A new method of calculating crown projection area and its comparative accuracy with conventional calculations for asymmetric tree crowns

This paper introduces a new method of calculating crown projection area(CPA),the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and integration.This novel method and other four existing methods of calculating CPA were compared using detailed crown radius measurements from 30 tall trees of Eucalyptus pilularis variable in crown size,shape,and asymmetry.The four existing methods included the polygonal approach and three ways of calculating CPA as the area of a circle using the arithmetic,geometric and quadratic mean radius.Comparisons were made across a sequence of eight non-consecutive numbers(from 2 to 16)of measured crown radii for each tree over the range of crown asymmetry of the 30 trees through generalized linear models and multiple comparisons of means.The sequence covered the range of the number of crown radii measured for calculating the CPA of a tree in the literature.A crown asymmetry index within the unit interval was calculated for each tree to serve as a normative measure.With a slight overestimation of 2.2%on average and an overall mean error size of 7.9%across the numbers of crown radii that were compared,our new method was the least biased and most accurate.Calculating CPA as a circle using the quadratic mean crown radius was the second best,which had an average overestimation of 4.5%and overall mean error size of 8.8%.These two methods remained by and large unbiased as crown asymmetry increased,while the other three methods showed larger bias of underestimation.For the conventional method of using the arithmetic mean crown radius to calculate CPA as a circle,bias correction factors were developed as a function of crown asymmetry index to delineate the increasing magnitude of bias associated with greater degrees of crown asymmetry.This study reveals and demonstrates such relationships between the accuracy of CPA calculations and crown asymmetry and will help increase awareness among researchers and practitioners on the existence of bias in their CPA calculations and for the need to use an unbiased method in the future.Our new method is recommended for calculating CPA where at least four crown radius measurements per tree are available because that is the minimum number required for its use.

Spatial modeling of the carbon stock of forest trees in Heilongjiang Province, China

Heilongjiang province is the largest forest zone in China and the forest coverage rate is 46%. Forests of Heilongjiang province play an important role in the forest ecosystem of China. In this study we investi- gated the spatial distribution of forest carbon storage in Heilongjiang province using 3083 plots sampled in 2010. We attempted to fit two global models, ordinary least squares model （OLS）, linear mixed model （LMM）, and a local model, geographically weighted regression model （GWR）, to the relationship between forest carbon content and stand, environment, and climate factors. Five predictors significantly affected forest carbon storage and spatial distribution, viz. average diameter of stand （DBH）, number of trees per hectare （TPH）, elevation （Elev）, slope （Slope） and the product of precipitation and temperature （Rain Temp）. The GWR model outperformed the two global models in both model fitting and prediction because it successfully reduced both spatial auto- correlation and heterogeneity in model residuals. More importantly, the GWR model provided localized model coefficients for each location in the study area, which allowed us to evaluate the influences of local stand conditions and topographic features on tree and stand growth, and forest carbon stock. It also helped us to better understand the impacts of silvi- cultural and management activities on the amount and changes of forest carbon storage across the province. The detailed information can be readily incorporated with the mapping ability of GIS software to provide excellent tools for assessing the distribution and dynamics of the for- est-carbon stock in the next few years.

Optimal management of Korean pine plantations in multifunctional forestry

Korean pine is one of the most important plantation species in northeast China. Besides timber, it produces edible nuts and plantations sequester carbon dioxide from the atmosphere. This study optimized the management of Korean pine plantations for timber production, seed production, carbon sequestration and for the joint production of multiple benefits. As the first step, models were developed for stand dynamics and seed production. These models were used in a simulation-optimization system to find optimal timing and type of thinning treatments and optimal rotation lengths. It was found that three thinnings during the rotation period were optimal. When the amount or profitability of timber production is maximized, suitable rotation lengths are 65-70 years and wood production is 5.5-6.0 m(3) ha(-1) a(-1). The optimal thinning regime is thinning from above. In seed production, optimal rotation lengths are over 100 years. When carbon sequestration in living biomass is maximized, stands should not be clear-cut until trees start to die due to senescence. In the joint production of multiple benefits, the optimal rotation length is 86 years if all benefits (wood, economic profits, seed, carbon sequestration) are equally important. In this management schedule, mean annual wood production is 5.5 m(2) ha(-1) and mean annual seed yield 141 kg ha(-1). It was concluded that it is better to produce timber and seeds in the same stands rather than assign stands to either timber production or seed production.

Individual-tree diameter growth model for Korean pine plantations based on optimized interpolation of meteorological variables

To explore the influence of meteorological variables on the growth of Korean pine(Pinus koraiensis Sieb.et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine,three approaches to interpolate meteorological variables during the growing season(i.e.,May-September) were compared in Heilongjiang Province,China.Optimized meteorological variable interpolation results were then combined with stand and individual tree variables,based on data from 56 sample plots and 2886 sample trees from Korean pine plantations in two regions of the province to develop an individualtree diameter growth model(Model I) and an individualtree diameter growth model with meteorological variables(Model Ⅱ) using a stepwise regression method.Moreover,an individual-tree diameter growth model with regional effects(Model Ⅲ) was developed using dummy variables in the regression,and the significance of introducing these dummy variables was verified with an F-test statistical analysis.The models were validated using an independent data set,and the predictive performance of the three models was assessed via the adjusted coefficient of determination(R_(a)^(2)) and root mean square error(RMSE).The results suggest that the growth increment in tree diameter of Korean pine plantations was significantly correlated with the natural logarithm of initial diameter(ln D),stand basal area(BAS),logarithmic deformation of the stand density index(ln SDI),ratio of basal area of trees larger than the subject tree to their initial diameter at breast height(DBH)(BAL/D),and the maximum growingseason precipitation(Pgmax).The individual-tree diameter growth models of Korean pine plantations developed in this study will provide a good basis for estimating and predicting growth increments of Korean pine forests over larger areas.

