Developing Height-Diameter Models for Natural Scots Pine Stands in Sinop Region
Yıl 2025,
Cilt: 27 Sayı: 3, 421 - 432, 15.12.2025
Hasan Aksoy
,
Alkan Günlü
,
Ferhat Bolat
Öz
In this study, diameter (D)-height (H) models were developed for natural Scots pine (Pinus sylvestris L.) stands in Sinop region. In the model development phase, a total of 904 D and H data obtained from 184 sample plots were used. In addition, various stand variables were measured and calculated. Within the scope of the study, various model forms including only diameter variable and diameter and stand variables were considered. The success and prediction behavior of the developed models were evaluated through various error criteria, prediction-observation and prediction-error graphs. According to the findings, the model including only diameter variable explained a significant part of the variance in measured height values, but showed a problem of varying variance in errors (Model coefficient of determination=0.90). The generalized H-D models including diameter and various stand variables were found to have a better variance explanation value (Model coefficient of determination=0.94) and showed a constant variance in errors. As a result of statistical and graphical evaluations, it was concluded that generalized H-D models can be used with confidence in pure and natural Scots pine stands in Sinop region.
Kaynakça
-
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.
-
Aksoy, H., & Günlü, A. (2025). UAV and satellite-based prediction of aboveground biomass in scots pine stands: a comparative analysis of regression and neural network approaches. Earth Science Informatics, 18(1), 66. https://doi.org/10.1007/s12145-024-01657-0
-
Aksoy, H. (2024). Estimation stand volume, basal area and quadratic mean diameter using Landsat 8 OLI and Sentinel‐2 satellite image with different machine learning techniques. Transactions in GIS, 28(8), 2687-2704. https://doi.org/10.1111/tgis.13265
-
Aksoy, H. (2022). Sinop Orman Bölge Müdürlüğü saf sarıçam meşcerelerinde farklı uzaktan algılama verileri kullanılarak bazı meşcere parametrelerinin modellenmesi (Doctoral dissertation, Dokto-ra Tezi, Çankırı Karatekin Üniversitesi, Çankırı).
-
Archontoulis, S. V., & Miguez, F. E. (2015). Nonlinear regression models and applications in agricul-tural research. Agronomy Journal, 107, 786–798.
-
Atar, D., & Bolat, F. (2025). Height-Diameter allometry of Calabrian pine within Anamur, Southern Türkiye. Forest and Wood Science, 1, 1–9.
-
Bolat, F. (2023). Gompertz büyüme modelinden türetilen farklı model formlarının bazı eğrisellik ve yanlılık ölçütleri ile değerlendirilmesi. Presented at the IV. International Applied Statistics Cong-ress, Tokat Gaziosmanpasa University, Sarajevo / Bosnia and Herzegovina, pp. 407–411. https://doi.org/10.5281/zenodo.10835021
-
Bolat, F. (2024). Antalya-Yeşilvadi yöresinde yayılış yapan kızılçam meşcereleri için yeni bir ağaç hacim modelinin geliştirilmesi. Anatolian Journal of Forest Research, 10, 108–113. https://doi.org/10.53516/ajfr.1566540
-
Bolat, F., Ürker, O., & Günlü, A. (2022). Nonlinear height-diameter models for Hungarian oak (Quer-cus frainetto Ten.) in Dumanlı Forest Planning Unit, Çanakkale/Turkey. Austrian Journal of Fo-rest Science, 139, 199–220.
-
Bolat, F., Ercanlı, İ., & Günlü, A. (2023). Yield of forests in Ankara Regional Directory of Forestry in Turkey: comparison of regression and artificial neural network models based on statistical and biological behaviors. iForest - Biogeosciences and Forestry, 16, 30–37. https://doi.org/10.3832/ifor4116-015
-
Carus, S., & Akguş, Y. (2018). Tarsus yöresi fıstıkçamı (Pinus pinea L.) meşcereleri için çap-boy mo-dellerinin geliştirilmesi. Turkish Journal of Forestry, 19, 1–8.
-
Çatal, Y. (2012). Göller yöresinde Yalancı akasya, Anadolu karaçamı ve Toros sediri ağaç türleri için çap-boy modeli. Süleyman Demirel Üniversitesi Orman Fakültesi Dergisi, 13, 92–96.
