## 1 Introduction  
The carbon flux of terrestrial ecosystems, with the greatest uncertainty, plays an important role in the carbon cycle [1]. Terrestrial carbon fluxes are fundamental to understand the feedback mechanism of terrestrial ecosystems to climate change [2]. However, the imbalance between carbon sources and carbon sinks results in the so-called \"mystery of the missing carbon\" [3,4]. Therefore, there is an urgent need to obtain accurate estimates of terrestrial carbon fluxes [5]. Gross primary productivity (GPP) is an important indicator for estimating terrestrial carbon fluxes. GPP refers to the amount of organic carbon fixed by green plants through photosynthesis per unit time; thus, it determines the initial substances and energy entering terrestrial ecosystems [6,7]. Therefore, an accurate estimation of GPP is an indispensable step to reduce the uncertainty of terrestrial carbon fluxes. The eddy covariance (EC) technology is seen as the most accurate method to estimate GPP. The main features obtained by the EC technology include semi-hourly/hourly fluxes of CO\({}_{2}\), heat and humidity. Ecosystem respiration (ER) is calculated by interpolating Net Ecosystem Exchange (NEE) and temperature (T) [8, 9, 10, 11]. Then, GPP is calculated as the difference between ER and NEE. The flux-tower-derived GPP products have clear advantages in the accuracy compared with remote sensing products. However, the footprint of observations of flux towers is small, resulting in a lack of spatial representativeness. Moreover, the number of flux towers is insufficient to monitoring GPP globally, and the uneven distribution of flux towers further left huge gaps in many regions. Satellite observations can serve as a good supplement to flux towers in terms of spatial coverage despite relatively lower accuracy of GPP estimates. For example, MODIS GPP is calculated using the light use efficiency (LUE) model [12]. The LUE model is the product of three variables fPAR (the proportion of PAR absorbed by plant canopies), PAR (photosynthetically active radiation) and LUE\({}_{\text{P}}\) (light use efficiency). LUE\({}_{\text{P}}\) indicates the efficiency of the radiation absorbed by the vegetation during photosynthesis [13]. LUE\({}_{\text{P}}\) is the critical input parameter of the LUE model, which is susceptible to plant growth status and ecological environments. Therefore, the light use efficiency should vary with different environments and growth stages of vegetation theoretically. However, LUE\({}_{\text{P}}\) is generally determined as a fixed parameter in the LUE model according to specific vegetation types, resulting in large uncertainties of estimated GPP. In addition, the LUE model requires a large number of ground parameter inputs, and the uncertainty of those parameters will also propagate to estimates of GPP [14,15]. Solar-induced chlorophyll fluorescence (SIF) is a probe of vegetation photosynthesis because most changes in photosynthesis can be reflected by SIF. Hence, SIF opens a new prospect for GPP estimations [16,17]. Previous studies have demonstrated that SIF-estimated GPP is more accurate than that of LUE model mainly because SIF is a byproduct of photosynthesis. Hence, water and heat stress on photosynthesis processes can be reflected by changes in chlorophyll fluorescence immediately [12,18]. Recent studies show that the accuracy of SIF-estimated GPP is evidently higher than those estimated by other vegetation indexes, such as the normalized difference vegetation index (NDVI) and enhanced vegetation index (EVI) [12,18,19]. Some researchers used SIF to calculate Vcmax (maximum carboxylation capacity), which presented a better GPP estimation accuracy [20,21]. SIF products from the Greenhouse Gases Observing Satellite (GOSAT) [22], the Global Ozone Monitoring Experiment-2 (GOME-2) [23] and the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) [24] were used to establish models to estimate GPP in the past a few years.