtropical climate	humid sub-tropical
Rainfall (mm)	1660	1364
Species	Bambusa balcooa, B. bambos, B. vulgaris, B. nutans, Dendrocalamus hamiltonii, D. stocksii and D. strictus	Bambusa balcooa, Bambusa bambos, Bambusa nutans, Dendrocalamus hamiltonii, and Dendrocalamus strictus
Year of plantation	2010 and 2 012	2005
Area of plantation	1.2 ha	3 ha

2.2 Sampling

For sampling, three plots of 0.018 ha (15m×12m) were selected for each species at site 1. For site 2, three plots of 0.0225 ha (15m×15m) were selected for each species. Each plot consisted of 9 bamboo clumps comprising of numerous bamboo culms (poles). Two-stage random sampling design was adopted for selecting the clumps (1st stage sampling unit) and culms (2nd stage sampling unit ). In total 39 plots (21 at site 1 and 18 at site 2) comprising of 351 clumps were demarcated to collect data every year from the year 2017 to 2020. For understanding the culm size distributions within the sample plots, three clumps were selected randomly and measured for its clump girth, crown diameter, culm number, culm diameter at breast height. Depending on the culm sizes, different diameter classes were recognized representing the whole diameter range and from each diameter class three mature culms (> 3 year old) were harvested randomly for each species in each clump. The age of mature culms in the clumps was determined on the basis of culm sheath, colour of culms, position of the culms, and growth and development of branches and leaves²⁵.The summary statistics for biometric parameters of different bamboo species studied is given in Table 1.The diameter of each bamboo culm was measured at breast height with the help of caliper. Culm height was measured with the help of tape after harvesting the culm. The harvested culms were separated into different components viz., leaf, branch and culm. Fresh weights were taken for respective components in the field. Subsamples from upper, middle, and lower portion of the culms of different ages were oven-dried at 65°C to constant weight for determining the ratio of dry weight to the fresh weight²⁶.

2.3. Development of allometric equations for biomass estimation

Two power equation forms of allometric equations were developed for biomass modelling of seven bamboo species. The first one was two-parameter general power form allometric equation as:

where ‘a’ denotes the constant of proportionality or scale constant, ‘b’ denotes the power or shape constant, and${\varepsilon _i}$ is the error component follow normal distribution with zero mean and non-constant variance $\sigma _{i}^{2}$ i.e.,${\varepsilon _i}\sim iid\,N(0,\sigma _{i}^{2})$. ‘x’ be a single predictor variable. Here, diameter at breast height (D) and culm volume (D²H) were used as x variable. Further, three parameter power form of allometric equationwas used as:

where ‘a’ denotes the scale constant, ‘b’ and ‘c’ denote the shape constant for the predictor variable x and z, respectively. ${\varepsilon _i}$ be the error component follow normal distribution with zero mean and non-constant variance $\sigma _{i}^{2}$ i.e.,${\varepsilon _i}\sim iid\,N(0,\sigma _{i}^{2})$. For biomass modelling D was used as x and Hused as z.

The error term of both the allometric forms already discussed, assuming as heteroscedastic (i.e., not constant variance). Therefore, a weighted fit model were used to calculate the variance of the residual variation using the function,$\,\sigma _{i}^{2}=Var({\varepsilon _i})={\hat {\sigma }^2}{({v_i})^{2\delta }}$;where ${\hat {\sigma }^2}$is the sum of the estimated errors of the squares; ${v_i}$ is the weighting variable associated with the i^th plant/clump sampled; and $\delta$is the coefficient of the variance function to be estimated²⁷⁻²⁹. Therefore, the weighted maximum likelihood nonlinear fixed effects modelling method was used to fit the biomass equations for the seven bamboo species using the ‘nlme’ package of R Studio statistical software (R version 4.1.0). The details of the allometric form of equations used for testing and validation of best fit are shown in Table 2. Statistical differences between the biomass components of the seven species were examined using analysis of variance and further post-hoc analysis was performed through Tukey’s Honest Significant Difference (HSD) test to achieve pair-wise comparison between species biomass components.

Table 2

Allometric models selected for comparison
Model Id.	Model name	Model Expression
A1	Allometric1	$y=a{D^b}+\varepsilon$
A2	Allometric2	$y=a{({D^2}H)^b}+\varepsilon$
A3	Allometric3	$y=a{D^b}{H^c}+\varepsilon$
Note: y denotes above ground fresh weight (kg), culm fresh weight (kg)

2.3.1 Model fit statistics and plot analysis to compare and choose the best model

Three popularly used model fit statistics viz. Akaike Information Criteria³⁰, Bayesian Information Criteria³¹, and adjusted R² (Adj.R²) were used to evaluate, compare and select the best allometric equations as per the following formulae:

(i) AIC=-2ln (L)+2p, where L is the likelihood of the model, and p is the number of the parameters of the model and n is the sample size.

(ii) BIC=-2ln(L)+pln (n), where L is the likelihood of the model, and p is the number of the parameters of the model and n is the sample size.

(iii) $Adj.{R^2}=1 - \frac{{RSS/(n - p)}}{{TSS/(n - 1)}}$ , where RSS=Residual sum of square, TSS=Total sum of square, and p is the number of the parameters of the model and n is the sample size.

Model with highest Adj.R² and lowest AIC, lowest BIC value was chosen as the best model³¹. Diagnostic plots of observed values versus fit and residual trends were also used to assess model performance.

