## 1 Introduction  
Gross primary productivity (GPP) of the terrestrial ecosystem, which reflects the carbon dioxide (CO\({}_{2}\)) flux fixed by plants through the process of photosynthesis, is a crucial factor in the global carbon cycle. Conventionally, the eddy covariance (EC) technique is recognized as one of the best micrometeorological methods for measuring the net exchange (NEE) of CO\({}_{2}\) between the atmosphere and the surface of various ecosystems and ecosystem respiration (ER) across diverse terrestrial ecosystems. The observed NEE, partitioned into GPP and ecosystem respiration, can be used for indirect GPP estimation [1]. EC flux measurements from continental or global flux networks provide fundamental data for calibrating and validating the parameters of ecological models to improve GPP estimation capability, facilitating numerous studies of carbon fluxes over various terrestrial ecosystems [2]. These flux sites' data integrated with satellite remote sensing and climate data have been widely used to support the development of GPP estimation models at the site, regional, and global scales [3; 4]. Light use efficiency (LUE) models, driven by vegetation indices (e.g., the enhanced vegetation index, EVI) obtained from remotely sensed imagery and climate data, have been extensively used for estimating GPP from site scale to global scale due to their advantages of a well-accepted explanation, few input parameters, and ease of operation. These models estimate GPP as a product of absorbed photosynthetically active radiation (APAR) and LUE (\(\epsilon_{\rm g}\)) (GPP = APAR \(\times\)\(\epsilon_{\rm g}\)), which is derived from downscaling the maximum LUE (LUE\({}_{\rm max}\), denoted as \(\varepsilon_{0}\)) by the scaling of environmental constraints (e.g., temperature, water, CO\({}_{2}\), etc.). Generally, the \(\epsilon_{0}\) is initially regarded as a constant for global vegetation in LUE models, such as C-Fix [5] and EC-LUE [6], and then considered as a biome-specific constant, as in MOD17 [7], or a constant dependent on product types of carbon (namely C3 and C4), as in VPM and TEC models [3; 8], as well as a two-leaf-specific constant in the TL-LUE model [9]. However, growing ecological communities think of \(\epsilon_{0}\) as a dynamic value rather than a constant [10; 11]. In reality, \(\epsilon_{0}\) was significantly influenced by vegetation canopy absorption of solar radiation [12] and the internal physiological characteristics (e.g., chlorophyll content) of plants [13] in earlier studies. Based on the fact that there is an essential increase in light use efficiency under overcast conditions, a cloudiness index was used to dynamically regulate \(\varepsilon_{0}\) in CFLUX and CI-LUE models [12; 14]. Considering the nonlinear response of vegetation photosynthesis to solar radiation induced by vegetation photosynthesis varies with the dynamics of solar radiation, [PERSON] et al. (2023) [10] proposed a PAR-regulated dynamic \(\varepsilon_{0}\) in GPP estimation based on the LUE model, while several recent studies have shown that \(\varepsilon_{0}\) greatly varies during the vegetation growing season [15] as a result of the varying correlation between chlorophyll content and photosynthesis efficiency at various growing stages [16]. Dynamic \(\epsilon_{0}\) was parameterized in the phenological transitions of paddy rice [17] and the leaf area index (LAI)-based green-up stage and senescence stage [11] at flux sites to improve agroecosystem GPP estimation. So far, studies on the comprehensive performances of phenology-based dynamic \(\varepsilon_{0}\) for GPP estimation in broader terrestrial ecosystems (such as forests, grasslands, and wetlands) are few, but performance evaluation can provide a deep understanding of dynamic \(\varepsilon_{0}\) in GPP estimation. More specifically, [PERSON] et al. (2021) [17] estimated \(\varepsilon_{0}\) during four phenological stages corresponding to the physiological features of paddy rice.