Indirect Measurement of Forest LAI to Deal with the Underestimation Problem Based on Beer-Lambert Law

  • State Key Laboratory of Remote Sensing Science, Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities, School of Geography, Beijing Normal University, Beijing 100875, China

Received date: 2011-10-27

  Revised date: 2012-05-06

  Online published: 2012-06-25

Supported by



Leaf area index (LAI) defined as one half of the total green leaf area per unit ground surface area. It is an important parameter of canopy structure, because it relates to many biophysical and physiological processes of canopy, including photosynthesis, respiration, transpiration, carbon cycling, net primary productivity, precipitation interception, and energy exchange, etc. Accurate measurement of forest leaf area index by means of remote sensing has been an important task in remote sensing research. The direct method of LAI measurement is time-consuming, labor-intensive and may destroy plants. Compared to the direct method, indirect methods by means of optical methods are quicker and more efficient. These methods are all based on the Beer-Lambert law. As an important means to validate remote sensing LAI products, indirect LAI ground measurement is the basis and standard of remote sensing inversion. However, indirect ground measurement method based on Beer-Lambert law has serious underestimation problem in forest. The derivation of Beer's law was originally in uniform gas medium, when applied to discrete vegetation measurement on a pixel scale. Its applicability has not got enough attention and validation. In this paper, by theory analysis, we find that the underestimation of leaf area index comes from the spatial heterogeneity of foliage area volume density, extinction depth and leaf angle projection function G if Beer-Lambert law is applied to LAI measurements in forest. Quantitative assessment of impact on LAI measurement from non-random distribution of canopy was made. It was shown that non-random distribution of canopy may bring 20-40% measurement error of LAI. An important conclusion is that the simple correction of Beer-Lambert law has significant limitations on the in situ forest LAI measurement. This method is not a fundamental solution to this underestimation problem, and the theories and methods for LAI indirect measurement need to be changed.

Cite this article

HU Ronghai, YAN Guangjian . Indirect Measurement of Forest LAI to Deal with the Underestimation Problem Based on Beer-Lambert Law[J]. Journal of Geo-information Science, 2012 , 14(3) : 366 -375 . DOI: 10.3724/SP.J.1047.2012.00366


[1] Jonckheere I, Fleck S, Nackaerts K, et al. Review of methods for in situ leaf area index determination: Part I. Theories, sensors and hemispherical photography[J]. Agricultural and Forest Meteorology, 2004, 121(1-2): 19-35.

[2] Weiss M, Baret F, Smith G J, et al. Review of methods for in situ leaf area index (LAI) determination: Part II. Estimation of LAI, errors and sampling[J]. Agricultural and Forest Meteorology, 2004, 121(1-2): 37-53.

[3] 张仁华,孙晓敏,朱治林. 叶面积指数的快速测定方法——植被定量遥感的地面标定技术[J]. 国土资源遥感, 1998 (1): 54-60.

[4] 徐希孺,范闻捷,陶欣. 遥感反演连续植被叶面积指数的空间尺度效应[J]. 中国科学(D辑:地球科学), 2009, 39(1): 79-87.

[5] 刘洋,刘荣高,刘斯亮,等. 基于物理模型训练神经网络的作物叶面积指数遥感反演研究[J]. 地球信息科学学报, 2010, 12(3): 426-435.

[6] 江东,付晶莹,黄耀欢,等. 地表环境参数时间序列重构的方法与应用分析[J]. 地球信息科学学报, 2011,13 (4): 439-446.

[7] Kvet J, Marshall J K. Assessment of leaf area and other assimilating plant surfaces [M]. The Hague: Dr W.Junk, 1971,517-555.

[8] Daughtry C S T. Direct measurements of canopy structure [J]. Remote Sensing Reviews, 1990, 5(1): 45-60.

[9] Smith N J. Estimating leaf area index and light extinction coefficients in stands of Douglas-fir (Pseudotsuga menziesii) [J]. CANADIAN JOURNAL OF FOREST RESEARCH, 1993, 23(2): 317-321.

[10] Cutini A, Matteucci G, Mugnozza G S. Estimation of leaf area index with the Li-Cor LAI 2000 in deciduous forests[J]. Forest Ecology and Management, 1998, 105(1-3): 55-65.

[11] Chen J M, Rich P M, Gower S T, et al. Leaf area index of boreal forests: Theory, techniques, and measurements[J]. J. Geophys. Res., 1997, 102(D24): 29429-29443.

[12] 邹杰,阎广建. 森林冠层地面叶面积指数光学测量方法研究进展 [J]. 应用生态学报, 2010, 21(11): 2971-2979.

[13] Lang A R G, Xiang Y. Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies[J]. Agricultural and Forest Meteorology, 1986, 37(3): 229-243.

[14] Miller E E, Norman J M. A sunfleck theory for plant canopies II. Penumbra effect: Intensity distributions along sunfleck segments[J]. Agronomy Journal, 1971, 63(5): 739-743.

[15] Chen J M, Cihlar J. Plant canopy gap-size analysis theory for improving optical measurements of leaf-area index[J]. Appl. Opt., 1995, 34(27): 6211-6222.

[16] Walter J-M N, Fournier R A, Soudani K,et al. Integrating clumping effects in forest canopy structure: An assessment through hemispherical photographs[J]. Canadian Journal of Remote Sensing, 2003, 29(3): 388-410.

[17] Zou J, Yan G, Zhu L,et al. Woody-to-total area ratio determination with a multispectral canopy imager[J]. Tree Physiology, 2009, 29(8): 1069-1080.

[18] Leblanc S G, Chen J M, Fernandes R,et al.Methodology comparison for canopy structure parameters extraction from digital hemispherical photography in boreal forests[J]. Agricultural and Forest Meteorology, 2005, 129(3-4): 187-207.

[19] Chen J M, Black T A. Defining leaf area index for non-flat leaves[J]. Plant, Cell & Environment, 1992, 15(4): 421-429.

[20] Myneni R B, Ross J, Asrar G. A review on the theory of photon transport in leaf canopies[J]. Agricultural and Forest Meteorology, 1989, 45(1-2): 1-153.

[21] Nilson T. A theoretical analysis of the frequency of gaps in plant stands [J]. Agricultural Meteorology, 1971(8): 25-38.

[22] 徐希儒. 遥感物理[M]. 北京: 北京大学出版社, 2005,80-82.

[23] Monteith J L. Light distribution and photosynthesis in field crops [J]. Annals of Botany, 1965, 29(1): 17-37.

[24] Chen J M, Leblanc S G. A four-scale bidirectional reflectance model based on canopy architecture[J]. IEEE Transactions on Geoscience and Remote Sensing, 1997, 35(5): 1316-1337.