-
Crecente-Campo, F., Tomé, M., Soares, P., & Diéguez-Aranda, U. (2010). A generalized nonlinear mixed-effects height–diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecology and Management, 259, 943–952. https://doi.org/10.1016/j.foreco.2009.11.036.
-
FAO. (2020). Global forest resources assessment 2020. Rome, Italy. https://doi.org/10.4060/ca9825en.
Fischer, C., & Schönfelder, E. (2017). A modified growth function with interpretable parameters app-lied to the age–height relationship of individual trees. Canadian Journal of Forest Research, 47, 166–173.
-
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 513–583.
-
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, 1297–1307.
-
Huang, S., S. J. Titus, Lakusta, T. W., & Held, R. J. (1994). Ecologically based individual tree height-diameter models for major Alberta tree species. Rep. No. 2, Alberta Environmental Protection, Land and Forest Service, Forest Management Division, Edmonton, AB, Canada. 27 p.
-
Huang, S., Price, D., & Titus, S. J. (2000). Development of ecoregion-based height–diameter models for white spruce in boreal forests. Forest ecology and management, 129(1-3), 125-141.
-
Lei, X., Peng, C., Wang, H., & Zhou, X. (2009). Individual height–diameter models for young black spruce (Picea mariana) and jack pine (Pinus banksiana) plantations in New Brunswick. Fo-restry Chronicle, 85, 43–56. https://doi.org/10.5558/tfc85043-1.
-
Mehtätalo, L., de-Miguel, S., & Gregoire, T. G. (2015). Modeling height-diameter curves for predic-tion. Canadian Journal of Forest Research, 45(7), 826-837.
-
McRoberts, R. E., & Westfall, J. A. (2014). Effects of uncertainty in model predictions of individual tree volume on large area volume estimates. Forest Science, 60, 34–42. https://doi.org/10.5849/forsci.12-141
-
Mirkovich J. L. (1958). Normale visinske krive za chrast kitnak I bukvu v NR Srbiji. Zagreb. Glasnik Sumarskog Fakulteta, 13, 43–56.
-
Nesha, M. K., Herold, M., De Sy, V., Duchelle, A. E., Martius, C., Branthomme, A., ... & Pekkarinen, A. (2021). An assessment of data sources, data quality and changes in national forest monitoring capacities in the Global Forest Resources Assessment 2005–2020. Environmental Research Let-ters, 16(5), 054029. https://doi.org/10.1088/1748-9326/abd81b.
-
OGM, (2022). Sinop Bölge Orman Müdürlüğü, Orman Planlama Birimleri, Orman Yönetim Planları. Türkiye Cumhuriyeti, Orman Genel Müdürlüğü, Orman İdaresi ve Planlama Dairesi, Ankara.
-
Özçelik, R., & Çapar, C. (2014). Antalya yöresi doğal kızılçam meşcereleri için genelleştirilmiş çap-boy modellerinin geliştirilmesi. Süleyman Demirel Üniversitesi Orman Fakültesi Dergisi, 15, 44–52.
-
Özçelik, R., Yavuz, H., Karatepe, Y., Gürlevik, N., & Kırış, R. (2014). Development of ecoregion-based height-diameter models for 3 economically important tree species of southern Turkey. Turkish Journal of Agriculture and Forestry, 38, 399–412.
-
R Core Team, 2022. R: A language and environment for statistical computing. R Foundation for Statis-tical Computing, Vienna, Austria. URL https://www.R-project.org/.
