McArthur's foliage height diversity (FHD) has been the gold standard in the determination of structural complexity of forests characterized by LiDAR vertical height profiles. It is based on Shannon's entropy index, which was originally designed to describe evenness in abundances among qualitative typologies, and thus the calculation of FHD involves subjective layering steps which are essentially unnatural to describe a continuous variable (X) such as height. In this contribution we aim to provide a mathematical framework for determining maximum entropy in 3D remote sensing datasets based on the Gini Coefficient of theoretical continuous distributions, intended to replace FHD as entropy measure in vertical profiles of LiDAR heights (1D, X), with extensions to variables expressing dimensions of higher order (2D or 3D, Z ∝ X² or X³). Then we apply this framework to Boreal forests in Finland to describe landscape heterogeneity with the intention to improve the modelling of forest aboveground biomass (AGB), hypothesizing that LiDAR models of AGB should essentially be different in areas of differing structural characteristics. We carried out a pre-stratification of LiDAR data collected in 2012 using simple rules applied to the L-skewness (L_skew) and L-coefficient of variation of LiDAR echo heights (L_cv; equivalent to the Gini coefficient, GC_H), determining a new threshold at GC_H = 0.33 as a consequence of the newly developed mathematical proofs. We observed only moderate improvements in terms of model accuracies: RMSDs reduced from 41.7% to 38.9 or 37.0%. More remarkably, we identified critical differences in the metrics selected at each stratum, which is useful to understand what predictor variables are more important for estimating AGB at each area of a forest. We observed that higher LiDAR height percentiles are more relevant at open canopies and heterogeneous forests, whereas closed canopies in homogeneous forests obtain most accurate predictions from a combination of cover metrics and percentiles around the median. Without stratification, the overall model would neglect explained variability in the structural types of lower occurrence, and predictions from a model influenced by structural types of higher occurrence would be biased at those areas. These results are thus useful in terms of improving our understanding on the relationships underlying LiDAR-AGB models.

麦克阿瑟（McArthur）的枝叶高度多样性（FHD）已成为确定以LiDAR垂直高度剖面为特征的森林结构复杂性的金标准。它基于Shannon的熵指数，该指数最初旨在描述定性类型之间的丰度均匀性，因此FHD的计算涉及主观分层步骤，而这些主观分层步骤本质上不适合描述连续变量（X），例如高度。在此贡献中，我们旨在提供一个基于理论连续分布的基尼系数确定3D遥感数据集最大熵的数学框架，以取代FHD作为LiDAR高度（1D，X），并扩展了表示高阶维度（2D或3D，Z  ∝  X ²或X ³）的变量。然后，我们将此框架应用于芬兰的北方森林，以描述景观异质性，目的是改善森林地上生物量（AGB）的建模，并假设AGB的LiDAR模型在结构特征不同的区域应基本不同。我们使用适用于LiDAR回波高度的L偏度（L _skew）和L系数变化的简单规则（L _cv；等效于Gini系数），对2012年收集的LiDAR数据进行了预分层。GC _H）， 由于新开发的数学证明，在GC _H = 0.33处确定了一个新的阈值。我们仅在模型准确性方面观察到了适度的改进：RMSD从41.7％降低到38.9或37.0％。更显着的是，我们确定了在每个层次选择的指标中的关键差异，这有助于了解哪些预测变量对于估计AGB更为重要在森林的每个区域。我们观察到，较高的LiDAR高度百分位数在开放式林冠和非均质森林中更为相关，而在均质林中的封闭式林冠通过覆盖度量和中位数附近的百分位数的组合获得最准确的预测。如果没有分层，整个模型将忽略发生率较低的结构类型的解释性可变性，而受发生率较高的结构类型影响的模型的预测将在那些区域出现偏差。因此，这些结果对于增进我们对LiDAR- AGB模型基础关系的理解很有用。