2.4 Model validation

Monte Carlo cross-validation method was applied to select, evaluate and compare the models^32–35. The method divide the dataset randomly into two parts, with about 80% for model development and 20% for cross-validation, repeated R times (about 100 times) to obtain stable statistics. Model fitting statistics and cross-validation criteria were calculated for each data series randomly selected and averaged over R (approximately 100) series. To evaluate the predictive reliability of the fitted model, three statistical validation criteria viz., bias (percentage), Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) were used^{27–29, 34–38} as per the following formulae:.

where${y_i}$= Observed value and ${\hat {y}_i}$=Predicated value, R=Number of times cross-validation occured. A model that has the lowest statistical error value in terms of bias, RMSE and MAPE was preferred as the best model.

2.5 Assessment of the relationship between height and diameter of bamboo

Allometric equation of the form H=𝑎𝐷^𝑏+e, was used to develop relationship between height (H) in meter with diameter at breast height(D) in cm, where ‘a’ is the normalization (scale) constant, ‘b’ is the shape parameter and e is error term follow normal distributionwith zero mean and non-constant variance $\sigma _{{Hi}}^{2}$ i.e.,${e_i}\sim iid\,N(0,\sigma _{{Hi}}^{2})$. The model development was done using the weighted maximum likelihood nonlinear fixed effects modelling methodand validation was done using Monte Carlo cross-validation method.

3.1 Biometric parameters of the seven bamboo species

Analysis of variance revealed that biometric parameters of the seven bamboo species viz., culm diameter, culm height, culm fresh weight, foliage fresh weight and fresh above ground biomass weight varied significantly (p<0.05). The post-hoc analysis through Tukey’s honest significant difference (HSD) test, revealed that D. hamiltonii has highest average culm diameter (5.99 cm), culm height (11.91m), culm fresh weight (16.92kg), foliage fresh weight (1.53kg) and fresh weight (20.39 kg). Average branch weight of D. hamiltonii though observed as highest (1.93kg) but not significantly differed from B. balcooa, B. bambos, B. nutans and B. vulgaris (Table 3). Further, Tukey’s HSD test, revealed that ratio of dry weight to fresh weight of different above ground biomass components viz., culm, branch, foliage and total above ground biomass (AGB) significantly differed for seven bamboo species. The highest dry to fresh weight ratio for culm (0.63), branch (0.62) and AGB (0.61) was observed in B. nutans. Whereas highest (0.53) dry to fresh weight ratio for foliage was found in D. strictus (Table 4). Biomass distribution for the different components of the seven species revealed that the culm component shares the highest proportion in percentage (69.56-78.71%), followed by branch (12.04-17.79%) and the foliage (3.50-16.94%). The allocation of branch biomass was highest (17.79%) in B. bambos. In D. stocksii highest allocation of culm (78.71%) and leaf biomass (16.94%) were found among the seven bamboo species (Figure 2).

Table 3

Summary statistics for different above ground biometric parameters of seven bamboo species grown in India.
Species (sample size)	Summary Statistics	Culm diameter (cm)	Culm height (m)	Culm weight (kg)	Branch weight (kg)	Foliage weight (kg)	Above ground weight (kg)
B. balcooa (97)	mean± SE	5.18±0.14^bc	8.85±0.33^c	9.62±0.68^b	1.85±0.12^a	1.29±0.09^bc	12.76±0.84^b
	Min.	2.55	3.30	0.70	0.10	0.05	1.03
	Max.	8.6	17.2	26.00	4.86	2.99	32.88
B. bambos (54)	mean± SE	5.37±0.30^bc	8.54±0.55^c	10.51±1.40^b	1.85±0.15^a	0.51±0.08^d	12.87±1.65^b
	Min.	2.17	0.90	1.15	0.04	0.05	1.46
	Max.	10.51	17.7	41.5	4.56	2.23	48.03
B. nutans (69)	mean± SE	4.74±0.16^cd	10.43±0.41^b	9.84±0.88^b	2.05±0.28^a	1.12±0.06^c	13.00±1.14^b
	Min.	2.23	3.80	0.56	0.05	0.12	0.86
	Max.	8.60	17.30	32.94	12.40	2.10	45.15
B. vulgaris (62)	mean± SE	5.56±0.18^ab	9.39±0.46^bc	12.41±0.95^b	1.80±0.17^a	1.51±0.11^ab	15.71±1.16^b
	Min.	2.77	2.7	0.9	0.08	0.04	1.15
	Max.	8.60	18.80	31.58	5.895	3.545	38.34
D. hamiltonii (121)	mean± SE	5.99±0.19^a	11.91±0.43^a	16.92±1.17^a	1.93±0.07^a	1.53±0.07^a	20.39±1.29^a
	Min.	1.91	2.80	0.49	0.29	0.10	1.05
	Max.	9.87	22.78	45.20	3.90	3.69	51.27
D. stocksii (83)	mean± SE	4.24±0.10^de	8.61±0.28^c	4.97±0.24^c	0.95±0.06^b	1.20±0.06^c	7.12±0.34^c
	Min.	1.91	1.60	0.72	0.10	0.05	1.20
	Max.	5.73	13.30	10.15	2.25	3.20	14.60
D. strictus (176)	mean± SE	3.78±0.11^e	6.24±0.21^d	3.96±0.33^c	0.84±0.08^b	0.59±0.03^d	5.38±0.43^c
	Min.	1.30	1.50	0.06	0.03	0.03	0.17
	Max.	8.60	13.5	28.27	6.73	1.95	34.17
Note: SE: Standard Error of mean, Min.: Minimum value and Max.: Maximum value; mean± SE value within biometric parameter, different superscript letters indicate significant differences (p<0.05) between the species.

