Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)
Abstract
:1. Introduction
2. Materials and Methods
2.1. Dataset
2.2. Lidar Metrics
2.3. Diameter Distribution Models and Fitting
2.3.1. The Weibull Function
2.3.2. The Beta Function
2.3.3. The Generalized Beta Distribution (GBD)
2.3.4. The Johnson’s SB Function
2.3.5. The Gamma Function
2.4. Goodness of Fit Evaluation
2.5. Recovering the Parameters of the Distributions from LiDAR Metrics
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Species | Variable | Mean | Max | Min | SD |
---|---|---|---|---|---|
Pinus halepensis | dg | 17.8 | 30.6 | 11.7 | 5.1 |
dmed | 17.3 | 29.6 | 11.4 | 4.8 | |
dmax | 25.7 | 49.6 | 18.8 | 7.4 | |
N | 1054 | 3200 | 176 | 588.4 | |
Ho | 10.1 | 19.1 | 6.2 | 3.2 | |
G | 24.1 | 58.9 | 6.3 | 11.9 | |
LRD | 1.070 | 2.222 | 0.453 | 0.421 |
Variables Related to Height Distribution (m) | Description |
LH_MIN, LH_MAX, LH_MEAN | Minimum, maximum and mean height |
LH_MODE, LH_MEDIAN, LH_SD, LH_CV | Mode, median, standard deviation and height’s coefficient of variation |
LH_SK, LH_KUR | Skewness and kurtosis |
LH_IQ | Interquartile amplitude |
LH_AAD | Mean absolute deviation |
LH_MAD_MEDIAN, LH_MAD_MODE | Median of the absolute deviations from the overall height median (LH_MAD_MEDIAN) and mode (LH_MAD_MODE) |
LH_L1, LH_L2…, LH_L4 | L moments |
INT_L_SK, INT_L_KUR | Linear combinations of L moments (skewness and kurtosis) |
LH_P05,…, LH_P95 | Percentiles |
LH_P25; LH_P75 | First and third quartiles |
Variables Related to Canopy Closure (%) | Description |
LFCC | Percentage of first returns above 2 m |
LFCC_MEAN | Percentage of first returns above LH_MEAN |
LFCC_MODE | Percentage of first returns above LH_MODE |
LFCC_ALL | Percentage of all returns above 2 m |
LFCC_ALL_MEAN | Percentage of all returns above LH_MEAN |
LFCC_ALL_MODE | Percentage of all returns above LH_MODE |
ALL_MEAN_FIRST | 100* all returns above LH_MEAN / total first returns |
ALL_FIRST | 100* all returns above 2 m / total first returns |
R2_COUNT | Number of first returns above 2 m |
CANOPY | Canopy relief ratio: (hmean − hmin)/(hmax − hmin) |
Function | Step | Param | Mean | SD | Min | Max |
---|---|---|---|---|---|---|
Weibull-2P | Fitting | b | 18.757 | 5.072 | 12.415 | 32.084 |
c | 4.905 | 1.125 | 2.163 | 8.020 | ||
Recovery | b | 18.918 | 4.614 | 13.699 | 33.740 | |
c | 4.873 | 0.825 | 2.215 | 6.577 | ||
Weibull-3P | Fitting | a | 7.184 | 1.750 | 5.625 | 14.100 |
b | 11.222 | 4.005 | 6.312 | 24.255 | ||
c | 2.598 | 0.460 | 1.535 | 3.560 | ||
Recovery | a | 7.500 | - | 7.500 | 7.500 | |
b | 11.008 | 4.637 | 5.513 | 25.319 | ||
c | 2.489 | 0.619 | 1.245 | 3.646 | ||
beta | Fitting | c | 0.006 | 0.015 | 1.47 × 10–6 | 0.107 |
L | 7.184 | 1.750 | 5.625 | 14.100 | ||
U | 25.739 | 7.403 | 16.700 | 49.600 | ||
α | 1.191 | 0.633 | 0.250 | 2.574 | ||
γ | 1.015 | 0.720 | 0.166 | 3.178 | ||
Recovery | c | 0.010 | 0.015 | 4.34 × 10–7 | 0.069 | |
L | 7.500 | - | 7.500 | 7.500 | ||
U | 26.100 | 7.229 | 18.000 | 55.000 | ||
α | 0.972 | 0.690 | 0.017 | 3.023 | ||
