2 Weiwei Huang: Ellipse or superellipse for tree-ring geometries? Evidence from six conifer species

Huan Wei-Wei is at Nanjing Forestry University. The report is based on joint work with Kehang Ma and Daniel K. Gladish

In nature, under environmental pressures, such as wind, slope, water availability, etc., tree-ring shapes in most cases appear to be elliptical rather than circular. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows the generation of a larger range of geometries: hypoellipse, ellipse, and hyperellipse. The more complex Gielis equation can generate asymmetrical shapes. In the present study, we modeled the geometries of tree-rings for six coniferous species using the superellipse equation (i.e., the three-parameter model) and the more complex Gielis equation (i.e., the five-parameter model). The species-specific mean value of n approached 2 and the k-value was lower than 1, which confirmed that most tree-ring shapes of the studied coniferous species were closer to an ellipse rather than a circle.
However, based on superellipse equation the n-value and k-value both showed an inter-annual fluctuation that ranged between 1.75–2.25 and 0.82–1.00, respectively. This suggests that most samples of tree-rings did not follow the typical ellipse equation, but the superellipse equation. Although the Gielis equation is slightly better in the goodness of fit than the superellipse equation, 86.67% of the percent errors (PEs) of RMSEadj between these two equations were smaller than 5%, which means that the superellipse equation is better given the trade-off between the model structural complexity and goodness of fit.
Most tree-ring shapes tend to be bilaterally symmetrical, and the three-parameter superellipse equation was verified to fit the tree-ring boundaries and estimate the inter-annual increments of tree-ring area well.