Mitigating the black-soil problem in the reflectance-to-fluorescence (R2F) relationship: A soil-adjusted reflectance-based approach for downscaling SIF

Solar-induced chlorophyll fluorescence (SIF) is an effective probe for photosynthesis, but this remote sensing signal is affected by multiple factors, including radiation intensity, canopy structure, sun-observer geometry, and leaf physiological status. The complex interplay among these factors causes substantial discrepancies among top-of-canopy (TOC) SIF, leaf-level average SIF and actual photosynthetic activity. Downscaling TOC SIF to the leaf-level and decoupling structural and physiological information remain major challenges in the use of SIF signals for remote sensing of photosynthesis. To address these challenges, the R2F (reflectance-to-fluorescence) theory was developed, grounded in the similarity in radiative transfer processes governing SIF and reflectance. This theory establishes a physical relationship between near-infrared reflectance ($R_{\mathrm{nir}}$) and the far-red SIF scattering coefficient (${\sigma }_F$). On this basis, SIF signals can be scaled from the canopy to the leaf level by normalizing ${\sigma }_F$, estimated from reflectance as ${\sigma }_F=R_{\mathrm{nir}}/i_0$, where $i_0$ denotes canopy interceptance. However, the original R2F formulation assumes a non-reflective soil. This simplification breaks down in sparse canopies, where soil contributions are non-negligible—an issue referred to as the “black-soil problem”. Soil enhances both $R_{\mathrm{nir}}$ and ${\sigma }_F$, distorting their intrinsic relationship. In this study, we show that soil effects manifest through two main mechanisms: (1) direct soil reflection, which significantly increases $R_{\mathrm{nir}}$ but has minimal impact on ${\sigma }_F$, and (2) soil–vegetation multiple scattering, which affects both $R_{\mathrm{nir}}$ and ${\sigma }_F$ but tends to have compensatory effects. Consequently, the dominant source of bias in the original R2F relationship is direct soil reflection that contributes to $R_{\mathrm{nir}}$—a mechanism that had not been explicitly isolated in previous studies. This finding allows us to narrow down the “black-soil problem” in the R2F framework to the specific impact of soil single scattering on $R_{\mathrm{nir}}$. To mitigate this bias, we propose a soil-adjusted R2F (saR2F) method, which estimates the direct soil contribution of $R_{\mathrm{nir}}$ using TOC red and blue reflectance. Correcting $R_{\mathrm{nir}}$ for the direct soil reflection results in a robust relationship between ${\sigma }_F$ and soil-adjusted $R_{\mathrm{nir}}\left(\mathrm{sa}{R}_{\mathrm{nir}}\right)$, notably ${\sigma }_F=\mathrm{sa}{R}_{\mathrm{nir}}/i_0$.

We evaluated the saR2F relationship using one field and two simulated datasets. In the field study, saR2F improved the estimation of ${\sigma }_F$ from TOC reflectance, with R² increasing ranging from 0.21 to 0.31 compared to the original R2F. In the two simulations, saR2F consistently outperformed the original R2F, especially under sparse canopy conditions. We also compared saR2F with NDVI-based (NIRv) and FCVI-based R2F approaches. In the available field observations collected under specific conditions (i.e., varying viewing azimuth angles), the three approaches showed similar performance and were better than the original R2F in explaining the viewing-angle dependence of ${\sigma }_F$. However, across the broader range of simulated scenarios and for estimating the exact ${\sigma }_F$, saR2F demonstrated better stability than NIRv and FCVI-based R2F methods. The NIRv-based and FCVI-based R2F methods yielded relatively low RMSE (0.092 and 0.075, respectively) but weak explanatory power, with R² values below 0.41 for canopies with LAI < 3. In contrast, saR2F achieved a much stronger relationship (R² = 0.80) and a low RMSE of 0.044. Furthermore, compared to the NIRv or FCVI-based approaches for R2F corrections, saR2F offers a more physically plausible and interpretable solution that can be applied to angular correction and total SIF estimation. The effective mitigation of the black-soil problem facilitates interpretation of raw SIF observations and enhances the monitoring of photosynthetic activity using SIF.