Height-diameter model for natural black pine stands in Eğirdir region: Quantile regression approach

Öz

Black pine (Pinus nigra JF Arnold.) is one of the most economically and ecologically important tree species in Turkey. In this context, reliable and accurate information about the current status, growth and yield characteristics of these forests is needed for the sustainable management of black pine forests. One of the most important components of growth and yield models is the height-diameter relationships. Diameter and height variables are also the most important measurement tools in forest inventory studies. Since the height of a standing tree cannot be measured as easily as the breast height diameter, tree height is often estimated as a function of diameter in forest inventory studies. For this reason, accurate and reliable estimation of tree height has a great importance for forestry activity. In this study, a height-diameter model was developed for natural black pine stands in Eğirdir region using Quantile Regression (QR) techniques. The measured data were randomly divided into two equal groups. Chapman-Richards height-diameter model was chosen as the base model for both methods since this model has been provided successful results in previous studies. QR models are developed based on three quantile (3, 5 and 9 quantiles) sets in this study. The most important advantage of QR approach over other estimation methods is that QR allows the calibration of the model with extra sample tree heights. For this purpose, different calibration alternatives were tested using a number of trees ranging from 1 to 10 in each sample plot. As a result of the study, it was seen that the 3QR approach performed better than both 5QR and 9QR approaches in terms of describing the height-diameter relationships. In addition, it has been determined that the calibration with five sample trees in each sample plot is appropriate in terms of both the estimation precision of the models and the sampling costs

Anahtar Kelimeler

• Black pine
• Height prediction
• Quantile regression
• Calibration

Eğirdir yöresi doğal karaçam meşcereleri için çap-boy modeli: Kantil regresyon yaklaşımı

Öz

Karaçam (Pinus nigra JF Arnold.) ekonomik ve ekolojik açıdan en önemli ağaç türlerimiz arasında yer almaktadır. Bu nedenle doğal karaçam meşcerelerinin bir taraftan korunması, diğer taraftan da sürdürülebilir yönetimi amacıyla, geleceğe dönük planlama ve stratejilerin oluşturulması için bu meşcerelerin büyüme ve gelişme özelliklerine ilişkin güvenilir bilgilere ihtiyaç duyulmaktadır. Büyüme ve hasılat modellerinin en önemli bileşenlerinden birisi de çap-boy ilişkileridir. Çap ve boy değişkenleri, orman envanteri çalışmalarının da en önemli ölçüm araçlarındadır. Dikili ağaçlarda ağaç boyu ölçümünün göğüs çapı ölçümü kadar kolay olmaması nedeniyle, ağaç boyları orman envanteri çalışmalarında genellikle göğüs çapının bir fonksiyonu olarak tahmin edilmektedir. Bu sebeple, ağaç boyunun doğru ve güvenilir bir şekilde tahmin edilmesi, ormancılık faaliyetleri açısından büyük önem arz etmektedir. Bu çalışmada, Eğirdir yöresi doğal karaçam meşcereleri için Kantil Regresyon (QR) yaklaşımı kullanılarak çap-boy modelleri geliştirilmiştir. Bu amaçla ölçümü yapılan veriler tesadüfi olarak eşit sayıda örnek alan içerecek şekilde iki gruba ayrılmıştır. Diğer modellere göre daha başarılı sonuçlar üretmesi nedeniyle çap-boy modellerinin geliştirilmesinde Chapman-Richards fonksiyonu temel alınmıştır. Çalışma kapsamında üç farklı kantil setini (3, 5 ve 9 katil) temel alan QR modelleri geliştirilmiştir. QR yaklaşımının geleneksel tahmin yöntemlerine göre en önemli üstünlüğü, her örnek alan için ekstra örnek ağaç boyları ile modelin kalibrasyonuna imkân sağlamasıdır. Bu amaçla, QR yöntemi kullanılarak modelin kalibrasyonu amacıyla her örnek alanda tesadüfi olarak seçilen 1-10 arasında değişen sayıda örnek ağaç kullanılarak farklı kalibrasyon alternatifleri test edilmiştir. Çap-boy ilişkilerinin modellenmesi amacıyla 5QR ve 9QR’ye göre daha başarılı sonuçlar üreten ve üç kantil setini temel alan QR’nin yeterli olduğu görülmüştür. Diğer yandan farklı sayıda örnek ağaç verisi kullanılarak yapılan kalibrasyon işleminin boy tahminlerinde önemli iyileşmeler sağladığı, her örnek alanda, beş ağaç kullanılarak yapılacak kalibrasyonun hem modellerin tahmin başarısı hem de örnekleme maliyetleri açısından uygun ve yeterli olduğu görülmüştür.

