Height and diameter are two factors that are considered when developing (volume and yield) tables, as well as for determining site quality and site index. Diameter is easily measured using precise and affordable instruments. However, height measurement is complex in terms of time, skill, and resource. So, developing allometric equation of height-diameter is useful to predict height from diameter to calculate tree volume, biomass, and carbon storage and survival analysis. The study was carried out in Nepal. The study area comprised of a total of 664 unique plots of Pinus roxburghii. Data was obtained from Forest Resource Assessment, 2018 undertaken by Forest Research and Training Centre (then Department of Forest Research and survey). Diameter was measured with a diameter tape at 1.3 m height above the ground level and total height was measured with a Vertex IV and Transponder. A two-phase cluster sampling was applied during data collection. Statistical software R and MS-Excel were used for data analysis. Correlation analysis showed significant positive correlation (r = 0.86) between DBH (diameter at breast height) and Height. The relationship between height as dependent variable to diameter was established through regression analysis, different suggested models were tested accordingly. Different forms of candidate models including linear, polynomial, logarithmic, and inverse were fitted to select the best height prediction model. The Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and Adjusted Coefficient of Determination (R^{2} adj.) were used to evaluate the model. Polynomial degree 2 form of equation (height=1.1052804+0.6252304*dbh−0.0021242*dbh^{2}) resulted as the best model with values of adj. R^{2} RMSE, and AIC; 0.720, 3.639 and 2735.253 respectively.
Published in | American Journal of Biological and Environmental Statistics (Volume 10, Issue 3) |
DOI | 10.11648/j.ajbes.20241003.12 |
Page(s) | 49-59 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Height, Diameter, Pinus roxburghii, Modeling, Height-Diameter Models
Model form | Model | Equation |
---|---|---|
Simple linear | M1 | Y= ax +b |
Polynomial degree 2 | M2 | Y= a x2+bx+ c |
Polynomial degree 3 | M3 | Y= ax3+bx2+ dx+c |
Logarithmic | M4 | Y= a * log(x) + c |
Inverse | M5 | Y= f(x) |
Criterion | Equation | Ideal Result |
---|---|---|
AIC | AIC = n ×ln (RSS/n) + 2K | Smaller AIC value |
Adjusted R^{2} | adj.R^{2} = 1 - $\frac{(n-\mathrm{}1)\sum _{i=1}^{n}{({Y}_{i}\mathrm{}-\mathrm{}{\mathrm{\u0176}}_{i})}^{2}\mathrm{}}{(n-p)\sum _{i=1}^{n}{({Y}_{i}\mathrm{}-\mathrm{}{\mathrm{\u0176}}_{i})}^{2}}$ | Higher adj. R², ideal value is 1 |
RMSE | RMSE= $\sqrt{\frac{1}{n-p-1}{\sum}_{i-1}^{n}({Y}_{i}\mathrm{}-\mathrm{}{\mathrm{\u0176}}_{i})}$ | Smaller RMSE value; ideal value is 0 |
DBH Class | No. of trees | Statistics | Diameter | Height |
---|---|---|---|---|
0-10 | 19 | 1st Q | 6.300 | 3.650 |
3^{rd} Q | 8.100 | 4.850 | ||
Mean | 7.326 | 4.579 | ||
Median | 7.200 | 4.000 | ||
10-20 | 88 | 1^{st} Q | 11.15 | 6.650 |
3^{rd} Q | 15.70 | 11.650 | ||
Mean | 13.47 | 9.328 | ||
Median | 12.80 | 9.000 | ||
20-30 | 208 | 1^{st} Q | 22.00 | 12.5 |
3^{rd} Q | 26.70 | 17.8 | ||
Mean | 24.53 | 15.2 | ||
Median | 24.50 | 15.5 | ||
30-40 | 175 | 1^{st} Q | 32.20 | 16.80 |
3^{rd} Q | 36.85 | 22.90 | ||
Mean | 34.47 | 20.38 | ||
Median | 34.20 | 20.20 | ||
40-50 | 75 | 1^{st} Q | 42.33 | 20.88 |
3^{rd} Q | 46.50 | 27.38 | ||
Mean | 44.45 | 24.41 | ||
Median | 44.25 | 24.30 | ||
>50 | 45 | 1^{st} | 54.23 | 26.62 |
3^{rd} Q | 66.60 | 35.40 | ||
Mean | 61.30 | 31.26 | ||
Median | 60.15 | 29.85 |
Model Form | Model | Formula |
---|---|---|
Simple Linear | M1 | height = 0.466 *dbh + 3.623 |
