A reinterpretation of the gap fraction of tree crowns from the perspectives of computer graphics and porous media theory

Yunfeng Zhu; Dongni Li; Jiangchuan Fan; Huaiqing Zhang; Markus P Eichhorn; Xiangjun Wang; Ting Yun

doi:10.3389/fpls.2023.1109443

A reinterpretation of the gap fraction of tree crowns from the perspectives of computer graphics and porous media theory

Front Plant Sci. 2023 Feb 6:14:1109443. doi: 10.3389/fpls.2023.1109443. eCollection 2023.

Authors

Yunfeng Zhu¹, Dongni Li¹, Jiangchuan Fan², Huaiqing Zhang³, Markus P Eichhorn^{4

5}, Xiangjun Wang⁶, Ting Yun^{1

7}

Affiliations

¹ School of Information Science and Technology, Nanjing Forestry University, Nanjing, China.
² National Engineering Research Center for Information Technology in Agriculture, Beijing, China.
³ Research Institute of Forestry Resource Information Techniques, Chinese Academy of Forestry, Beijing, China.
⁴ School of Biological, Earth and Environmental Sciences, University College Cork, Cork, Ireland.
⁵ Environmental Research Institute, University College Cork, Cork, Ireland.
⁶ Rubber Research Institute, Chinese Academy of Tropical Agricultural Sciences, Haikou, China.
⁷ Forestry College, Nanjing Forestry University, Nanjing, China.

Abstract

The gap fraction (GF) of vegetative canopies is an important property related to the contained bulk of reproductive elements and woody facets within the tree crown volume. This work was developed from the perspectives of porous media theory and computer graphics techniques, considering the vegetative elements in the canopy as a solid matrix and treating the gaps between them as pores to guide volume-based GF_vol calculations. Woody components and individual leaves were extracted from terrestrial laser scanning data. The concept of equivalent leaf thickness describing the degrees of leaf curling and drooping was proposed to construct hexagonal prisms properly enclosing the scanned points of each leaf, and cylinder models were adopted to fit each branch segment, enabling the calculation of the equivalent leaf and branch volumes within the crown. Finally, the volume-based GF_vol of the tree crown following the definition of the void fraction in porous media theory was calculated as one minus the ratio of the total plant leaf and branch volume to the canopy volume. This approach was tested on five tree species and a forest plot with variable canopy architecture, yielding an estimated maximum volume-based GF_vol of 0.985 for a small crepe myrtle and a minimal volume-based GF_vol of 0.953 for a sakura tree. The 3D morphology of each compositional element in the tree canopy was geometrically defined and the canopy was considered a porous structure to conduct GF_vol calculations based on multidisciplinary theory.

Keywords: computer graphics; equivalent leaf thickness; fine geometric characterization; porous media theory; volume-based gap fraction.

Grants and funding

This research was financially supported by the National Key R & D Program of China (2019YFD1000500). This research was also funded by the National Natural Science Foundation of China (grant numbers 31770591 and 32071681), the Natural Science Foundation of Jiangsu Province (BK20221337), China, the Jiangsu Provincial Agricultural Science and Technology Independent Innovation Fund Project (CX(22)3048) and Key Laboratory of Land Satellite Remote Sensing Application, Ministry of Natural Resources of the People’s Republic of China (Grant No. KLSMNR-G202208)