title: Capturing spiral radial growth of conifers using the superellipse to model tree-ring geometric shape.
abstract: Tree-rings are often assumed to approximate a circular shape when estimating forest productivity and carbon dynamics. However, tree rings are rarely, if ever, circular, thereby possibly resulting in under- or over-estimation in forest productivity and carbon sequestration. Given the crucial role played by tree ring data in assessing forest productivity and carbon storage within a context of global change, it is particularly important that mathematical models adequately render cross-sectional area increment derived from tree rings. We modeled the geometric shape of tree rings using the superellipse equation and checked its validation based on the theoretical simulation and six actual cross sections collected from three conifers. We found that the superellipse better describes the geometric shape of tree rings than the circle commonly used. We showed that a spiral growth trend exists on the radial section over time, which might be closely related to spiral grain along the longitudinal axis. The superellipse generally had higher accuracy than the circle in predicting the basal area increment, resulting in an improved estimate for the basal area. The superellipse may allow better assessing forest productivity and carbon storage in terrestrial forest ecosystems.
authors.affiliation: Co-Innovation Centre for Sustainable Forestry in Southern China, Bamboo Research Institute, Nanjing Forestry University Nanjing, China ; Key Laboratory of Vegetation Restoration and Management of Degraded Ecosystems, South China Botanical Garden, Chinese Academy of Sciences Guangzhou, China.
authors.forename: Pei-Jian
authors.initials: PJ
authors.lastname: Shi
authors.affiliation: Key Laboratory of Vegetation Restoration and Management of Degraded Ecosystems, South China Botanical Garden, Chinese Academy of Sciences Guangzhou, China ; Provincial Key Laboratory of Applied Botany, South China Botanical Garden, Chinese Academy of Sciences Guangzhou, China.
authors.forename: Jian-Guo
authors.initials: JG
authors.lastname: Huang
authors.affiliation: Department of Mathematical Sciences, Centre for Invasion Biology, Stellenbosch University Matieland, South Africa ; Mathematical and Physical Biosciences, African Institute for Mathematical Sciences Cape Town, South Africa.
authors.forename: Cang
authors.initials: C
authors.lastname: Hui
authors.affiliation: Department of Geography, The University of Tennessee Knoxville, TN, USA.
authors.forename: Henri D
authors.initials: HD
authors.lastname: Grissino-Mayer
authors.affiliation: Centre for Forest Interdisciplinary Research, University of Winnipeg Winnipeg, MB, Canada.
authors.forename: Jacques C
authors.initials: JC
authors.lastname: Tardif
authors.affiliation: Key Laboratory of Vegetation Restoration and Management of Degraded Ecosystems, South China Botanical Garden, Chinese Academy of Sciences Guangzhou, China ; Provincial Key Laboratory of Applied Botany, South China Botanical Garden, Chinese Academy of Sciences Guangzhou, China.
authors.forename: Li-Hong
authors.initials: LH
authors.lastname: Zhai
authors.affiliation: Co-Innovation Centre for Sustainable Forestry in Southern China, Bamboo Research Institute, Nanjing Forestry University Nanjing, China.
authors.forename: Fu-Sheng
authors.initials: FS
authors.lastname: Wang
authors.affiliation: Ecological Complexity and Modelling Laboratory, Department of Botany and Plant Sciences, University of California, Riverside Riverside, CA, USA.
authors.forename: Bai-Lian
authors.initials: BL
authors.lastname: Li
keywords: basal area; cross section; major semi-axis; polar coordinate; rotation; tree-rings