Modelling individual tree diameter growth for Norway spruce in the Czech Republic using a generalized algebraic difference approach

Individual tree-based growth models precisely describe the growth of individual trees irrespective of stand complexity. These models are more useful than the stand-based growth models for effective management of forests. We developed an individual tree diameter growth model for Norway spruce (Picea abies /Linnaeus/ H. Karsten) using permanent research plot data collected from Krkonoše National Park in the Czech Republic. The model was tested against a part of the Czech National Forest Inventory (NFI) data that originated from the western region of the country. Among various models derived by a generalized algebraic difference approach (GADA), the GADA model derived from the Chapman-Richards function best suited to our data. Tree-specific parameters unique to each growth series, which describe tree-specific growth conditions, were estimated simultaneously with global parameters common to all growth series using the iterative nested regressions. The model described most of the variations in diameter growth for model calibration data (R2adj = 0.9901, RMSE = 0.5962), leaving no significant trends in the residuals. A test against NFI data also confirms that the model is precise enough for predictions of diameter growth for ranges of site quality, tree size, age, and growth condition. The model also possesses biologically desirable properties because it produces the curves with growth rates and asymptotes that increase with increasing site quality. The GADA model is path-invariant and therefore applicable for both forward and backward predictions, meaning that the model can precisely predict diameter growth at any past ages of the trees.