Estimating structural parameters of agricultural crops from ground-based multi-angular digital images with a fractional model of sun and shade components

Accurate and efficient in situ measurement methods of leaf area index (LAI) and leaf angle distribution (LAD) are needed to estimate the fluxes of water and energy in agricultural settings. However, available methods: to estimate these two parameters, especially LAD, are limited. In this study, we propose a field measurement method using multi-angular digital images to estimate LAI and LAD simultaneously from the area proportions of: (i) sunlit soil; (ii) sunlit leaves; (iii) shaded soil; and (iv) shaded leaves. A new expression of the fraction of sunlit leaves is developed based on the radiative transfer theory. Coupling the measured and modeled fractions with an optimization scheme, LAI and the LAD parameters are derived from inverting a fractional model of sunlit and shaded leaves and soil. Through four tests using simulated scenes and in situ measurements for row crops, it is determined that our method performs well. The absolute error of LAI estimation is less than 0.1 when LAI is low (i.e., < 1.2), and the absolute deviations of LAI estimates are approximately 0.5 when the reference LAI is 3.5. The estimation errors of LAI and the G function (a representative of LAD which quantifies the projection of unit foliage area) for in situ measurements are respectively less than 0.2 and 0.06 in general. In addition, the accuracy of estimation is even higher when leaves are simulated as randomly distributed disks or observations from multiple azimuth planes are used. One of the most interesting features of this method is its ability to estimate reasonable LAD directly from the fractions of sunlit and shaded leaves, even when LAI is high (i.e., > 3), so little background soil is seen. The sensitivity and uncertainty analysis is consistent with the estimation errors. Theoretically, the application of this method is not limited to row crops or to field measurement, as the derived formulae of sunlit and shaded components can be used for other types of vegetation by introducing the clumping index and can be used in the modeling of canopy vegetation parameters (e.g., canopy reflectance).