Modeling of stem taper model with mixed effects approach for oriental spruce

Year 2017, Volume: 18 Issue: 2, 110 - 118, 28.07.2017

Ramazan Özçelik , Ahmet Sarıtaş Manuel Arias-rodil

https://doi.org/10.18182/tjf.302073

Abstract

Oriental spruce (Picea orientalis
L.) is one of the most important tree species in Turkey. Therefore, the
information is necessary about growth and yield of the species for developing
future management and planning strategies. The one of the essential building
blocks in forest growth and yield prediction models is the equations for
estimating individual tree volume. One of the most accurate and reliable
approaches for estimating stem total volume and merchantable volume is the use
of taper models. In this study, a taper model was developed by using nonlinear
mixed effects modeling approach (NLME) using data from 170 trees felled in
oriental spruce stands from Ardahan-Posof Region. An NLME approach accounted
for within-and between tree variations in stem form. In the first stage, all
possible combinations of expansion with random effects in one and two model
parameters were tested, selecting then the best one. The inclusion of random
effects was not enough to account for the existing autocorrelation between the
residuals and then the variance-covariance matrix of the error term was
modelled through a first order autocorrelation structure AR (1). In a second
step, we evaluated the response obtained by calibration (which implies
estimation of random effects for a new tree) based on upper-stem diameter
measurements at different points. The selected mixed-effects model produced the
best results both in fitting and calibration process. It was found that an
upper-stem diameter measurement at 40-80% of total height was best suited for
calibrating tree-specific predictions. As a result, model calibration should be
considered an essential criterion in mixed model selection.           

Keywords

Picea orientalis, Taper model, Autocorrelation, Calibration, Ardahan-Posof

Doğu ladini için gövde çapı modelinin karışık etkili yaklaşım ile geliştirilmesi

Abstract

Doğu ladini (Picea orientalis L.)
ülkemizin önemli ağaç türlerinden birisidir. Bu nedenle, ladin ormanlarının
bugün ve geleceğe dönük yönetim ve planlama stratejilerinin geliştirilmesinde,
türün büyüme ve hasılatına ilişkin bilgilere ihtiyaç duyulmaktadır. Ormanların
büyüme ve hasılatına ilişkin tahminlerde kullanılan en önemli yapı taşlarından
birisi, ağaç hacim tahminleridir. Gövde çapı denklemleri, bir ağaca ilişkin
toplam ve ticari hacim tahminlerinde en güvenilir ve doğru yaklaşımlardan biri
olarak kabul edilmektedir. Bu çalışmada, Ardahan-Posof Yöresi doğu ladini
meşcerelerinden elde edilen 170 ağaç kullanılarak doğrusal olmayan karışık
etkili modelleme (NLME) yaklaşımı ile gövde çapı modeli geliştirilmiştir.
Karışık etkili modelleme, bir ağacın kendi içinde ve ağaçlar arasında gövde
formu açısından değişimin hesaplanmasına imkân sağlamaktadır. Çalışmanın
birinci aşamasında, öncelikle hangi parametrelerin tesadüfi etkili
parametrelerle genişletilmesi gerektiğinin ortaya konması için modelin bir ve
iki parametresine tesadüfi parametreler eklenerek olası tüm kombinasyonlar test
edilmiştir. Modele tesadüfi etkili parametrelerin eklenmesi aynı ağaç için elde
edilen hatalar arasında var olan korelasyonun hesaplanması için yeterli
olmamış, hata terimine ilişkin varyans-kovaryans matrisi birinci derece
otoregresif hata yapısı AR(1) ile modellenmiştir. Karışık etkili modele
AR(1)’in eklenmesi ile hatalar arasındaki otokorelasyonun tamamının
uzaklaştırılması mümkün olmuştur. İkinci aşamada, gövde üzerinde farklı noktalarda
ölçülen çap değerleri kullanılarak kalibrasyon sonuçları değerlendirilmiştir.
Seçilen karışık etkili model, hem model geliştirme hem de kalibrasyon için en
iyi sonuçları üretmiştir. Genel olarak, kalibrasyon için toplam boyun %40-80
arasında ölçülen ekstra çapların gövde çapı modelinin tahmin performansını
arttırdığı gözlenmiştir. Sonuç olarak model kalibrasyonu, karışık etkili model
seçiminde önemli bir kriter olarak göz önünde bulundurulmalıdır.    

