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Revista mexicana de ciencias agrícolas

versión impresa ISSN 2007-0934

Rev. Mex. Cienc. Agríc vol.7 no.3 Texcoco abr./may. 2016



Allometric equations for estimating biomass and carbon from the aerial part of Pinus hartwegii in Ixta-Popo National Park, Mexico

Fernando Carrillo Anzures1 

Miguel Acosta Mireles1  § 

Carmen del R. Jiménez Cruz2 

Lucila González Molina1 

Jorge D. Etchevers Barra3 

1 Campo Experimental Valle de México-INIFAP. Carretera Los Reyes-Texcoco, Coatlinchán, Texcoco, km 13.5, Estado de México. C. P. 56250. (;;

2 Universidad Autónoma Chapingo-División de Ciencias Forestales, Carretera México-Texcoco, km 38.5 Chapingo Estado de México, C. P. 56230.

3 Colegio de Postgraduados-Campus Montecillo. Carretera México-Texcoco, km 36.5, Montecillos, Texcoco, Estado de México, C. P. 56230. (


To determine the biomass in trees of Pinus hartwegii and estimate the carbon content air, allometric equations with 29 trees of that species of Izta-Popo National Park, Mexico were calculated. The 57.9% of wet weight of biomass trees was 48.6% and this was carbon. The distribution of biomass in the trees was: 65.3% in the shaft, 23.8% at branches and 10.9% the foliage. The carbon content was distributed similarly: 64.9% in the shaft, 24.2% at 10.9% branches and the foliage. The adjusted model is of the form Y= bXk where the dependent variable (Y) or biomass carbon is expressed in kilograms and the independent variable taken the normal diameter 1.3 m (DN) expressed in centimeters. The parameters "b" and "k" model were obtained by linear regression by the method of least squares; "b" measures the intercept and "k" slope model. The resulting equation for estimating biomass was B = 0.0635DN2.4725 and carbon content: C= 0.0309 DN2.4722, in both the value of R2 was 0.98. It was possible to adjust the allometric equation for estimating biomass and carbon content of Pinus hartwegii with a high coefficient of determination. With the equation obtained was possible to determine that trees of this species concentrate most air bole carbon followed by the branches and finally the foliage.

Keywords: allometry; climate change; pine forest; store carbon


Para determinar la biomasa en árboles de Pinus hartwegii y estimar el contenido de carbono aéreo, se calcularon ecuaciones alométricas con 29 árboles de dicha especie del Parque Nacional Izta-Popo, México. El 57.9% del peso húmedo de los árboles fue biomasa y de esta 48.6% fue carbono. La distribución de la biomasa en los árboles fue: 65.3% en el fuste, 23.8% en las ramas y 10.9% en el follaje. El contenido de carbono se distribuyó de manera similar: 64.9% en el fuste, 24.2% en las ramas y 10.9% en el follaje. El modelo ajustado es de la forma Y= bXk donde la variable dependiente (Y) es biomasa o carbono, expresada en kilogramos y la variable independiente el diámetro normal tomado a 1.3 m de altura (DN) expresado en centímetros. Los parámetros “b” y “k” del modelo fueron obtenidos por regresión lineal por el método de mínimos cuadrados; “b” mide el intercepto y “k” la pendiente del modelo. La ecuación resultante para la estimación de la biomasa fue B= 0.0635D N2.4725 y para el contenido de carbono: C= 0.0309DN2.4722, en ambas el valor de R2 fue de 0.98. Fue posible ajustar la ecuación alométrica para estimar la biomasa y el contenido de carbono de Pinus hartwegii con un alto coeficiente de determinación. Con la ecuación obtenida fue posible determinar que los árboles de esta especie concentran la mayor parte del carbono aéreo en el fuste seguido por las ramas y por último el follaje.

Palabras clave: alometría; almacén de carbón; bosque de pino; cambio climático


Global warming or increase in global temperature, physical phenomenon that has arisen in recent years, is related to the increased concentrations of greenhouse gases among which the principal is CO2, Intergovernmental Panel on Climate Change (IPCC, 2007). In 2005, concentrations of CO2 and CH4 in the atmosphere exceeded considerably the range of natural values of the last 650 000 years (IPCC, 2007), a situation that certainly threatens the climate balance of the planet. Although the concentrations of all greenhouse gases and aerosols in the levels reached in 2000 remained constant at present, one would expect an additional global warming of about 0.1°C in temperature every 10 years.

