叶面积指数田间测量中有限长度平均法的改进

doi:10.11983/CBB17083

植物学报 ›› 2018, Vol. 53 ›› Issue (5): 671-685.DOI: 10.11983/CBB17083

叶面积指数田间测量中有限长度平均法的改进

刘强^1,^2,^*(), 蔡二丽¹, 张嘉琳¹, 宋翘¹, 李秀红^1,², 窦宝成^1,²

¹北京师范大学全球变化与地球系统科学研究院, 北京 100875
²北京师范大学-中国科学院遥感与数字地球研究所遥感科学国家重点实验室, 北京 100875

收稿日期:2017-04-14 接受日期:2017-08-30 出版日期:2018-09-01 发布日期:2018-11-29
通讯作者: 刘强
作者简介:
† 共同第一作者。
基金资助:
国家自然科学基金(No.41476161, No.41331171)、遥感科学国际重点实验室开放基金(No.OFSLRSS201626)和国家重点研发计划(No.2016YFA0600102)

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

Liu Qiang^1,^2,^*(), Cai Erli¹, Zhang Jialin¹, Song Qiao¹, Li Xiuhong^1,², Dou Baocheng^1,²

¹College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China
²State Key Laboratory of Remote Sensing Science, Jointly Sponsored by Beijing Normal University and Institute of Remote Sensing and Digital Earth, Chinese Academy and Sciences, Beijing 100875, China

Received:2017-04-14 Accepted:2017-08-30 Online:2018-09-01 Published:2018-11-29
Contact: Liu Qiang
About author:
† These authors contributed equally to this paper

摘要/Abstract

摘要：

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。

关键词: 叶面积指数, 聚集指数, 比尔定律, 采样方法

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

刘强, 蔡二丽, 张嘉琳, 宋翘, 李秀红, 窦宝成. 叶面积指数田间测量中有限长度平均法的改进. 植物学报, 2018, 53(5): 671-685.

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. Chinese Bulletin of Botany, 2018, 53(5): 671-685.

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链接本文: https://www.chinbullbotany.com/CN/10.11983/CBB17083

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

图/表 11

图1 模拟的3种叶形(条形、方形和梭形)

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

图2 在不同长度(r)条件下的叶面积指数投影均值($\overline{PLA}$)和标准差随冠层孔隙率(P)的变化(梭形叶片)(A) 样线采样的均值; (B) 样方采样的均值; (C) 样线采样的标准差; (D) 样方采样的标准差

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

图3 梭形叶片在样线/样方尺度上估算叶面积指数投影(PLA)的误差(A) 样线采样方式使用ƒ*的均方根误差RMSE; (B) 样方采样方式使用ƒ*的均方根误差RMSE; (C) 样线采样方式使用ƒ*的相对误差RRMSE; (D) 样方采样方式使用ƒ*的相对误差RRMSE; (E) 样线采样方式使用比尔定律的相对误差RRMSE; (F) 样方采样方式使用比尔定律的相对误差RRMSE

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

图4 样线长度(r)与样线数量(n)对应的样方叶面积指数投影均值($\overline{PLA}$)估算误差RMSE黑线为n∙r等值线($\overline{PLA}$约等于2, 样线采样方式, 叶片为梭形叶片, 样地内叶片为均匀随机分布)。

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).

图5 测量均匀样地时严格、普通或宽松精度要求下的长度(r)和数量(n)的取值范围(梭形叶片)(A) 样线采样+ƒ*; (B) 样线采样+比尔定律; (C) 样方采样+ƒ*; (D) 样方采样+比尔定律

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

图6 模拟的叶片非均匀分布的场景A和场景B局部的孔隙情况(A) 场景A平均叶面积指数(LAI)约为1; (B) 场景A平均LAI约为4; (C) 场景B平均LAI约为1; (D) 场景B平均LAI约为4

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

图7 对于模拟的非均匀场景选取不同的长度(r)估算叶面积指数投影(PLA)的RMSE(A) 场景A样线采样; (B) 场景A样方采样; (C) 场景B样线采样; (D) 场景B样方采样

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

表1 样线采样方式下使用不同公式估算的叶面积指数(LAI)和聚集指数(CI)

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

表2 样方采样方式下使用不同公式估算的叶面积指数(LAI)和聚集指数(CI)

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

图8 河北怀来遥感综合试验站内玉米样地观测点自动拍照相片提取的叶片掩膜图时间序列(A) 5月30日; (B) 6月7日; (C) 6月13日; (D) 6月20日; (E) 7月4日; (F) 7月16日

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

表3 河北怀来遥感综合试验站内玉米样地田间测量参数以及从照片估算的叶面积指数(LAI)

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

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叶面积指数田间测量中有限长度平均法的改进

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

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