A Modification of the Finite-length Averaging Method in Measuring Leaf Area Index in Field

doi:10.11983/CBB17083

Abstract

Abstract: 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.

Key words: leaf area index, clumping index, Beer’s law;, sampling method

Liu Qiang, Cai Erli, Zhang Jialin, Song Qiao, Li Xiuhong, Dou Baocheng. A Modification of the Finite-length Averaging Method in Measuring Leaf Area Index in Field[J]. Chinese Bulletin of Botany, 2018, 53(5): 671-685.

Add to citation manager EndNote|Ris|BibTeX

URL: https://www.chinbullbotany.com/EN/10.11983/CBB17083

https://www.chinbullbotany.com/EN/Y2018/V53/I5/671

Figures/Tables 11

Figure 1 The 3 kinds of leaf shapes used in the simulation (strip, square and fusiform)

Figure 2 The mean and standard deviation (stdev) of projected leaf area ($\overline{PLA}$) with respect to different length (r) and canopy porosity (P) (fusiform leaves)(A) Mean of sample lines; (B) Mean of sample squares; (C) Stdev of sample lines; (D) Stdev of sample squares

Figure 3 The root mean square error (RMSE) and relative root mean square error (RRMSE) of the estimated projected leaf area (PLA) on the scale of sample line and sample square, simulated with fusiform leaf(A) RMSE using ƒ* in sample line; (B) RMSE using ƒ* in sample square; (C) RRMSE using ƒ* in sample line; (D) RRMSE using ƒ* in sample square; (E) RRMSE using Beer’s law in sample line; (F) RRMSE using Beer’s law in sample square

Figure 4 The RMSE of the estimated scene average projected leaf area ($\overline{PLA}$) with respect to sample line length r and sample number nThe black lines are contour lines of n∙r (Leaves are in fusiform shape and uniformly distributed in the scene, and the value of $\overline{PLA}$ is about 2).

Figure 5 The required range of r and n in measuring LAI with different accuracy criterion, in homogeneous scene (fusiform leaves)(A) Sample line+ƒ*; (B) Sample line+Beer’s law; (C) Sample square+f *; (D) Sample square+Beer’s law

Figure 6 The local gap image of the simulated scene A and scene B(A) Scene A with leaf area index (LAI) around 1; (B) Scene A with LAI around 4; (C) Scene B with LAI around 1; (D) Scene B with LAI around 4

Figure 7 The RMSE of estimated projected leaf area (PLA) in heterogeneous scene with respect to different length (r)(A) Scene A with sample line; (B) Scene A with sample square; (C) Scene B with sample line; (D) Scene B with sample square

Table 1 Estimated LAI and CI with sample line and different formulas

Scene ID	True values		Beer’s law			ƒ* of fusiform leaves			ƒ* of square leaves			ƒ* of strip leaves
Scene ID	LAI	CI	LAI	RMSE	CI	LAI	RMSE	CI	LAI	RMSE	CI	LAI	RMSE	CI
A	1.03	0.94	1.05	0.06	0.91	1.05	0.06	0.91	1.05	0.06	0.92	1.05	0.06	0.92
A	2.06	0.88	2.11	0.12	0.87	2.10	0.11	0.87	2.11	0.12	0.87	2.10	0.11	0.87
A	3.07	0.84	3.13	0.18	0.82	3.08	0.15	0.84	3.09	0.15	0.83	3.08	0.15	0.84
A	4.10	0.79	4.25	0.30	0.76	4.03	0.20	0.80	4.05	0.19	0.80	4.03	0.20	0.81
A	5.14	0.76	5.66	0.64	0.69	4.92	0.30	0.79	4.93	0.30	0.79	4.93	0.30	0.79
B	1.03	0.92	1.09	0.09	0.88	1.09	0.09	0.88	1.08	0.09	0.88	1.08	0.09	0.88
B	2.06	0.85	2.17	0.17	0.80	2.16	0.17	0.80	2.18	0.18	0.80	2.16	0.17	0.80
B	3.08	0.79	3.46	0.46	0.71	3.30	0.30	0.74	3.32	0.32	0.74	3.30	0.30	0.74
B	4.11	0.74	5.03	1.00	0.62	4.37	0.35	0.71	4.37	0.36	0.70	4.38	0.36	0.70
B	5.12	0.70	6.66	1.63	0.54	5.18	0.27	0.69	5.17	0.26	0.69	5.22	0.29	0.68

Table 2 Estimated leaf area index (LAI) and clumping index (CI) with sample square and different formulas

