Fitting and Evaluating Taper Functions to Predict Upper Stem Diameter of Planted Teak (Tectona grandis L.f.) in Eastern and Central Regions of Nepal
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Sampling and Measurements
2.3. Taper Equations
2.4. Model Fitting and Evaluation
3. Results
3.1. Taper Equations and Performance
3.2. Residual Diagnostic
3.3. Model Comparison
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Diameter Class | n | D (cm) | H (m) | ||||
---|---|---|---|---|---|---|---|
(cm) | Mean ± sd | Min | Max | Mean ± sd | Min | Max | |
<25 | 19 | 21.84 ± 2.73 | 14.64 | 24.83 | 17.15 ± 3.01 | 12.22 | 21.25 |
25–30 | 25 | 27.71 ± 1.54 | 25.15 | 29.92 | 20.77 ± 2.40 | 14.23 | 25.32 |
30–35 | 18 | 32.14 ± 1.06 | 30.24 | 33.74 | 21.4 ± 2.44 | 15.19 | 25.23 |
35–40 | 13 | 36.58 ± 1.45 | 35.01 | 39.15 | 22.87 ± 2.04 | 19.24 | 25.31 |
40+ | 25 | 43.96 ± 3.86 | 40.11 | 54.11 | 23.58 ± 2.30 | 18.21 | 28.27 |
Overall | 100 | 33.48 ± 8.23 | 14.64 | 54.11 | 21.43 ± 3.23 | 12.22 | 28.27 |
Model | Equations | Authors |
---|---|---|
M1 | Kozak et al. (1969) [51] | |
M2 | Bennett and Swindel (1972) [34] | |
M3 | Cervera (1973) [57] | |
M4 | Amidon (1984) [58] | |
M5 | Oderwald and Rayamajhi (1991) [59] | |
M6 | Ormerod (1973) [60] | |
M7 | Clutter (1980) [61] | |
M8 | Sharma and Oderwald (2001) [62] | |
M9 | Sharma and Zhang (2004) [63] | |
M10 | where , , | Kozak (2004) [4] |
M11 | Sharma and Parton (2009) [52] | |
M12 | Arias-Rodil (2015) [64] | |
M13 | García (2015) [53] | |
M14 | where | Max and Burkhart (1976) [14] |
M15 | Modified Bi (2000) [56] |
Model | Fit Statistics | Validation Statistics | Total Ranking | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
MB | MAB | RMSE | Adj.R2 | Rank | MB | MAB | RMSE | Adj.R2 | Rank | ||
M1 | 0.275 (8.5) | 2.222 (14.3) | 2.886 (12.8) | 0.908 (12.3) | 48 (12.2) | 0.005 (1.0) | 2.318 (14.1) | 2.979 (13.4) | 0.89 (13.1) | 41.6 (12.0) | 89.6 (12.2) |
M2 | 0.170 (5.5) | 1.787 (7.7) | 2.371 (7.1) | 0.938 (6.3) | 26.6 (6.4) | −0.208 (5.0) | 1.933 (8.8) | 2.64 (9.8) | 0.913 (9.0) | 32.6 (8.8) | 59.2 (7.5) |
M3 | −0.198 (6.3) | 1.674 (5.9) | 2.294 (6.3) | 0.942 (5.5) | 24.0 (7.0) | −0.446 (9.8) | 1.66 (5.0) | 2.203 (5.1) | 0.94 (4.3) | 24.2 (7.5) | 48.2 (5.8) |
M4 | 0.438 (13.2) | 2.268 (15.0) | 3.083 (15.0) | 0.895 (15.0) | 58.2 (10.2) | 0.176 (4.4) | 2.382 (15.0) | 3.124 (15) | 0.879 (15) | 49.4 (7.5) | 107.6 (15) |
M5 | −0.454 (13.6) | 2.114 (12.6) | 2.84 (12.3) | 0.911 (11.8) | 50.4 (7.1) | −0.707 (15) | 2.14 (11.7) | 2.849 (12.0) | 0.9 (11.3) | 50 (4.2) | 100.4 (13.9) |
M6 | 0.055 (2.2) | 2.178 (13.6) | 2.939 (13.4) | 0.905 (13.0) | 42.3 (5.4) | −0.211 (5.1) | 2.243 (13.1) | 2.959 (13.2) | 0.892 (12.7) | 44.1 (7.7) | 86.4 (11.7) |