Anahtar Kelimeler

• Karaçam
• Boy tahmini
• Kantil regresyon
• Kalibrasyon

Kaynakça

1. Adame, P., del Río, M., Canellas, I., 2008. A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.). Forest ecology and management, 256 (1-2): 88-98.
2. Avery, T.E., Burkhart, H.E., 2002. Forest Measurements. McGraw-Hill Book Company, New York, NY.
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. Bronisz, K., Mehtätalo, L., 2020. Seemingly Unrelated Mixed-Effects Biomass Models for Young Silver Birch Stands on Post-Agricultural Lands. Forests, 11 (4): 381.
5. Calama, R., Montero, G., 2004. Interregional nonlinear height diameter model with random coefficients for stone pine in Spain. Canadian Journal of Forest Research, 34: 150-163.
6. Cao, Q. V., Wang, J., 2015. Evaluation of methods for calibrating a tree taper equation. Forest Science, 61: 213-219.
7. Chen, C., Wei, Y., 2005. Computational ıssues on quantile regression. Special Issue on Quantile Regression and Related Methods, 67: 399-417.
8. Ciceu, A., Garcia-Duro, J., Seceleanu, I., Badea, O., 2020. A generalized nonlinear mixed-effects height–diameter model for Norway spruce in mixed-uneven aged stands. Forest Ecology and Management, 477: 118507.

