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.

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:

2)

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.

Biomass

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= bX^k, 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= β₀+β₁D N²H; however, this value r² decreased to 0.9684. Another models tested was: B= β₀D N^β1H^β2 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.