Scene ID	True values		Beer’s law			ƒ* of fusiform leaves			ƒ* of square leaves			ƒ* of strip leaves
Scene ID	LAI	CI	LAI	RMSE	CI	LAI	RMSE	CI	LAI	RMSE	CI	LAI	RMSE	CI
A	1.03	0.94	1.04	0.04	0.92	1.03	0.03	0.93	1.03	0.03	0.93	1.04	0.03	0.92
A	2.06	0.88	2.11	0.08	0.87	2.10	0.07	0.87	2.10	0.07	0.87	2.10	0.08	0.87
A	3.08	0.83	3.10	0.09	0.83	3.08	0.09	0.83	3.08	0.09	0.83	3.08	0.09	0.83
A	4.11	0.79	4.15	0.13	0.79	4.12	0.12	0.80	4.12	0.12	0.80	4.13	0.12	0.80
A	5.14	0.76	5.20	0.18	0.76	5.09	0.15	0.77	5.08	0.16	0.77	5.12	0.14	0.77
B	1.03	0.92	1.06	0.05	0.89	1.05	0.05	0.90	1.05	0.05	0.90	1.06	0.05	0.89
B	2.06	0.85	2.13	0.10	0.82	2.11	0.09	0.83	2.12	0.09	0.83	2.12	0.10	0.82
B	3.08	0.79	3.23	0.18	0.76	3.21	0.17	0.77	3.21	0.17	0.77	3.23	0.18	0.77
B	4.11	0.74	4.34	0.27	0.71	4.30	0.24	0.71	4.30	0.24	0.72	4.31	0.24	0.71
B	5.14	0.70	5.49	0.40	0.65	5.34	0.27	0.67	5.33	0.25	0.67	5.37	0.29	0.67

Figure 8 The time series of extracted leaf-cover from the digital photos acquired by the wireless LAI-Sensor in the corn field in Huailai Remote Sensing Test Station of Hebei province(A) May 30th; (B) June 7th; (C) June 13th; (D) June 20th; (E) July 4th; (F) July 16th

Table 3 The measured corn canopy parameters and estimated leaf area index (LAI) from digital photo of the corn field in Huailai Remote Sensing Test Station of Hebei province

Observation date	Measured LAI	Average single leaf area (cm²)	Leaf age	Average plants density	Equivalent leaf side length (cm)	Estimated LAI
Observation date	Measured LAI	Average single leaf area (cm²)	Leaf age	Average plants density	Equivalent leaf side length (cm)	Setting A	Setting B	Setting C	Setting D
May 30^th	0.1359	40.74	6	5.56	4.0368	0.1885	0.1916	0.1929	0.1963
June 7^th	0.5507	133.93	8	5.14	7.3193	0.5149	0.5206	0.5041	0.5124
June 13^th	0.8898	173.12	10	5.14	8.3215	0.9626	0.9669	0.9377	0.9500
June 20^th	1.3663	300.96	10	4.54	10.972	1.4123	1.4170	1.3702	1.3858
June 27^th	-	-	-	-	12.323	2.5817	2.6493	2.4040	2.4331
July 4^th	3.1837	467.50	15	4.54	13.675	3.4230	3.4990	3.1904	3.2443
July 16^th	3.7523	550.99	15	4.54	14.846	4.6051	4.8787	4.1786	4.3009

