[Prediction models of knot volume inside the stem for Korean pine plantation]

Based on 1207 knots from 49 sample trees of 29 standard plots of Korean pine plantations in Linkou and Dongjingcheng Forest Bureau of Heilongjiang Province, China, we extracted longitudinal sections of knots using the image processing software Digimizer and represented the shape of knots using two-dimensional scatter plots. According to the two-dimensional scatter plots, knots of Korean pine plantation were divided into three types: 1) alive knots (whole knot contained only sound knot portion); 2) non-occluded dead knots (whole knot contained both sound and loose knot portions); 3) occluded dead knots (the sound and loose portion of the knot were partially occluded by the bark). For all the three types of knots, the volume of sound knot was calculated by mathematical integral of the sound knot shape equation. The volume of loose knot was calculated using the volume equation of a cylinder. The total volume of knots was calculated as the sum of sound and loose knot volume. Finally, based on knot variables (diameter, relative height and total length of knots) and tree variable (diameter at breast height), we established the prediction models for sound knot volume, loose knot volume, and total volume of knot using the linear mixed model at plot level and tree level. Compared with fixed-effects model, the mixed effects models of the volume of sound knot, loose knot, and total knots provided more accurate parameter estimation, more uniform residual distribution, and higher model fitting precision. The validation results showed that prediction precision of each fixed-effect model was higher than 90%, while that of the mixed models with plot and tree effect was above 93%, indicating that the established model could well predict the volume of knot for Korean pine plantation.