Modelling individual tree height to crown base of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.)

Abstract

Height to crown base (HCB) of a tree is an important variable often included as a predictor in various forest models that serve as the fundamental tools for decision-making in forestry. We developed spatially explicit and spatially inexplicit mixed-effects HCB models using measurements from a total 19,404 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) on the permanent sample plots that are located across the Czech Republic. Variables describing site quality, stand density or competition, and species mixing effects were included into the HCB model with use of dominant height (HDOM), basal area of trees larger in diameters than a subject tree (BAL- spatially inexplicit measure) or Hegyi’s competition index (HCI—spatially explicit measure), and basal area proportion of a species of interest (BAPOR), respectively. The parameters describing sample plot-level random effects were included into the HCB model by applying the mixed-effects modelling approach. Among several functional forms evaluated, the logistic function was found most suited to our data. The HCB model for Norway spruce was tested against the data originated from different inventory designs, but model for European beech was tested using partitioned dataset (a part of the main dataset). The variance heteroscedasticity in the residuals was substantially reduced through inclusion of a power variance function into the HCB model. The results showed that spatially explicit model described significantly a larger part of the HCB variations [R2adj = 0.86 (spruce), 0.85 (beech)] than its spatially inexplicit counterpart [R2adj = 0.84 (spruce), 0.83 (beech)]. The HCB increased with increasing competitive interactions described by tree-centered competition measure: BAL or HCI, and species mixing effects described by BAPOR. A test of the mixed-effects HCB model with the random effects estimated using at least four trees per sample plot in the validation data confirmed that the model was precise enough for the prediction of HCB for a range of site quality, tree size, stand density, and stand structure. We therefore recommend measuring of HCB on four randomly selected trees of a species of interest on each sample plot for localizing the mixed-effects model and predicting HCB of the remaining trees on the plot. Growth simulations can be made from the data that lack the values for either crown ratio or HCB using the HCB models.

Generalized Nonlinear Mixed-Effects Individual Tree Crown Ratio Models for Norway Spruce and European Beech

“…Most of the existing CR models have included the measures describing the effects of competition (e.g., stand basal area, crown competition factor, and spacing index), the effects of size of trees (e.g., diameter, height, height-to-diameter ratio, and stand age), and the effects of site characteristics (e.g., altitude, slope, and aspect), but not the measures that describe the effects of intra-or inter-species interactions and canopy height differentiation on the CR variation. The effects of species mixture on tree and stand characteristics have been thoroughly analyzed in several studies [42,44,48,56,[58][59][60]. These studies confirm that species-mixing effect on tree characteristics is highly significant; therefore, this cannot be disregarded when measurements from mixed stands are used.…”

“…The studied forests consist of the monospecific stands and mixed stands of Norway spruce and European beech. Most of these sample plot data have been used in other studies [42,48,56,61,63,64] with different objectives. Therefore, more information about sample plots and sampling designs can be obtained from this literature.…”

“…Area of the sample plots varies from 2500 to 4900 m 2 , and they have square and rectangular shapes. The sample plots are representative of a wide range of altitudes (240-1370 m), temperatures (4-9.5 • C of mean annual temperature), precipitation (500-1450 mm of mean annual precipitation), and growing periods (45-180 days of growing season length) [48,56]. The canopy layers, mortality, regeneration, dead wood stocking, stand density, and stand development stage were taken into account while laying out the sample plots [65].…”

“…We considered HCB as the lowest point of the crown on the bole where continuous whorl with all living branches was formed. However, we did not consider a whorl as a continuous if there were one or more dead whorls above it [48,56]. We recorded 1-26 species per sample plot.…”

“…In this situation, the mixed-effects modeling approach, which allows to include both fixed and random effects into the model, may be the most appropriate [54]. The fixed parameters in the mixed-effects model account for the effects of main and covariate predictors as in the ordinary least square regression, while the random component accounts for variability caused by stochastic factors [41,[53][54][55][56][57].…”