-
Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany, 10, 290–301. https://doi.org/10.1093/jxb/10.2.290
-
Sağlam, F., & Sakıcı, O. (2024). Ecoregional height–diameter models for Scots pine in Turkiye. Jour-nal of Forestry Research, 35, 103. https://doi.org/10.1007/s11676-024-01757-z
-
Sağlam, F., & Sakıcı, O. E. (2025). Height-diameter relationships for Pinus brutia Ten. in the Adana-Karaisali Region of Türkiye. Dendrobiology, 93, 121–131. https://doi.org/10.12657/denbio.093.009
-
Seki M., & Sakıcı, O.E. (2022). Ecoregion-based height-diameter models for Crimean pine. Journal of Forest Research, 27(1), 36-44, https://doi.org/10.1080/13416979.2021.1972511
-
Sharma, M., & Parton, J. (2007). Height–diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management, 249, 187–198. https://doi.org/10.1016/j.foreco.2007.05.006
-
Şahin, A. (2025). Nonlinear mixed-effect models for height-diameter relationships of Oriental beech trees in Artvin region, Eastern Black Sea Region of Türkiye. Scandinavian Journal of Forest Re-search, 1–12. https://doi.org/10.1080/02827581.2025.2533378
-
Şenyurt, M. (2011). Batı Karadeniz yöresi sarıçam meşcerelerinde artım ve büyüme. Doktora Tezi, İstanbul Üniversitesi Fen Bilimleri Enstitüsü, 215 s., İstanbul.
-
Tjørve, K. M. C., & Tjørve, E. (2017). The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family. Plos One, 12, e0178691. https://doi.org/10.1371/journal.pone.0178691
-
Vanclay JK (1994). Modelling forest growth and yield: applications to mixed tropical forests. CAB International, Wallingford, UK, pp. 329.
-
Zobel, J. M. (2024). Measurement error effects on estimates from linear and nonlinear regression who-le-stand yield models. Natural Resource Modeling, 37, e12384. https://doi.org/10.1111/nrm.12384
-
Yuancai, L., & Parresol, B. R. (2001). Remarks on Height-Diameter Modeling. Res. Note SE-10. As-heville, NC: U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Sta-tion. 8 p.
Sinop Yöresi Saf ve Doğal Sarıçam Meşcereleri için Çap-Boy Modellerinin Geliştirilmesi
Yıl 2025,
Cilt: 27 Sayı: 3, 421 - 432, 15.12.2025
Hasan Aksoy
,
Alkan Günlü
,
Ferhat Bolat
Öz
Bu çalışmada, Sinop yöresi doğal Sarıçam (Pinus sylvestris L.) meşcereleri için çap (D)-boy (H) modelleri geliştirilmiştir. Model geliştirme aşamasında, 184 örnek alandan elde edilen toplam 904 adet D ve H verisi kullanılmıştır. Bununla birlikte çeşitli meşcere değişkenleri de ölçülmüş ve hesaplanmıştır. Çalışma kapsamında sadece çap değişkeni ve çap ile birlikte meşcere değişkenlerini içeren çeşitli model formları dikkate alınmıştır. Geliştirilen modellerin başarısı ve tahmin davranışı çeşitli hata ölçütleri, tahmin-gözlem ve tahmin-hata grafikleri üzerinden değerlendirilmiştir. Elde edilen bulgulara göre, sadece çap değişkenini içeren model ölçülen boy değerlerindeki varyansın önemli bir kısmını açıklasa da hatalarda değişen varyans problemi göstermiştir (Model belirtme katsayısı=0.90). Çap ile birlikte çeşitli meşcere değişkenlerini içeren genelleştirilmiş H-D modelleri ise hem daha iyi bir varyans açıklama değerine sahip (Model belirtme katsayısı=0.94) hem de hatalarda sabit bir varyans göstermiştir. İstatistiksel ve grafiksel değerlendirmelerin sonucu olarak, genelleştirilmiş H-D modellerinin Sinop yöresinde yayılış yapan doğal Sarıçam meşcerelerinde güvenle kullanılabileceği söylenebilir.
Destekleyen Kurum
Bu çalışma Çankırı Karatekin Üniversitesi Bilimsel Araştırmalar Proje Birimi tarafından desteklenmiştir. Proje No: OF211221D08.
Teşekkür
Desteklerinden dolayı Çankırı Karatekin Üniversitesi Bilimsel Araştırmalar Proje Birimine teşekkür ederiz.
Kaynakça
-
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.
