Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters
Abstract
:1. Introduction
2. Literature Search and Compilation
3. Frequency and Geographic Distribution of Taper Functions
4. Forest Types of Studied Taper Functions
5. A Brief History of Taper Functions
6. Types of Taper Function
6.1. Parametric Taper Equations
6.1.1. Static Taper Equations
Polynomial Form Models
Sigmoid Taper Equations
Segmented Polynomial Taper Equations
Variable Exponent Form Models
Trigonometric Models
6.1.2. Complex Taper Functions
Compatible Taper Models
Whole-Bole Systems Models
Dynamic Taper Models
Other Complex Taper Models
Contemporary Taper Models
6.2. Non-Parameric Taper Equations
7. Parameters and Accuracy of Taper Functions
Types of Taper Functions | Species | Country | Reference |
---|---|---|---|
Non-parametric (ML) | Acacia mearnsii (De Wild.) | BRA | Schikowski, et al. [62] |
Static, segmented polynomial, and variable-exponent | Abies nordmanniana (subsp. bornmulleriana Mattf.) | TUR | Sakici, et al. [63] |
Variable-exponent equation | Alnus rubra (Bong.) | USA, CAN | Hibbs, et al. [64] |
Static polynomial equation | Araucaria cunninghamii (Ait. ex D. Don) | AUS | Allen, et al. [65] |
Segmented polynomial | Betula platyplhylla (Sukaczev) | CHN | Shahzad, et al. [66] |
Single and segmented polynomial | Betula alnoides | CHN | Tang, et al. [67] |
Segmented polynomial | Calocedrus formosana | TWN | Wang, et al. [68] |
Non-parametric (AI) | Cryptomeria japónica | BRA | Sanquetta, et al. [69] |
Sigmoid equation | Cryptomeria japónica. D. Don. | JPN | Hada [70] |
Segmented polynomial | Eucalyptus grandis × E. urophylla (Hybrid) E. grandis × E. camaldulensis (Hybrid) | ZAF | Morley and Little [71] |
Static polynomial | Eucalyptus grandis × Eucalyptus urophylla (Hybrid) | BRA | Da Silva, et al. [72] |
Compatible taper equation | Eucalyptus pilularis; E. obliqua; E. andrewsii; E.saligna; Corymbia maculata | AUS | Muhairwe [30] |
Static polynomial | Eucalyptus cloeziana (f. Muell.) | ZMB | Eerikäinen, et al. [73] |
Variable-exponent equation | Eucalyptus saligna | CMR | Fonweban [74] |
Non-parametric (ANN) | Fagus orientalis Abies nordmanniana | TUR | Sakici and Ozdemir [75] |
Segmented polynomial | Larix gmelinii (Rupr.) | CHN | Liu, et al. [76] |
Dynamic taper equation | Nothofagus spp. | CHL | Valenzuela, et al. [77] |
Segmented polynomial | Picea abies (L.) H. Karst. | CZE | Adamec, et al. [78] |
Sigmoid (Spline) taper equation | Picea abies (L. Karst.) | CZE | Kuželka and Marušák [79] |
Variable-exponent | Picea sitchensis (Bong. Carr.) Pinus sylvestris (L.) | GBR | Fonweban, et al. [10] |
Variable-exponent equation | Picea glauca (Moench. Voss) | CAN | Huang, et al. [80] |
Polynomial | Pinus nigra (J.F. Arnold) | ITA | Marchi, et al. [81] |
Segmented polynomial | Pinus elliottii × P. caribaea var. hondurensis (Pexc) | ZAF | Algera, et al. [82] |
Compatible taper equation | Pinus cooperi Pinus durangensis | MEX | Corral-Rivas, et al. [83] |
