基于贝尔定律的叶面积指数测定适用性分析与改进

Leaf area index is an important parameter to related studies on geosciences, its measurement accuracy directly determines the simulation precision of net primary productivity from leaf level to the canopy scale by using carbon cycle model. Optical instruments were developed to measure leaf area index based on the theory of Bell-Lambert’s law. However, Bell-Lambert’s law with the assumption of continuous vegetation of uniform vertical stratification, and the mismatch between Bell-Lambert’s law and geometrical optics model make some limitations of leaf area index measurement based on Bell-Lambert’s law. In view of this problem, this study focuses on the method improvement of leaf area index measurement combining the theoretical derivation with experimental data validation. From three scales, including a single tree scale, sample area scale (or pixel scale), and regional scale (it can be thought as infinite dimension from the mathematics), the consistency of mathematical formula for the background visual probability calculation from Bell-Lambert’s law and geometrical optics model was studied, and the application condition of Bell-Lambert’s law is analyzed, to find the spatial scale at which Bell-Lambert’s law is ineffective and impracticable. When Bell-Lambert’s law is ineffective and impracticable, taking clumping index as the breakthrough point, the quantitative relationship between canopy clumping index and leaf clumping index in the canopy is developed to determine the final total clumping index of the pixel, put forward the improvement method for the true leaf area index measurement, and improve its measurement accuracy.

叶面积指数是地学相关研究领域重要参数，其测定精度直接决定着碳循环模型从单位叶片推算到冠层尺度的净初级生产力的模拟精度。光学仪器法测定叶面积指数的基础是贝尔定律，然而贝尔定律的连续植被水平均一垂直分层的假定以及贝尔定律与几何光学模型的不协调使得贝尔定律测定叶面积指数存在局限性。针对该问题本研究采用理论推导与实验数据验证相结合的方法重点研究森林植被叶面积指数测定的改进方法，从单棵树、样地尺度（或像元尺度）及区域尺度（从数学角度可认为像元无限大尺度）三种尺度研究贝尔定律与几何光学模型背景可视概率数学公式的一致性，分析贝尔定律的适用条件，从而找到贝尔定律失效的像元空间尺度。在贝尔定律失效的像元空间尺度下以聚集度指数为突破点，研究树冠空间分布与树冠内叶子聚集分布的定量关系，进而确定像元尺度内总冠层聚集度指数，提出叶面积指数测定的改进方法，提高真实叶面积指数的测定精度。

贝尔定律是光学仪器法测定叶面积指数的基础，然而对于森林植被，无论树冠分布是随机分布还是丛生分布，亦或是规则分布，应用贝尔定律的形式都是不变的。针对贝尔定律测定叶面积指数存在局限性问题，项目在帽儿山实验林场设置针叶、阔叶、针阔混交3块100m*100m的样地，每隔10m设置落叶框收集装置，利用LAI-2200与TRAC仪器测量样地的有效叶面积指数和叶聚集度指数，二者联合获得光学仪器测量的真实叶面积指数，与凋落物法测量的样地真实叶面积指数进行比较，从理论推导、数据模拟到实验数据验证，讨论贝尔定律的适用性；将样地划分为20m*20m，30m*30m，40m*40m，50m*50m和100m*100m五种尺度，研究四尺度模型与贝尔定律计算孔隙率的关系，确定贝尔定律测定叶面积指数的适用尺度范围；提出贝尔定律失效时，根据不同尺度的聚集度指数（树冠尺度聚集度指数、树冠内叶子尺度聚集度指数、针簇比）与非连续植被孔隙率调整比例因子（1-P，P表示树冠为刚体的树冠间孔隙率）修正贝尔定律测得的孔隙率。结果表明：(1)贝尔定律的适用条件为单株树或像元（或样地）无穷大；(2)在任何有限尺度下采用贝尔定律测定的真实叶面积指数均存在较大误差；(3)采用三种尺度的聚集度指数调整有效叶面积指数校正贝尔定律计算的冠层孔隙率效果不佳，而采用比例因子校正贝尔定律计算的孔隙率，与四尺度模型计算的背景可视概率差值小于0.1；(4)校正后的贝尔定律测得的叶面积指数除以叶子间的聚集度指数，针叶树种再除以针簇比，获到真实叶面积指数，在三块样地内精度均提高10%以上，三块样地叶面积指数提高的最高精度分别可达到39.48%、32.19%和26.73%。因此，采用比例因子1-P校正贝尔定律获得的真实叶面积指数是可行的。研究结果为进一步提高叶面积指数测定精度提供理论方法与参考依据，为大区域尺度叶面积指数估算提供校正方法。