-
Aksoy, H., & Günlü, A. (2025). UAV and satellite-based prediction of aboveground biomass in scots pine stands: a comparative analysis of regression and neural network approaches. Earth Science Informatics, 18(1), 66. https://doi.org/10.1007/s12145-024-01657-0
-
Aksoy, H. (2024). Estimation stand volume, basal area and quadratic mean diameter using Landsat 8 OLI and Sentinel‐2 satellite image with different machine learning techniques. Transactions in GIS, 28(8), 2687-2704. https://doi.org/10.1111/tgis.13265
-
Aksoy, H. (2022). Sinop Orman Bölge Müdürlüğü saf sarıçam meşcerelerinde farklı uzaktan algılama verileri kullanılarak bazı meşcere parametrelerinin modellenmesi (Doctoral dissertation, Dokto-ra Tezi, Çankırı Karatekin Üniversitesi, Çankırı).
-
Archontoulis, S. V., & Miguez, F. E. (2015). Nonlinear regression models and applications in agricul-tural research. Agronomy Journal, 107, 786–798.
-
Atar, D., & Bolat, F. (2025). Height-Diameter allometry of Calabrian pine within Anamur, Southern Türkiye. Forest and Wood Science, 1, 1–9.
-
Bolat, F. (2023). Gompertz büyüme modelinden türetilen farklı model formlarının bazı eğrisellik ve yanlılık ölçütleri ile değerlendirilmesi. Presented at the IV. International Applied Statistics Cong-ress, Tokat Gaziosmanpasa University, Sarajevo / Bosnia and Herzegovina, pp. 407–411. https://doi.org/10.5281/zenodo.10835021
-
Bolat, F. (2024). Antalya-Yeşilvadi yöresinde yayılış yapan kızılçam meşcereleri için yeni bir ağaç hacim modelinin geliştirilmesi. Anatolian Journal of Forest Research, 10, 108–113. https://doi.org/10.53516/ajfr.1566540
-
Bolat, F., Ürker, O., & Günlü, A. (2022). Nonlinear height-diameter models for Hungarian oak (Quer-cus frainetto Ten.) in Dumanlı Forest Planning Unit, Çanakkale/Turkey. Austrian Journal of Fo-rest Science, 139, 199–220.
-
Bolat, F., Ercanlı, İ., & Günlü, A. (2023). Yield of forests in Ankara Regional Directory of Forestry in Turkey: comparison of regression and artificial neural network models based on statistical and biological behaviors. iForest - Biogeosciences and Forestry, 16, 30–37. https://doi.org/10.3832/ifor4116-015
-
Carus, S., & Akguş, Y. (2018). Tarsus yöresi fıstıkçamı (Pinus pinea L.) meşcereleri için çap-boy mo-dellerinin geliştirilmesi. Turkish Journal of Forestry, 19, 1–8.
-
Çatal, Y. (2012). Göller yöresinde Yalancı akasya, Anadolu karaçamı ve Toros sediri ağaç türleri için çap-boy modeli. Süleyman Demirel Üniversitesi Orman Fakültesi Dergisi, 13, 92–96.
-
Crecente-Campo, F., Tomé, M., Soares, P., & Diéguez-Aranda, U. (2010). A generalized nonlinear mixed-effects height–diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecology and Management, 259, 943–952. https://doi.org/10.1016/j.foreco.2009.11.036.
-
FAO. (2020). Global forest resources assessment 2020. Rome, Italy. https://doi.org/10.4060/ca9825en.
Fischer, C., & Schönfelder, E. (2017). A modified growth function with interpretable parameters app-lied to the age–height relationship of individual trees. Canadian Journal of Forest Research, 47, 166–173.
-
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 513–583.
-
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, 1297–1307.
-
Huang, S., S. J. Titus, Lakusta, T. W., & Held, R. J. (1994). Ecologically based individual tree height-diameter models for major Alberta tree species. Rep. No. 2, Alberta Environmental Protection, Land and Forest Service, Forest Management Division, Edmonton, AB, Canada. 27 p.
-
Huang, S., Price, D., & Titus, S. J. (2000). Development of ecoregion-based height–diameter models for white spruce in boreal forests. Forest ecology and management, 129(1-3), 125-141.
-
Lei, X., Peng, C., Wang, H., & Zhou, X. (2009). Individual height–diameter models for young black spruce (Picea mariana) and jack pine (Pinus banksiana) plantations in New Brunswick. Fo-restry Chronicle, 85, 43–56. https://doi.org/10.5558/tfc85043-1.
