Journal of Geographical Sciences >
Measurement of vegetation parameters and error analysis based on Monte Carlo method
Author: Liang Boyi, Email: liangboyi@pku.edu.cn
Received date: 20170630
Accepted date: 20171208
Online published: 20180620
Supported by
National Natural Science Foundation of China, No.41171262
Copyright
In this paper we bring up a Monte Carlo theory based method to measure the ground vegetation parameters, and make quantitative description of the error. The leaf area index is used as the example in the study. Its mean and variance stability at different scales or in different time is verified using both the computer simulation and the statistics of remotely sensed images. And the error of Monte Carlo sampling method is analyzed based on the normal distribution theory and the centrallimit theorem. The results show that the variance of leaf area index in the same area is stable at certain scales or in the same time of different years. The difference between experimental results and theoretical ones is small. The significance of this study is to establish a measurement procedure of ground vegetation parameters with an error control system.
Key words： remote sensing; vegetation parameter; error analysis; GLASS LAI
LIANG Boyi , LIU Suhong . Measurement of vegetation parameters and error analysis based on Monte Carlo method[J]. Journal of Geographical Sciences, 2018 , 28(6) : 819 832 . DOI: 10.1007/s1144201815078
Figure 1 Vegetation scenarios simulated by computer and their leaf area index frequency curves (a. low level; b. median level; c. high level) 
Figure 2 LAI variations in computer simulation 
Figure 3 GLASS LAI of the study area 
Figure 4 Frequency curves of GLASS LAI (a. low level. b. median level. c. high level) 
Figure 5 Verification of normal distribution (a. low level of computer simulation; b. low level of GLASS LAI; c. median level of computer simulation; d. median level of GLASS LAI; e. high level of computer simulation; f. high level of GLASS LAI) 
Table 1 Verification of mean and variation 
Sampling quantity  30  50  70  100  150  200  300  500  

Low level  Computer simulation  Variation  Theoretical value  0.049  0.029  0.021  0.015  0.010  0.007  0.005  0.003 
Real value  0.056  0.032  0.022  0.016  0.011  0.008  0.006  0.003  
Mean  Theoretical value  2.535  2.535  2.535  2.535  2.535  2.535  2.535  2.535  
Real value  2.531  2.546  2.541  2.536  2.537  2.534  2.540  2.537  
GLASS LAI  Variation  Theoretical value  0.028  0.017  0.012  0.008  0.006  0.004  0.003  0.002  
Real value  0.031  0.018  0.013  0.009  0.006  0.005  0.003  0.002  
Mean  Theoretical value  1.234  1.234  1.234  1.234  1.234  1.234  1.234  1.234  
Real value  1.243  1.240  1.228  1.231  1.230  1.233  1.231  1.231  
Median level  Computer simulation  Variation  Theoretical value  0.212  0.127  0.091  0.064  0.042  0.032  0.021  0.013 
Real value  0.245  0.153  0.105  0.076  0.047  0.035  0.024  0.015  
Mean  Theoretical value  5.086  5.086  5.086  5.086  5.086  5.086  5.086  5.086  
Real value  5.073  5.091  5.097  5.079  5.083  5.084  5.087  5.091  
GLASS LAI  Variation  Theoretical value  0.039  0.023  0.017  0.012  0.008  0.006  0.004  0.002  
Real value  0.038  0.024  0.016  0.011  0.008  0.006  0.004  0.002  
Mean  Theoretical value  2.115  2.115  2.115  2.115  2.115  2.115  2.115  2.115  
Real value  2.099  2.122  2.118  2.117  2.113  2.115  2.115  2.115  
High level  Computer simulation  Variation  Theoretical value  0.495  0.297  0.212  0.148  0.099  0.074  0.049  0.030 
Real value  0.532  0.352  0.270  0.176  0.122  0.085  0.054  0.035  
Mean  Theoretical value  8.086  8.086  8.086  8.086  8.086  8.086  8.086  8.086  
Real value  8.089  8.096  8.087  8.081  8.103  8.090  8.081  8.096  
GLASS LAI  Variation  Theoretical value  0.056  0.033  0.024  0.017  0.011  0.008  0.006  0.003  
Real value  0.047  0.030  0.020  0.015  0.009  0.007  0.005  0.003  
Mean  Theoretical value  4.498  4.498  4.498  4.498  4.498  4.498  4.498  4.498  
Real value  4.493  4.498  4.501  4.503  4.504  4.505  4.502  4.500 
Figure 6 Error distribution (a. three dimensional graph; b. orthographic projection) 
Table 2 Statistics of error distribution 
Sampling quantity  03%  3%5%  5%10%  10%20%  >20%  Average 

30  3.07%  0.18%  0.75%  3.24%  0.76%  1.60% 
50  1.95%  1.60%  1.45%  1.86%  0.24%  1.42% 
70  3.33%  2.34%  1.94%  3.07%  0.66%  2.27% 
100  2.82%  2.84%  1.35%  1.36%  0.03%  1.68% 
150  3.20%  0.95%  1.59%  0.52%  1.57%  
200  3.97%  1.55%  2.12%  0.30%  1.99%  
300  3.31%  1.96%  1.32%  0.03%  1.66%  
500  5.99%  3.75%  2.24%  3.99% 
Figure 7 Error distribution under different sampling quantities (a. 30; b. 50; c. 70; d. 100; e. 150; f. 200; g. 300; h. 500) 
The authors have declared that no competing interests exist.
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