FSM: A Reflectance Reconstruction Method to Retrieve Full-Spectrum Sun-Induced Chlorophyll Fluorescence From Canopy Measurements

Full-spectrum Sun-induced chlorophyll fluorescence (SIF) offers profound physiological insights into plant functional status compared to single-band SIF. We propose a Fourier series-based method (FSM) for retrieving full-spectrum SIF, aiming to address the limitations of existing methods, such as reliance on reflectance training datasets and the limited spectral range of retrieved SIF spectrum. The core principle of the FSM involves modeling reflectance as a wavelength-dependent function, which can be approximated by successive summations using high-order expansions of the Fourier series. The performance of the FSM was thoroughly evaluated through a combination of simulations and field measurements. The findings illustrate FSM’s capability to achieve high-precision full-spectrum SIF retrieval, with an average relative root-mean-square error (RRMSE) of 2.468% based on synthetic data. Moreover, the corresponding RRMSE values in the O2-A and O2-B bands, at 1.1% and 3.724%, respectively, indicate accuracy comparable to the spectral fitting method (SFM) and advanced FSR (aFSR) methods and superior to the SpecFit method. In the field full-spectrum SIF retrieval, FSM exhibited improved reflectance reconstruction and produced more reasonable results for the diurnal variation of full-spectrum SIF. The diurnal comparison of single-band SIF at both Italian and German sites further highlights the close alignment between FSM-retrieved SIF and the SFM SIF, with $R^{2}$ values exceeding 0.96 and a maximum RMSE of 0.118 mW/m2/sr/nm. Conversely, the aFSR method encountered challenges stemming from an under-representation of the training dataset, resulting in the maximum RMSE at the Italian site reaching 0.506 mW/m2/sr/nm, along with a minimum $R^{2}$ of 0.809. The FSM demonstrates the promising potential for full-spectrum SIF retrieval, accompanied by fewer limitations.