Development of stem diameter model using quantile regression

Öz

Tree volume estimates are one of the most important components of growth and yield models. Stem diameter models are one of the most modern approaches used for stem volume estimation. Different regression methods, especially the nonlinear least squares (ONLS) method, were used to develop stem diameter models. Recently, the quantile regression (QR) method has also been used in forestry applications for the development of taper models. In this study, a stem diameter model based on Max and Burkhart (1976) model was developed using ONLS and QR methods for natural black pine stands. For this purpose, sample tree data were obtained from two different black pine stands, and some of the data (group I) were used to develop the models and the rest of the data (group II) was used to test the models developed. In the study, the QR technique was used based on two different quantile sets (3QR and 5QR). The results were compared for the whole tree stem and ten different relative height classes using four different evaluation criteria. Evaluation statistics showed that both quantile regression models provided better results as compared to ONLS and 3QR model performed relatively better than 5QR. In conclusion, QR technique is an approach that can be used as an alternative to other regression techniques for stem diameter estimations.

Anahtar Kelimeler

• Quantile regression
• Quantile set
• Stem diameter
• Black pine

Kantil regresyon ile gövde çapı modelinin geliştirilmesi

Öz

Büyüme ve hasılat modellerinin en önemli bileşenlerinden birisi ağaç hacim tahminleridir. Hacim tahminleri amacıyla kullanılan en modern yaklaşımlardan birisi de gövde çapı modelleridir. Günümüze kadar farklı formlarda pek çok gövde çapı modeli geliştirilmiştir. Gövde çapı modellerinin geliştirilmesi amacıyla geleneksel doğrusal olmayan en küçük kareler (ONLS) yöntemi başta olmak üzere farklı regresyon teknikleri kullanılmıştır. Son yıllarda, ormancılık uygulamalarında ve gövde çapı modellerinin geliştirilmesi amacıyla Kantil Regresyon (QR) tekniği de kullanılmaya başlamıştır. Bu çalışmada, doğal karaçam meşcereleri için ONLS ve QR teknikleriyle Max ve Burkhart (1976) modelini temel alan gövde çapı modeli geliştirilmiştir. Bu amaçla, birbirinden bağımsız iki farklı karaçam meşceresinden örnek ağaç verileri elde edilmiş ve verilerin bir kısmı (grup I) model geliştirmek, diğer kısmı ise (grup II) ise geliştirilen modelin test edilmesi amacıyla kullanılmıştır. Çalışmada, QR tekniği iki farklı kantil setini (3QR ve 5QR) esas alarak kullanılmıştır. Sonuçlar, dört farklı değerlendirme ölçütü kullanılarak tüm ağaç gövdesi ve on farklı nisbi boy sınıfı için karşılaştırılmıştır. QR tekniği ile elde edilen gövde çapı tahminlerinin hem tüm gövde hem de farklı nispi boy sınıfları için ONLS ile elde edilen sonuçlara göre daha başarılı olduğu görülmüştür. Çap tahminleri için 3QR ile elde edilen sonuçlar, 5QR ile elde edilen sonuçlara göre nispeten daha başarılıdır. Sonuç olarak, QR tekniği de, gövde çapı tahminleri için diğer regresyon tekniklerine alternatif olarak kullanılabilecek bir yaklaşımdır.

Anahtar Kelimeler

• Kantil regresyon
• Kantil seti
• Gövde çapı
• Karaçam

Kaynakça

1. Alkan, O., Özçelik, R., Alkan, H., 2019. Türkiye’nin bazı önemli ağaç türleri için yöresel gövde çapı modellerinin geliştirilmesi: Bucak örneği. Turkish Journal of Forestry, 20(4): 333-340.
2. Biging, G.S., 1984. Taper equations for second-growth mixed conifers of Northern California. Forest Science, 30(4): 1103-1117.
3. Bohora, S.B., Cao, Q.V., 2014. Prediction of tree diameter growth using quantile regression and mixed-effects models. Forest Ecology and Management, 319: 62–66.
4. Cao, Q.V., Burkhart, H.E., Max, T.A., 1980. Evaluation of two methods for cubic-volume prediction of loblolly pine to any merchantable limit. Forest Science, 26(1): 71-80.
5. Cao, Q.V., Wang, J., 2015. Evaluation of methods for calibrating a tree taper equation. Forest Science, 61(2): 213–219.
6. Castedo-Dorado, F., Gómez-García, E., Diéguez-Aranda, U., Barrio-Anta, M., Crecente-Campo, F., 2012. Aboveground stand-level biomass estimation: a comparison of two methods for major forest species in northwest Spain. Annals of Forest Science, 69(6): 735-746.
7. Chen, C., Wei, Y., 2005. Computational issues for quantile regression. Sankhyā: The Indian Journal of Statistics, 67(2): 399-417.
8. Clark, A., Souter, R.A., Schlaegel, B.E., 1991. Stem profile equations for southern tree species. Research paper SE (USA).