The Kyoto Protocol includes three mechanisms (articles 6, 12 and 17) designed to increase the cost-effectiveness and mitigate climate change, by creating options for countries listed in annex I to that protocol to reduce emissions, or increase its carbon sinks more cheaply in other countries than their own (Guzman et al., 2004). These mechanisms are: emissions trading (article 17), joint implementation (article 6) and through clean development mechanism (MDL) (article 12).

Rosa et al. (2004) mention that environmental services are defined as "the benefits that people obtain from ecosystems" and according to the assessment ecosystematic millennium, classified provisioning services; regulation of ecosystem processes; cultural and supporting. Among the environmental services provided by forests are contributing to basic cycles (water, carbon and other nutrients); climate stability; carbon sequestration, protection and maintenance of biodiversity; watershed protection for water catchment quality and scenic beauty (Torres and Guevara, 2002).

Forest ecosystems can store significant amounts of CO2; however, under certain circumstances they can become a source of this gas. In recent decades there has been considerable interest in increasing the carbon content by increasing the terrestrial vegetation, preserving the forest cover, reforestation, proper implementation of agroforestry practices and other methods of soil conservation (De Jong et al., 2004).

With respect to carbon storage, the Kyoto protocol granted official recognition to the role of forests as "sinks" in mitigating global climate change by reducing atmospheric concentrations of CO2; it has also tried to promote the potential market for carbon sequestration in forest areas (Bull et al., 2006). However, there is controversy as to this mechanism as there are those who argue that they have not yet perfected reliable mechanisms to monitor and verify catch and release of carbon from forested areas, making it difficult to confirm what is being marketed (Bishop and Landell-Mills, 2003).

To estimate the carbon stored in forest biomass have been developed direct and indirect methods. Direct consist destructive analysis for estimating the green weight and dry of each of the components of the selected trees (Hitchcock and McDonnell, 1979) weight. The latter are based on the use of mathematical models that estimate the weight of the different fractions of the tree from individual variables; however, in order to develop indirect methods it is necessary to have data from direct methods. In indirect methods it has also been estimated biomass by using remote sensing (aerial photographs, satellite images, radar images, etc.).

When you want to know the biomass of trees, a practical response is the use of allometric equations; i.e. by indirect estimates of plant material whose quantity is desired to know prior collection data obtained from direct sampling. These functions, consider the relationship between the total biomass that counts the tree and some of its dimensions are usually the most commonly used: height, normal diameter or sapwood area (Acosta et al., 2002) also they can be considered not only morphological variables, but also physiological or biochemical (Lopez, 1995). Allometric equations are used especially for small-scale projects. When it comes to estimating biomass in large areas (region or country level) is preferable to use methods based on spectrometry, such as REDD or REDD +.

In many parts of the world they have conducted studies to determine the parameters of allometric equations to help calculate the biomass contained in forest species (Gaillard et al., 2002). In Mexico, such studies exist for calculating biomass of conifers, and comparisons have been made regarding the models used (Domínguez et al., 2009; Montes de Oca et al. 2009; Pimienta et al., 2007). Of the variables taken into account, the main ones are normal diameter and height (Vidal et al., 2004; Díaz et al., 2007; Avendaño et al., 2009; Carrillo et al., 2014). In these cases the sample size or number of measured trees has varied.

Therefore, in the present work objectives were to determine the parameters of two allometric equations for calculating biomass and carbon content of the air portion of Pinus hartwegii, based on the normal diameter by sampling destructive type selected trees in the Izta-Popo National Park covering the State of Mexico and the states of Puebla and Morelos.

Materials and methods

Study area

Sampling was done within the Izta-Popo National Park in the area called "Paso de Cortes", 24 km southeast of the town of Amecameca, State of Mexico (19° 16' 25" north latitude, 98° 34' 54" west longitude). The park is located in the central part of the transverse volcanic axis of Mexico. The Popocatepetl and Iztaccihuatl volcanoes are the highest mountains of the Sierra Nevada. The prevailing climate is cold high mountain humid, with annual average temperature of 5 to 12 °C, the coldest month from 3 to 8 °C and an average annual rainfall of 928 mm. The andosols soils are derived from volcanic ash (Garcia, 1988).

