<p>Timber quality modeling is essential for value-oriented forest management since the traditional, volume-only yield models often ignore internal defects (notably knots) and overestimate usable wood. In this study, we developed an integrated framework to quantify knot-free and knotty core volumes in Korean pine (<i>Pinus koraiensis</i>) plantations in Northeast China. The framework couples a re-parameterized Kozak (For Chron 80:507-515, 2004) taper equation with a bark factor model to convert outside- to inside-bark diameters and two height-dependent functions to describe sound- and loose-knot vertical distribution. Nonlinear mixed-effects models were employed with climatic, stand, competition, and tree predictors (e.g., <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$DBH$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">DBH</mi> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$CR$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CR</mi> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$Hegyi$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">Hegyi</mi> </mrow> </math></EquationSource> </InlineEquation> index,<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$SI$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">SI</mi> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$CMD$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CMD</mi> </mrow> </math></EquationSource> </InlineEquation>) to partition each stem into knot-free and knotty core sections (sound- and loose-knot) based on the heights to crown base (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$HCB$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">HCB</mi> </mrow> </math></EquationSource> </InlineEquation>) and lowest dead branch (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">$HDB$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">HDB</mi> </mrow> </math></EquationSource> </InlineEquation>), ensuring consistency with observed stem–crown structure. Model evaluation showed high accuracy for all three curves (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$RMSE$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">RMSE</mi> </mrow> </math></EquationSource> </InlineEquation> 0.70–1.04 cm; <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$MAE$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">MAE</mi> </mrow> </math></EquationSource> </InlineEquation> 0.72–0.98 cm), supporting reliable prediction of stem profiles and internal knot distributions. We further identified the drivers of section yields at tree and stand scales: at the tree scale, climate, stand, competition, and tree attributes contributed comparably to knot-free yield; for the loose-knot (lowest-quality) section, climate (51%) and tree factors (37%) dominated. At the stand scale, knot-free proportion was accurately predicted using only basal area (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$BAS$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">BAS</mi> </mrow> </math></EquationSource> </InlineEquation>), dominant height (<InlineEquation ID="IEq11"> <EquationSource Format="TEX">${H}_{dom}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mrow> <mi mathvariant="italic">dom</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>), and mean annual temperature (<InlineEquation ID="IEq12"> <EquationSource Format="TEX">$MAT$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">MAT</mi> </mrow> </math></EquationSource> </InlineEquation>), with an <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$RMSE$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">RMSE</mi> </mrow> </math></EquationSource> </InlineEquation> of 0.03. The framework delivers fast, reliable estimates of timber quantity and quality under varying stand and climate conditions, supporting higher-value management of Korean pine.</p>

Integrating stem taper and knot-length models to simulate internal knotty structure and quantify knot-free and knotty core volumes in Korean pine plantation

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2026年1月11日

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Zheng Miao,
Xuehan Zhao,
Yumeng Jiang,
Timo Pukkala,
Lihu Dong,
Fengri Li

摘要

Timber quality modeling is essential for value-oriented forest management since the traditional, volume-only yield models often ignore internal defects (notably knots) and overestimate usable wood. In this study, we developed an integrated framework to quantify knot-free and knotty core volumes in Korean pine (Pinus koraiensis) plantations in Northeast China. The framework couples a re-parameterized Kozak (For Chron 80:507-515, 2004) taper equation with a bark factor model to convert outside- to inside-bark diameters and two height-dependent functions to describe sound- and loose-knot vertical distribution. Nonlinear mixed-effects models were employed with climatic, stand, competition, and tree predictors (e.g., $DBH$ $DBH$ , $CR$ $CR$ , $Hegyi$ $Hegyi$ index, $SI$ $SI$ , $CMD$ $CMD$ ) to partition each stem into knot-free and knotty core sections (sound- and loose-knot) based on the heights to crown base ( $HCB$ $HCB$ ) and lowest dead branch ( $HDB$ $HDB$ ), ensuring consistency with observed stem–crown structure. Model evaluation showed high accuracy for all three curves ( $RMSE$ $RMSE$ 0.70–1.04 cm; $MAE$ $MAE$ 0.72–0.98 cm), supporting reliable prediction of stem profiles and internal knot distributions. We further identified the drivers of section yields at tree and stand scales: at the tree scale, climate, stand, competition, and tree attributes contributed comparably to knot-free yield; for the loose-knot (lowest-quality) section, climate (51%) and tree factors (37%) dominated. At the stand scale, knot-free proportion was accurately predicted using only basal area ( $BAS$ $BAS$ ), dominant height ( ${H}_{dom}$ $H_{dom}$ ), and mean annual temperature ( $MAT$ $MAT$ ), with an $RMSE$ $RMSE$ of 0.03. The framework delivers fast, reliable estimates of timber quantity and quality under varying stand and climate conditions, supporting higher-value management of Korean pine.