Mixed segmented compatible | Pinus brutia (Ten.) Pinus nigra (Arnold.) | TUR | Özçelik, et al. [84] |
Segmented polynomial | Pinus sylvestris (L.); Pinus pinaster (Ait.); Quercus pyrenaica (Willd.); Populus x euramericana (Dode); Pinus pinea (L.); Juniperus thurifera (L.); Pinus nigra (Arnold.); Fagus sylvatica (L.) | ESP | Rodríguez, et al. [85] |
Semi-parametric | Pinus spp. and Quercus spp. | MEX | Návar [86] |
Variable-exponent equation | Pinus banksiana (Lamb.) Picea mariana (Mill. BSP) | CAN | Subedi, et al. [87] |
Segmented polynomial | Pinus contorta Larix sibirica | ISL | Heidarsson and Pukkala [88] |
Segmented polynomial | Pinus sylvestris (L.) | TUR | Özçelik [89] |
Compatible taper equation | Pinus taeda (L.) | USA | Coble and Hilpp [90] |
Variable-exponent equation | Pinus pinaster (Ait.) | ESP | Rojo, et al. [91] |
Variable-exponent equation | Pinus taeda (L.) | USA | Bullock and Burkhart [92] |
Static polynomial equation | Pinus kesiya, Pinus oocarpa, Pinus merkusii, Pinus michoacana, Eucalyptus grandis, Eucalyptus doeziana | ZMB | Heinonen, et al. [93] |
Segmented polynomial | Populus hybrids (P. trichocarpa/P. deltoids) | FRA | Benbrahim and Gavaland [94] |
Segmented polynomial | Pseudotsuga menziesii | ESP | López-Sánchez, et al. [95] |
Compatible taper equation | Quercus variabilis | CHN | Zheng, et al. [96] |
Dynamic taper equation | Quercus robur (L.) | ESP | Gómez-García, et al. [97] |
Segmented polynomial | Quercus fagaceae | MEX | Pompa-García, et al. [98] |
Compatible taper equation | Quercus robur L. Q petraea (Matt) Liebl | DNK | Tarp-Johansen, et al. [99] |
Compatible taper equation | Quercus robur (L.) | ZAF | Trincado, et al. [100] |
Compatible taper equations | Salix schwerinii (E. L. Wolf) | FIN | Salam, et al. [101] |
Segmented polynomial | Taiwania cryptomerioides | TWN | Wang, et al. [102] |
Mixed polynomial | Tectona grandis (L.f.) | BRA | Lanssanova, et al. [103] |
Non-parametric (ANN) | Tectona grandis (Linn.) | BRA | Leite, da Silva, Binoti, Fardin and Takizawa [31] |
Spline regression | Not defined | DEU | Kublin, et al. [104] |
8. Applications of Taper Functions
9. Opportunities for Taper Function Development
10. Summary and Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Equation | Coefficients | Species | Stat., Unit | Value | Country | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | - | - | - | - | ||||||||
2 | * * * * Form class = 75 | Picea abies (L.) Karst. | - | - | USA | |||||||
3 | * * * Form class = 75 | Picea abies (L.) Karst. | SEE vol. (%) | ±13.74 | USA | |||||||
4 | Tsuga heterophylla (Raf.) Sarg. | - | - | USA | ||||||||
5 | , −1.976 8.238, −4.964 , −7.417 | Alnus rubra (Bong.) | SEE, in | 0.0704 | USA | |||||||
6 | Pinus resinosa Sol. Ex Aiton | SSE, D (cm) | 446.634 | USA | ||||||||
Pinus taeda L. | SSE, D (cm) | 526.285 | USA | |||||||||
7 | Not available | Populus tremuloides Michx. | - | - | CAN | |||||||
8 | Populus tremuloides Michx. (Coastal) | SEE, D (inch) | 0.59 | CAN | ||||||||
