A fine-scale model for area-based predictions of tree-size-related attributes derived from LiDAR canopy heights

Abstract

We propose a conceptual (generic) allometric (power function) relationship between tree-size-related forest inventory attributes (e.g. biomass, volume, basal area, quadratic mean diameter, Lorey's height) and canopy height (CH) as estimated from first-return airborne light detection and ranging (LiDAR) pulses. A data-driven estimation of the parameters in the power function is complicated, so we recommend an alternative approximation obtained via a linearisation step. Only two predictors appear in the approximation: the mean CH and the variance of CHs within the spatial domain supported by field data. The proposed model eliminates an otherwise complex search for the best predictors amongst a large number of candidate LiDAR metrics. It also facilitates model comparisons and interpretation. Fit statistics estimated for volume, basal area, quadratic mean diameter and Lorey's height – using three separate datasets from Norway – were compelling.

Keywords:

• Forest inventory
• Gaussian kernel
• non-linear least squares
• variance functions
• power function
• allometric relationship

Acknowledgements

The authors would like to thank Mr Marius Hauglin, Mr Vegard Lien and Mr John Gunnar Dokk at the Norwegian University of Life Sciences (UMB) for well-conducted fieldwork and Dr Ole Martin Bollandsås (UMB) for computing the field values of the sample plots collected in Aurskog-Høland municipality. We are also grateful to Mjøsen Skog BA for organising the fieldwork in the Kongsvinger and Sør-Odal municipalities. Mike Wulder provided helpful comments to an earlier draft of the manuscript. Two anonymous referees helped us with many constructive suggestions for improvement.