Polynomial (2) | M2 | height=1.1052804+0.6252304*dbh−0.0021242*dbh^{2} |
Polynomial (3) | M3 | height=1.569+0.5791*dbh−0.0008634⋅*dbh^{2}−0.000009678* dbh^{3} |
Logarithmic | M4 | log(height) = -0.075 + 0.862 * log(dbh) |
Inverse | M5 | height= 27.261 + -227 * (1/dbh) |
Model | Coefficients/Parameters | Estimates | Std error | t-value | p-value |
---|---|---|---|---|---|
M1 | intercept | 3.6231 | 0.4557 | 7.95 | 1.31e-14 |
diameter | 0.4657 | 0.0134 | 34.74 | < 2e-16 | |
M2 | Intercept | 1.1052804 | 0.8007517 | 1.38 | 0.168129 |
poly (diameter, degree = 2)1 | 0.6252304 | 0.0440294 | 14.20 | < 2e-16 | |
poly (diameter, degree = 2)2 | -0.0021242 | 0.0005591 | -3.80 | 0.000163 | |
M3 | (Intercept) | 1.569 | 1.28 | 1.226 | 0.221 |
poly (diameter, degree = 3)1 | 0.5791 | 0.1086 | 5.331 | 1.5e-07 | |
poly (diameter, degree = 3)2 | −0.0008634 | 0.002769. | -0.312 | 0.755 | |
poly (diameter, degree = 3)3 | −0.000009678 | 0.00002082 | -0.465 | 0.642 | |
M4 | (Intercept) | -0.07519 | 0.07566 | -0.994 | 0.321 |
Log (diameter) | 0.86165 | 0.02244 | 38.398 | <2e-16 | |
M5 | (Intercept) | 27.2610 | 0.4688 | 58.15 | <2e-16 |
I(1/diameter) | -227.2172 | 10.0655 | -22.57 | <2e-16 |
Model | Intercept | a | b | d | Adj. R^{2} | RMSE | AIC |
---|---|---|---|---|---|---|---|
M1 | 3.578 | 0.466 | N/A | N/A | 0.712 | 3.718 | 2747.567 |
M2 | 18.168 | -15.08 | 139.782 | N/A | 0.720 | 3.639 | 2735.253 |
M3 | 18.168 | -1.847 | -15.08 | 139.782 | 0.720 | 3.642 | 2737.035 |
M4 | -0.075 | 0.862 | N/A | N/A | 0.75 | 3.695 | 2703.218 |
M5 | 27.365 | N/A | N/A | N/A | 0.511 | 5.731 | 3006.688 |
Model | Fitting Rank | RMSE | AIC | Total | Rank |
---|---|---|---|---|---|
Adj. R^{2} | |||||
M1 | 3 | 4 | 4 | 11 | 6 |
M2 | 2 | 1 | 2 | 5 | 1 |
M3 | 2 | 2 | 3 | 7 | 4 |
M4 | 1 | 3 | 1 | 5 | 2 |
M5 | 4 | 5 | 5 | 14 | 7 |
adj.R^{2} | Adjusted Coefficient of Determination |
AIC | Akaike Information Criterion |
CCSPs | Concentric Circular Sample Plots |
CO_{2} | Carbon Dioxide |
DBH | Diameter at Breast Height |
FRA | Forest Resource Assessment |
FRTC | Forest Research and Training Centre |
RMSE | Root Mean Square Error |
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APA Style
Upadhyay, J., Khadka, S. (2024). Modelling Height-Diameter Relationship of Pinus Roxburghii in Nepal. American Journal of Biological and Environmental Statistics, 10(3), 49-59. https://doi.org/10.11648/j.ajbes.20241003.12
ACS Style
Upadhyay, J.; Khadka, S. Modelling Height-Diameter Relationship of Pinus Roxburghii in Nepal. Am. J. Biol. Environ. Stat. 2024, 10(3), 49-59. doi: 10.11648/j.ajbes.20241003.12
AMA Style
Upadhyay J, Khadka S. Modelling Height-Diameter Relationship of Pinus Roxburghii in Nepal. Am J Biol Environ Stat. 2024;10(3):49-59. doi: 10.11648/j.ajbes.20241003.12
@article{10.11648/j.ajbes.20241003.12, author = {Jharana Upadhyay and Shiva Khadka}, title = {Modelling Height-Diameter Relationship of Pinus Roxburghii in Nepal }, journal = {American Journal of Biological and Environmental Statistics}, volume = {10}, number = {3}, pages = {49-59}, doi = {10.11648/j.ajbes.20241003.12}, url = {https://doi.org/10.11648/j.ajbes.20241003.