Modeling Small-Footprint Airborne Lidar-Derived Estimates of Gap Probability and Leaf Area Index
Abstract
:1. Introduction
2. Theoretical Background and Implementations in DART
2.1. Lidar Pulse
2.2. Lidar Point Cloud and the Corresponding Radiometric Quantities
- Rapid detected peak amplitude by first-derivative zero-crossing (without GD).
- Fitted peak amplitude (after GD by non-linear least-squares minimization [63]).
- Standard deviation (after GD).
- Power integral of a return (after GD):
2.3. Radiative Transfer under Realistic Conditions
3. LPI Estimation and LAI/PAI Inversion from Small-Footprint ALS Point Clouds
3.1. Estimation of and LAI
3.1.1. Theoretical Approaches
3.1.2. Practical Empirical Correlation
3.2. Review of LPI Computation
3.2.1. Point-Number-Based (PNB) Methods for LPI Computation
3.2.2. “Intensity”-Based (IB) Methods for LPI Computation
4. Comparative Sensitivity Study of Estimation Approaches Using DART Simulations
4.1. DART Simulations
4.1.1. Homogeneous Scenes
4.1.2. Heterogeneous Scenes
4.2. Results and Analyses
4.2.1. Homogeneous Scene
4.2.2. Heterogeneous Scene
5. Discussion
6. Conclusions and Outlook
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Receiver telescope area | |
Footprint area at a certain distance | |
Projection area | |
A calibration constant with pre-defined instrumental and experimental configurations | |
The beam cross-section diameter at the “exit gate” of the laser generator | |
Diameter of the receiver telescope | |
eLAI | Effective LAI |
Proportion of crown vertical projection area by neglecting the within-crown gaps | |
Leaf angle distribution function | |
G | Unit leaf area projection along the pulse direction |
Integral of a return Gaussian power profile, total power of a return | |
The distance-weighted power integral (), proportional to | |
of pulses with only single ground return | |
For a pure vegetation or vegetation-ground pulse, refer to For the nearest pure ground pulse | |
i | Return index of a lidar pulse |
IB | Intensity-based |
LAI | Leaf area index |
Estimated LAI from lidar points without using correlation coefficient | |
Laser penetration index | |
Penetration index of a single pulse | |
Number of returns | |
Number of first returns | |
Number of last returns | |
Number of pulses with only a single return | |
Peak amplitude of a return Gaussian profile | |
Time-dependent amplitude profile of a lidar waveform recorded by the receiver | |
Total pulse power | |
Total incident power onto the ground | |
Total incident power onto the vegetation part | |
Gap probability of zenith angle | |
The gap probability along vertical direction adapted in most airborne lidar processing | |
PNB | Point-number-based |
Distance from lidar | |
Footprint radius | |
Peak amplitude of transmitted laser pulse | |
The temporal standard deviation of the convolved transmitted pulse and receiver response function | |
The temporal standard deviation of a returned Gaussian profile of return index i | |
The temporal standard deviation broadening of a return Gaussian profile (index i) from target interaction | |
The standard deviation of the angular energy distribution within footprint | |
Back-scatter transfer function of of return index i | |
Correlation coefficient to link LPI with (exponential) and with eLAI (linear) | |
The angular offset from the pulse direction | |
Footprint divergence | |
Ratio of ground apparent reflectance over vegetation apparent reflectance | |
Radar back-scattering differential cross-section | |
Natural reflectivity of a target | |
Apparent reflectance of a target | |
Direction and solid angle from target to the receiver of return index i | |
Leaf normal direction | |
System and atmospheric transmission factor | |
The overall clumping index for LAI estimation over an area | |
Index of clumping that is induced by only crown shape and within-crown clumping | |