Table 4

Description about ratio of dry to fresh weight of different above ground biomass components for seven bamboo species.
Species	Ratio=W_{sample dry weight}/ W_{sample wet weight}
Species	Culm	Branch	Foliage	AGB
B. balcooa	0.59^b	0.60^b	0.48^d	0.58^b
B. bambos	0.52^e	0.49^e	0.51^c	0.51^f
B. nutans	0.63^a	0.62^a	0.46^e	0.61^a
B. vulgaris	0.51^f	0.57^c	0.52^b	0.52^e
D. hamiltonii	0.47^g	0.49^e	0.46^e	0.47^g
D. stocksii	0.56^c	0.45^f	0.45^f	0.53^d
D. strictus	0.53^d	0.53^d	0.53^a	0.53^c
Note: Dry weight (kg) = Ratio × Fresh weight (kg). Within biometric parameter, different superscript letters indicate significant differences (p<0.05) between the species.

3.2 Development and validation of allometric models

3.2.1Above ground biomass prediction

Three allometric equations [allometric form (1) in A1 and A2; allometric form (2) in A3] were developed for fresh above ground biomass (AGB) and fresh weight for the seven bamboo species using the data collected from harvested culms from >3 years old bamboo plantation. Further, allometric model A1 were again developed for bamboo height prediction (H) using diameter at breast height (H). Results of allometric models development revealed ranged value of adjusted-R² (Adj.R²) (0.82-0.97), AIC (190.24-562.79) and BIC (205.57-580.74), suggested differential fitting accuracy, whereas high Adj.R² and low AIC and BIC value for the three model, evidenced appropriateness of using allometric models (Table 5).

Table 5

Parameter estimates of allometric models fitted on 80% dataset of seven bamboo species for above ground fresh weight prediction.
Species	Model Id.	Weight variable	Parameter [Estimate± std. error]			Adj.R²	AIC	BIC
Species	Model Id.	Weight variable	a	b	c	Adj.R²	AIC	BIC
B. balcooa	A1	1/D^2.41	0.10±0.02	2.87±0.11	-	0.85	375.02	391.42
	A2	1/D^0.40	0.15±0.03	0.79±0.04	-	0.83	387.65	404.05
	A3	1/D^2.18	0.10±0.02	2.45±0.19	0.31±0.14	0.87	372.10	390.88
B. bambos	A1	1/D^1.10	0.35±0.06	2.04±0.09	-	0.94	209.02	221.35
	A2	1/D^0.29	0.24±0.06	0.69±0.04	-	0.92	225.08	237.40
	A3	1/D^1.16	0.40±0.06	2.34±0.24	-0.29±0.20	0.94	215.00	234.37
B. nutans	A1	1/D^2.02	0.21±0.04	2.56±0.11	-	0.82	269.03	283.08
	A2	1/D^0.34	0.15±0.04	0.80±0.05	-	0.85	306.83	320.89
	A3	1/D^1.99	0.16±0.03	2.34±0.17	0.27±0.14	0.85	273.51	295.59
D. hamiltonii	A1	1/D^1.58	0.29±0.05	2.29±0.08	-	0.87	562.79	580.74
	A2	1/D^0.58	0.16±0.03	0.77±0.03	-	0.88	552.35	570.30
	A3	1/D^1.54	0.20±0.03	1.88±0.13	0.43±0.12	0.89	550.55	564.76
D. stocksii	A1	1/D^1.48	0.37±0.05	2.01±0.9	-	0.86	208.4	223.72
	A2	1/D^0.23	0.30±0.04	0.62±0.02	-	0.91	190.24	205.57
	A3	1/D^0.78	0.29±0.04	1.31±0.16	0.58±0.11	0.90	198.21	222.30
D .strictus	A1	1/D^1.78	0.15±0.01	2.48±0.04	-	0.96	357.64	378.24
	A2	1/D^0.48	0.10±0.01	0.82±0.01	-	0.97	347.55	368.14
	A3	1/D^1.75	0.11±0.01	1.92±0.1	0.57±0.09	0.97	335.17	367.52
B. vulgaris	A1	1/D^0.95	0.30±0.08	2.23±0.15	-	0.84	275.31	288.56
	A2	1/D^0.32	0.27±0.07	0.70±0.04	-	0.87	264.20	277.45
	A3	1/D^1.20	0.26±0.06	1.50±0.21	0.63±0.14	0.87	268.31	289.12

Monte Carlo cross-validation method unfolded prediction accuracy of the fitted allometric models with the extended value of ABias (-14.62 to 8.90%), ARMSE (0.98 to 5.12) and AMAPE (11.28 to 30.29%), revealed differential prediction accuracy of the fitted model, whereas low error valuesfor the three model, indicating their prediction capabilities (Table 6).

Table 6

Validation of allometric models of above ground fresh weight prediction on 20% dataset of seven bamboo species.
Species	Model Id.	ABias (%)	ARMSE	AMAPE (%)
B. balcooa	A1	-7.13	3.09	21.67
	A2	-11.52	2.87	24.85
	A3	-7.10	2.97	21.22
B. bambos	A1	-2.74	4.02	25.88
	A2	2.77	4.17	27.95
	A3	-14.62	5.12	30.29
B. nutans	A1	0.50	2.14	10.83
	A2	-8.87	2.22	13.96
	A3	-1.64	2.02	11.28
D. hamiltonii	A1	-9.13	3.90	23.93
	A2	-2.57	3.71	19.59
	A3	-1.87	3.24	18.96
D. stocksii	A1	-8.11	1.62	24.44
	A2	-4.08	1.31	17.66
	A3	-4.98	1.33	18.68
D. strictus	A1	-3.98	0.98	24.22
	A2	-0.65	1.12	27.28
	A3	-0.47	1.03	23.45
B. vulgaris	A1	5.68	4.94	30.80
	A2	8.46	3.91	22.50
	A3	8.90	4.03	23.05