M7 | 0.133 (4.4) | 1.989 (10.7) | 2.816 (12.1) | 0.913 (11.5) | 38.7 (1.0) | −0.096 (2.8) | 2.021 (10.0) | 2.707 (10.5) | 0.909 (9.7) | 33.1 (1.0) | 71.8 (9.5) |
M8 | 0.459 (13.8) | 1.700 (6.3) | 2.186 (5.1) | 0.947 (4.3) | 29.5 (6.4) | 0.247 (5.8) | 1.651 (4.9) | 2.116 (4.1) | 0.945 (3.4) | 18.3 (8.8) | 47.8 (5.7) |
M9 | −0.253 (7.9) | 1.537 (3.8) | 2.170 (4.9) | 0.948 (4.2) | 20.8 (5.7) | −0.489 (10.6) | 1.552 (3.5) | 2.122 (4.2) | 0.944 (3.5) | 21.9 (5.9) | 42.7 (5.0) |
M10 | −0.013 (1.0) | 1.883 (9.1) | 2.514 (8.7) | 0.930 (7.9) | 26.7 (15.0) | −0.315 (7.2) | 1.933 (8.8) | 2.531 (8.6) | 0.919 (7.9) | 32.5 (14.8) | 59.2 (7.5) |
M11 | −0.150 (4.9) | 1.833 (8.3) | 2.460 (8.1) | 0.933 (7.2) | 28.6 (12.9) | −0.405 (9.0) | 1.799 (6.9) | 2.376 (6.9) | 0.93 (6.0) | 28.9 (15.0) | 57.5 (7.2) |
M12 | 0.501 (15.0) | 1.851 (8.6) | 2.538 (9.0) | 0.929 (8.1) | 40.7 (10.7) | 0.286 (6.6) | 1.834 (7.4) | 2.467 (7.9) | 0.925 (7.0) | 28.9 (12.9) | 69.6 (9.1) |
M13 | 0.460 (13.8) | 1.666 (5.8) | 2.196 (5.2) | 0.947 (4.4) | 29.3 (9.7) | 0.198 (4.8) | 1.677 (5.2) | 2.208 (5.1) | 0.939 (4.4) | 19.6 (9.0) | 48.9 (5.9) |
M14 | −0.285 (8.8) | 1.573 (4.4) | 2.199 (5.2) | 0.947 (4.5) | 22.9 (7.2) | −0.56 (12.1) | 1.704 (5.6) | 2.306 (6.2) | 0.934 (5.4) | 29.2 (3.8) | 52.1 (6.4) |
M15 | −0.107 (3.7) | 1.352 (1.0) | 1.815 (1.0) | 0.964 (1.0) | 6.7 (4.8) | −0.326 (7.4) | 1.37 (1.0) | 1.824 (1.0) | 0.958 (1.0) | 10.4 (5.1) | 17.1 (1.0) |
Model | Mixed Effects Parameter | Fit Statistics | Test Statistics | ||||||
---|---|---|---|---|---|---|---|---|---|
MB | MAB | RMSE | Adj.R2 | MB | MAB | RMSE | Adj.R2 | ||
M15-Fixed | - | −0.1222 | 1.3546 | 1.8144 | 0.9630 | 0.6846 | 1.3782 | 1.9475 | 0.9575 |
M15-Mixed | β2 | −0.1652 | 1.1587 | 1.5781 | 0.9720 | 0.6888 | 1.3884 | 1.9853 | 0.9558 |
M9-Fixed | - | −0.2678 | 1.5376 | 2.1624 | 0.9475 | 0.6045 | 1.4331 | 1.9881 | 0.9560 |
M9-Mixed | β3 | −0.1424 | 1.0878 | 1.5466 | 0.9732 | 0.6165 | 1.4301 | 1.9867 | 0.9561 |
M8-Fixed | - | 0.3889 | 1.6828 | 2.1686 | 0.9473 | 1.2721 | 1.8352 | 2.3853 | 0.9375 |
M8-Mixed | β1 | 0.3423 | 1.4934 | 1.9117 | 0.9591 | 1.2027 | 1.7858 | 2.3398 | 0.9399 |
M3-Fixed | - | −0.2116 | 1.6663 | 2.2784 | 0.9417 | 0.6368 | 1.5802 | 2.1536 | 0.9482 |
M3-Mixed | β0 | −0.0413 | 1.3606 | 1.8605 | 0.9611 | 0.5492 | 1.6368 | 2.1463 | 0.9485 |
M13-Fixed | - | 0.4342 | 1.6568 | 2.1767 | 0.9469 | 1.2842 | 1.8774 | 2.3614 | 0.9382 |
M13-Mixed | β3 | 0.1430 | 1.5932 | 2.1483 | 0.9483 | 0.9780 | 1.7786 | 2.3859 | 0.9369 |
Model | Mixed Effects Parameter | Fixed Effects Parameters | Variance–Covariance Parameters | Fit Statistics | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
