Compatible Biomass Model with Measurement Error Using Airborne LiDAR Data
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Data Collection
2.2.1. Field Data Collection
2.2.2. Airborne LiDAR Data Acquisition
2.2.3. LiDAR-Based Extraction of Individual Tree Characteristics
2.3. Method
2.3.1. Variables Selection and Determination of the LiDAR-DBH Base Model
2.3.2. Developing Form of a Model System
2.3.3. Nonlinear Error-in-Variable Models (NEIVM) and Nonlinear Seemingly Unrelated Regression (NSUR)
2.3.4. Heteroscedasticity
3. Results
3.1. LiDAR-DBH Models
3.2. Model Parameter Estimates
3.3. Model Evaluation
3.4. Reduction of Heteroscedasticity
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Variable | Min | Mean | Max | SD |
---|---|---|---|---|
WP (kg) | 0.24 | 42.51 | 164.08 | 29.76 |
WB (kg) | 0.22 | 16.5 | 53.5 | 10.1 |
WBK (kg) | 0.12 | 8.11 | 25.53 | 4.85 |
WF (kg) | 0.17 | 4.82 | 12.59 | 2.44 |
WS (kg) | 0.37 | 50.62 | 189.61 | 34.59 |
WC (kg) | 0.38 | 21.32 | 66.09 | 12.53 |
WAG (kg) | 0.75 | 71.94 | 55.70 | 47.09 |
LH (m) | 1.05 | 9.68 | 17.27 | 3.07 |
DBH (cm) | 2.1 | 15.76 | 29.4 | 5.40 |
CD (m) | 0.79 | 2.69 | 5.52 | 0.8 |
CPA (m2) | 0.35 | 6.17 | 24 | 3.66 |
Biomass | Model |
---|---|
Protoxylem | WP = 0.0388DBH2.4696 |
Branch | WB = 0.0462DBH2.0865 |
Bark | WBK = 0.0274DBH2.0222 |
Foliage | WF = 0.0496DBH1.6375 |
Stem | WS = 0.0618DBH2.3723 |
Crown | WC = 0.0837DBH1.9946 |
Above-ground | WAG = 0.1431DBH2.2193 |
Model | Model | Model Form | RMSE | R2 | TRE | |
---|---|---|---|---|---|---|
I.1 | Linear | 4.0462 | 0.51626 | 0.00000 | 6.0526 | |
I.2 | Empirical | 4.0276 | 0.52072 | −0.01672 | 5.9935 | |
I.3 | Logistic | 4.0127 | 0.52439 | −0.005258 | 5.9469 | |
I.4 | Richards | 4.0154 | 0.52362 | −0.01672 | 5.9551 | |
I.5 | Exponential | 4.1903 | 0.48120 | −0.04616 | 6.5199 |
Model | Model | Components | RMSE | R2 | TRE | |
---|---|---|---|---|---|---|
II.1 | Protoxylem | 8.6527 | 0.5900 | −0.0717 | 11.8530 | |
II.2 | Branch | 22.7314 | 0.5657 | −0.1633 | 15.8248 | |
II.3 | Bark | 3.1095 | 0.5882 | −0.0257 | 12.1274 | |
II.4 | Foliage | 6.5137 | 0.5839 | −0.0534 | 12.7763 | |
II.5 | Aboveground | 31.5338 | 0.5753 | −0.2478 | 14.1597 | |
II.6 | Stem | 19.7480 | 0.5598 | −0.1305 | 16.9231 | |
II.7 | Crown | 1.5162 | 0.6143 | −0.0114 | 8.5341 |
Parameters | Model I.4 | Model II | TSEM | NSUR | ||||
---|---|---|---|---|---|---|---|---|
Model (6) | Model (7) | Model (8) | Model (6) | Model (7) | Model (8) | |||
49.7128 | ||||||||
0.04028 | ||||||||
0.0768 | 0.0667 | 0.0735 | 0.0859 | 0.0108 | 3.2675 | 0.0794 | ||
2.2550 | 2.3065 | 2.2827 | 2.2280 | 2.3317 | 1.7254 | 2.2435 | ||
0.1266 | 0.0735 | 0.0691 | 0.0721 | 0.0107 | 0.0603 | 0.0737 | ||
1.8635 | 1.9435 | 0.0477 | 1.9545 | 2.0060 | 2.5465 | 1.9387 | ||
0.0737 | 0.0431 | 1.8584 | 0.0406 | 0.0062 | 0.5010 | 0.0409 | ||
1.9386 | 1.8826 | 2.2196 | 1.9064 | 1.9466 | 1.7892 | 1.8961 | ||
0.0421 | 0.0726 | 0.0667 | 0.0555 | 0.0107 | 0.0007 | 0.0449 | ||
1.8861 | 1.5177 | 1.5461 | 1.6099 | 1.5746 | 1.6928 | 1.6776 | ||