Allometric model A1 unveiled highest adj.R² (0.94) for B. bambos, lowest AIC (209.02-269.03) and BIC (221.35-283.08) for B. bambos and B. nutans. Further, it unveiled lowest prediction error with lowest ABias (-2.74 to 0.50%) ARMSE (2.14 to 4.02) and AMAPE (10.83 to 25.88%) for B. bambos and B. nutans. A2 model revealed lowest prediction error for D. stocksii and B. vulgaris with lowest AMAPE (17.66 to 22.50%) and ARMSE (1.31 to 3.91). Moreover, A2 found lowest ABias (-4.08%) for B. vulgaris. Model A3 has unveiled highest adj.R² (0.87 to 0.97), lowest AIC (335.17-550.55) and BIC (367.52-564.76) for B. balcooa, D. hamiltonii and D. strictus. Further, it achieved lowest prediction error for B. balcooa, D. hamiltonii and D. strictus with lowest ABias (-7.13 to -0.47%) and AMAPE (18.96 to 23.45%) for B. balcooa, D. hamiltonii and lowest ARMSE (2.97 to 23.45) found for B. balcooa and D. hamiltonii. Overall results of above ground biomass modelling evidenced that A1 allometric model was most efficient for B. bambos and B.nutans, whereas A2 was most reliable for D. stocksii and B. vulgaris, further A3 was most suitable for B. balcooa, D. hamiltonii, and D. strictus (Table 5, Table 6). Figure 3 and Figure 4 demonstrates the results of best fitted allometric models for above ground fresh weight prediction. The results show that the weighted best fitted allometric models capture heteroscedasticity well in residuals and produced much lower residuals. Further, residuals found to be random (lack of any pattern) visually which indicate high fitting accuracy.

3.2.2 Culm biomass prediction

Results of allometric models development for fresh culm biomass extended value of Adj.R² (0.80-0.96), AIC (200.39-554.83) and BIC (205.72-578.54) lower than fitted model for fresh above ground biomass, suggested higher consistency of the allometric models (Table 7). Cross-validation results of the fitted allometric models unfolded low prediction error with extended value of ABias (-11.68 to 7.03%), ARMSE (0.79 to 4.70) and AMAPE (11.10 to 30.10%), revealed high prediction accuracy of the the three model (Table 8).

Table 7

Parameter estimates of allometric models of culm fresh weight fitted on 80% dataset of seven bamboo species.
Species	Model Id	Weight variable	Parameter [Estimate± std. error]			Adj.R²	AIC	BIC
Species	Model Id	Weight variable	a	b	c	Adj.R²	AIC	BIC
B. balcooa	A1	1/D^2.91	0.06±0.01	3.00±0.10	-	0.81	324.18	340.59
	A2	1/D^0.61	0.07±0.13	0.87±0.03	-	0.89	311.20	337.61
	A3	1/D^2.67	0.05±0.01	2.33±0.17	0.54±0.12	0.85	315.14	340.92
B. bambos	A1	1/D^0.74	0.16±0.03	2.33±0.10	-	0.95	200.39	212.72
	A2	1/D^0.22	0.10±0.03	0.79±0.04	-	0.93	216.08	228.41
	A3	1/D^1.04	0.25±0.05	2.61±0.25	-0.39±0.22	0.94	206.16	225.53
B. nutans	A1	1/D^2.28	0.11±0.02	2.75±0.13	-	0.80	297.12	267.17
	A2	1/D^0.41	0.10±0.03	0.83±0.06	-	0.81	291.67	205.72
	A3	1/D^1.68	0.09±0.02	2.11±0.165	0.49±0.15	0.80	550.33	578.54
D. hamiltonii	A1	1/D^1.77	0.13±0.03	2.59±0.11	-	0.84	554.83	572.78
	A2	1/D^0.61	0.07±0.01	0.87±0.03	-	0.88	545.05	563.01
	A3	1/D^1.68	0.09±0.02	2.12±0.166	0.49±0.14	0.87	550.33	578.54
D. stocksii	A1	1/D^1.35	0.20±0.06	2.31±0.18	-	0.81	268.19	281.43
	A2	1/D^0.38	0.18±0.05	0.723±0.04	-	0.84	253.26	265.50
	A3	1/D^1.39	0.175±0.05	1.37±0.24	0.80±0.165	0.84	258.48	279.28
D. strictus	A1	1/D^1.39	0.087±0.01	2.63±0.05	-	0.95	287.58	308.17
	A2	1/D^0.43	0.06±0.01	0.86±0.02	-	0.96	309.38	329.97
	A3	1/D^1.82	0.07±0.01	2.17±0.11	0.46±0.11	0.96	283.21	315.57
B. vulgaris	A1	1/D^1.35	0.20±0.06	2.31±0.18	-	0.81	268.18	281.43
	A2	1/D^0.38	0.18±0.05	0.72±0.04	-	0.84	253.26	266.50
	A3	1/D^1.38	0.18±0.05	1.37±0.24	0.798±0.16	0.83	258.47	279.28

Table 8

Validation of allometric models of culm fresh weight on 20% dataset of seven bamboo species.
Species	Model Id	ABias (%)	ARMSE	AMAPE (%)
B. balcooa	A1	-9.71	2.96	25.23
	A2	-7.52	2.56	20.38
	A3	-8.69	2.71	21.98
B. bambos	A1	-4.99	3.16	23.14
	A2	7.03	3.56	24.50
	A3	-11.68	4.70	29.30
B. nutans	A1	2.27	1.76	12.91
	A2	-2.05	1.71	11.10
	A3	-3.03	1.79	18.86
D. hamiltonii	A1	-7.08	4.16	26.07
	A2	-8.24	3.93	23.98
	A3	-11.28	3.57	24.56
D. stocksii	A1	7.01	4.70	27.66
	A2	6.11	3.87	21.46
	A3	6.92	3.89	22.44
D. strictus	A1	-5.32	0.86	28.15
	A2	-3.06	0.81	30.10
	A3	-2.62	0.79	27.21
B. vulgaris	A1	7.01	4.70	29.66
	A2	6.11	3.77	22.46
	A3	6.92	3.83	25.44