Determination of biomass

The methodology used was similar to that applied by Avendaño et al. (2009), Carrillo et al. (2014), Diaz et al. (2007), and to estimate biomass and carbon in different species of trees. A representative sample of 29 healthy trees of Pinus hartwegii was selected, the trees had different normal diameter (1.3 m. Height) (DN) ranging from 3.3 to 57.2 cm. The number of trees sampled by diameter class was not uniform due to the restrictions of the National Park as only few trees downing larger and most of them were small diameter were allowed. The average age of the stand is 86 years, with a density of 200 trees ha and an average height woodland of 21.7 m.

Before the demolition, each tree was measured normal diameter (DN) with diameter tape and once knocked down was measured total height with a tape measure and height of the felling cut (stump height). The trees were separated into branches, foliage and trunk, the latter was split into logs, logs the first 3 m long and 1.25 m the past. Before cutting the logs, the base of each slice of about 5 cm thick was obtained. The fresh weight of each log was obtained in the same place where he was shot down every tree with a weighing capacity of 200 kg and 1 kg precision. For those logs exceeding 200 kg and for the stump, its wet weight was obtained from the linear equation generated by the volume- weight ratio of logs whose weight itself could be obtained directly in the field. Huber's formula modified (Romahn et al., 1987) and the stump truncated neiloide formula used for calculating volume of logs. The slices obtained from logs, samples of branches and foliage samples were weighed wet field, with a weighing capacity of 15 kg and 10 g precision. The slices, branches and foliage, were carefully labeled for identification in the laboratory.

The branches were placed in bags and heavy sectional shape with the scale of 200 kg capacity, the wet weight of the branches corresponded to the sum of the weight of the sections. The same procedure was carried out for foliage. Of total branches and leaves they were obtained two to three samples per tree about 1 to 3 kg for large trees and small trees.

Once heavy samples were transported to the Valley of Mexico Experimental Station of the National Institute of Forestry, Agriculture and Livestock (INIFAP), and placed in a greenhouse to reduce humidity. Because the gases does not result in a total drying subsamples they were taken some samples to carry them dry weight; subsamples of slices and branches were dried in an oven at 103°C for 72 h and foliage at 60°C for 48 h to constant weight with this information the dry weight of the material being weighed field was calculated log, branches and leaves, or biomass thus each component was obtained. The wet/dry weight of the first slice weight ratio was also used to calculate the biomass of stump and by adding biomass of each log and stump, the total biomass of the bole of each tree was obtained. The same was done for the branches and foliage and determine the biomass of each tree crown.

A potential model (Ter-Mikaelian and Korzukhin, 1997) was used to estimate the biomass according to the normal diameter, the parameters were obtained using least squares. The general representation of the model is shown in Equation 1.


Where:Y= biomass or carbon (kg); X= normal diameter; DN (cm); b and k= model parameters.

The model [1] can be linearized to facilitate regression analysis: Little and Jackson (1976) recommend logarithmic transformations do so by adopting the form:


Where: Y, X, b and k have the same meaning as in equation 1; ln (Y), ln (b) and ln (X) are natural logarithms of Y; b and X, respectively. In fact, to identify the effectiveness of the model used, first linearized and then the residual dispersion were graphed.

Determination of carbon

Of the 29 trees selected for estimating biomass 13 they were chosen to determine percent carbon of each of its components (stem, branches and leaves). This selection was made equally within the range of diameters became available. To determine the carbon content of the samples of sliced, branches and leaves was obtained a subsample of about 50 g, respectively, with the features mentioned by Acosta et al. (2002). The subsamples were ground and dried for two hours at 60°C and then carbon content was determined by dry combustion method using the Total Organic Carbon Analyzer Carbon Analyzer (TOC-5050A). For the carbon content of the stem, branches and foliage around the tree the total biomass of each component was multiplied by the average carbon content fraction obtained from the subsamples of each component. The carbon content of the whole tree was the result of the sum of carbon stump, stem, branches and leaves.

After obtaining the data carbon content of each tree in kilograms, the allometric model developed was used to estimate biomass and correlated the carbon content according to the normal diameter, using data on both variables for each tree (D Nandbiomass). As in the case of the model to determine biomass, it was linearized and then the residual dispersion to identify the effectiveness of the model used were graphed. In addition to testing the model including the DN as the only independent variable, they were also tested other models where the total height (m) was included to determine whether it was significant inclusion or not in the same model.

Results and discussion


The fresh weight of the 29 trees used to generate the equation is placed in the range of 1.7 to 2 917.9 kg. Tree biomass was 1.37 to 1 142 kg, corresponding to trees with less DN (3.3 cm) and most DN (57.2 cm), respectively.