β1 | β2 | β3 | β4 | β5 | β6 | σβ | Φ | δ | MB | MAB | RMSE | Adj.R2 | ||
M15-Fixed | - | 0.8631 (0.1006) | −0.5631 (0.0517) | −0.0740 (0.0100) | −0.2816 (0.0563) | 0.0646 (0.0069) | −0.0322 (0.0126) | −0.1086 | 1.3522 | 1.8291 | 0.9626 | |||
M15-Mixed | β2 | 0.6199 (0.0711) | −0.3909 (0.036) | −0.0409 (0.0078) | −0.1629 (0.0379) | 0.0613 (0.0028) | −0.0382 (0.0053) | 0.0254 | 0.0004 | −0.1570 | −0.1469 | 1.1409 | 1.5766 | 0.9722 |
M9-Fixed | - | 0.9565 (0.0047) | 2.1915 (0.0033) | −0.2846 (0.0339) | −0.1497 (0.0442) | - | - | −0.2606 | 1.5315 | 2.1652 | 0.9476 | |||
M9-Mixed | β3 | 0.9555 (0.0094) | 2.1923 (0.0058) | −0.3080 (0.0362) | −0.1849 (0.0472) | - | - | 0.1815 | 0.6664 | −0.4017 | −0.1304 | 1.0705 | 1.5395 | 0.9735 |
M8-Fixed | - | 2.1635 (0.0020) | - | - | - | - | - | 0.4684 | 1.6917 | 2.1886 | 0.9465 | |||
M8-Mixed | β1 | 2.1564 (0.0060) | - | - | - | - | - | 0.0385 | 0.7640 | −0.3765 | 0.3901 | 1.4998 | 1.9373 | 0.9581 |
M3-Fixed | - | 0.2498 (0.0132) | 0.1496 * (0.1402) | 3.9458 (0.4665) | −7.3717 (0.6006) | 4.0500 (0.2616) | - | −0.2045 | 1.6621 | 2.2818 | 0.9418 | |||
M3-Mixed | β0 | 0.2276 (0.0096) | 0.2828 (0.1099) | 4.0384 (0.4095) | −8.1436 (0.561) | 4.6339 (0.2525) | - | 0.0424 | 0.7351 | −0.2895 | −0.4000 | 1.3644 | 1.8750 | 0.9607 |
M13-Fixed | - | 0.6823 (0.1254) | 0.9335 (0.0204) | 1.0981 (0.021) | - | - | - | 0.4130 | 1.6503 | 2.1793 | 0.9469 | |||
M13-Mixed | β3 | 1.2923 (0.1626) | 1.0132 (0.0346) | 0.7791 (0.0344) | - | - | - | 0.2102 | 0.7870 | −0.3719 | 0.1191 | 1.5654 | 2.1259 | 0.9495 |
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Pokhrel, N.R.; Subedi, M.R.; Malego, B. Fitting and Evaluating Taper Functions to Predict Upper Stem Diameter of Planted Teak (Tectona grandis L.f.) in Eastern and Central Regions of Nepal. Forests 2025, 16, 77. https://doi.org/10.3390/f16010077
Pokhrel NR, Subedi MR, Malego B. Fitting and Evaluating Taper Functions to Predict Upper Stem Diameter of Planted Teak (Tectona grandis L.f.) in Eastern and Central Regions of Nepal. Forests. 2025; 16(1):77. https://doi.org/10.3390/f16010077
Chicago/Turabian StylePokhrel, Nawa Raj, Mukti Ram Subedi, and Bibek Malego. 2025. "Fitting and Evaluating Taper Functions to Predict Upper Stem Diameter of Planted Teak (Tectona grandis L.f.) in Eastern and Central Regions of Nepal" Forests 16, no. 1: 77. https://doi.org/10.3390/f16010077
APA StylePokhrel, N. R., Subedi, M. R., & Malego, B. (2025). Fitting and Evaluating Taper Functions to Predict Upper Stem Diameter of Planted Teak (Tectona grandis L.f.) in Eastern and Central Regions of Nepal. Forests, 16(1), 77. https://doi.org/10.3390/f16010077