A Nonlinear Mixed-Effects Height-to-Diameter Ratio Model for Several Tree Species Based on Czech National Forest Inventory Data
Abstract
1. Introduction
2. Materials and Methods
2.1. Data Materials
2.2. Training Dataset
2.3. Validation Dataset
2.4. Data Analysis
2.4.1. Deriving Stand-Level Variables
2.4.2. Model Construction
Canopy Height Class | CC1 | CC2 |
CHC1 | 0 | 0 |
CHC2 | 1 | 0 |
CHC3 | 0 | 1 |
Tree Species | TS1 | TS2 | TS3 | TS4 | TS5 | TS6 |
Norway spruce | 0 | 0 | 0 | 0 | 0 | 0 |
Scots pine | 1 | 0 | 0 | 0 | 0 | 0 |
European larch | 0 | 1 | 0 | 0 | 0 | 0 |
Fir species | 0 | 0 | 1 | 0 | 0 | 0 |
European beech | 0 | 0 | 0 | 1 | 0 | 0 |
Oak species | 0 | 0 | 0 | 0 | 1 | 0 |
Birch and alder speices | 0 | 0 | 0 | 0 | 0 | 1 |
2.4.3. Estimating Model Parameters and Evaluation
2.4.4. Calibrating Mixed-Effects Model and Predicting Sample Plot-Specific HDR
3. Results
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Variables | Statistics (Mean ± Standard Deviation (Range)) | |
---|---|---|
Training Data | Validation Data | |
Number of sample plots | 13,875 | 220 |
Number of HDR sample trees | 348,980 | 25,146 |
Number of HDR sample trees per sample plot | 36.5 ± 15.9 (4–90) | 232.3 ± 167.8 (8–664) |
Number of stems (N ha−1) | 1514 ± 671 (40–5460) | 940 ± 711 (32–4700) |
Stand basal area (BA, m2 ha−1) | 38.3 ± 13.5 (0.07–85.4) | 41.3 ± 14.4 (0.1–81.1) |
BA of trees lager than a subject tree (BAL, m2 ha−1) | 28.5 ± 14.4 (0–83.3) | 32.2 ± 17.6 (0–79.5) |
Quadratic mean DBH per sample plot (QMD, cm) | 27.3 ± 6.9 (8.7–84.2) | 28.6 ± 10.3 (9.6–87.3) |
DBH-to-QMD ratio (dq) | 0.95 ± 0.31 (0.13–4.5) | 0.86 ± 0.52 (0.04–7) |
Arithmetic mean DBH per sample plot (AMD, cm) | 25.8 ± 6.6 (8.5–78.4) | 24.9 ± 10.6 (9.1–84.4) |
Dominant height per sample plot (HDOM, m) | 23.2 ± 6.2 (4.4–42.4) | 27.5 ± 6.9 (8–42.8) |
Dominant diameter (DDOM, cm) | 31.5 ± 8.1 (8.6–78.4) | 49.7 ± 14.2 (13.3–84.4) |
Total height (H, m) | 21.1 ± 7.1 (1.5–54.3) | 17.2 ± 9.3 (1.4–50.6) |
Diameter at breast height (DBH, cm) | 26.4 ± 11.6 (7–117.3) | 25.2 ± 17.4 (2–118.1) |
Height-to-DBH ratio (HDR, m cm−1) | 0.85 ± 0.19 (0.08–2.15) | 0.81 ± 0.28 (0.11–2.3) |
Estimate | Standard Error | t-Value | Pr > |t| | |
---|---|---|---|---|
Fixed | ||||
α1 | −0.4005 | 0.001765 | −226.98 | <0.0001 |
α2 | −1.0526 | 0.004407 | −238.81 | <0.0001 |
α3 | 0.7998 | 0.004939 | 161.95 | <0.0001 |
α4 | 0.4568 | 0.002249 | 203.06 | <0.0001 |
α5 | −0.02188 | 0.000223 | −97.98 | <0.0001 |
α6 | 0.1236 | 0.01565 | 7.90 | <0.0001 |
α7 | −0.4599 | 0.002771 | −165.97 | <0.0001 |
α8 | 0.01049 | 0.001457 | 7.20 | <0.0001 |
α9 | 0.07762 | 0.002047 | 37.91 | <0.0001 |
α10 | −0.04291 | 0.003544 | −12.11 | <0.0001 |
α11 | 0.01252 | 0.002087 | 6.00 | <0.0001 |
α12 | −0.04845 | 0.002019 | −23.99 | <0.0001 |
α13 | 0.04806 | 0.001804 | 26.65 | <0.0001 |
b2 | 0.1823 | 0.000747 | 244.09 | <0.0001 |
Variance | ||||
σ2ui | 0.01109 | |||
σ2 | 0.006923 | |||
Fit statistics | ||||
RMSE | 0.0923 | |||
R2adj | 0.7863 | |||
AIC | −729778 |
Species | RMSE | R2 |
---|---|---|
Norway spruce | 0.0673 | 0.8922 |
Scots pine | 0.0657 | 0.9039 |
European larch | 0.0667 | 0.8821 |
Fir species | 0.0654 | 0.8574 |
European beech | 0.0676 | 0.9605 |
Oak species | 0.0681 | 0.9176 |
Birch and alder species | 0.0668 | 0.9328 |
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Sharma, R.P.; Vacek, Z.; Vacek, S.; Kučera, M. A Nonlinear Mixed-Effects Height-to-Diameter Ratio Model for Several Tree Species Based on Czech National Forest Inventory Data. Forests 2019, 10, 70. https://doi.org/10.3390/f10010070
Sharma RP, Vacek Z, Vacek S, Kučera M. A Nonlinear Mixed-Effects Height-to-Diameter Ratio Model for Several Tree Species Based on Czech National Forest Inventory Data. Forests. 2019; 10(1):70. https://doi.org/10.3390/f10010070
Chicago/Turabian StyleSharma, Ram P., Zdeněk Vacek, Stanislav Vacek, and Miloš Kučera. 2019. "A Nonlinear Mixed-Effects Height-to-Diameter Ratio Model for Several Tree Species Based on Czech National Forest Inventory Data" Forests 10, no. 1: 70. https://doi.org/10.3390/f10010070
APA StyleSharma, R. P., Vacek, Z., Vacek, S., & Kučera, M. (2019). A Nonlinear Mixed-Effects Height-to-Diameter Ratio Model for Several Tree Species Based on Czech National Forest Inventory Data. Forests, 10(1), 70. https://doi.org/10.3390/f10010070