Most biomass in Pinus hartwegii corresponded to the accumulated in the shaft, with 45.5 to 84.6% by individual, and 65.3% average. The biomass of branches represented 11.4 to 37.4% of the tree, with an average of 23.8% and foliage from 2.0 to 29.2%, with 10.9% average.

Biomass equations

The equation to determine the biomass according to the normal diameter presented a determination coefficient R2= 0.986 (Figure 1) considered very acceptable, plus the original model (equation 2) was linearized and after adjustment, the residuals were plotted (Figure 2), where a clear trend that invalidates the model used is appropriate for the data used in the regression analysis (Montgomery, 2006) therefore the model used may be considered appropriate for the data analyzed in this species is not evidence.

Figure 1 Dispersion biomass values for Pinus hartwegii its regression line generated and its equation. 

Figure 2 Residual equation for ln(B)=-2.7 564 + 2.4 725 ln (DN).  

The percentage of stem biomass, branches and foliage of Pinus hartwegii, was within the ranges found for other species in Mexico, both coniferous and broadleaved (Castellanos, 1993; Monroy and Návar, 2004; Díaz et al., 2007; Avendaño et al., 2009; Montes de Oca et al., 2009; Carrillo et al. 2014; although it is clear that the proportion of biomass between the parts of the tree can vary considerably with respect to other species according to their morphology.

Carbon concentration

The average percentage of carbon found in the samples for the shaft was 48.2%, 49.4% for branches and foliage 48.5%. Therefore, the simple average percentage of carbon to the total biomass of each tree in the 29 sampled individuals of Pinus Hartwegii was 48.5%.

The distribution of carbon among the components had the following characteristics: the shaft was located in the range 52.6 to 84.3% with an average of 64.9%, in the branches of 11.6 to 38% with an average of 24.2% and finally in the foliage ranged from 2 to 29.1% with a mean of 10.9%.

Carbon equations

The fit of the model Y= bXk, for carbon content data presented the values displayed along with the scattering of data and adjustment line in Figure 3.

Figure 3 Dispersion of the carbon content values for Pinus hartwegii, its generated regression line and its equation. 

When tested others including height (m), the model did not change substantially in the coefficient of determination (r2), unlike in some models this value decreased slightly, for example in the model: B= β0D N2H (B= kg biomass, DN= normal diameter in cm and H the total height of the trees in m), with this model the value of r2 = 0.9819, slightly lower than the value obtained when only the DN is used as an independent variable. The model was also tested: B= β01D N2H; however, this value r2 decreased to 0.9684. Another models tested was: B= β0D Nβ1Hβ2 in which r2= 0.9868 if it was slightly higher than that obtained with the model where only the DN was used as independent variable.

The percentage of carbon considering the whole tree is within the range of values found for other species (Diaz et al., 2007; Avendaño et al., 2009; Carrillo et al., 2014) to which they have given a similar allometric equation.

However, it should be noted that this study does not allow for measurement of biomass and carbon in roots, so can be under-estimating the amount of CO2 retained by these trees, since in some species the underground proportion can conifers represent up to 18% and 17.1% leaves to 36.2% of the total biomass (Kurz et al., 1996; Gargaglione et al., 2010).

It was decided not to include height in the model to determine the biomass and carbon, because the variable height is a more difficult parameter to measure in the field, in one way or another can make more errors in measurement and invests more time for measurement, plus it did not improve substantially the value of r2 in the model where it was used.


It was possible to adjust the allometric equation to estimate the biomass of Pinus hartwegii with a high coefficient of determination. It was also possible to adjust the equation for estimating the carbon content per tree with the same coefficient of determination. With the equation obtained was possible to determine that trees of this species concentrate most air bole carbon followed by the branches and finally the foliage.

To make complete this type of study is necessary to determine the carbon of the underground part in the ecosystems studied, since it must take into account that many forest species, according to several authors much carbon we concentrate also on the roots.

Because the normal diameter is one of the variables that usually are measured in field when making forest inventories or measurements of temporary or permanent sites, with the equations obtained in this work can be made practical and accurate estimates of the amount carbon captured by forests of Pinus hartwegii, and be in a position to request a payment for environmental services through clean development mechanisms specified in the Kyoto protocol.

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Received: October 2015; Accepted: January 2016

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