9. Coble, D.W., Hilpp, K., 2006. Compatible cubic-foot stem volume and upper-stem diameter equations for semi-intensive plantation grown loblolly pine trees in East Texas. Southern Journal of Applied Forestry, 30(3): 132-141.
10. Crecente-Campo, F., Alboreca, A.R., Diéguez-Aranda, U., 2009. A merchantable volume system for Pinus sylvestris L. in the major mountain ranges of Spain. Annals of forest science, 66(8): 808.
11. de-Miguel, S., Mehtätalo, L., Shater, Z., Kraid, B., Pukkala, T., 2012. Evaluating marginal and conditional predictions of taper models in the absence of calibration data. Canadian Journal of Forest Research, 42(7): 1383-1394.
12. Diéguez-Aranda, U., Castedo-Dorado, F., Álvarez-González, J.G., Rojo, A., 2006. Compatible taper function for Scots pine plantations in northwestern Spain. Canadian Journal of Forest Research, 36(5): 1190-1205.
13. Ducey, M.J., Knapp, R.A., 2010. A stand density index for complex mixed species forests in the northeastern United States. Forest Ecology and Management, 260(9): 1613-1622.
14. Evans, A.M., Finkral, A.J., 2010. A new look at spread rates of exotic diseases in North American forests. Forest Science, 56: 453–459.
15. Evans, A.M., Gregoire, T.G., 2007. A geographically variable model of hemlock woolly adelgid spread. Biological Invasions, 9(4): 369-382.
16. Fang, Z., Borders, B.E., Bailey, R.L., 2000. Compatible volume taper models for loblolly and slash pine based on system with segmented-stem form factors. Forest Science, 46: 1–12.
17. Farias, A.A., Soares, C.P.B., Leite, H.G., da Silva, G.F., 2021. Quantile regression: Prediction of growth and yield for a eucalyptus plantation in northeast Brazil. European Journal of Forest Research, 1-7.
18. Figueiredo-Filho, A., Borders, B.E., Hitch, K.L., 1996. Taper equations for Pinus taeda plantations in Southern Brazil. Forest Ecology and Management, 83(1-2): 39-46.
19. Gomez-Garcia, E., Fonseca, T.F., Crecente-Campo, F., Almeida, L.R., Dieguez-Aranda, U., Huang, S., Marques, C.P., 2015. Height-diameter models for maritime pine in Portugal: a comparison of basic, generalized and mixed-effects models. iForest-Biogeosciences and Forestry, 9(1): 72.
20. He, P., Hussain, A., Shahzad, M.K., Jiang, L., Li, F., 2021. Evaluation of four regression techniques for stem taper modeling of Dahurian larch (Larix gmelinii) in Northeastern China. Forest Ecology and Management, 494: 119336.
21. Huang, Q., Zhang, H., Chen, J., He, M.J.J.B.B., 2017. Quantile regression models and their applications: A review. Journal of Biometrics & Biostatistics, 8(3): 354.
22. Jiang, L., Brooks, J.R., Wang, J., 2005. Compatible taper and volume equations for yellow-poplar in West Virginia. Forest ecology and management, 213(1-3): 399-409.
23. Jiang, L. 2004. Compatible taper and volume equations for yellow-poplar in West Virginia. PhD Thesis, West Virginia University, Morgantown
24. Koenker, R., Bassett, G., 1978. Regression quantiles. Econometrica 46: 33–50.
25. Koenker, R., 2004. Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1): 74-89.
26. Kozak, A., 2004. My last words on taper equations. The Forestry Chronicle, 80(4): 507-515.
27. Kozak, A., Munro, D.D., Smith, J.H.G., 1969. Taper functions and their application in forest inventory. The Forestry Chronicle, 45(4): 278-283.
28. Kozak, A., Kozak, R., 2003. Does cross validation provide additional information in the evaluation of regression models?. Canadian Journal of Forest Research, 33(6): 976-987.
29. Ma, Y., Jiang, L., 2019. Stem taper function for Larix gmelinii based on nonlinear quantile regression. Scientia Silvae Sinicae, 55(10): 68-75.
30. Mäkinen, A., Kangas, A., Kalliovirta, J., Rasinmäki, J., Välimäki, E., 2008. Comparison of treewise and standwise forest simulators by means of quantile regression. Forest Ecology and Management, 255(7): 2709-2717.
