Weibull models for single-tree increment of Norway spruce, Scots pine, birch and other broadleaves in Norway

Abstract

Distance-independent, non-linear models of 5-year diameter increment for Norway spruce, Scots pine, birch and other broadleaved trees were developed, evaluated and compared on data from the Norwegian National Forest Inventory. The models were based on a Weibull curve dependent on diameter and a modifier function dependent on site parameters. A non-linear mixed model approach was used to fit the models. Model fit was assessed by the Pseudo-R ² on total level and on plot level reflecting a random plot effect. The values were 0.31, 0.20, 0.13 and 0.10 for Norway spruce, Scots pine, birch and other broadleaves, respectively. The bias estimates from an independent validation were 0.1, 0.0, 0.1 and 0.3 mm for Norway spruce, Scots pine, birch and other broadleaves, respectively. The results from the independent validation were compared with results from identical tests of three other sets of models. The comparison indicated good model performance of the current models. The models were also compared by evaluating their behaviour when the tree size component was extrapolated beyond the range of the model development data. The results indicated that an additive model of diameter increment and the current non-linear Weibull and modifier model of diameter increment performed best.

Keywords:

• Mixed models
• NFI data
• radial growth
• single tree
• Weibull

Acknowledgements

The research leading to this article was funded by the Research Council of Norway (research project no. 153185/110). We wish to thank Associate Professor Terje Gobakken, Professor Tron Eid (Norwegian University of Life Sciences) and two referees for very useful comments. Thanks also to Rune Eriksen at the Norwegian Institute of Land Inventory for supplying the data.