Needle-Like Leaf Organs of Conifers. Part II. Modeling the Needle Surface Area

In ecological and physiological studies of plant cover, the predominant participation of leaves in the processes of photosynthesis, transpiration and respiration determines the key role of such a morphometric parameter as leaf surface area. The estimation of the area of needle-like leaf organs of conifers often requires an individual approach. The diversity of needle shapes is determined by species affiliation, morphological structure, ecological conditions and age, and, in turn, determines the diversity of methods for estimating the needle surface area. Therefore, the search for simple standard methods for determining the surface area of leaf organs of conifers is an urgent task for plant physiologists. The aim of this work has been to create a universal model for estimating the needle surface area, independent of species. To achieve it, the needle cross-section model proposed by the authors has been used, based on the transformation of the perimeter of the cross-section into an equivalent circle, the perimeter of which is associated with the parameters of the needle cross-section before the transformation. To estimate the surface area of the needle, it is possible to approximate the needle with a geometric body, which is a combination of an ellipsoid of revolution, a cone and a cylinder, with the radius of the cylinder being estimated using the needle cross-section model. The model allows to estimate the surface area of the needle by its 4 morphometric parameters: thickness, width, length of the middle part and total length. Full verification of the model proposed in the article has turned out to be impossible due to the lack of methods for accurate estimation of the needle surface area. The developed method has been compared to other methods for estimating the surface area of needle-like samples by the examples of the needles of Siberian fir (Abies sibirica L.) and common juniper (Juniperus communis L.), as well as banana fruits (Musa paradisiaca L.), and the good predictive ability of the model has been demonstrated. It can be characterized as universal with a theoretical relative error of no more than 5 %.