Toros göknarında gövde çapı modelinin doğrusal olmayan karışık etkili modelleme yaklaşımı ile geliştirilmesi

Abstract

Bu çalışmada, doğal Toros göknarı (Abies cilicica Carr.) meşcereleri için karışık etkili modelleme tekniği ile Max ve Burkhart parçalı gövde çapı modeli kullanılarak gövde formundaki birey içi ve bireyler arası değişkenlikler ortaya konmuştur. Bu amaçla 327 örnek ağaç ölçülerek, rasgele yöntemle iki gruba ayrılmış ve 203 adet örnek ağaç (%60) model geliştirmek için, geri kalan 124 adet (%40) ağaç ise geliştirilen modelin test edilmesi amacıyla kullanılmıştır. Model ölçüt değerlerine göre, en başarılı tesadüfi etkili parametre kombinasyonu olarak β1, β3, β4 bulunmuştur. Modele tesadüfi etkilerin eklenmesi, hata korelasyonunu tamamen ortadan kaldırmamıştır. Hatalar arasındaki ağaç içi ve ağaçlar arası varyans ve otokorelasyon için modele sırasıyla bir hata varyans fonksiyonu ve otoregresif hata yapısı eklenmiştir. Bu işlem sonucunda, hata korelasyonu hemen hemen ortadan kalkmıştır. Diğer yandan, yeni bir ağaç için modelin kalibrasyonu amacıyla uygun bir Bayesian tahmincisi yardımı ile tesadüfi etkileri tahmin etmek amacıyla ekstra çap ölçümleri kullanılmıştır. Elde edilen sonuçlar test verileri ile denetlenmiştir. Ölçüt değerleri (ortalama hata, tutarlılık ve RMSE), ekstra çap ölçümleri ile tesadüfi etkilerin tahmini sonucunda, özelikle gövdenin ilk yarısındaki çap tahminlerinin oldukça başarılı olduğunu göstermiştir. Çalışmanın sonuçları, kalibrasyon için tek ve iki çap ölçümü arasında önemli farklılıkların olmadığını da ortaya koymuştur. Bu çalışmada kullanılan yöntem, doğal Toros göknarı meşcerelerinde uygulanacak farklı yönetim stratejileri ve farklı yetişme ortamlarındaki ağaçlar için gövde formundaki değişimin ortaya konması amacıyla kullanılabilir. Diğer yandan, bu çalışmanın sonuçları, karışık etkili modelleme tekniğinin, çap tahminleri için gövde çapı modellerinin etkinliğini ve esnekliğini arttırdığı yönündeki bulguları destekler niteliktedir.

Keywords

• Gövde çapı modeli,Tesadüfi parametre,Hata varyansı,Kalibrasyon

Developent of stem taper equation using nonlinear mixed-effects modeling approach for Taurus fir

Abstract

The Max and Burkhart segmented taper equation was fitted using nonlinear mixed-effects modeling techniques to account for within- and between-individual variation in Taurus fir (Abies cilicica Carr.) stem profiles. Totally 327 sample trees measured and about 60% (203 trees) of the trees were randomly selected for model development and the reminder 40% (124 trees) of the trees used for model validation. Based on goodness-of-fit criteria, the model including three random-effects parameters β1, β3, and β4 was the best. An error variance function and a continuous auto correlation structure incorporated in model to within and between-tree residual variances and spatial autocorrelation between residuals. However, most of the residual autocorrelation was accounted for by including random effects. Upper stem diameter measurements were used to estimate random effects parameters using an approximate Bayesian estimator, which localized stem profile curves for individual trees. The procedure was tested with a validation data set. The goodness-of-fit statistics (Bias, precision, and RMSE) showed that upper stem diameter measurements and subsequent estimates of random effects improved the predictive capability of the taper equation mainly in the lower portion of the bole. Accordingly results of this research, there is no big differences between one and two additional upper stem diameter measurements for predictive capability of model. The method can localize stem curves for trees growing under different site and management conditions in natural Taurus fir stands. The results of this study support previous findings that mixed-effect modeling approach increases flexibility and efficiency of taper equations for upper stem diameter prediction.

Keywords

• Stem diameter model,Random parameter,Residual variance,Calibration

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