ModelA1 found to be outperformer for fresh culm biomass prediction of B. bambos as it has highest fitting accuracy with highest adj.R² (0.95), lowest AIC(200.39) and BIC (212.72) and lowest prediction error with ABias (-4.99%) ARMSE (3.16) and AMAPE (23.14%). A2 model was found to be outperformer with maximum fitting and prediction accuracy over A1 and A3 model for five bamboo species viz., B. balcooa, B. nutans, D. hamiltonii, D. stocksii and B. vulgaris. For the five mambo species, A2 model shown maximum fitting accuracy with highest Adj.R² (0.80-0.89), lowest AIC (253.26-545.05) and BIC(205.72-563.01). Further, highest prediction accuracy of A2 by lowest ABias (-8.24 to 6.11%), ARMSE (1.71 to 3.93) and AMAPE (11.10-23.98%).Whereas A3 was found to be most suitable for D. strictus, as it has highest fitting accuracy [highestAdj.R² (0.96), lowest AIC (283.21) and BIC (315.57)] and lowest prediction error [ABias (-2.62%) ARMSE (0.79) and AMAPE (27.21%)].

3.3 Generate synthetic values as a proxy height using H-D model

The results of fitted general power form allometric model for H-D modelling in the seven bamboo species revealed that the Adj.R² value of the fitted model for the seven bamboo species was found to be >0.7 except the species B. nutans with Adj.R²=0.69 (Table 9). Whereas, highest Adj.R² (0.89) was observed in B. bambos. Lowest AIC (156.04) and BIC (497.83) was observed in B. bambos. While highest AIC (497.83) and BIC (485.78) value was found in D. hamiltonii. Further, evaluation results about prediction accuracy of the fitted models H-D were done and found that bias of the fitted models was extended between -1.57 (in B. vulgaris) and-3.91 (in D. stocksii). The RMSE ranged between 1.16 (in D. strictus) and 2.70 (in D. hamiltonii). Lowest value of MAPE (9.34) was found in B. bambos, whereas highest MAPE (20.52) was observed for D. hamiltonii (Table 10).

Table 9

Parameter estimates of H-D allometric model fitted on 80% dataset of seven bamboo species.
Species	Weight variable	Parameter [Estimate± std. error]		Adj.R²	AIC	BIC
Species	Weight variable	a	b	Adj.R²	AIC	BIC
B. balcooa	1/D^0.91	1.28±0.19	1.17±0.09	0.70	318.85	335.26
B. bambos	1/D^0.45	1.29±0.15	1.11±0.06	0.89	156.04	168.37
B. nutans	1/D^1.07	2.58±0.37	0.89±0.09	0.69	254	260.74
D. hamiltonii	1/D^0.38	2.30±0.30	0.92±0.06	0.70	497.83	485.78
D. stocksii	1/D^0.41	1.55±0.21	1.18±0.09	0.76	232.66	247.99
D. strictus	1/D^0.13	1.73±0.10	0.96±0.03	0.84	438.77	459.36
B. vulgaris	1/D^1.057	1.09±0.22	1.24±0.11	0.71	220.15	224.39

Table 10

Validation of H-D allometric model on 20% dataset of seven bamboo species.
Species	Bias (%)	RMSE	MAPE (%)
B. balcooa	-3.33	1.61	13.73
B. bambos	-2.26	1.25	9.34
B. nutans	2.14	1.47	12.80
D. hamiltonii	-3.65	2.70	20.52
D. stocksii	-3.91	1.58	12.61
D. strictus	-1.72	1.16	16.66
B. vulgaris	-1.57	1.48	10.67

Biometric parameters of the seven bamboo species

In bamboo culm has surprising biomass productivity due to its habit of producing sprouting from horizontal rhizome systems annually that allows annual harvesting without exposing the soil surface. Bamboo plays an important role in global carbon cycle, by sequestering atmospheric carbon through its biomass accumulation process^39–42. In seven bamboo species studied, among three major biomass component (culm, branch and foliage), culm is the most important with highest share (69.56 to 78.71%) to above ground biomass which is more than double to combine biomass share of branch and foliage. Moreover, bamboo culm has high commercial value due its multi-purpose utility⁴³. Distribution of percentage (%) share of culm, branch and foliage to above ground fresh weight varies significantly between different bamboo species (Figure 2).

Analysis of variance (ANOVA) analysis revealed significant (p<0.05) differential productivity of above ground biometric components (culm diameter, culm height, culm fresh weight, foliage fresh weight and above ground fresh weight) for the seven bamboo species. Tukey’s HSD post-hoc test, revealed that on an average D. hamiltonii has highest biometric productivity for culm diameter D (5.99 cm), culm height H (11.91m), culm fresh weight (16.92kg), foliage fresh weight (1.53kg) and above ground fresh weight (20.39kg). Forbranch fresh weight, though D. hamiltonii was found to be have the highest productivity but not significantly higher than B. balcooa, B. bambos, B. nutans and B. vulgaris (Table 3). Differential growth rate of the seven bamboo species, evidenced need of species specific relationship rather general relationship study for establishing model for biomass prediction.

Ratio of dry to fresh weight of seven bamboo species were estimated for culm, branch, foliage and above ground biomass to convert fresh weight to dry weight using the formula: dry weight (kg) = Ratio × fresh weight (kg). The ratio in different biomass components within species found significantly different. The highest dry to fresh weight ratio was found for culm (0.63), branch (0.62) and above ground biomass (0.61) in B. nutans, where as, in foliage highest ratio (0.53) was achieved for in D. strictus. The relationship equation between dry weight and fresh weight indicated that variability of fresh weigh directly proportional to dry weight (biomass) (Table 4).

