Developing a 3D clumping index model to improve optical measurement accuracy of crop leaf area index

The clumping index reflects the state of leaf aggregation, which is an essential structural parameter for calculating the leaf area index (LAI). Most of the previous clumping index models are one-dimensional (1D) models, in which the input parameters are measured in a long truncated manner (i.e., one-dimensional measurement path, line data), so that is not practical in the measurement of a dense crop canopy with no branch height. To address this issue, it is necessary to develop an area-based clumping index model that is suitable for measuring the LAI of crops. Taking the digital cover photography of crops captured by digital cameras as a case study, we derived equations with the gap fraction to describe the gap distribution which indirectly reflected the anisotropy in the horizontal distribution of leaves. Using the gap fraction as a variable, we established a three-dimensional (3D) clumping index model. Validation on the proposed 3D model using computer simulations shows that the system deviation of the clumping index derived from the model is less than − 4.64%. In the validation using in-situ measurements, compared with the 1D clumping index model, the 3D clumping index model improved the prediction accuracy of LAI by 20.9%. This study demonstrated that the proposed 3D clumping index model successfully addresses the issue about underestimation of LAI by previous models, facilitates the optical measurement, and improves the calculation accuracy in the quadrat. This study provides theoretical assistance for the development of optical equipment in agriculture.