To represent commonly used approaches, two different estimators were tested (for case a in Table 2): an estimator adapted for buy OSI-906 a paired sample approach (representing a design with permanent sample units) and an estimator for an independent sample approach (representing a design with temporary sample units). For both approaches, the test data were based on paired samples, and therefore the estimates of biomass should have been the same. However, in principle, estimates of variance should be smaller for the paired sample approach.
The variance estimators are described in Appendix A. To investigate the effect of different BEFs on estimates of biomass, individual BEFs were derived from estimates of biomass and volume, using standing stock data, for the
years 1990 and 2005. To estimate the change in biomass stock, each BEF was multiplied by the change in stem volume using either the paired sample or independent sample approach (b in Table 2). The corresponding variance estimators were derived by Taylor series expansion (Appendix B). The change in biomass between 1990 and 2005 ΔBˆ, a in Table 2) was estimated directly from BiEqs for different tree fractions using the following ratio estimator (Thompson, 1992): equation(1) ΔBˆi=AiAˆiT2·ΔBˆiT2-T1=Ai·∑j=1niΔbij∑j=1niaijwhere AiAi is the official land and fresh water area of stratum or region i (http://www.lantmateriet.se; 2011-12-12), AˆiT2 is the estimated land area of stratum i in 2005, ΔBˆiT2-T1 is the estimated change in biomass from 1990 to 2005 Vorinostat manufacturer based on paired samples, ΔbijΔbij is the change in biomass per sample unit j and aij is the inventoried area for sample unit j . The change in biomass at a national scale, ΔBˆ, is estimated by summing over all strata. A similar estimator, where Farnesyltransferase the biomasses were estimated using an independent sample approach, was also derived: equation(2) BˆT2∗-BˆT1∗=Ai∑j=1niaij·∑j=1nibijT2-∑j=1nibijT1where BˆT1 and BˆT2 are
the estimated biomasses for 1990 and 2005, respectively. The variance of both estimators described by (1) and (2) was estimated by a standard variance estimator for a ratio estimator (Appendix A, Thompson, 1992). In the alternative method, using stem volume regression equations, two BEFs were calculated as follows: equation(3) BEF∧T1=BˆT1∗VˆT1∗=AAˆT1·BˆT1AAˆT1·VˆT1=BˆT1VˆT1 equation(4) BEF∧T2=BˆT2VˆT2where VˆT1 and VˆT2 are the estimated stem volumes in 1990 and 2005, respectively. A is the measured land area and AˆT1 is the estimated land area at 1990. The annual change in biomass from 1990 to 2005 was estimated based on paired samples as follows: equation(5) BEF∧T2·ΔVˆ=BˆT2VˆT2·AAˆT2·ΔVˆT2-T1where ΔVˆT2-T1 is the estimated change in volume between 1990 and 2005.