-
Mehtätalo, L., de-Miguel, S., & Gregoire, T. G. (2015). Modeling height-diameter curves for predic-tion. Canadian Journal of Forest Research, 45(7), 826-837.
-
McRoberts, R. E., & Westfall, J. A. (2014). Effects of uncertainty in model predictions of individual tree volume on large area volume estimates. Forest Science, 60, 34–42. https://doi.org/10.5849/forsci.12-141
-
Mirkovich J. L. (1958). Normale visinske krive za chrast kitnak I bukvu v NR Srbiji. Zagreb. Glasnik Sumarskog Fakulteta, 13, 43–56.
-
Nesha, M. K., Herold, M., De Sy, V., Duchelle, A. E., Martius, C., Branthomme, A., ... & Pekkarinen, A. (2021). An assessment of data sources, data quality and changes in national forest monitoring capacities in the Global Forest Resources Assessment 2005–2020. Environmental Research Let-ters, 16(5), 054029. https://doi.org/10.1088/1748-9326/abd81b.
-
OGM, (2022). Sinop Bölge Orman Müdürlüğü, Orman Planlama Birimleri, Orman Yönetim Planları. Türkiye Cumhuriyeti, Orman Genel Müdürlüğü, Orman İdaresi ve Planlama Dairesi, Ankara.
-
Özçelik, R., & Çapar, C. (2014). Antalya yöresi doğal kızılçam meşcereleri için genelleştirilmiş çap-boy modellerinin geliştirilmesi. Süleyman Demirel Üniversitesi Orman Fakültesi Dergisi, 15, 44–52.
-
Özçelik, R., Yavuz, H., Karatepe, Y., Gürlevik, N., & Kırış, R. (2014). Development of ecoregion-based height-diameter models for 3 economically important tree species of southern Turkey. Turkish Journal of Agriculture and Forestry, 38, 399–412.
-
R Core Team, 2022. R: A language and environment for statistical computing. R Foundation for Statis-tical Computing, Vienna, Austria. URL https://www.R-project.org/.
-
Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany, 10, 290–301. https://doi.org/10.1093/jxb/10.2.290
-
Sağlam, F., & Sakıcı, O. (2024). Ecoregional height–diameter models for Scots pine in Turkiye. Jour-nal of Forestry Research, 35, 103. https://doi.org/10.1007/s11676-024-01757-z
-
Sağlam, F., & Sakıcı, O. E. (2025). Height-diameter relationships for Pinus brutia Ten. in the Adana-Karaisali Region of Türkiye. Dendrobiology, 93, 121–131. https://doi.org/10.12657/denbio.093.009
-
Seki M., & Sakıcı, O.E. (2022). Ecoregion-based height-diameter models for Crimean pine. Journal of Forest Research, 27(1), 36-44, https://doi.org/10.1080/13416979.2021.1972511
-
Sharma, M., & Parton, J. (2007). Height–diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management, 249, 187–198. https://doi.org/10.1016/j.foreco.2007.05.006
-
Şahin, A. (2025). Nonlinear mixed-effect models for height-diameter relationships of Oriental beech trees in Artvin region, Eastern Black Sea Region of Türkiye. Scandinavian Journal of Forest Re-search, 1–12. https://doi.org/10.1080/02827581.2025.2533378
-
Şenyurt, M. (2011). Batı Karadeniz yöresi sarıçam meşcerelerinde artım ve büyüme. Doktora Tezi, İstanbul Üniversitesi Fen Bilimleri Enstitüsü, 215 s., İstanbul.
-
Tjørve, K. M. C., & Tjørve, E. (2017). The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family. Plos One, 12, e0178691. https://doi.org/10.1371/journal.pone.0178691
-
Vanclay JK (1994). Modelling forest growth and yield: applications to mixed tropical forests. CAB International, Wallingford, UK, pp. 329.
-
Zobel, J. M. (2024). Measurement error effects on estimates from linear and nonlinear regression who-le-stand yield models. Natural Resource Modeling, 37, e12384. https://doi.org/10.1111/nrm.12384
-
Yuancai, L., & Parresol, B. R. (2001). Remarks on Height-Diameter Modeling. Res. Note SE-10. As-heville, NC: U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Sta-tion. 8 p.