References 21

1	王锦地, 张戈, 肖月庭, 屈永华 (2007). 基于地物波谱库构造农作物生长参数的时空分布先验知识. 北京师范大学学报(自然科学版) 43, 284-291.
2	吴朝阳, 牛铮 (2008). 基于辐射传输模型的高光谱植被指数与叶绿素浓度及叶面积指数的线性关系改进. 植物学通报 25, 714-721.
3	杨贵军, 黄文江, 王纪华, 邢著荣 (2010). 多源多角度遥感数据反演森林叶面积指数方法. 植物学报 45, 566-578.
4	姚延娟, 范闻捷, 刘强, 李丽, 陶欣, 辛晓洲, 柳钦火 (2010). 玉米全生长期叶面积指数收获测量法的改进. 农业工程学报26(8), 189-194.
5	Baret F, De Solan B, Lopez-Lozano R, Ma K, Weiss M (2010). GAI estimates of row crops from downward looking digital photos taken perpendicular to rows at 57.5° zenith angle: theoretical considerations based on 3D architecture models and application to wheat crops.Agric Forest Meteor 150, 1393-1401.
6	Chen JM, Cihlar J (1995). Plant canopy gap-size analysis theory for improving optical measurements of leaf-area index.Appl Opt 34, 6211-6222.
7	Guo QH, Wu FF, Pang SX, Zhao XQ, Chen LH, Liu J, Xue BL, Xu GC, Li L, Jing HC, Chu CC (2016). Crop 3D: a platform based on LiDAR for 3D high-throughput crop phenotyping.Sci Sin Vitae 46, 1210-1221.
8	Hu RH, Yan GJ, Mu XH, Luo JH (2014). Indirect measurement of leaf area index on the basis of path length distribution.Remote Sens Environ 155, 239-247.
9	Jonckheere I, Fleck S, Nackaerts K, Muys B, Coppin P, Weiss M, Baret F (2004). Review of methods for in situ leaf area index determination: Part I. Theories, sensors and hemispherical photography. Agric Forest Meteor 121, 19-35.
10	Lang ARG, Xiang YQ (1986). Estimation of leaf area index from transmission of direct sunlight in discontinuous cano- pies.Agric Forest Meteor 37, 229-243.
11	Leblanc SG, Chen JM, Fernandes R, Deering DW, Conley A (2005). Methodology comparison for canopy structure parameters extraction from digital hemispherical photography in boreal forests.Agric Forest Meteor 129, 187-207.
12	Li XH, Liu Q, Yang RJ, Zhang HJ, Zhang JL, Cai EL (2015). The design and implementation of the leaf area index sensor.Sensors 15, 6250-6269.
13	Liu JG, Pattey E (2010). Retrieval of leaf area index from top-of-canopy digital photography over agricultural crops.Agric Forest Meteor 150, 1485-1490.
14	Liu YK, Mu XH, Wang HX, Yan GJ (2012). A novel method for extracting green fractional vegetation cover from digital images.J Veg Sci 23, 406-418.
15	Myneni RB, Hoffman S, Knyazikhin Y, Privette JL, Glassy J, Tian Y, Wang Y, Song X, Zhang Y, Smith GR, Lotsch A, Friedl M, Morisette JT, Votava P, Nemani RR, Running SW (2002). Global products of vegetation leaf area and fraction absorbed PAR from year one of MODIS data.Remote Sens Environ 83, 214-231.
16	Piayda A, Dubbert M, Werner C, Correia AV, Pereira JS, Cuntz M (2015). Influence of woody tissue and leaf clum- ping on vertically resolved leaf area index and angular gap probability estimates.Forest Ecol Manage 340, 103-113.
17	Wang HX, Zhang WM, Zhou GQ, Yan GJ, Clinton N (2009). Image-based 3D corn reconstruction for retrieval of geometrical structural parameters.Int J Remote Sens 30, 5505-5513.
18	Weiss M, Baret F, Smith GJ, Jonckheere I, Coppin P (2004). Review of methods for in situ leaf area index (LAI) determination: Part II. Estimation of LAI, errors and samp- ling. Agric Forest Meteor 121, 37-53.
19	Woodgate W, Disney M, Armston JD, Jones SD, Suarez L, Hill MJ, Wilkes P, Soto-Berelov M, Haywood A, Mellor A (2015). An improved theoretical model of canopy gap probability for leaf area index estimation in woody ecosys- tems.Forest Ecol Manage 358, 303-320.
20	Xiao ZQ, Liang SL, Wang JD, Chen P, Yin XJ, Zhang LQ, Song JL (2014). Use of general regression neural networks for generating the glass leaf area index product from time-series MODIS surface reflectance.IEEE Trans Geosci Remote Sens 52, 209-223.
21	Xu XR, Fan WJ, Tao X (2009). The spatial scaling effect of continuous canopy leaves area index retrieved by remote sensing.Sci China Ser D: Earth Sci 52, 393-401.