Keywords

Picea orientalis, Gövde çapı modeli, Otokorelasyon, Kalibrasyon, Ardahan-Posof

References

• Akaike, H., 1974. A new look at the statistical model identification. IEEE transactions on automatic control, 19(6): 716-723.
• Arias-Rodil, M., Diéguez-Aranda, U., Rodríguez Puerta, F., López-Sánchez, C.A., Canga Líbano, E., Cámara Obregón, A., Castedo-Dorado, F., 2015a. Modelling and localizing a stem taper function for Pinus radiata in Spain. Canadian Journal of Forest Research, 45(6): 647-658.
• Arias-Rodil, M., Castedo-Dorado, F., Cámara-Obregon, A., Diéguez-Aranda,U., 2015b. Fitting and Calibrating a Multilevel Mixed-Effects Stem Taper Model for Maritime Pine in NW Spain. PLoS One, 10(12): e0143521.
• Bueno-López, S.W., Bevilacqua, E., 2012. Nonlinear mixed model approaches to estimating merchantable bole volume for Pinus occidentalis. Biogeosciences and Forestry, 5: 247-254.
• Calama, R., Montero, G., 2004. Multilevel linear mixed model for tree diameter increment in Stone Pine (Pinus pinea): A calibrating approach. Silva Fennica, 39(1): 37-54.
• Cao, Q.V., 2009. Calibrating a segmented taper equation with two diameter measurements. Southern Journal of Applied Forestry, 33(2): 58–61.
• Cao, Q.V., Wang, J., 2011. Calibrating fixed- and mixed-effects taper equations. Forest Ecology and Management, 262: 671-673.
• 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: 735-746.
• Clark, III A., Souter, R.A., Schlaegel, B.E., 1991. Stem profile equations for southern tree species. United States Department of Agriculture Forest Service Research Paper, SE-282.
• Cochran, W.G., 2007. Sampling Techniques. John Wiley & Sons.
• Corral-Rivas, J.J., Barrio-Anta, M., Aguirre-Calderón, O.A., Diéguez-Aranda, U., 2007. Use of stump diameter to estimate diameter at breast height and tree volume for major pine species in El Salto Durango (Mexico). Forestry, 80: 29-40.
• Crecente-Campo, F., Rojo Alboreca, A., Diéguez-Aranda, U., 2009. A Merchantable volume system for Pinus sylvestris L. in the major mountain ranges of Spain. Annals of Forest Science, 66-808.
• 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: 1383-1394.
• Diéguez-Aranda, U., Castedo-Dorado, F., Álvarez-González, J.G., Rojo, A., 2006. Compatible taper function for Scots Pine plantations in Nortwestern Spain. Canadian Journal of Forest, 36(5): 1190-1205.
• Ercanlı, İ., Kurt, A.K., Bolat, F., 2014. Adana-Feke kızılçam (Pinus brutia Ten.) meşcereleri için gövde çapı ve gövde hacim denklemlerinin karışık etkili modelleme ile geliştirilmesinde bazı varyans yapılarının karşılaştırılması. II. Ulusal Akdeniz Orman ve Çevre Sempozyumu, Bildiriler Kitabı, Isparta, 585-591.
• 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.
• Fang, Z., Bailey, R.L., 2001. Nonlinear mixed effects modeling for Slash Pine dominant height growth following intensive silvicultural treatments. Forest Science, 47: 287-300.
• Garber, S.M., Maguire, D.A., 2003. Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures. Forest Ecology and Management, 179: 507-507.
• Gómez-García, E., Crecente-Campo, F., Diéguez-Aranda, U., 2013. Selection of mixed effects parameters in a variable exponent taper equation for birch trees in northwestern Spain. Annals of Forest Science, 70(7): 707-715.
• Gómez-García, E., Crecente-Campo, F., Barrio-Anta, M., Diéguez-Aranda, U., 2015. A disaggregated dynamic model for predicting volume, biomass and carbon stocks in even-aged pedunculate oak stands in Galicia (NW Spain). European Journal of Forest research, 134: 569-583.
• Gómez-García, E., Diéguez-Aranda, U., Özcelik, R., Sal-Cando, M., Castedo-Dorado, F., Crecente-Campo, F., Corral-Rivas, J.J., Arias-Rodil, M., 2016. Desarrollo de una función de perfil mediante modelos mixtos para Pinus sylvestris en Turquía: selección de parámetros fijos a expandir. Bosque, 37(1): 159-167.
• Gregoire, T.G., Schabenberger, O., 1996. A non-linear mixed-effects model to predict cumulative bole volume of standing trees. Journal of Applied Statistics, 23: 257-271.
• Jiang, L., Brooks, J.R., Wang, J., 2005. Compatible taper and volume equations for yellow-poplar in West Virginia. Forest Ecology and Management, 213: 399-409.
• Klos, R.J., Wang, G.G., Dang, Q.L., East, E.W., 2007. Taper equations for five majör commercial tree species in Manitoba, Canada. Western Journal of Applied Research, 22: 163-170.
• Kozak, A. 1988. A variable exponent taper equation. Canadian Journal of Forest Research, 18: 1363-1368.
• Kozak, A., 2004. My last words on taper equations. Forestry Chronicle, 80: 507–515.
