A longitudinal height–diameter model for Norway spruce in Finland

A height–diameter (H–D) model for Norway spruce (Picea abies (L.) Karst.) was estimated from longitudinal data. The Korf growth curve was used as the H–D curve. Firstly, H–D curves for each stand at each measurement time were fitted, and the trends in the parameters of the H–D curve were modeled. Secondly, the trends were included in the H–D model to estimate the whole model at once. To take the hierarchy of the data into account, a mixed-model approach was used. This makes it possible to calibrate the model for a new stand at a given point in time using sample tree height(s). The heights may be from different points in time and need not be from the point in time being predicted. The trends in the parameters of the H–D curve were not estimated as a function of stand age but as a function of the median diameter of basal area weighted diameter distribution (dGm). This approach was chosen because the stand ages may differ substantially among stands with similar current growth patterns. This is true especially with shade-tolerant tree species, which can regenerate and survive for several years beneath the dominant canopy layer and start rapid growth later. The growth patterns in stands with a given dGm, on the other hand, seem not to vary much. This finding indicates that the growth pattern of a stand does not depend on stand age but on mean tree size in the stand.