Comparison between artificial neural networks and some mathematical models in leaf area estimation of Red Chief apple variety

Abstract

Leaf area index is an important variable in ecological and physiological studies. This study was aimed to determine the most suitable model explaining the leaf area estimation and weekly growth of leaf parameters in Red Chief apple variety. In the first part of the study, the leaf area was modeled through two different models (Model-1 and Model-2) developed based on ANN and power function (LA= AxB). In the second part, the weekly growth of each of the leaf width, length and area parameters were analyzed according to the Gompertz and Logistics function. The results of analysis revealed that leaf area estimations performed by ANN (Training: R2= 0.98, RMSE= 0.922, MAD= 0.614, MAPE= 4.22; Testing: R2= 0.94, RMSE= 3.346 MAD= 1.889 MAPE= 4.88) were more successful than Model-1 and Model-2. In addition, Gompertz has come to the fore as the model that best describes the weekly growth in all leaf parameters (Width: R2= 0.98, RMSE= 0.154, MAD= 0.134, MAPE= 3.65, Length: R2= 0.98, RMSE= 0.180, MAD= 0.145, MAPE= 2.26 and Leaf area: R2= 0.99, RMSE= 0.73, MAD= 0.654, MAPE= 4.60).

Keywords

• ANN,Leaf area index,Growth,Apple,Mathematical model

Red Chief elma çeşidinde yapay sinir ağları ve bazı matematiksel modeller kullanılarak yaprak alan tahminlerinin karşılaştırılması

Abstract

Yaprak alan indeksi ekolojik ve fizyolojik çalışmalarda önemli bir değişkendir. Çalışmada, Red Chief elma çeşidinde yaprak alan tahmini ve yaprak parametrelerinin haftalık büyümesini açıklayan en uygun modelin belirlenmesi amaçlanmıştır. Bu amaçla çalışmanın ilk kısmında ANN ve power fonksiyonuna (LA= AxB) dayalı geliştirilen iki farklı model (Model-1 ve Model-2) aracılığıyla yaprak alanı modellenmekte, ikinci kısmında yaprak en, boy ve alan parametrelerinin her birinin haftalık büyümeleri Gompertz ve Lojistik fonksiyona göre analiz edilmektedir. Analiz sonuçlarına göre yaprak alan tahmininde ANN’nin (Eğitim: R2= 0.98, RMSE= 0.922, MAD= 0.614, MAPE= 4.22; Test: R2= 0.94, RMSE= 3.346, MAD= 1.889, MAPE= 4.88) Model-1 ve Model-2’den daha başarılı tahminlerde bulunduğu gözlemlenmiştir. Bunun yanında yaprak parametrelerinin tamamında haftalık büyümeyi en iyi açıklayan modelin Gompertz olduğu (En: R2= 0.98, RMSE= 0.154, MAD= 0.134, MAPE= 3.65, Boy: R2= 0.98, RMSE= 0.180, MAD= 0.145, MAPE= 2.26 ve Yaprak alanı: R2= 0.99, RMSE= 0.73, MAD= 0.654, MAPE= 4.60) görülmüştür.

Keywords

• ANN,Yaprak alan indeksi,Büyüme,Elma,Matematiksel model

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