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

Abstract 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.