ALBERT

Description: Both aggregative and disaggregative strategies were used to develop additive nonlinear biomass equations for slash pine (Pinus elliottii Engelm. var. elliottii) trees in the southeastern United States. In the aggregative approach, the total tree biomass equation was specified by aggregating the expectations of component biomass models, and their parameters were estimated by jointly fitting all component and total biomass equations using weighted nonlinear seemingly unrelated regression (NSUR) (SUR1) or by jointly fitting component biomass equations using weighted NSUR (SUR2). In an alternative disaggregative approach (DRM), the biomass component proportions were modeled using Dirichlet regression, and the estimated total tree biomass was disaggregated into biomass components based on their estimated proportions. There was no single system to predict biomass that was best for all components and total tree biomass. The ranking of the three systems based on an array of fit statistics followed the order of SUR2 〉 SUR1 〉 DRM. All three systems provided more accurate biomass predictions than previously published equations.

Description: Since 1977, the extent of forest wildfires in the boreal and western regions of North America increased 6- to 9-fold over long-term trends, and an estimated 132 × 106 ha of temperate and boreal forest burned across the northern hemisphere. Emissions during and after burning may have been a significant feedback to global warming. Simulated carbon budgets indicated a hemispheric release of 1.4 Pg C during burning and 4.1 Pg C gross from CO2 fluxes postfire. The total release (5.5 Pg C) was 43% of the biospheric CO2 release to the atmosphere, 1977–1990. Over the next century (1991–2090), continuing emissions from wood and soil decomposition will release an additional 6.9 Pg C gross. A large CO2 release was contrary to assumptions of little net carbon flux in the temperate and boreal forests. The pattern of attenuated CO2 release in northern forests also contrasted with sharp emission peaks in tropical deforestation. A simulation experiment indicated that the CO2 pulse from direct emissions per unit area was 10-fold larger in tropical deforestation than in northern forest wildfires on average; postfire release in the northern systems, however, was about 10 times longer in duration and only slightly less overall than in tropical deforestation fires.

Description: Canadian Journal of Forest Research, Volume 0, Issue 0, Page 272-278, e-First articles.

Description: Canadian Journal of Forest Research, e-First Articles. The typical “double counting” application of the mirage method of boundary correction cannot be applied to sampling systems such as critical height sampling (CHS) that are based on a Monte Carlo sample of a tree (or debris) attribute because the critical height (or other random attribute) sampled from a mirage point is generally not equal to the critical height measured from the original sample point. A generalization of the mirage method is proposed for CHS and related techniques in which new samples of critical heights or other dimensions are obtained from mirage points outside the tract boundary. This is necessary because, in the case of CHS, the critical height actually depends on the distance between the tree and a randomly located sample point. Other spatially referenced individual tree attribute or coarse woody debris (CWD) estimators that use Monte Carlo integration with importance sampling have been developed in which the tree or CWD attribute estimate also depends on the distance between the tree and the sample point. The proposed modified mirage method is shown to be design unbiased. The proof includes general application to Monte Carlo integration estimators for objects such as CWD sampled from points.

Description: Canadian Journal of Forest Research, Volume 0, Issue 0, Page 1151-1161, e-First articles. Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the “antithetic variate” associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 − b/B), where b is the cross-sectional area at “borderline” condition and B is the tree’s basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias.

Description: Canadian Journal of Forest Research, e-First Articles. The typical “double counting” application of the mirage method of boundary correction cannot be applied to sampling systems such as critical height sampling (CHS) that are based on a Monte Carlo sample of a tree (or debris) attribute because the critical height (or other random attribute) sampled from a mirage point is generally not equal to the critical height measured from the original sample point. A generalization of the mirage method is proposed for CHS and related techniques in which new samples of critical heights or other dimensions are obtained from mirage points outside the tract boundary. This is necessary because, in the case of CHS, the critical height actually depends on the distance between the tree and a randomly located sample point. Other spatially referenced individual tree attribute or coarse woody debris (CWD) estimators that use Monte Carlo integration with importance sampling have been developed in which the tree or CWD attribute estimate also depends on the distance between the tree and the sample point. The proposed modified mirage method is shown to be design unbiased. The proof includes general application to Monte Carlo integration estimators for objects such as CWD sampled from points.

Description: Critical height sampling (CHS) estimates cubic volume per unit area by multiplying the sum of critical heights measured on trees tallied in a horizontal point sample (HPS) by the HPS basal area factor. One of the barriers to practical application of CHS is the fact that trees near the field location of the point-sampling sample point have critical heights that occur quite high on the stem, making them difficult to view from the sample point. To surmount this difficulty, use of the “antithetic variate” associated with the critical height together with importance sampling from the cylindrical shells integral is proposed. This antithetic variate will be u = (1 − b/B), where b is the cross-sectional area at “borderline” condition and B is the tree’s basal area. The cross-sectional area at borderline condition b can be determined with knowledge of the HPS gauge angle by measuring the distance to the sample tree. When the antithetic variate u is used in importance sampling, the upper-stem measurement will be low on tree stems close to the sample point and high on tree stems distant from the sample point, enhancing visibility and ease of measurement from the sample point. Computer simulations compared HPS, CHS, CHS with importance sampling (ICHS), ICHS and an antithetic variate (AICHS), and CHS with paired antithetic varariates (PAICHS) and found that HPS, ICHS, AICHS, and PAICHS were very nearly equally precise and were more precise than CHS. These results are favorable to AICHS, since it should require less time than either PAICHS or ICHS and is not subject to individual-tree volume equation bias.

Description: Procedures are described which estimate the locational advantages of mill sites in terms of wood procurement costs and the relative competition among mills in a region. At the heart of the process a transportation matrix links individual harvestable timber stands to mill locations in the region. The procedures estimate delivered wood cost curves for individual mills or mill sites, and indices that measure the degree of competition for wood among mills. The procedures arc completely automated. They enable planners to examine the impact of different demand scenarios in terms of relative ability of mills to obtain wood.

Description: The design bias in the sample mean obtained from sampling the trees nearest to points randomly and uniformly distributed over a forested area can be exactly quantified in terms of the Voronoi polygons (V polygons) surrounding each tree in the forest of interest. For this sampling method, the V polygon for a prospective sample tree is its inclusion zone. The sides of such polygons are perpendicular to a line joining adjacent trees and equidistant from these trees. For any individual tree attribute Y, the design bias in such a sample mean for estimating the population mean of Y will be equal to the covariance between Y and V-polygon area V divided by the mean V-polygon area. The bias as a percent of the population mean of Y is the product of the correlation coefficient between Y and V and the coefficients of variation for Y and V multiplied by 100. This implies that attempts to estimate the means of commonly measured individual tree variables such as DBH, basal area, and crown diameter or the area from sampling trees nearest to randomly located points will likely be positively biased, and the magnitude of that bias will depend on the strength of the linear relationship to the V-polygon area, as well as the variability among the V-polygon areas and the variable of interest. It is not obvious whether increment core data will be positively or negatively biased, because this depends on the characteristics of the forest of interest. The main conclusion of the study is that the bias formula derived for unweighted estimation from sampling the tree nearest to a point indicates that bias in the range of 5%–10% or greater can occur in many forest populations.