叶面积指数(LAI)的田间测量是生态和农业等领域的常规工作之一, 测量方法分为直接测量和间接测量, 间接测量中有一类方法基于数字相机照片提取冠层孔隙率, 再用有限长度平均法同时估算LAI和聚集指数。然而, 有限长度平均法自提出以来缺少进一步的发展, 在有限长度的样线/样方上应用比尔定律的方式具有理论缺陷, 可能造成无效值或高估LAI。从模拟的训练数据中提取经验公式以取代比尔定律进行样线/样方的LAI估算, 提高了有限长度平均法的精度和鲁棒性。进一步分析在一定精度需求下对样线/样方大小和数量的要求, 对于非均匀样地, 提出样线长度为8倍等效叶片边长、样方边长为3倍等效叶片边长的推荐设置。在基于数字相机照片提取非均匀样地LAI的应用中, 使用样方采样比样线采样更为适宜。

Measuring leaf area index (LAI) in the field is a common task in ecological and agricultural studies. There are direct and indirect methods for the task. One of the frequently used indirect methods is to acquire a digital photo of the vegetation canopy and extract the area ratio of green leaf, then simultaneously estimate LAI and clumping index with the finite-length averaging method proposed by Lang and Xiang (1986). However, the finite-length averaging method still needs improvement. For example, using Beer’s law for estimating leaf area in the sample’s line of finite length is theoretically incompatible with its basic assumption of heterogeneous canopy, resulting in over-estimation or even invalid value of the calculated LAI. Thus, this study proposed empirical formulas to replace Beer’s law in characterizing the relation between gap ration and LAI in the sample line (or sample square) based on computer simulations. The new formulas correct the shortcomings of over-estimation and instability of Beer’s law when the canopy is dense and the length of sample line (or sample square) is short. Then, the optimal setting for the length of sample line (or sample square) in a heterogeneous field is discussed: the length of 8 times an equivalent leaf length for sample line and 3 times an equivalent leaf length for a sample square were recommended in most cases of crop or grass scenes. As well, a sample square was superior to a sample line in applications estimating LAI of a heterogeneous field.