Mathematical Modeling to Estimate the Leaf Area of Dalbergia frutescens from Linear Dimensions

Abstract

The objective of this work was to obtain mathematical equations and indicate the most appropriate estimation of the leaf area of Dalbergia frutescens, by a non-destructive method through the linear dimensions of the leaves. A total of 370 leaves of D. frutescens were collected, 270 of which were used to adjust the equations and 100 for validation. The length (L) along the main vein, the maximum width (W), the product of multiplying the length and width (LW), and the observed leaf area (OLA) was measured for all leaves. First degree, quadratic, and power linear equation models were fitted, where OLA was the dependent variable as a function of L, W and LW. From the 100 leaves destined for validation, and using the adjusted equations for each mathematical model, the estimated leaf area (ELA) was obtained. The means obtained from ELA and OLA were compared using Student's t test at 5% probability. The mean absolute error, the root mean square error, and the d Willmott index were also determined. The first-degree linear model represented  based on the product of multiplying the length by the width is the most suitable to determine the leaf area of D. frutescens with high precision.