The use of numerical methods in the design of a formula that returns the surface of the leaves of Phragmites australis (Cav.) Trin. Ex Steud.

Abstract

Abstract The paper presents the results of calculations and a verification of numerical models developed for estimating the surface of leaves of the common reed (Phragmites australis (Cav.) Trin. Ex Steud.). The research sample consisted of 137 leaves collected from the rush zone of Lake Raduńskie Górne in 2018. The total area of leaves obtained for testing was 1932.3 cm2. To derive a formula that returns the surface of common reed foliage regression models were used – MLR (Multiple Linear Regression) and SLR (Stepwise Linear Regression). It has been shown that the measurement of basic leaf dimensions (i.e. length – L, mid-width – WM and maximum width – WX) makes it possible to define an empirical formula which, with an average accuracy of 99.9%, allows the real surface of leaves to be estimated. The modelling results were compared with formulas currently used in practice, and the measurement errors were determined using these formulas. It has been shown that the formulas used to date are subject to RMSE to the value of 1.19-2.52. The application of the developed formula (A = 0.4486 – 0.046 L + 7.9267 WM – 5.8121 WX + 0.5853 L • WX) will significantly reduce errors in leaf surface estimation (RMSE = 0.86) and thus the amount of reed transpiration and evapotranspiration, especially in the case of handling small samples (number of leaves and measurements).