31. Martin, A.J., 1981. Taper and volume equations for selected Appalachian hardwood species. Research Paper. NE-490. Broomall, PA: US Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 22p., 490.
32. Max, T.A., Burkhart, H.E., 1976. Segmented polynomial regression applied to taper equations. Forest Science, 22(3): 283-289.
33. Mehtätalo, L., Gregoire, T.G., Burkhart, H.E., 2008. Comparing strategies for modeling tree diameter percentiles from remeasured plots. Environmetrics: The Official Journal of The International Environmetrics Society, 19(5): 529-548.
34. OGM, 2019. Ormancılık İstatistikleri. https://www.ogm.gov.tr/tr/ ormanlarimiz/resmi-istatistikler, Erişim: 18.06.2021.
35. Özçelik, R., Alkan, H., 2011. Okaliptüs ağaçlandırmaları için uyumlu gövde çapı ve gövde hacim modellerinin geliştirilmesi. I. Ulusal Akdeniz Orman ve Çevre Sempozyumu, 26-28 Ekim, Kahramanmaraş, s. 720-730
36. Özçelik, R., Crecente-Campo, F., 2016. Stem taper equations for estimating merchantable volume of Lebanon cedar trees in the Taurus Mountains, Southern Turkey. Forest Science, 62(1): 78-91
37. Özçelik, R., Cao, Q.V., Trincado, G., Göçer, N., 2018a. Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey. Forest Ecology and Management, 419: 240–248.
38. Özçelik, R., Alkan, O., Korkmaz, M., 2018b. Local Volume Equations for Eucalyptus Plantations. International Congress on Agriculture and Animal Sciences, Kasım 7-9, Antalya, s. 383-396.
39. Özçelik, R., Diamantopoulou, M.J., Trincado, G., 2019. Evaluation of potential modeling approaches for Scots pine stem diameter prediction in north-eastern Turkey. Computers and Electronics in Agriculture, 162: 773-782.
40. Paulo, J.A., Firmino, P.N., Faias, S.P., Tomé, M., 2021. Quantile regression for modelling the impact of climate in cork growth quantiles in Portugal. European Journal of Forest Research, 1-14.
41. Rodriguez, F., Lizarralde, I., Fernández-Landa, A., Condés, S., 2014. Non-destructive measurement techniques for taper equation development: a study case in the Spanish Northern Iberian Range. European journal of forest research, 133(2): 213-223.
42. Rust, S., 2014. Analysis of regional variation of height growth and slenderness in populations of six urban tree species using a quantile regression approach. Urban Forestry & Urban Greening, 13(2): 336-343.
43. Sharma, M., Parton, J., 2009. Modeling stand density effects on taper for jack pine and black spruce plantations using dimensional analysis. Forest science, 55(3): 268-282.
44. Sharma, M., Zhang, S., 2004. Height–diameter models using stand characteristics for Pinus banksiana and Picea mariana. Scandinavian Journal of Forest Research, 19(5): 442-451.
45. West, P.W., Ratkowsky, D.A., Davis, A.W., 1984. Problems of hypothesis testing of regressions with multiple measurements from individual sampling units. Forest Ecology and Management, 7(3): 207-224.
46. Xin, S., Jiang, L., 2020. Modeling stem taper profile for Pinus sylvestris plantations using nonlinear quantile regression. Journal of Beijing Forestry University, 42(2): 1-8.
47. Yang, Y., Huang, S., Trincado, G., Meng, S.X., 2009. Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta, Canada. European Journal of Forest Research, 128(4): 415-429.
48. Zang, H., Lei, X., Zeng, W., 2016. Height–diameter equations for larch plantations in northern and northeastern China: A comparison of the mixed-effects, quantile regression and generalized additive models. Forestry, 89(4): 434–445.
49. Zhang, L., Bi, H., Gove, J.H., Heath, L.S., 2005. A comparison of alternative methods for estimating the self-thinning boundary line. Canadian Journal of Forest Research, 35(6): 1507-1514.