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

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

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