Development and validation of allometric models

From the analysis of above ground and culm biomass, it was found that biomass production in the seven bamboo species has a high positive correlation with diameter at breast height (D) and culm height (H) but did not have significant correlation with age. This was similar to findings point out by Yen et al.⁴² for bamboo species S. dullooa, P. polymorphum and M. baccifera. So, D, combination of D and H was used for prediction of biomass using combine data of more than three years oldbamboo plantation. Many authors already observed D and D²H as good predictor variable for bamboo allometric modelling ^{27–29, 34–35}. The results revealed that D was a valid independent variable but using volume (D²H) as compound independent variable or incorporation of H as separate independent variable, further improved prediction accuracy for both above ground biomass and culm biomass except bamboo species B. bambos and B. nutans for fresh above ground biomass and B. bambos for fresh culm weight prediction (Table 5-8). Here, use of H as additional independent variable did not improve prediction accuracy but increase prediction error may be due to measurement error in H data or incorporation of H may have masking effect on D during model fitting. A1 with D as independent variable alone, performed very well and usually very close to A2 and A3 model. Further biomass equation using D as independent variable has practical advantage of easy measurement^45–46. A1 model was also reported as reliable model for biomass prediction by Yen et al.²⁵, Kaushal et al.²¹.

General power form allometric equation A2 with volume (D²H) as an independent variable, found to be most reliable for above ground fresh weight prediction in bamboo species D. stocksii and B. vulgaris, whereas for fresh culm weight prediction A2 to be outperformer forfive bamboo species viz., B. balcooa, B. nutans, D. hamiltonii, D. stocksii and B. vulgaris. This finding was consistent with allometric models established for biomass prediction in thin-walled bamboo species by Singnar et al.⁴⁷ and general findings of Chave et al.³⁷ in woody species for above ground biomass prediction using bole volume (D²H).

Moreover, three parameter allometric equation A3 with D and H as independent variables, found to be most reliable in bamboo species B. balcooa, D. hamiltonii and D. strictus for above ground fresh weight prediction, whereas for fresh culm weight prediction A3was most appropriate model in D. strictus. For A3 use of D and H as independent variable provided more flexibility to establish relationship with biomass response.

The fitting and prediction accuracy of best fitted allometric models for fresh above weight prediction were visually investigated through line plots. The residual plot of prediction error values evidenced that allometric models using weighted maximum likelihood nonlinear fixed effects modelling method capture heteroscedastic relationship between the biomass response and the predictor variables well and produced much lower residuals. Further, residuals found to be random (lack of any pattern) visually which indicate high fitting accuracy (Fig. 3-4).

Generate synthetic values as a proxy height using H-D model

It was very often that best fitted allometric models were not possible to apply due to missing observation of H⁴⁸. To get H value, synthetic H values were generated as proxy H using H-D allometric model. H-D allometric equation developed for the seven bamboo species revelaed high fitting accuracy with high Adj.R² (>0.7) except B. nutans (0.69). Highest fitting accuracy was observed in B. bambos, whereas lowest value observedin D. hamiltoni i(Table 9-10). Similar, result was also pointed out by Kempes et al.⁹ and Sileshi¹⁰. H-D relationship was developed using >3 year old bamboo plantation where H reached to plateau i.e., there is no growth in diameter and height⁴⁹. As per our knowledge, for the first time this study has established allometric modelling for quantifying H-D relationship between the seven bamboo species viz., B. bambos, B. nutans, D. stocksii, B. vulgaris, B. balcooa, D. hamiltonii, and D. strictus.

In this study species-specific two-parameter allometric equations with simple as well as compound regressor variable and three parameter allometric equations were developed for above ground biomass. Further, species specific height-diameter models were also developed to predict bamboo height, which can be used as a proxy of height variable and used for allometric equation without measuring height of bamboo. Since the allometric equations were developed using rigorous criteria, we can also conclude that the developed biomass estimation equations provides better biomass predication for culm as well as above ground biomass. The models can expected to be increase accuracy in estimation of biomass and carbon sequestration in bamboo based ecosystems of India under managed natural stands or plantation grown under similar condition. Moreover, considering the wide multipurpose use of the bamboo species, the developed models may give provide useful information about culm biomass and above ground biomass to forestry professionals, bamboo farmers, and other stakeholders.

Competing interests

The authors declare that they have no competing interests.

Declarations

The planting material was obtained from different Government nurseries from different part of the country and for which all the permissions were obtained. All the collection complies with relevant institutional, national, and international guidelines and legislation.

Funding

This research was funded by National Bamboo Mission, New Delhi, State Forest Department, Uttarakhand, India and International Bamboo and Rattan Organisation (INBAR) through its grants from IFAD and Dutch Government and from the CGIAR Research Program on Forests, Trees and Agroforestry (FTA).

Acknowledgements

The financial help received from both the funding agency is duly acknowledged. We also thank ICAR and Director ICAR-IISWC for providing the permission to conduct the experiment. The technical assistance provided by Mr. UVS Chauhan and Mr. Ravish is gratefully acknowledged.

Author contributions

R.K., S.I., S.T., J.D. conceptualized the research and design the experiments; R.K. contributed to experimental materials; J.M.S.T., S.T., executed the experimental data collection, R.K., S.I. conducted data analysis and interpretation; S.I., R.K., M.M. prepared the manuscript; T.L.T. and J.D. secured funding and edited the manuscript. All authors reviewed the manuscript.

