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A radiative transfer model for solar induced fluorescence using spectral invariants theory

Solar Induced chlorophyll Fluorescence (SIF) shows promise as an approach for estimating gross primary production (GPP) remotely. However, sun-target-sensor geometry and within-canopy absorption of SIF can alter the relationship between measured SIF and GPP, because sensors can only retrieve some unknown fraction of the total emitted SIF. Radiative transfer models that allow for variation in canopy structure and sensor angles are therefore needed to properly interpret SIF measurements. Spectral invariants allow decoupling of the wavelength-independent canopy structure and the wavelength-dependent leaf and soil spectrum in the radiative transfer process. Here we develop a simple analytical Fluorescence Radiative Transfer model based on Escape and Recollision probability (FluorRTER) to investigate the impact of canopy structure and sun-target-sensor geometry on SIF emissions. SIF simulations using the FluorRTER model agreed well the one-dimensional Soil-Canopy Observation of Photochemistry and Energy balance (SCOPE) model and the three-dimensional Fluorescence model with Weighted Photon Spread (FluorWPS) model. The fractional vegetation cover (FVC) and clumping effect have a large influence the SIF emission of 3D discontinuous canopies. For a moderate solar zenith angle (30°) and a clumped canopy (FVC = 0.6), the difference between the directional observed SIF of a 3D discontinuous canopy and a 1D homogeneous canopy was as large as 43.2% and 38.4% for Photosystem I + II fluorescence at 685 nm and at 740 nm, respectively. By bridging the gap between observed SIF and total emitted SIF over 3D heterogeneous vegetation canopies, the FluorRTER model can assist with the angular normalization of SIF measurements and enable the more robust interpretation of how variations in SIF from directional and hemispherical in-situ, airborne and satellite observations relate to leaf and whole-canopy physiological processes.