Chin Bull Bot ›› 2018, Vol. 53 ›› Issue (5): 671-685.doi: 10.11983/CBB17083

• TECHNIQUES AND METHODS • Previous Articles     Next Articles

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

Liu Qiang1,2,*(), Cai Erli1, Zhang Jialin1, Song Qiao1, Li Xiuhong1,2, Dou Baocheng1,2   

  1. 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:2018-11-29 Published:2018-09-10
  • Contact: Liu Qiang E-mail:toliuqiang@bnu.edu.cn
  • About author:

    † These authors contributed equally to this paper

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

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
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
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
Setting A Setting B Setting C Setting D
May 30th 0.1359 40.74 6 5.56 4.0368 0.1885 0.1916 0.1929 0.1963
June 7th 0.5507 133.93 8 5.14 7.3193 0.5149 0.5206 0.5041 0.5124
June 13th 0.8898 173.12 10 5.14 8.3215 0.9626 0.9669 0.9377 0.9500
June 20th 1.3663 300.96 10 4.54 10.972 1.4123 1.4170 1.3702 1.3858
June 27th - - - - 12.323 2.5817 2.6493 2.4040 2.4331
July 4th 3.1837 467.50 15 4.54 13.675 3.4230 3.4990 3.1904 3.2443
July 16th 3.7523 550.99 15 4.54 14.846 4.6051 4.8787 4.1786 4.3009
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