Deriving leaf-scale chlorophyll index (CIleaf) from canopy reflectance by correcting for the canopy multiple scattering based on spectral invariant theory

Leaf chlorophyll content (LCC) is a crucial biochemical parameter for monitoring the plant's nutritional status and photosynthetic capacity. However, retrieving LCC from canopy reflectance is challenging due to the coupling influence of LCC and canopy structure, particularly leaf area index (LAI). The isolation of leaf-scale information from canopy signals is therefore essential to improve the LCC estimation. This study proposed an approach for deriving the leaf-scale chlorophyll index (CI_leaf) from the canopy bidirectional reflectance factor (BRF) based on the spectral invariant theory (p-theory). Six widely used canopy-scale chlorophyll indices (CI_canopy) were selected to derive the corresponding CI_leaf. The CI_leaf is expressed as the product of its original CI_canopy and a scale conversion factor (SCF) (CI_leaf = CI_canopy × SCF). The SCF is determined by two spectral invariants of p-theory (recollision probability p and directional area scattering factor DASF), as well as canopy BRFs at specific wavelengths, and it corrects for the contribution of canopy multiple scattering to CI_canopy. The analysis through radiative transfer model simulations showed that CI_leaf exhibited more unified relationships with LCC across LAI conditions than the original CI_canopy and substantially eliminated the influence of LAI on the CI-based model. Validation results demonstrated that CI_leaf improved the accuracy of LCC estimation compared to CI_canopy. The leaf-scale MERIS terrestrial chlorophyll index (MTCI_leaf) exhibited the most prominent improvements, reducing the root-mean-square error (RMSE) by 6.68 μg/cm² for ground spectra and 2.33–4.21 μg/cm² for Sentinel-2 images with multi-ecosystem datasets. Additionally, the influence of vegetation types on the CI-based model was mitigated by CI_leaf. MTCI_leaf reduced the RMSE values by 3.8 %–34.0 % for different plant functional types, giving more consistent accuracies across species than MTCI_canopy. Our results show that the proposed CI_leaf combines the robustness of the physically-based method with the simplicity of the CI-based method, thus providing a practical approach for large-scale high-resolution LCC mapping. Moreover, the method holds promise for designing leaf-scale vegetation indices sensitive to various leaf biochemical parameters beyond LCC, extending its utility to broader leaf-scale remote sensing retrieval (e.g., leaf carotenoid content and leaf dry mass).