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China

Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.

A management planning system for even-aged and uneven-aged forests in northeast China

The most common scientific approach to numerical landscape-level forest management planning is combinatorial optimization aimed at finding the optimal combination of the treatment alternatives of stands. The selected combination of treatments depends on the conditions of the forest, and the objectives of the forest landowners. A two-step procedure is commonly used to derive the plan. First, treatment alternatives are generated for the stands using an automated simulation tool. Second,the optimal combination of the simulated treatment schedules is found by using mathematical programming or various heuristics. Simulation of treatment schedules requires models for stand dynamics and volume for all important tree species and stand types present in the forest.A forest planning system was described for Northeast China. The necessary models for stand dynamics and tree volume were presented for the main tree species of the region. The developed models were integrated into the simulation tool of the planning system. The simulation and the optimization tools of the planning system were described. The optimization tool was used with heuristic methods, making it possible to easily solve also spatial forest planning problems, for instance aggregate cuttings.Finally, the use of the system is illustrated with a case study, in which nonspatial and spatial management plans are developed for the Mengjiagang Forest District.

Stochastic frontiers or regression quantiles for estimating the self-thinning surface in higher dimensions?

Stochastic frontier analysis and quantile regression are the two econometric approaches that have been commonly adopted in the determination of the self-thinning boundary line or surface in two and higher dimensions since their introduction to the field some 20 years ago.However,the rational for using one method over the other has,in most cases,not been clearly explained perhaps due to a lack of adequate appreciation of differences between the two approaches for delineating the self-thinning surface.Without an adequate understanding of such differences,the most informative analysis may become a missed opportunity,leading to an inefficient use of data,weak statistical inferences and a failure to gain greater insight into the dynamics of plant populations and forest stands that would otherwise be obtained.Using data from 170 plot measurements in even-aged Larix olgensis(A.Henry) plantations across a wide range of site qualities and with different abundances of woody weeds,i.e.naturally regenerated non-crop species,in northeast China,this study compared the two methods in determining the self-thinning surface across eight sample sizes from 30 to 170 with an even interval of 20 observations and also over a range of quantiles through repeated random sampling and estimation.Across all sample sizes and over the quantile range of 0.90 ≤τ≤0.99,the normal-half normal stochastic frontier estimation proved to be superior to quantile regression in statistical efficiency.Its parameter estimates had lower degrees of variability and correspondingly narrower confidence intervals.This greater efficiency would naturally be conducive to making statistical inferences.The estimated self-thinning surface using all 170 observations enveloped about 96.5% of the data points,a degree of envelopment equivalent to a regression quantile estimation with aτ of 0.965.The stochastic frontier estimation was also more objective because it did not involve the subjective selection of a particular value of τ for the favoured self-thinning surface from several mutually intersecting surfaces as in quantile regression.However,quantile regression could still provide a valuable complement to stochastic frontier analysis in the estimation of the self-thinning surface as it allows the examination of the impact of variables other than stand density on different quantiles of stand biomass.

Two-level optimization approach to tree-level forest planning

Background:Laser scanning and individual-tree detection are used increasingly in forest inventories.As a consequence,methods that optimize forest management at the level of individual trees will be gradually developed and adopted.Results:The current study proposed a hierarchical two-level optimization method for tree-level planning where the cutting years are optimized at the higher level.The lower-level optimization allocates the trees to the cutting events in an optimal way.The higher-level optimization employed differential evolution whereas the lower-level problem was solved with the simulated annealing metaheuristic.The method was demonstrated with a 30 m30 m sample plot of planted Larix olgensis.The baseline case maximized the net present value as the only management objective.The solution suggested heavy thinning from above and a rotation length of 62 years.The baseline problem was enhanced to mixed stands where species diversity was used as another management objective.The method was also demonstrated in a problem that considered the complexity of stand structure,in addition to net present value.The objective variables that were used to measure complexity were the Shannon index(species diversity),Gini index(tree size diversity),and the index of Clark and Evans,which was used to describe the spatial distribution of trees.The article also presents a method to include natural advance regeneration in the optimization problem and optimize the parameters of simulated annealing simultaneously with the cutting years.Conclusions:The study showed that optimization approaches developed for forest-level planning can be adapted to problems where treatment prescriptions are required for individual trees.

Erratum to: Optimal management of Korean pine plantations in multifunctional forestry

In the original publication of Fig. 11 have been the article, Eq. 14 and text in online published incorrectly version is provided in this er The correct ratum (Eq. 14; Fig. 11).