γ | 0.734 | 0.488 | 0.046 | 2.003 | ||
Generalized beta | Fitting | 471.180 | 925.744 | 1.251 | 5827.044 | |
B1 | 7.184 | 1.750 | 5.625 | 14.100 | ||
B2 | 25.739 | 7.403 | 16.700 | 49.600 | ||
B3 | 2.253 | 1.034 | 0.543 | 4.885 | ||
B4 | 4.285 | 1.806 | 0.358 | 9.363 | ||
Recovery | 365.657 | 868.723 | 1.428 | 5125.128 | ||
B1 | 7.500 | - | 7.500 | 7.500 | ||
B2 | 26.104 | 7.222 | 18.286 | 55.318 | ||
B3 | 2.057 | 1.100 | 0.435 | 4.647 | ||
B4 | 4.116 | 1.015 | 0.974 | 6.354 | ||
Johnson’s SB | Fitting | ε | 7.184 | 1.750 | 5.625 | 14.100 |
λ | 25.739 | 7.403 | 16.700 | 49.600 | ||
γ | 0.727 | 0.344 | 0.027 | 1.379 | ||
δ | 1.327 | 0.235 | 0.630 | 1.879 | ||
Recovery | ε | 7.500 | - | 7.500 | 7.500 | |
λ | 26.104 | 7.222 | 18.286 | 55.318 | ||
γ | 0.801 | 0.409 | −0.152 | 1.457 | ||
δ | 1.295 | 0.190 | 0.698 | 1.724 | ||
gamma-2P | Fitting | α | 19.906 | 8.426 | 4.636 | 48.331 |
β | 1.062 | 0.815 | 0.382 | 5.329 | ||
Recovery | α | 18.594 | 5.410 | 4.398 | 31.558 | |
β | 1.089 | 0.802 | 0.562 | 5.093 |
Function | Dn | W2 | Bias | MSE |
---|---|---|---|---|
Weibull-2P | 0.146922 | 0.081863 | 0.003424 | 0.002009 |
Weibull-3P | 0.150761 | 0.046157 | 0.002637 | 0.001904 |
beta | 0.138560 | 0.062044 | 0.001643 | 0.001851 |
Generalized beta | 0.153656 | 0.048215 | 0.002563 | 0.001879 |
Johnson’s SB | 0.162578 | 0.043088 | 0.002276 | 0.001892 |
gamma-2P | 0.164750 | 0.054360 | 0.002736 | 0.001996 |
Equation | Dep var | Independent Variable | Param | Param Estim | R2 | RMSE | RMSE% | |
---|---|---|---|---|---|---|---|---|
(28) | dmax | Intercept | 6.733 | <0.0001 | 0.873 | 2.758 | 10.56 | |
LH_AAD | 8.143 | <0.0001 | ||||||
LH_P95 | 7.728 | <0.0001 | ||||||
(29) | dg | Intercept | 5.329 | <0.0001 | 0.750 | 2.542 | 14.24 | |
LH_P90 | 1.335 | <0.0001 | ||||||
(30) | dmed | Intercept | −1.789 | <0.0001 | 0.724 | 2.549 | 14.72 | |
LH_MAD_MEDIAN | 1.049 | <0.0001 |
Function | Dn | W2 | Bias | MSE | KS Acceptance (%) |
---|---|---|---|---|---|
Weibull-2P | 0.282500 | 0.498277 | 0.004303 | 0.002732 | 28 (56%) |
Weibull-3P | 0.286170 | 0.497091 | 0.003619 | 0.002746 | 26 (52%) |
beta | 0.254078 | 0.381916 | 0.003744 | 0.002649 | 35 (70%) |
Generalized beta | 0.264840 | 0.389917 | 0.003673 | 0.002711 | 33 (66%) |
Johnson’s SB | 0.273945 | 0.411657 | 0.003578 | 0.002851 | 32 (64%) |
Gamma-2P | 0.272107 | 0.398073 | 0.004047 | 0.002792 | 34 (68%) |
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Gorgoso-Varela, J.J.; Ponce, R.A.; Rodríguez-Puerta, F. Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain). Remote Sens. 2021, 13, 2307. https://doi.org/10.3390/rs13122307
Gorgoso-Varela JJ, Ponce RA, Rodríguez-Puerta F. Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain). Remote Sensing. 2021; 13(12):2307. https://doi.org/10.3390/rs13122307
Chicago/Turabian StyleGorgoso-Varela, J. Javier, Rafael Alonso Ponce, and Francisco Rodríguez-Puerta. 2021. "Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)" Remote Sensing 13, no. 12: 2307. https://doi.org/10.3390/rs13122307