Pseudotsuga menziesii (Mirbel) Franco (Interior) | SEE, D (inch) | 1.33 | CAN | |||||||||
9 | , , , | Pinus taeda L. | MAD, D (cm) | 0.53–0.86 | USA | |||||||
10 | , , 0.914280, | Pinus resinosa Sol. Ex Aiton | SSE, D (inch) | 268.918 | USA | |||||||
, , , | Pinus taeda L. | SSE, D (inch) | 294.163 | |||||||||
11 | Pinus resinosa Sol. Ex AitonPicea mariana (Mill.) Britton | ME % Vol. | 3.92 | CAN | ||||||||
12 | , , , , | Pinus contorta | SEE, D (cm) | 1.39 | CAN | |||||||
, , , , | Thuja plicata | SEE, D (cm | 6.67 | |||||||||
13 | Quercus phellos (L.) | SEE d (cm) | 1.284 | USA | ||||||||
14 | Species | Region | K1 × 102 | K2 | Mixed Species | Bias % vol. | −8.2 | USA | ||||
Cottonwood | C + I | 0.20302 | 0.37223 | |||||||||
Douglas-Fir | C | 0.167216 | 0.306585 | |||||||||
Douglas-Fir | I | 0.181694 | 0.33313 | Bias % vol. | −12.2 | |||||||
Lodgepole pine | C + I | 0.226124 | 0.41459 | |||||||||
Yellow cedar | C + I | 0.219329 | 0.402132 | |||||||||
Yellow pine | C + I | 0.208576 | 0.382417 | Bias % vol. | −7.7 | |||||||
Region: C= Coastal, I = Interior | ||||||||||||
19 | , −44.310 26.708, −3.5452 , 0.33021 17.070 | Pinus radiata D.Don | SEE, D (cm) | 1.43 | NZL | |||||||
20/21 | Not available | Pseudotsuga menziesii (Mirbel) Franco; Acer spp. (L.) | SEE D (inch) | 0.72/0.49 | CAN | |||||||
22 | , , , | Pinus contorta | SEE, D (cm) | 0.6468 | CAN | |||||||
23 | , , , , | Pinus spp. | SEE, D (%) | 3.63 | CAN | |||||||
24 | u | Coefficient | Pinus sylvestris (L.) | RMSE, vol. (%) | 3.5 | FIN | ||||||
a0 | a1 | a2 | a3 | |||||||||
1 | 0.784 | 0.958 | 0.034 | −0.118 | ||||||||
2 | 0.793 | 0.897 | 0.043 | −0.123 | ||||||||
3 | 0.746 | 0.853 | 0.052 | −0.124 | ||||||||
4 | 0.558 | 0.933 | 0.033 | −0.111 | ||||||||
5 | 0.521 | 0.903 | 0.038 | −0.101 | ||||||||
6 | 0.483 | 0.862 | 0.046 | −0.09 | ||||||||
7 | 318 | 0.866 | 0.042 | −0.057 | ||||||||
8 | 0.065 | 0.939 | 0.019 | −0.011 | ||||||||
9 | −0.313 | 1.054 | −0.018 | 0.056 | ||||||||
10 | −0.644 | 1.12 | −0.044 | 0.113 | ||||||||
11 | −1.141 | 1.194 | −0.073 | 0.169 | ||||||||
12 | −1.798 | 1.23 | −0.093 | 0.206 | ||||||||
13 | −0.63 | 1.276 | −0.108 | 0.23 | ||||||||
14 | −2.168 | 1.396 | −0.162 | 0.524 |
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Salekin, S.; Catalán, C.H.; Boczniewicz, D.; Phiri, D.; Morgenroth, J.; Meason, D.F.; Mason, E.G. Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters. Forests 2021, 12, 913. https://doi.org/10.3390/f12070913
Salekin S, Catalán CH, Boczniewicz D, Phiri D, Morgenroth J, Meason DF, Mason EG. Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters. Forests. 2021; 12(7):913. https://doi.org/10.3390/f12070913
Chicago/Turabian StyleSalekin, Serajis, Cristian Higuera Catalán, Daniel Boczniewicz, Darius Phiri, Justin Morgenroth, Dean F. Meason, and Euan G. Mason. 2021. "Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters" Forests 12, no. 7: 913. https://doi.org/10.3390/f12070913