Over the past 50 years,crown asymmetry of forest trees has been evaluated through several indices constructed from the perspective of projected crown shape or displacement but often on an ad hoc basis to address speci...Over the past 50 years,crown asymmetry of forest trees has been evaluated through several indices constructed from the perspective of projected crown shape or displacement but often on an ad hoc basis to address specifi c objectives related to tree growth and competition,stand dynamics,stem form,crown structure and treefall risks.Although sharing some similarities,these indices are largely incoherent and non-comparable as they diff er not only in the scale but also in the direction of their values in indicating the degree of crown asymmetry.As the fi rst attempt at devising normative measures of crown asymmetry,we adopted a relative scale between 0 for perfect symmetry and 1 for extreme asymmetry.Five existing crown asymmetry indices(CAIs)were brought onto this relative scale after necessary modifi cations.Eight new CAIs were adapted from measures of circularity for digital images in computer graphics,indices of income inequality in economics,and a bilateral symmetry indicator in plant leaf morphology.The performances of the 13 CAIs were compared over diff erent numbers of measured crown radii for 30 projected crowns of mature Eucalyptus pilularis trees through benchmarking statistics and rank order correlation analysis.For each CAI,the index value based on the full measurement of 36 evenly spaced radii of a projected crown was taken as the true value in the benchmarking process.The index(CAI 13)adapted from the simple bilateral symmetry measure proved to be the least biased and most precise.Its performance was closely followed by that of three other CAIs.The minimum number of crown radii that is needed to provide at least an indicative measure of crown asymmetry is four.For more accurate and consistent measures,at least 6 or 8 crown radii are needed.The range of variability in crown morphology of the trees under investigation also needs to be taken into consideration.Although the CAIs are from projected crown radii,they can be readily extended to individual tree crown metrics that are now commonly extracted from LiDAR and other remotely sensed data.Adding a normative measure of crown asymmetry to individual tree crown metrics will facilitate the process of big data analytics and artifi cial intelligence in forestry wherever crown morphology is among the factors to be considered for decision making in forest management.展开更多
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 inte...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.展开更多
基金the Heilongjiang Touyan Innovation Team 747 Program(Technology Development Team for High-effi cient Silviculture of Forest Resources).
文摘Over the past 50 years,crown asymmetry of forest trees has been evaluated through several indices constructed from the perspective of projected crown shape or displacement but often on an ad hoc basis to address specifi c objectives related to tree growth and competition,stand dynamics,stem form,crown structure and treefall risks.Although sharing some similarities,these indices are largely incoherent and non-comparable as they diff er not only in the scale but also in the direction of their values in indicating the degree of crown asymmetry.As the fi rst attempt at devising normative measures of crown asymmetry,we adopted a relative scale between 0 for perfect symmetry and 1 for extreme asymmetry.Five existing crown asymmetry indices(CAIs)were brought onto this relative scale after necessary modifi cations.Eight new CAIs were adapted from measures of circularity for digital images in computer graphics,indices of income inequality in economics,and a bilateral symmetry indicator in plant leaf morphology.The performances of the 13 CAIs were compared over diff erent numbers of measured crown radii for 30 projected crowns of mature Eucalyptus pilularis trees through benchmarking statistics and rank order correlation analysis.For each CAI,the index value based on the full measurement of 36 evenly spaced radii of a projected crown was taken as the true value in the benchmarking process.The index(CAI 13)adapted from the simple bilateral symmetry measure proved to be the least biased and most precise.Its performance was closely followed by that of three other CAIs.The minimum number of crown radii that is needed to provide at least an indicative measure of crown asymmetry is four.For more accurate and consistent measures,at least 6 or 8 crown radii are needed.The range of variability in crown morphology of the trees under investigation also needs to be taken into consideration.Although the CAIs are from projected crown radii,they can be readily extended to individual tree crown metrics that are now commonly extracted from LiDAR and other remotely sensed data.Adding a normative measure of crown asymmetry to individual tree crown metrics will facilitate the process of big data analytics and artifi cial intelligence in forestry wherever crown morphology is among the factors to be considered for decision making in forest management.
基金supported by the Natural Science Foundation of China (32071758)the Fundamental Research Funds for the Central Universities of China (No. 2572020BA01)
文摘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.