0.2465 | 0.1514 | 0.1769 | 0.2096 | 0.1924 | ||||
2.0474 | 2.1951 | 2.1359 | 2.0877 | 2.1169 | ||||
0.1160 | 1.9600 | 0.1925 | ||||||
2.1738 | 0.0995 | 2.3012 | ||||||
0.0613 | 0.1289 | 0.3223 | ||||||
1.5708 | 1.8295 | 1.8211 |
Component | Method | R2 | TRE | RMSE | |
---|---|---|---|---|---|
Protoxylem | TSEM-one-step | 0.5585 | 0.7367 | 17.3555 | 19.7769 |
TSEM-two-step | 0.5571 | 1.3899 | 18.1241 | 19.8083 | |
TSEM-summation | 0.5567 | −1.6579 | 15.9434 | 19.8157 | |
NSUR-one-step | 0.5598 | −0.1139 | 16.9208 | 19.7469 | |
NSUR-two-step | 0.5598 | −0.1386 | 16.9182 | 19.7470 | |
NSUR-summation | 0.5597 | −0.1631 | 16.9260 | 19.7482 | |
Branch | TSEM-one-step | 0.5831 | 0.2232 | 13.0848 | 6.5200 |
TSEM-two-step | 0.5818 | 0.4157 | 13.5562 | 6.5306 | |
TSEM-summation | 0.5820 | −0.4344 | 12.2372 | 6.5287 | |
NSUR-one-step | 0.5841 | −0.0557 | 12.7713 | 6.5124 | |
NSUR-two-step | 0.5843 | 0.0163 | 12.7756 | 6.5111 | |
NSUR-summation | 0.5839 | −0.0522 | 12.7779 | 6.5137 | |
Bark | TSEM-one-step | 0.5875 | 0.1046 | 12.4149 | 3.1123 |
TSEM-two-step | 0.5861 | 0.1944 | 12.8460 | 3.1175 | |
TSEM-summation | 0.5864 | −0.1985 | 11.6462 | 3.1163 | |
NSUR-one-step | 0.5883 | −0.0306 | 12.1221 | 3.1089 | |
NSUR-two-step | 0.5710 | 0.2621 | 12.7672 | 3.1736 | |
NSUR-summation | 0.5882 | −0.0190 | 12.1310 | 3.1096 | |
Foliage | TSEM-one-step | 0.6141 | 0.0445 | 8.7044 | 1.5164 |
TSEM-two-step | 0.6126 | 0.0829 | 8.9405 | 1.5195 | |
TSEM-summation | 0.6131 | −0.0693 | 8.3161 | 1.5185 | |
NSUR-one-step | 0.6139 | −0.0333 | 8.5344 | 1.5169 | |
NSUR-two-step | 0.5840 | −0.1341 | 9.2154 | 1.5746 | |
NSUR-summation | 0.6125 | 0.0268 | 8.5872 | 1.5196 | |
Above-ground | TSEM-one-step | 0.5753 | −0.2478 | 14.1597 | 31.5338 |
TSEM-two-step | 0.5753 | −0.2478 | 14.1597 | 31.5338 | |
TSEM-summation | 0.5685 | −2.3602 | 14.0111 | 30.9364 | |
NSUR-one-step | 0.5753 | −0.2478 | 14.1597 | 31.5338 | |
NSUR-two-step | 0.5753 | −0.2478 | 14.1597 | 31.5338 | |
NSUR-summation | 0.5710 | −0.2075 | 14.7572 | 30.8468 |
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Chen, X.; Xie, D.; Zhang, Z.; Sharma, R.P.; Chen, Q.; Liu, Q.; Fu, L. Compatible Biomass Model with Measurement Error Using Airborne LiDAR Data. Remote Sens. 2023, 15, 3546. https://doi.org/10.3390/rs15143546
Chen X, Xie D, Zhang Z, Sharma RP, Chen Q, Liu Q, Fu L. Compatible Biomass Model with Measurement Error Using Airborne LiDAR Data. Remote Sensing. 2023; 15(14):3546. https://doi.org/10.3390/rs15143546
Chicago/Turabian StyleChen, Xingjing, Dongbo Xie, Zhuang Zhang, Ram P. Sharma, Qiao Chen, Qingwang Liu, and Liyong Fu. 2023. "Compatible Biomass Model with Measurement Error Using Airborne LiDAR Data" Remote Sensing 15, no. 14: 3546. https://doi.org/10.3390/rs15143546
APA StyleChen, X., Xie, D., Zhang, Z., Sharma, R. P., Chen, Q., Liu, Q., & Fu, L. (2023). Compatible Biomass Model with Measurement Error Using Airborne LiDAR Data. Remote Sensing, 15(14), 3546. https://doi.org/10.3390/rs15143546