## 1 Introduction  
Gross primary production (GPP) is the largest terrestrial carbon flux, and its accurate estimation is crucial for global carbon cycle studies [1]. However, large uncertainties exist in global to regional GPP estimates, including interannual variations. One important factor attributed to this uncertainty is the poor representation of climate extreme impacts on GPP in models. Regional GPP is often influenced by climate extremes (e.g., droughts and heatwaves) [2, 3, 4, 5]. For example, the 2003 heatwave and drought in Europe caused a 30% drop in GPP in the context of global warming [6]. The frequency and intensity of droughts have increased significantly in recent years [7], and the occurrence of future droughts is predicted to cause more GPP losses, resulting in ecological and agricultural economic losses. Extreme drought significantly impacts gross primary productivity (GPP) by causing water stress, inhibiting photosynthesis, degrading vegetation structure, and triggering ecosystem feedback [8]. Soil water deficiency leads to stomatal closure, reducing carbon dioxide absorption and suppressing photosynthesis [9; 10]. Drought also lowers Rubisco activity, increases photorespiration, and hinders water transport due to hydraulic failure [11]. Vegetation may shed leaves, curl, or lose chlorophyll, further reducing photosynthetic capacity [12]. Prolonged drought shifts plant communities toward drought-tolerant species, reducing high-GPP species and overall productivity. Vegetation degradation and reduced cover exacerbate soil erosion and weaken carbon sink functions, creating a feedback loop of drought, climate change, and carbon emissions, with both short- and long-term impacts on regional and global carbon cycles [13]. How to accurately simulate GPP under drought conditions is a challenge for carbon cycle modeling. Light-use efficiency (LUE) models calculate GPP as the product of the energy absorbed by vegetation and the actual light energy used for converting energy into fixed carbon during photosynthesis [14], where the key variables can be obtained directly from satellite remote sensing. Since LUE models are simple to use [15], computationally efficient, and easily integrated with remote sensing [16; 17], LUE models were widely applied to regional to global carbon cycle studies [18; 19]. LUE models have two basic assumptions: (1) GPP and Absorbed Photosynthetic Active Radiation (APAR) are linearly correlated; (2) the actual LUE is influenced by environmental conditions (temperature, moisture, etc.). Most LUE models rely on the fraction of absorbed photosynthetically active radiation (FAPAR) and the atmospheric saturated water vapor pressure difference (VPD) to characterize the response of GPP to drought, but FAPAR or VPD do not necessarily capture the effect of soil moisture (SM) deficit on GPP [20]. [PERSON] et al. found that under severe drought conditions, VPD and SM gradually decouple, and GPP becomes progressively disconnected from FAPAR due to the changes in stomatal and biochemical responses and resulting variations in LUE. By quantifying the effect of SM on the terrestrial carbon cycle, [PERSON] et al. emphasized that the future ability of continents to become carbon sinks depends largely on SM and the nonlinear terrestrial-atmospheric response [21]. A recent study investigating global changes in water use efficiency and its relationship with both biotic (i.e., leaf area index, LAI) and abiotic (i.e., SM, VPD) factors reported that SM dominates GPP in more than 63% of the global land [22]. Incorporating SM information into models may improve GPP simulations under water stress or drought conditions, which has gained increasing research attention recently. Traditionally, most ecological process models use empirical water stress functions dependent on soil water content to reflect the effects of soil water stress on the carbon cycle [23]. For example, the BEPS model takes into account SM by superimposing environmental effects on stomatal conductance through a layered simulation [24].