Vorontsova, M.S., Clark, L.G., Dransfield, J., Govaerts, R.H.A. & Baker, W.J. World Checklist of Bamboos and Rattans. Science Press, Beijing, 102 (2017).
https://www.inbar.int/global-programmes/ (Accessed November 18 2021).
Lobovikov, M., Paudel, S., Ball, L., Piazza, M., Guardia, M., Ren, H., Russo, L., Wu, J. World bamboo resources: a thematic study prepared in the framework of the global forest resources assessment 2005. Food & Agriculture Org., (2007).
https://www.fao.org/3/ca9825en/ca9825en.pdf
ISFR (2019). http://www.indiaenvironmentportal.org.in/files/file/isfr-fsi-vol1.pdf (Accessed November 18 2021).
Salam, K. Connecting the poor: Bamboo, Problems and prospect. South Asia Bamboo Foundation (SABF) (2013) retrieved 17 December 2013 from jeevika.org/bamboo/2g-article-fornbda.docx.
http://pib.nic.in/newsite/PrintRelease.aspx?relid=180805 (Accessed April 25, 2018).
IPCC (2003). shorturl.at/bguxF (Accessed November 18 2021).
Kempes, C.P., West, G.B., Crowell, K. & Girvan, M. Predicting maximum tree heights and other traits from allometric scaling and resource limitations. PLoS ONE, 6(6), e20551 (2011).
Sileshi, G.W. A critical review of forest biomass estimation models, common mistakes and corrective measures. Forest Ecology and Management, 329, 237–254 (2014).
Verma, A., Kaushal, R., Alam, N.M., Mehta, H., Chaturvedi, O.P., Mandal, D., Kaushal, R., Subbulakshmi, V., Tomar, J.M.S., Alam, N.M., Jayaparkash, J., Mehta, H., & Chaturvedi, O.P. Predictive models for biomass and carbon stock estimation in male bamboo (Dendrocalamus strictus L.) in Doon valley, India. Acta Ecol. Sin.36, 469–476 (2016).
Gao, X., Li, Z., Yu, H., Jiang, Z., Wang, C., Zhang, Y., Qi, L. & Shi, L. Modeling of the height–diameter relationship using an allometric equation model: a case study of stands of Phyllostachys edulis. J. For. Res.27, 339–347 (2016).
Huy, B. and Long, T.T. A manual for bamboo forest biomass and carbon assessment, INBAR technical report (2019). https://www.inbar.int/resources/inbar_publications/a-manual-for-bamboo-forest-biomass-and-carbon-assessment/. Accessed November 18 2021.
Brahma, B., Nath, A.J., Deb, C., Sileshi, G.W., Sahoo, U.K., & Das, A.K. A critical review of forest biomass estimation equations in India Trees, Forests and People, 5, 100098 (2021). https://doi.org/10.1016/j.tfp.2021.100098.
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, Forest Ecology and Management, 260, 339–344 (2010). doi:10.1016/j.foreco.2010.04.021.
FAO. Guidelines on Destructive Measurement for Forest Biomass Estimation (FAO, Rome, 2012).
Yen, T.M. Comparing aboveground structure and aboveground carbon storage of an age series of moso bamboo forests subjected to different management strategies. J. For. Res.20, 1–8 (2015).
Yuen, J.Q., Fung, T. & Ziegler, A.D. Carbon stocks in bamboo ecosystem worldwide: estimates and uncertainties, Forest Ecology and Management, 393, 113-138 (2017).
Nath, A.J., Das, G., Das, A.K. Above ground standing biomass and carbon storage in village bamboos in North East India, Biomass and bioenergy, 33, 1188–11 96 (2009).
Rawat, R.S., Arora, G., Rawat, V.R.S., Borah, H.R., Singson, M.Z., Chandra, G., Nautiyal, R. & Rawat, J. Estimation of Biomass and Carbon Stock of Bamboo Species through Development of Allometric Equations. Indian Council of Forestry Research and Education, Dehradun, INDIA (2018).
Tripathi, S.K., Singh, K.P. Productivity and nutrient cycling in recently harvested and mature bamboo savannas in the dry tropics. Journal of Applied Ecology, 31, 109–24 (1994).
Kaushal, R., Subbulakshmi, V., Tomar, J.M.S., Alam, N.M., Jayaparkash, J., Mehta, H. & Chaturvedi, O.P. Predictive models for biomass and carbon stock estimation in male bamboo (Dendrocalamus strictus L.) in Doon valley, India. Acta Ecol. Sin.36, 469–476 (2016).
Das, D. & Chaturvedi, O.P. Bambusa bambos (L.) Voss plantation in eastern India: I. Culm recruitment, dry matter dynamics and carbon flux, Journal of Bamboo and Rattan,5(1&2), 47-59 (2006).
Shanmughavel, P. & Francis, K. Above ground biomass production and nutrient distribution in growing bamboo (Bambusa bambos (L.) Voss). Biomass and Bioenergy, 10 (5/6), 383–91(1996).
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, Forest Ecology and Management, 260, 339–344(2010). doi:10.1016/j.foreco.2010.04.021.
FAO. Guidelines on Destructive Measurement for Forest Biomass Estimation (FAO, Rome, 2012).
Huy, B., Kralicek, K., Poudel, K.P., Phuong, V.T., Khoa, P.V., Hung, N.D. & Temesgen, H. Allometric equations for estimating tree aboveground biomass in evergreen broadleaf forests of Vietnam, Forest Ecology and Management, 382, 193-205 (2016a).
Huy, B., Poudel, K.P., Kralicek, K., Hung, N.D., Khoa, P.V., Phuong, V.T. & Temesgen, H. Allometric equations for estimating tree aboveground biomass in tropical dipterocarp forests of Vietnam’, Forests, 7(180), 1-19 (2016b).
