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

Yıl 2017, Cilt: 18 Sayı: 2, 110 - 118, 28.07.2017

Ramazan Özçelik , Ahmet Sarıtaş Manuel Arias-rodil

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

Öz

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.           

Anahtar Kelimeler

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

Doğu ladini için gövde çapı modelinin karışık etkili yaklaşım ile geliştirilmesi

Öz

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.    

Anahtar Kelimeler

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

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