Cross-sectional interpolation of annual rings within a 3D root model

Ring width of a given year can be highly variable throughout the cross section of a stem. This is especially true for roots. Therefore, the entire circumference of tree rings is often needed for studies focusing on specific reactions of individual trees on certain environmental conditions. Also, ring reconstructions are of interest for biomass calculations estimated by the cross-sectional area. The aim of the study is thus to reconstruct tree rings of cross sections within a 3D root-surface model, which will be the basis for an upcoming 3D root-development model. A FARO ScanArm was used for the acquisition of the 3D root structure (Technologies Inc., 2010). Afterwards ring-width data was measured along 4 radii per cross section and the resulting ring boundaries were integrated into the 3D root model. A weighted interpolation algorithm was used to reconstruct entire ring-width profiles of the cross sections. The algorithm considered the ring-width variations of the adjacent radii as well as the outer shape of the cross section. Hence, the intention was to estimate ring width around the root circumference using ring widths measured along 4 radii and the surface dimensions of roots. Interpolated ring-width data was compared to the measured tree-ring data as a control for the developed interpolation algorithm. Comparisons between modelled and empirical values showed a mean absolute error of about 0.06 mm deviation, and with a few exceptions the growth patterns could be accurately simulated. This has permitted additional radii measurements to be replaced by model interpolations.