Huy, B., Poudel, K.P. & Temesgen, H. Aboveground biomass equations for evergreen broadleaf forests in South Central coastal ecoregion of Vietnam: selection of eco-regional or pantropical models’, Forest Ecology and Management, 376, 276-283 (2016c).
Akaike, H. Information theory as an extension of the maximum likelihood principle’ in Petrov, B.N. & Csaki, F.E. (eds.) Proceedings of the 2nd international symposium on information theory. Budapest: Akademiai Kiado, 267-281 (1973).
Schwarz, G. E. Estimating the dimension of a model, Annals of statistics, 6(2), 461-464 (1978)
Huy, B. Methodology for developing and cross-validating allometric equations for estimating forest tree biomass. HCM City: Science & Technology, 238 (2017a).
Huy, B. Statistical informatics in forestry. HCM City: Science & Technology, 282 (2017b).
Huy, B., Tinh, N.T., Poudel, K.P., Frank, B.M. & Temesgen, H. Taxon-specific modeling systems for improving reliability of tree aboveground biomass and its components estimates in tropical dry dipterocarp forests, Forest Ecology and Management, 437, 156-174 (2019a).
Huy, B., Thanh, G.T., Poudel, K.P. & Temesgen, H. Individual Plant Allometric Equations for Estimating Aboveground Biomass and Its Components for a Common Bamboo Species (Bambusa procera A. Chev. and A. Camus) in Tropical Forests, Forests, 10, 1-17 (2019b).
Mayer, D.G. & Butler, D.G. Statistical validation, Ecological Modelling, 68, 21-32 (1993).
Chave, J., Andalo, C., Brown, S., Cairns, M.A., Chambers, J.Q., Eamus, D., Folster, H., Fromard, F., Higuchi, N., Kira, T., Lescure, J.P., Nelson, B.W., Ogawa, H., Puig, H., Rier, B. & Yamakura, T. Tree allometry and improved estimation of carbon stocks and balance in tropical forests, Oecologia, 145, 87-99 (2005).
Basuki, T.M., van Laake, P.E., Skidmore, A.K. & Hussin, Y.A. Allometric equations for estimating the above-ground biomass in the tropical lowland Dipterocarp forests’, Forest Ecology and Management, 257, 1684-1694 (2009).
Kaushal, R., Singh, I., Thapliyal, S.D., Gupta, A.K., Mandal, D., Tomar, J.M.S., Kumar, A., Alam, N.M., Kadam, D., Singh, D.V., Mehta, H., Dogra, P., Ojasvi, P.R., Reza, S., & Durai, J. Rooting behavior and soil properties in different bamboo species of Western Himalayan Foothils, India, Scientific Reports, 10, 4966 (2020).
Kramer, P.J. & Kozlowski, T.T. Physiology of Wood Plants. McGraw Hill, New York, 628–702 (1979).
IPCC, 2008.Availableat http://www.ipcc.ch. AccessedOctober2008.
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. Forest Ecology and Management, 260, 339–344 (2010)
Inoue A., Sakamoto, S., Suga, H., Kitazato, H. & Sakuta, K. Construction of One-way volume table for the three major useful bamboos in Japan, Journal of Forestry Research, 18, 323-334 (2013).
Kralicek, K., Huy, B., Poudel, K.P., Temesgen, H. & Salas, C. Simultaneous estimation of above- and below-ground biomass in tropical forests of Vietnam, Forest Ecology and Management, 390, 147-156 (2017).
Montes N., Gauquelin, W., Badri, V., Bertaudiere, E.H. & Zaoui, A. A non-destructive method for estimating above-ground forest biomass in threatended woodlands, Forest Ecology and Management, 130, 37-46 (2000).
Verma, A., Kaushal, R., Alam, N.M., Mehta, H. Chaturvedi, O.P. Mandal, D. Tomar, J. M. S. Rathore, A. C., Singh, C. Predictive models for biomass and carbon stocks estimation in Grewia optiva on degraded lands in western Himalaya, Agroforestry Systems, 88:895–905 (2014). Doi: 10.1007/s10457-014-9734-1.
Singnar, P., Das, M.C., Sileshi, G. W., Brahma, B., Nath, A. J. & Das, A. K. Allometric scaling, biomass accumulation and carbon stocks in different aged stands of thin-walled bamboos Schizostachyum dullooa, Pseudostachyum polymorphum and Melocanna baccifera, Forest Ecology and Management, 395, 81–91 (2017). http://dx.doi.org/10.1016/j.foreco.2017.04.001.
Huang, S., Price, D., Titus, S.J. Development of ecoregion-based height diameter models for white spruce in boreal forests. Forest Ecology and Management, 129, 125–141 (2000).
Yen, T.M. Culm height development, biomass accumulation and carbon storage in an initial growth stage for a fast-growing moso bamboo (Phyllostachy pubescens), Bot. Stud.57, 10 (2016).

No competing interests reported.

An Allometric Model Based Approach For Estimating Biomass In Seven Indian Bamboo Species In Western Himalayan Foothills, India

Status:

Version 1

Abstract

Figures

1. Introduction

2. Materials And Methods

2.1 Study area

2.2 Sampling

2.3. Development of allometric equations for biomass estimation

2.4 Model validation

3. Results

3.1 Biometric parameters of the seven bamboo species

3.2 Development and validation of allometric models

3.2.2 Culm biomass prediction

3.3 Generate synthetic values as a proxy height using H-D model

4. Discussion

5. Conclusions

Declarations

References

Additional Declarations

Status:

Version 1

Model Id.	Model name	Model Expression
A1	Allometric1	\(y=a{D^b}+\varepsilon\)
A2	Allometric2	\(y=a{({D^2}H)^b}+\varepsilon\)
A3	Allometric3	\(y=a{D^b}{H^c}+\varepsilon\)
Note: y denotes above ground fresh weight (kg), culm fresh weight (kg)