• Leites, L., Robinson, A., 2004. Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework. Forest Science, 50(2): 204-212.
• Lejeune, G., Ung, C.H., Fortin, M., Guo, X.J., Lambert, M.C., Ruel, J.C. 2009. A simple stem taper model with mixed effects for boreal black spruce. European Journal of Forest Research, 128: 505-513.
• Li, R., Weiskittel, A.R., 2010. Estimating and predicting bark thickness for seven conifer species in the Acadian Region of North America using a mixed-effects modeling approach: comparison of model forms and subsampling strategies. European Journal of Forest Research, 130: 219-233.
• Lindstrom, M.J., Bates, D.M., 1990. Nonlinear mixed effects models for repeated measures data. Biometrics, 46: 673-687.
• Max, T.A., Burkhart, H.E., 1976. Segmented polynomial regression applied to taper equations. Forest Science, 22: 283-289.
• Meng, S.X., Huang, S., Vanderschaaf, C.L., Yang, Y. Trincado, G,. 2011. Accounting for serial correlation and its impact on forecasting ability of a fixed and mixed-effects basal area model: a case study. European Journal of Forest Research, 131(3): 541-552.
• Newnham, R.M., 1988. A Variable form Taper Function. Information Report PI-X-83. Forestry, 33p. Canada.
• Newnham, R.M., 1992. A variable-form taper function four Alberta tree species. Canadian Journal of Forest Research, 22: 210-223.
• Özcelik, R., Brooks, J.R., Jiang, L., 2011. Modeling stem profile of Lebanon cedar, Brutian pine,and Cilicica fir in Southern Turkey using nonlinear mixed-effects models. European Journal of Forest Research, 130: 613-621.
• Özçelik, R., Karatepe, Y., Gürlevik, N., Canellas, I., Crecente-Campo, F. 2016. Development of ecoregion-based merchantable volume systems for Pinus brutia Ten. and Pinus nigra Arnold. in Southern Turkey. J For Res. 27: 101-117.
• 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: 78-91.
• Özçelik, R., Yaşar, Ü., 2015. Sinop Yöresi Uludağ Göknarı (Abies nordmanniana (Stev.) subsp. bornmülleriana (Mattf.)) meşcereleri için gövde çapı modelinin karışık etkili modelleme tekniği ile geliştirilmesi.Turkish Journal of Forestry | Türkiye Ormancılık Dergisi, 16: 86-95. Pinheiro, J.C., Bates, D.M., 2000. Mixed Effects Models in S and S-plus. Springer, Heidelberg, 528p. R Core Team, 2013. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available from http://www.r-project.org/ (28 Mart 2017).
• Rojo, A., Perales, X., Sánchez-Rodríguez, F., Álvarez-González, J.G., Gadow, K., 2005. Stem taper functions for maritime pine (Pinus pinaster Ait.) in Galicia (Northwestern Spain). European Journal of Forest Research, 124: 177–186.
• Sabatia, C.O., Burkhart, H.E., 2015. On the use of upper stem diameters to localize a segmented taper equation to new trees. Forest Science, 61(3): 411-423.
• Schröder, T.A., Healey, S.P., Moisen, G.G., Frescino, T.S., Cohen, W.B., Huang, C., Kennedy, R.E., Yang, Z., 2014. Improving estimates of forest disturbance by combining observations from landsat time series with U.S. Forest Service Forest Inventory and Analysis data. Remote Sensing of Environment, 154(1): 61-73.
• Schwarz, G.E., 1978. Estimating the dimension of a model. Ann. Stat., 6(2): 461–46., doi:10.1214/aos/1176344136.
• Şenyurt, M., Ercanlı, İ., Saraçoğlu, Ö., 2014. Batı Karadeniz yöresi sarıçam meşcereleri için uyumlu gövde çapı ve gövde hacim denklemlerinin karışık etkili modelleme ile geliştirilmesi. II. Ulusal Akdeniz Orman ve Çevre Sempozyumu, Antalya, Bildiriler Kitabı, s.601-607.
• Sharma, M., Parton, J., 2009. Modeling stand density effects on taper for jack pine black spruce plantations using dimensional analysis. Forest Science, 55(3): 268-282.
• Trincado, G,. Burkhart, H.E., 2006. A generalized approach for modeling and localizing stem profile curve. Forest Science, 52: 670-682.
• Valentine, H.T., Gregorie, T.G., 2001. A switching model of bole taper. Canadian Journal of Forest Research, 31(8):1400-1409.
• Vonesh, E.F., Chinchilli, V.M., 1997. Linear and Nonlinear Models for the Analysis of Repeated Measurements, Marcel Dekker, New York.
• Yang, Y., Huang, S., Trincado, G., Meng, S.X., 2009a. Nonlinear mixed effects modelling of variable exponent taper equations for Lodgepole pine in Alberta, Canada, European Journal of Forest Research, 128: 415-429.
• Yang, Y., Huang, S., Meng, S.X., 2009b. Development of a Tree-Specific Stem Profile Model for White spruce: A Nonlinear Mixed Model Approach with a Generalized Covariance Structure. Forestry, 82(5): 541-555.
• Yang, Y., Huang, S., 2013. On the statistical and biological behaviors of nonlinear mixed forest models. European Journal of Forest Research, 132(5–6): 727–736. doi:10.1007/s10342-013-0705-2.