## 1 Introduction  
Gross primary production (GPP) is defined as the rate of carbon (C) fixation through the process of vegetation photosynthesis. It drives both ecosystem function and C cycling [1,2]. GPP accounts for approximately 120 Pg-C:yr-1, and is the largest component of the global C cycle [3]. It is critically important to precisely simulate GPP in order to accurately estimate C sequestration and the response of terrestrial ecosystems to climate change. Nevertheless, huge uncertainties remain in estimating the spatiotemporal changes of GPP, which limits our understanding of elevated atmospheric carbon dioxide (CO\({}_{2}\)) in the context of global climate change [4, 5, 6]. The utilization of eddy covariance (EC) technology is the most direct and accurate means to obtain real-time canopy level GPP. However, EC measurements usually have a spatial footprint in the range of 1 km\({}^{2}\)[7]. This limitation necessitates the combination of remote sensing data with field-based EC measurements for the estimations of GPP at regional to global spatial scales [8]. Light use efficiency (LUE) models are broadly used to analyze terrestrial GPP utilizing remote sensing data and utilizes a simple model structure that require less input variables [9, 10, 11, 12]. GPP is generally expressed in LUE models as the product of LUE and absorbed photosynthetically active radiation (APAR). APAR can be calculated by multiplying the total photosynthetically active radiation (PAR) incident on a vegetation canopy and the fraction of PAR absorbed by the canopy (FPAR). Meteorological observations provide the total incident PAR, and FPAR can be acquired using remote sensing data [13,14]. The accuracy of APAR and LUE are critical inputs for the estimation of GPP. The photochemical reflectance index (PRI) is the most representative index of the xanthophyll cycle in the photoprotective mechanisms of photosynthesis and is regarded as a promising method for accurate estimation of LUE [15, 16, 17]. Numerous studies have reported that PRI is an effective spectral index that can reveal spatial and temporal changes in LUE across various ecosystems [18, 19, 20, 21, 22], PRI-based LUE models enable an improved assessment of GPP in terrestrial vegetation canopies. Although the correlation between PRI and LUE has been examined across various spatial scales and ecosystems, the underlying mechanism of the correlation between PRI and LUE remains controversial. The uncertainty is partly attributed to the impact of canopy structure on sun-view geometry and various illuminations. Vegetation canopies are non-Lambertian and exhibit varying degrees of anisotropy, leading to their reflectance changes with viewed angles. The PRI signal and its interpretation of LUE can be significantly influenced by angular effects, inclusive of leaf angle distribution and sun-view geometry [16, 22, 23, 24]. Multi-angle spectral observations can provide information of the vegetation canopy and describe the variation in the observed fractions of the canopy with view angles. This approach improves the monitoring and inversion accuracy of crop biochemical parameters for the entire canopy [25, 26]. Recent studies have reported that the long-term variation in PRI was ascribed to the dynamics of the pigment pool size in vegetation, which also affected the tracking of LUE by PRI [27, 28, 29]. Such studies have concentrated on responses of evergreen vegetation, with only limited reporting of long-term PRI responses in annual vegetation such as crops [30, 31]. Environmental variables also affect the correlation between PRI and photosynthesis. The ability of PRI to estimate LUE varies with environmental factors, i.e., the ability of PRI in tracking diurnal variations of LUE increases with PAR, vapor pressure deficit (VPD), and air temperature (T\({}_{\text{a}}\)) for a subtropical coniferous forest [18]. Therefore, further studies are needed to improve our knowledge of varying environmental conditions on the effectiveness of PRI in the estimation of GPP using LUE models.