## 1 Introduction  
Photosynthesis, the most important biochemical process in terrestrial ecosystems, is an essential part of the global carbon cycle [1; 2]. Therefore, as an indicator of photosynthetic carbon exchange in ecosystems, accurate observations of the gross primary production (GPP) and a clear explanation of its response to environmental conditions are required, in order to help solve the problem of climate change [3; 4; 5]. The eddy covariance (EC) technique is a terrestrial observation method used to estimate the GPP, and the continuously measured data are relatively accurate [6]. However, an EC tower only has a small field of view and limited aerodynamic properties [7], which makes it difficult to measure GPP at larger scales using this method. At larger spatial scales, a measured approach using models and algorithms that integrate tower-based measurements with remotely sensed data offers the possibility to estimate GPP [8; 9]. [PERSON] [10] proposed the light-use efficiency (LUE) based model, validated using tower-based data from an EC tower, which is well-known for its simplicity and efficiency and has been widely applied for remote sensing estimates of GPP. LUE model approaches are commonly based on reflectance vegetation indices [11], such as the normalized difference vegetation index (NDVI) and the enhanced vegetation index (EVI) [12; 13]. However, the NDVI and EVI are related to changes in the canopy structure and biomass, and, therefore, it is hard to capture the diurnal and seasonal dynamics of vegetation photosynthesis in this way [14]. As a result, estimating the GPP using these traditional remote sensing methods remains a challenge, and there is a critical need to develop a more accurate method to estimate GPP and characterize its temporal variations for different vegetation types and environmental conditions [7; 15; 16]. During photosynthesis, green components absorb sunlight covering the 400-700 nm range of the electromagnetic spectrum, triggering chlorophyll to emit the red and far-red light known as solar-induced chlorophyll fluorescence (SIF). Numerous studies have demonstrated a strong relationship between GPP and SIF based on satellite, airborne, tower-based and ground platforms [2; 6; 7; 9; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. Airborne and satellite remote sensing can only offer a snapshot of the SIF at a certain time (for example, 13:30 local time in the case of the OCO-2 satellite), while the influence of the temporal scale used is difficult to assess using instantaneous observations [27; 28; 29]. Automated, continuous, tower-based SIF observation systems have been developed to explore the dynamic mechanism between SIF and GPP [25; 26]. Tower-based SIF studies are continuing to collect long-term data sets for different ecosystems, including wheat [29], maize [30], rice paddy [31], soybean [32], sorghum [33], shrub [34], temperate forest [35], deciduous forest [26], and evergreen forest [36]. These observations provide direct and reliable evidence that can be used to explore the correlation between SIF and GPP at different temporal scales. Although multiple studies have found that SIF demonstrates a strong linear relationship with gross primary production (GPP), the SIF-GPP relationship at different temporal scales and under different environmental conditions has not been well explored. Some studies have found that the relationship has a weaker empirical linear correlation over shorter time scales than at the seasonal scale [29; 37]. [PERSON] et al. [38] demonstrated that the relationship between SIF and GPP can be nonlinear over short temporal scales. [PERSON] et al. [39] assessed the relationship between airborne-measured SIF and field-measured leaf CO\({}_{2}\) assimilation in a citrus crop field, and, using second-order polynomial regression, found that the SIF and leaf carbon assimilation exhibited a statistically significant relationship at the diurnal scale. However, [PERSON] et al.