We present a new algorithm for the estimation of the plant area density (PAD) profiles and plant area index (PAI) for forested areas based on data from airborne lidar. The new element in the algorithm is to scale and average returned lidar intensities for each lidar pulse, whereas other methods do not use the intensity information at all, use only average intensity values, or do not scale the intensity information, which can cause problems for heterogeneous vegetation. We compare the performance of the new algorithm to three previously published algorithms over two contrasting types of forest: a boreal coniferous forest with a relatively open structure and a dense beech forest. For the beech forest site, both summer (full-leaf) and winter (bare-tree) scans are analyzed, thereby testing the algorithm over a wide spectrum of PAIs. Whereas all tested algorithms give qualitatively similar results, absolute differences are large (up to 400?% for the average PAI at one site). A comparison with ground-based estimates shows that the new algorithm performs well for the tested sites. Specific weak points regarding the estimation of the PAD from airborne lidar data are addressed including the influence of ground reflections and the effect of small-scale heterogeneity, and we show how the effect of these points is reduced in the new algorithm, by combining benefits of earlier algorithms. We further show that low-resolution gridding of the PAD will lead to a negative bias in the resulting estimate according to Jensen's inequality for convex functions and that the severity of this bias is method dependent. As a result, the PAI magnitude as well as heterogeneity scales should be carefully considered when setting the resolution for the PAD gridding of airborne lidar scans.
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