9. 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: 1-12.
10. Curtis, R.O., 1967. Height-diameter and height-age equations for second-growth Douglas-fir. Forest Science, 13: 365-375.
11. Çatal, Y., Carus, S., 2018. A heigt-diameter model for brutian pine ( Pinus brutia Ten.) plantations in soutwestern Turkey. Applied Ecology and Environmental Research, 16: 1445-1459.
12. Diamantopoulou, M.J., Özçelik, R., 2012. Evaluation of different modeling approaches for total tree-height estimation in Mediterranean Region of Turkey. Forest Systems, 21(3): 383-397.
13. Diéguez-Aranda, U., Barrio, A.M., Castedo, D.F., Álvarez, J., 2005. Relación altura-diámetro generalizada para masas de Pinus sylvestris L. procedentes de repoblación en el noroeste de España. Forest Systems, 14 (2): 229-241.
14. Dubrasich, M.E., Hann, D.W., Tappeiner II, J.C., 1997. Methods for evaluating crown area profiles of forest stands. Canadian Journal of Forest Research, 27 (3): 385-392.
15. 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: 1613-1622.
16. Ercanlı, İ., 2020. Innovative deep learning artificial intelligence applications for predicting relationships between individual tree height and diameter at breast height. Forest Ecosystems, 7:12.
17. 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.
18. Evans, A.M., Gregoire, T.G., 2007. A geographically variable model of hemlock woolly adelgid spread. Biological Invasions, 9: 369 –382.
19. Fang, Z., Bailey, R.L., 1998. Height-diameter models for tropical forest on Hainan Island in southern China. Forest Ecology and Management, 110: 315-327.
20. Fekedulegn, D., Siurtain, M.P.M., Colbert, J.J., 1999. Parameter estimation of nonlinear growth models in forestry. Silva Fennica, 33: 327-336.
21. Gadow, K.V., Real, P., Alvarez Gonzalez, J. G., 2001. Modelizacion del Crecimiento y la Evolucion de los Bosques. Vienna, Austria: IUFRO World Series, Vol. 12 242p. (in Spanish).
22. Geraci, M., Bottai, M., 2007. Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics, 8 (1): 140-154.
23. Gómez-García, E., Diéguez-Aranda, U., Castedo-Dorado, F., Crecente-Campo, F., 2014. A comparison of model forms for the development of height-diameter relationships in even-aged stands. Forest Science, 60: 560-568.
24. Gómez-García, 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: 72.
25. 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.
26. Huang, S., Price, D., Morgan, D., Peck, K., 2000. Kozak’s variable-exponent taper equation regionalized for white spruce in Alberta. Western journal of Applied Forest, 15: 75-85.
27. Huang, S., Titus, S.J., Wiens, D.P., 1992. Comparison of nonlinear height–diameter functions for major Alberta tree species. Canadian Journal of Forest Research, 22(9): 1297-1304.
28. Huang, S., Wiens, D.P., Yang, Y., Meng, S.X., Vanderschaaf, C.L., 2009. Assessing the impacts of species composition, top height and density on individual tree height prediction of quaking aspen in boreal mixed woods. Forest Ecology and Management, 258: 1235-1247.
29. Huang, Q., Zhang, H., Chen, J., He, M., 2017. Quantile regression models and their applications: A review. Journal of Biometrics & Biostatistics, 8: 3.
30. Koenker, R., Bassett Jr, G., 1978. Regression quantiles. Econometrica: Journal of the Econometric Society, 33-50.
31. Koenker, R., 2004. Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91 (1): 74-89.
32. Lhotka, J.M., 2012. Height-diameter relationships in Sweetgum (Liquidambar styraciflua)-dominated stands. Southern Journal of Applied Forestry, 36 (2): 98-106.
33. Lhotka, J. M., Loewenstein, E.F., 2008. An examination of species-specific growing space utilization. Canadian Journal of Forest Research, 38 (3): 470-479.
34. López-Sánchez, C.A., Varela, J.G., Dorado, F.C., Alboreca, A.R., Soalleiro, R.R., González, J.G.Á., Rodríguez, F.S., 2003. A height-diameter model for Pinus radiata D. Don in Galicia (Northwest Spain). Annals of forest science, 60 (3): 237-245.
35. 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.
36. Mehtätalo, L., Gregoire, T.G., Burkhart, H.E., 2008. Comparing strategies for modeling tree diameter percentiles from remeasured plots. Environmetrics, 19: 529-548.
37. Mehtätalo, L., 2005. Height-diameter models for Scots pine and birch in Finland. Silva Fennica, 39 (1): 55-66.
38. Mısır, N., 2010. Generalized height-diameter models for Populus tremula L. Stands. African Journal of Biotechnology, 9(28): 4348-4355.
39. Özçelik, R., Cao, Q.V., Trincado, G., Göçer, N., 2018. 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, 419-420: 240-248.
40. Özçelik, R., Diamantopoulou, M.J., Crecente-Campo, F., Eler, U., 2013. Estimating Crimean juniper tree height using nonlinear regression and artificial neural network models. Forest Ecology and Management, 306, 52-60.
41. Özçelik, R., Diamantopoulou, M., 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.
42. Parresol, B.R., 1992. Baldcypress height-diameter Equations and their prediction confidence intervals. Canadian Journal of Forest Ressearch, 22: 1429-1434.
43. Poudel, K.P., Cao, Q.V., 2013. Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. Forest Science, 59 (2): 243-252.
44. Seki, M., Sakıcı, O.E., 2022. Ecoregion-based height-diameter models for Cremian pine. Journal of Forest Research, 27: 36-44.
45. Soares, P., Tome, M., 2002. Height-diameter equation for first rotation eucalypt plantations in Portugal. Forest Ecology and Management, 166: 99-109.
46. Temesgen, H., Monleon, V., Hann, D., 2008. Analysis and comparison of nonlinear tree height prediction strategies for Douglas-fir forests. Canadian Journal of Forest Research, 38, 553-565.
47. Trincado, G., VanderSchaaf, C.L., Burkhart, H.E., 2007. Regional mixed-effects height–diameter models for loblolly pine (Pinus taeda L.) plantations. European Journal of Forest Research, 126: 253-262.
48. Wang, J., Jiang, L., Gaire, D., He, P., Yan, Y., Xin, S., 2022. Predicting and calibrating height to crown base: a case for Dahurian larch (Larix gmalinii Rupr.) in Northeastern China. Canadian Journal of Forest Research, e-First.
49. 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: 207–224.
50. Xie, L., Widagdo, F.R.A., Miao, Z., Dong, L., Li, F., 2022. Evaluation of the mixed-effects model and quantile regression approaches for predicting tree height in larch (Larix olgensis) plantations in northeastern China. Canadian Journal of Forest Research, 52(3): 309-319.
51. Yang, Y., Huang, S., Trincado, G., Meng, S.X., 2009. Nonlinear Mixed Effects Modelling of Variable Exponent Taper Equations for Lodgepole pine in Alberta, Canada. European Journal of Forest Research, 128: 415-429.
52. Yuancai, L., Parresol, B.R. 2001. Remarks on height-diameter modeling. Res. Note. SRS-10. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 6p.
53. 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: An International Journal of Forest Research, 89 (4): 434-445.
54. 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: 1507–1514.
55. Zhang, B., Sajjad, S., Chen, K., Zhou, L., Zhang, Y., Yong, K.K., Sun, Y., 2020. Predicting tree height‒diameter relationship from relative competition levels using quantile regression models for Chinese Fir (Cunninghamia lanceolata) in Fujian province, China. Forests, 11(2): 183.
56. Zhang, L., 1997. Cross-validation of non-linear growth functions for modeling tree height-diameter relationship. Annals of Botany, 79: 251-257.