Derivations of stand heights from airborne laser scanner data with canopy-based quantile estimators

The distribution of canopy heights obtained with an airborne laser scanner over a field trial with Douglas-fir (Pseudotsuga menziesii (Mirb.) France) was a function of the vertical distribution of foliage area. Over a wide range of canopy structures, the proportion of laser pulses returned from or above a given reference height was proportional to the fraction of leaf area above it. We hypothesized that the quantile of the laser canopy heights matching in probability the fraction of leaf area above a desired height would be an unbiased estimator of same. This was confirmed in 36 (20 x 20 m) plots and 6 older validation plots. Canopy-based quantiles of the laser canopy height data were within 6% (mean 3%) of the field estimates. Laser and field estimates were strongly correlated (r similar to 0.8), and statistical tests supported the null hypotheses of no difference in mean stand height (P > 0.3). A geometric model successfully predicted the mean difference between the laser canopy heights and the mean tree height. Our results explicate why estimation of stand heights from laser scanner data based on the maximum canopy height value in each cell of a fixed area grid has been successful in practice.