Non-linearity between gross primary productivity and far-red solar-induced chlorophyll fluorescence emitted from canopies of major biomes

Solar-induced chlorophyll fluorescence (SIF) observed from vegetation has been considered as a promising proxy of gross primary productivity (GPP) in several studies, and recent work has shown advantages of using the total emitted SIF (SIFtotal) to capture the variation of GPP. The non-linearity between SIF and GPP at the canopy level was often observed in many previous studies, but the non-linearity between SIFtotal and GPP has not yet been systematically investigated. In this study, based on a theoretical analysis of the relationship between SIF and GPP at the leaf level and how it propagates to the canopy level with the consideration of sunlit and shaded leaf fractions in the canopy, we asserted that non-linear relationships between SIFtotal and GPP at the canopy level are general and physically sound. We derived SIFtotal from two different approaches using TROPOMI SIF data. One is based on the canopy escape ratio of SIF signals observed by satellite sensors (SIFobs), and the other is an angular normalization method. At the site level, we established linear and non-linear (exponential, hyperbolic, and polynomial) regressions between TROPOMI SIF and GPP data from 25 flux tower sites covering the eight biomes. The results indicate that non-linearity between SIFtotal and GPP exists among eight major biomes, and exponential regression is the best regression method to capture the non-linearity between SIF and GPP at the site level. We developed a simple variable, SIFnon-linear, to capture the non-linearity between SIFtotal and GPP. R2 values of the linear correlations between SIFnon-linear and GPP are equal or close to those of exponential correlations between SIFtotal and GPP. SIFnon-linear captures the non-linearity well, even though different biomes have different degrees of non-linearity. On the global scale, TROPOMI SIF was compared with GPP simulations of the BEPS model and the SMAP GPP product, showing that SIFnon-linear is a better proxy of GPP than SIFobs and SIFtotal. We find that the non-linearity between SIFtotal and GPP generally exists among eight major biomes regardless of the spatial or temporal scales. The non-linearity is driven by the seasonal variation of the absorbed photosynthetically active radiation (APAR). The degree of the non-linearity varies among different biomes, and it is controlled by three factors: the light saturation point of GPP, the variation of APAR during the growing season, and the ratio between the sunlit and shaded portion of the canopy. Temporal aggregation of SIFtotal reduces the non-linearity. Our results indicate that the simple variable SIFnon-linear can replace SIFobs or SIFtotal to improve global SIF-GPP related studies in the future.