The relationship between the ratio of far-red to red leaf SIF and leaf chlorophyll content: Theoretical derivation and experimental validation

Abstract

Leaf chlorophyll content (LCC) is an important indicator of photosynthetic capacity. Sun-induced chlorophyll fluorescence (SIF) is an optical signal emitted from the leaf interior, providing a unique technique for accurately estimating LCC. The far-red to red ratio of chlorophyll fluorescence (F_ratio) has been used to empirically estimate LCC in some previous studies. While these studies support the use of the F_ratio for LCC estimation, its theoretical underpinning remains less well-defined and its effectiveness across a wider range of scenarios remains unclear. In this study, we established the relationship between the F_ratio and LCC using the light use efficiency (LUE)-based SIF model and spectral invariant radiative transfer theory. Firstly, the LUE-based SIF model demonstrates that the change in the leaf F_ratio is controlled by the ratio of the fluorescence escape fraction (i.e., f_esc from the photosystem to the leaf surface) at the corresponding bands. Secondly, a f_esc modeling approach is presented using the spectral invariant theory and thus the f_esc ratio is linked to LCC. Theoretical analysis shows that the F_ratio has a strong correlation with LCC, which explains over 90 % of the variation in F_ratio. Both experimental measurements and model simulations from a radiative transfer model Fluspect were used to validate the relationship between LCC and three F_ratio (i.e., $F_{\text{ratio}}^{\uparrow }$, $F_{\text{ratio}}^{\downarrow }$ and $F_{\text{ratio}}^{\mathrm{tot}}$), which were derived from the upward and downward SIF of leaves, as well as the total SIF observed from both sides. The Fluspect simulations were used to assess the sensitivity of the F_ratio-LCC relationship to the leaf structure. Two types of experimental measurements, including the field measurements of three crops and the laboratory measurements of 20 tundra plants, were employed to examine the species dependence of the F_ratio-LCC relationship. The performance of F_ratio for LCC estimation was evaluated and compared with spectral indices and the PROSPECT model using the experimental measurements and leave-one-out cross-validation (LOOCV) approach. Both the Fluspect simulations and the experimental measurements indicate that the F_ratio is strongly correlated with LCC for a wide range of leaf scenarios. The F_ratio-LCC relationship remains relatively stable across different leaf structures and plant species, since the relationship is almost consistent. The LOOCV of experimental measurements shows that the F_ratio provides promising and robust LCC estimates, with the $F_{\text{ratio}}^{\mathrm{tot}}$ performing the best. The $F_{\text{ratio}}^{\mathrm{tot}}$ outperforms spectral indices, reducing the RMSE for LCC estimation by 19.5 %–93.9 %. Furthermore, compared to the PROSPECT model, the F_ratio achieves a reduction in RMSE by 30.4 %–77.8 %. These results demonstrate that the F_ratio is effective for estimating LCC of diverse plant species. This study advances our understanding of the relationship between the F_ratio and LCC, supporting the use of SIF signals for remote sensing of LCC.