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.

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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

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