Appendix B. Carbon book-keeping model.
Overview of Carbon Calculations
For each year over the period from 1984 to 1995 and every two years thereafter, we estimated the pools of carbon related to aboveground biomass that were sequestered or decomposed (returned to the atmosphere), on an individual tree basis. We chose to treat each of the 1.56 ha plots as independent for two reasons. First, this finer spatial scale is more appropriate to analyze harvest intensity which varies greatly among plots. Second, this scale provides some comparison with other studies generally conducted at the 1 ha scale (Clark 2002, Malhi et al. 2004).
All analyses were performed using the R project software (http://R-project.org/).
Calculation of Biomass Change due to Tree Growth
For each stem at each inventory date, above-ground biomass was calculated using formulas (Chave et al. 2005) for moist tropical forests using wood specific gravity (WSG) and tree diameter (DBH) as predictor variables:
AGB = WSG*e (-1.499+2.148*ln(DBH)+0.207*((ln(DBH))2)-0.0281*((ln(DBH))3))
Wood specific gravity values were obtained from a large database at the species level compiled by Cirad (unpublished data). We note that some of the identifications in this database were made using conversions from common names for which no herbarium vouchers were available. In these cases, we applied the mean values for all sampled species within the respective genus to all species within that genus (Chave et al. 2006). In cases where no data were available, we applied the mean of all species in the database (0.654 g cm-3). Values were converted from 12% humidity to dry mass density using the formulas described by (Chave et al. 2006). Aboveground biomass was converted into carbon by assuming that oven-dry biomass contains 50% of carbon.
Calculation of Biomass Change due to Tree Recruitment
Biomass accumulation due to newly-recruited stems (DBH = 10 cm) was calculated using formula 1, and was considered as growth from null diameter in the previous year. While this rapid entry of biomass into stored carbon pools might bias short-term studies (Clark 2002), recruitment at Paracou stabilized within 10 years (see Fig. 2) after logging. Thus, over the 23-year period of the study this effect should not bias the result.
Calculation of Biomass Change due to Tree Mortality
For decomposition, it is important to separate the Fine Woody Biomass (FWB) that will decompose rapidly (leaves, twigs and small diameter branches), from the coarse or Large Woody Biomass which decomposes more slowly (LWB; Chambers et al. 2004, Keller et al. 2004). Chambers et al. (2004) propose a separation of decomposing aboveground biomass into fine wood and larger wood. Their measurements suggest that larger trees tend to have a greater fraction of aboveground biomass in large wood, giving the following estimate LWB fraction based on DBH.
fLWB = 0.774 +0.0018*DBH
(B.2)Using this formula, the fine debris pool (FWB) could be calculated as the difference between total aboveground biomass and large wood biomass, as:
FWB = AGB - LWB = AGB*(0.226 - 0.0018*DBH)
We set the decomposition rates of LWB and FWB pools based on reported values from the literature, using an exponential decay formula
Mt = Mo e (-kt)
(B.4)First, we assumed that FWB pools decomposed rapidly, with kFWB = 0.2 (a half-life of about three years (Keller et al. 2004). Second, several methods have been proposed to estimate the decomposition rate of LWB pools. (Chambers et al. 2000) presented a polynomial model as a function of diameter and wood specific gravity. However, this model was calibrated with a data set predominated by small-diameter trees and very few species with high wood density. The application of such a model to large diameter trees and high wood density species is then unsatisfying. Indeed, when applied to the Paracou data set it results in unrealistic rapid rates of decomposition for large diameter dense woods (Fig. B1). Alternatively, (Chambers et al. 2000) propose simpler models based on either DBH or wood density. We chose to use the later model for our data set both because it avoids the problems of bigger DBH and because it results in the best Akaike’s Information Criteria (AIC) values when fit to Chambers’ data.
kLWB = (0.918 - 0.738*WSG)2
We limited the slowest decomposition rate to 2% yr-1, as done by Chambers et al. (2000).
Calculation of Initial Decomposing Carbon Stocks
We estimated the stock of decomposing aboveground biomass in the soil at the first census date using simulated data based on observed mortality in the unlogged plots from the Paracou experimental site. At the first census date in 1984, each plot was attributed a set of decomposing trees in the soil. This set is obtained at the end of three consecutive series dating back from 1984, each of which duplicated the mortality events observed in the 1984–2007 period in the unlogged plot from the same block. Our simulations showed that soil carbon stocks from dead trees stabilized between 15 and 20 Mg C per hectare between two and three cycles of 21 years, similar to that measured in other tropical forests (Chambers et al. 2000, Chambers et al. 2004).
Calculation of Biomass Change due to Tree Harvest
These calculations are based on formulas used for natural tree death, except that the trunk biomass is divided into pieces of about 2m length for which basal and apical circumferences were measured at the time of harvest (Fig. A2). The volume in logs was calculated for pieces of approximately 2 m in length (h), using basal and apical circumference measures and the formula for cone piece.