The angle between ground normal and the incident direction of a pulse |
Appendix A. DART Workflow of Point-Cloud Modeling
Appendix B. Influence of Peak Detection Threshold
Variables | PNB Methods | IB Methods | References | |||||||
---|---|---|---|---|---|---|---|---|---|---|
LAI = 2 (Random) | 0.47 | 0.94 | 0.64 | 6.11 | 1.44 | 1.05 | 1.00 | 1.07 | 1.00 | |
1.70 | 2.01 | 1.26 | 7.26 | 3.35 | 2.10 | 2.10 | 2.10 | 1.98 | ||
computed | 0.28 | 0.47 | 0.51 | 0.84 | 0.43 | 0.50 | 0.48 | 0.51 | 0.51 | |
R2 | 0.90 | 0.87 | 0.78 | 0.78 | 0.91 | 0.89 | 0.89 | 0.89 | 0.90 | |
LAI = 2 (Clumping) | 0.49 | 1.03 | 0.71 | 4.85 | 1.45 | 1.04 | 1.02 | 1.07 | 1.00 | |
1.66 | 2.36 | 1.51 | 6.99 | 3.51 | 2.29 | 2.27 | 2.34 | 2.23 | ||
computed | 0.30 | 0.44 | 0.47 | 0.69 | 0.41 | 0.45 | 0.45 | 0.46 | 0.45 | |
R2 | 0.82 | 0.86 | 0.81 | 0.81 | 0.94 | 0.89 | 0.89 | 0.89 | 0.90 | |
LAI = 1 | 0.33 | 0.71 | 0.47 | 18.69 | 1.18 | 1.09 | 1.00 | 1.11 | 1.00 | |
0.90 | 1.11 | 0.67 | 0.81 | 2.10 | 1.59 | 1.48 | 1.63 | 1.48 | ||
computed | 0.37 | 0.64 | 0.70 | 1.73 | 0.56 | 0.69 | 0.68 | 0.68 | 0.68 | |
R2 | 0.91 | 0.87 | 0.81 | 0.14 | 0.82 | 0.95 | 0.95 | 0.95 | 0.95 |
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Deviation | Full Waveform Storage | ||||
---|---|---|---|---|---|
V-line | × | × ** | × | ||
Q-line | × | × * | × | × |
Representation | Expressions | Reference Examples | ||
---|---|---|---|---|
Point Number Based (PNB) Methods | Luo et al. [36] Hu et al. [23] | |||
Fleck et al. [68] Schneider et al. [35] Grau et al. [28] | ||||
Solberg et al. [30,31,32] Riaño et al. [69] Lovell et al. [70] Morsdorf et al. [33] Korhonen et al. [34] Cook et al. [71] | ||||
“Intensity” Based (IB) Methods | Empirical constant | Lefsky et al. [72] Luo et al. [36] | ||
Statistically derived | Armston et al. [16] Chen et al. [17] | |||
Milenković, et al. [64] |
Parameter | Value | Parameter | Value |
---|---|---|---|
Wavelength | 1550 nm | Scanning speed | 100 lines/second |
Laser sampling interval | 1 ns | Laser pulse repetition rate | 200 kHz |
Laser beam divergence | 0.3 mrad |
Variables | PNB Methods | IB Methods | References | |||||||
---|---|---|---|---|---|---|---|---|---|---|
LAI = 2 (Random) | 0.40 | 0.97 | 0.60 | 27.14 | 1.56 | 1.00 | 1.00 | 1.02 | 1.00 | |
1.57 | 1.84 | 1.16 | 22.08 | 3.90 | 1.98 | 1.98 | 2.01 | 1.98 | ||
computed | 0.25 | 0.53 | 0.52 | 1.23 | 0.40 | 0.51 | 0.51 | 0.51 | 0.51 | |
R2 | 0.88 | 0.84 | 0.77 | 0.19 | 0.79 | 0.89 | 0.89 | 0.89 | 0.90 | |
LAI = 2
(Clumping) | 0.42 | 0.97 | 0.67 | 24.20 | 1.62 | 1.01 | 1.03 | 1.03 | 1.00 | |
1.50 | 2.20 | 1.42 | 21.11 | 4.2 | 2.24 | 2.28 | 2.28 | 2.23 | ||
computed | 0.28 | 0.44 | 0.47 | 1.15 | 0.39 | 0.45 | 0.45 | 0.45 | 0.45 | |
R2 | 0.71 | 0.80 | 0.80 | 0.34 | 0.84 | 0.89 | 0.89 | 0.89 | 0.90 | |
LAI = 1 | 0.27 | 0.61 | 0.42 | - | 1.10 | 1.00 | 1.02 | 1.03 | 1.00 | |
0.77 | 0.92 | 0.59 | - | 1.95 | 1.49 | 1.49 | 1.52 | 1.48 | ||
computed | 0.35 | 0.66 | 0.71 | - | 0.56 | 0.67 | 0.68 | 0.68 | 0.68 | |
R2 | 0.90 | 0.84 | 0.78 | - | 0.77 | 0.94 | 0.95 | 0.94 | 0.95 |
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Yin, T.; Qi, J.; Cook, B.D.; Morton, D.C.; Wei, S.; Gastellu-Etchegorry, J.-P. Modeling Small-Footprint Airborne Lidar-Derived Estimates of Gap Probability and Leaf Area Index. Remote Sens. 2020, 12, 4. https://doi.org/10.3390/rs12010004
Yin T, Qi J, Cook BD, Morton DC, Wei S, Gastellu-Etchegorry J-P. Modeling Small-Footprint Airborne Lidar-Derived Estimates of Gap Probability and Leaf Area Index. Remote Sensing. 2020; 12(1):4. https://doi.org/10.3390/rs12010004
Chicago/Turabian StyleYin, Tiangang, Jianbo Qi, Bruce D. Cook, Douglas C. Morton, Shanshan Wei, and Jean-Philippe Gastellu-Etchegorry. 2020. "Modeling Small-Footprint Airborne Lidar-Derived Estimates of Gap Probability and Leaf Area Index" Remote Sensing 12, no. 1: 4. https://doi.org/10.3390/rs12010004