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajbes.20241003.12}, abstract = {Height and diameter are two factors that are considered when developing (volume and yield) tables, as well as for determining site quality and site index. Diameter is easily measured using precise and affordable instruments. However, height measurement is complex in terms of time, skill, and resource. So, developing allometric equation of height-diameter is useful to predict height from diameter to calculate tree volume, biomass, and carbon storage and survival analysis. The study was carried out in Nepal. The study area comprised of a total of 664 unique plots of Pinus roxburghii. Data was obtained from Forest Resource Assessment, 2018 undertaken by Forest Research and Training Centre (then Department of Forest Research and survey). Diameter was measured with a diameter tape at 1.3 m height above the ground level and total height was measured with a Vertex IV and Transponder. A two-phase cluster sampling was applied during data collection. Statistical software R and MS-Excel were used for data analysis. Correlation analysis showed significant positive correlation (r = 0.86) between DBH (diameter at breast height) and Height. The relationship between height as dependent variable to diameter was established through regression analysis, different suggested models were tested accordingly. Different forms of candidate models including linear, polynomial, logarithmic, and inverse were fitted to select the best height prediction model. The Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and Adjusted Coefficient of Determination (R2 adj.) were used to evaluate the model. Polynomial degree 2 form of equation (height=1.1052804+0.6252304*dbh−0.0021242*dbh2) resulted as the best model with values of adj. R2 RMSE, and AIC; 0.720, 3.639 and 2735.253 respectively. }, year = {2024} }
TY - JOUR T1 - Modelling Height-Diameter Relationship of Pinus Roxburghii in Nepal AU - Jharana Upadhyay AU - Shiva Khadka Y1 - 2024/09/20 PY - 2024 N1 - https://doi.org/10.11648/j.ajbes.20241003.12 DO - 10.11648/j.ajbes.20241003.12 T2 - American Journal of Biological and Environmental Statistics JF - American Journal of Biological and Environmental Statistics JO - American Journal of Biological and Environmental Statistics SP - 49 EP - 59 PB - Science Publishing Group SN - 2471-979X UR - https://doi.org/10.11648/j.ajbes.20241003.12 AB - Height and diameter are two factors that are considered when developing (volume and yield) tables, as well as for determining site quality and site index. Diameter is easily measured using precise and affordable instruments. However, height measurement is complex in terms of time, skill, and resource. So, developing allometric equation of height-diameter is useful to predict height from diameter to calculate tree volume, biomass, and carbon storage and survival analysis. The study was carried out in Nepal. The study area comprised of a total of 664 unique plots of Pinus roxburghii. Data was obtained from Forest Resource Assessment, 2018 undertaken by Forest Research and Training Centre (then Department of Forest Research and survey). Diameter was measured with a diameter tape at 1.3 m height above the ground level and total height was measured with a Vertex IV and Transponder. A two-phase cluster sampling was applied during data collection. Statistical software R and MS-Excel were used for data analysis. Correlation analysis showed significant positive correlation (r = 0.86) between DBH (diameter at breast height) and Height. The relationship between height as dependent variable to diameter was established through regression analysis, different suggested models were tested accordingly. Different forms of candidate models including linear, polynomial, logarithmic, and inverse were fitted to select the best height prediction model. The Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and Adjusted Coefficient of Determination (R2 adj.) were used to evaluate the model. Polynomial degree 2 form of equation (height=1.1052804+0.6252304*dbh−0.0021242*dbh2) resulted as the best model with values of adj. R2 RMSE, and AIC; 0.720, 3.639 and 2735.253 respectively. VL - 10 IS - 3 ER -