Vlog = (1/12)*h*π*( C1² + C2² + C1*C2)
The biomass in logs was then calculated as:
Blog = WSG*Vlog
Two-thirds of roundwood biomass was estimated as byproducts of sawmill transformation (Fig. A2). This estimate is based on surveys of sawmills in French Guiana. In the Brazilian Amazon where secondary transformation is performed on some smaller wood pieces, this value may be slightly reduced to about 58% (Lentini et al. 2005). Roundwood sawmill waste was assumed to be burned as it is a common practice in French Guiana and other Amazonian locations, and were immediately decomposed with a kwaste set to 1 in Eq. B.5.
One-third of roundwood biomass was thus estimated to be incorporated in construction as sawnwood products. We assigned a conservative estimate of decomposition rate to these wood products, with a kwood set to 0.005 after Keller et al. (2004) and Houghton et al. (2000).
Logs that were cut and not skidded or transported to a sawmill were treated as field debris. Field debris included lower and upper purges of trunk adjacent to the removed log, as well as the stump. The circumference of each of these pieces was measured at the time of logging, with incremental measures every 2 m along larger pieces. The volume and biomass of wood in these pieces was calculated in the same manner as described above for the skidded log pieces.
To confirm these field-measures of large wood, they were compared to LWB. When LWB was observed to represent a surplus, we supposed these pieces were not measured in the field and added their biomass to the large wood pool.
We applied decomposition rates to these pieces based on the average diameter of the piece, to account for tapering relative to DBH, using formulas B.4 and B.5.
Projection of Future Carbon Stocks
We examined the amount of time required to recover carbon stocks using simulations of carbon sequestered due to growth and recruitment and lost from mortality in all plots beginning in 2007. To achieve this, we constructed a model assuming that the observed net carbon sequestration until 2007 in the logged plots will diminish through time towards a maximum value. We set this maximum value as the value observed in each plot at the original census date, modified by the mean change in carbon flux observed over the census period in the adjacent four control plots of a given floristic block. We calculated the change in two-year intervals from 2007 as:
dC(t)/dt = R * [1-(Ct-C2007)/(Cmax-C2007)
with C(t) being the carbon stock at each time step, R being the mean net carbon flux between 2001 and 2007, and C2007 the carbon balance at the last census in 2007. Cmax is calculated as the sum of carbon stock at the first census in 1984 and a mean annual net C flux (calculated over the period 2001–2007 for the control plots of the same block) integrated across the observation period.
FIG. B1. Results of polynomial model of decomposition of coarse woody debris as a function of wood density and tree DBH proposed by Chambers et al. (2000, 2004), as applied to the broader range of values in the Paracou data set.
Chambers, J. Q., N. Higuchi, J. P. Schimel, L. V. Ferreira, and J. M. Melack. 2000. Decomposition and carbon cycling of dead trees in tropical forests of the central Amazon. Oecologia 122:380–388.
Chambers, J. Q., N. Higuchi, L. M. Teixeira, J. dos Santos, S. G. Laurance, and S. E. Trumbore. 2004. Response of tree biomass and wood litter to disturbance in a Central Amazon forest. 141:596–611.
Chave, J., C. Andalo, S. Brown, M. A. Cairns, J. Q. Chambers, D. Eamus, H. Folster, F. Fromard, N. Higuchi, T. Kira, J. P. Lescure, B. W. Nelson, H. Ogawa, H. Puig, B. Riera, and T. Yamakura. 2005. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia 145:87–99.
Chave, J., H. Muller-Landau, T. Baker, T. Easdale, H. ter Steege, and C. O. Webb. 2006. Regional and phylogenetic variation of wood density across 2,456 neotropical tree species. Ecological Applications 16:2356–2367.
Clark, D. A. 2002. Are tropical forests an important carbon sink? Reanalysis of the long-term plot data. Ecological Applications 12:3-7. Houghton, R. A., D. L. Skole, C. A. Nobre, J. L. Hackler, K. T. Lawrence, and W. H. Chomentowski. 2000. Annual ¯uxes of carbon from deforestation and regrowth in the Brazilian Amazon. Nature 403:301–304.
Houghton, R. A., D. L. Skole, C. A. Nobre, J. L. Hackler, K. T. Lawrence, and W. H. Chomentowski. 2000. Annual fluxes of carbon from deforestation and regrowth in the Brazilian Amazon. Nature 403:301–304.
Keller, M., M. Palace, G. P. Asner, R. Pereira, and J. N. M. Silva. 2004. Coarse woody debris in undisturbed and logged forests in the eastern Brazilian Amazon. Global Change Biology 10:784–795.
Lentini, M., D. Pereira, D. Celentano, and R. Pereira. 2005. Fatos florestais de Amazônica. Imazon, Belem.
Malhi, Y., T. R. Baker, O. L. Phillips, S. Almeida, E. Alvarez, L. Arroyo, J. Chave, C. I. Czimczik, A. Di Fiore, N. Higuchi, T. J. Killeen, S. G. Laurance, W. F. Laurance, S. L. Lewis, L. M. M. Montoya, A. Monteagudo, D. A. Neill, P. N. Vargas, S. Patino, N. C. A. Pitman, C. A. Quesada, R. Salomao, J. N. M. Silva, A. T. Lezama, R. V. Martinez, J. Terborgh, B. Vinceti, and J. Lloyd. 2004. The above-ground coarse wood productivity of 104 Neotropical forest plots. Global Change Biology 10:563–591.
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