[1]	Xue Yao, Xing Chen, Zun Dai, Kun Song, Shichen Xing, Hongyu Cao, Lu Zou, Jian Wang. Importance of collection strategy on detection probability and species diversity of epiphyllous liverworts [J]. Biodiv Sci, 2023, 31(4): 22685-.
[2]	Jiesheng Rao, Tao Yang, Xi Tian, Wencong Liu, Xiaofeng Wang, Hengjun Qian, Zehao Shen. Vertical structural characteristics of a semi-humid evergreen broad-leaved forest and common tree species based on a portable backpack LiDAR [J]. Biodiv Sci, 2023, 31(11): 23216-.
[3]	ZHENG Zhou-Tao, ZHANG Yang-Jian. Variation in ecosystem water use efficiency and its attribution analysis during 1982-2018 in Qingzang Plateau [J]. Chin J Plant Ecol, 2022, 46(12): 1486-1496.
[4]	LIU Bing-Bing, WEI Jian-Xin, HU Tian-Yu, YANG Qiu-Li, LIU Xiao-Qiang, WU Fa-Yun, SU Yan-Jun, GUO Qing-Hua. Validation and uncertainty analysis of satellite remote sensing products for monitoring China’s forest ecosystems—Based on massive UAV LiDAR data [J]. Chin J Plant Ecol, 2022, 46(10): 1305-1316.
[5]	LIU Chao, LI Ping, WU Yun-Tao, PAN Sheng-Nan, JIA Zhou, LIU Ling-Li. Estimation of grassland aboveground biomass using digital photograph and canopy structure measurements [J]. Chin J Plant Ecol, 2022, 46(10): 1280-1288.
[6]	Zun Dai, Xing Chen, Jianhang Zhang, Maojie Zhu, Kun Song, Shichen Xing, Shuwen Tu, Lu Zou, Zupei Lei, Hongqing Li, Jian Wang. Species diversity of epiphyllous liverworts and host plants in the Wuyanling National Nature Reserve, Zhejiang Province [J]. Biodiv Sci, 2022, 30(1): 21229-.
[7]	Shichen Xing, Luyan Tang, Zun Dai, Shuwen Tu, Xing Chen, Jianhang Zhang, Hongqing Li, Tao Peng, Jian Wang. Bryophyte diversity in Shitai County and Qingyang County, Anhui Province [J]. Biodiv Sci, 2022, 30(1): 21186-.
[8]	Meichun Duan, Ruxia Qin, Hongbin Zhang, Baoxiong Chen, Bin Jin, Songbo Zhang, Shaopeng Ren, Shuquan Jin, Shenghai Zhu, Jianing Hua, Yunhui Liu, Zhenrong Yu. Comprehensive comparison of different sampling methods for arthropod diversity in farmland [J]. Biodiv Sci, 2021, 29(4): 477-487.
[9]	HUANG Song-Yu, JIA Xin, ZHENG Jia-Jia, YANG Rui-Zhi, MU Yu, YUAN He-Di. Characteristics and influencing factors of Bowen ratio variation in typical terrestrial ecosystems in China [J]. Chin J Plant Ecol, 2021, 45(2): 119-130.
[10]	YANG Huan-Ying, SONG Jian-Da, ZHOU Tao, JIN Guang-Ze, JIANG Feng, LIU Zhi-Li. Influences of stand, soil and space factors on spatial heterogeneity of leaf area index in a spruce-fir valley forest in Xiao Hinggan Ling, China [J]. Chin J Plant Ecol, 2019, 43(4): 342-351.
[11]	Ze-Bin LIU, Yan-Hui WANG, Yu LIU, Ao TIAN, Ya-Rui WANG, Hai-Jun ZUO. Spatiotemporal variation and scale effect of canopy leaf area index of larch plantation on a slope of the semi-humid Liupan Mountains, Ningxia, China [J]. Chin J Plant Ecol, 2017, 41(7): 749-760.
[12]	GAO Lin, WANG Xiao-Fei, GU Xing-Fa, TIAN Qing-Jiu, JIAO Jun-Nan, WANG Pei-Yan, LI Dan. Exploring the influence of soil types underneath the canopy in winter wheat leaf area index remote estimating [J]. Chin J Plant Ecol, 2017, 41(12): 1273-1288.
[13]	Ming ZHOU, Zhi-Li LIU, Guang-Ze JIN. Improving the accuracy of indirect methods in estimating leaf area index using three correction schemes in a Larix gmelinii plantation [J]. Chin J Plant Ecol, 2016, 40(6): 574-584.
[14]	ZHU Xu-Chao, YUAN Guo-Fu, SHAO Ming-An, YI Xiao-Bo, DU Tao. Spatial pattern of riparian vegetation in desert of the lower Tarim River basin [J]. Chin J Plan Ecolo, 2015, 39(11): 1053-1061.
[15]	LIU Zhi-Li, JIN Guang-Ze, ZHOU Ming. Measuring seasonal dynamics of leaf area index in a mixed conifer-broadleaved forest with direct and indirect methods [J]. Chin J Plant Ecol, 2014, 38(8): 843-856.