## 1 Introduction  
Drought is a persistent environmental challenge for global ecosystems [1, 2], significantly impacting vegetation growth and the regional and global water balance [3, 4, 5]. Gross Primary Production (GPP), a key indicator of the organic carbon fixed by plants via photosynthesis over a given period, is important for regulating atmospheric CO\({}_{2}\) concentrations, understanding the global carbon cycle, and ecosystem service functions [6, 7]. GPP estimation methods include the eddy correlation method [8], light use efficiency (LUE) [9] models, and ecological process models [10]. The primary models for estimating GPP using remote sensing data include the CASA [11], VPM [12], DTEC [13], and EC-LUE models [14]. Commonly used GPP products derived using the normalised difference vegetation index (NDVI) and enhanced vegetation index (EVI) include MOD17 and GLASS GPP. However, when the vegetation chlorophyll content is high, traditional vegetation indices become saturated, rendering NDVI and EVI insufficiently sensitive to the rapid physiological responses of plants to short-term environmental changes, such as water stress, pests, and diseases [15]. This limitation increases the GPP estimation uncertainty and restricts its application to complex environments, particularly in arid zones. Recent advances in satellite-based observations of solar-induced chlorophyll fluorescence (SIF) have provided innovative techniques for directly monitoring GPP [16]. SIF, the red and near-infrared photons re-emitted by green plants after absorbing light energy during photosynthesis, is a by-product of photosynthesis and provides an ideal indicator of transient photosynthetic activity in vegetation [17]. Compared to NDVI and EVI, SIF exhibits greater sensitivity to vegetation photosynthesis and is closely linked to light-dependent photosynthetic processes [18]. SIF data exhibit a strong correlation with GPP [19] and can be used to monitor and estimate GPP more directly and effectively [20; 21]. As big data and machine learning technologies continue to evolve, using machine learning algorithms in GPP estimation has garnered increasing attention [22; 23]. Machine learning has become a crucial method for estimating GPP. In particular, the extreme Gradient Boosting (XGBoost) and random forest (RF) models were selected in this study because they are good at dealing with complex nonlinear relationships and large datasets and can effectively control overfitting [24]. To assess the model's strengths and weaknesses, a comparative analysis with the classical GPP estimation method, the LUE model, was also conducted to verify the applicability and advantages of machine learning models in GPP estimation in arid zones. [PERSON] et al. employed five machine learning algorithms to extrapolate point-scale GPP to the regional level. The RF model demonstrated higher accuracy in simulating regional-scale GPP [25]. Integrating machine learning algorithms with SIF further enhances the simulation accuracy of GPP and offers novel insights into GPP estimation. The spatial pattern of global GPP simulated using SIF and other auxiliary data in combination with machine learning algorithms can exhibit plausible spatial and seasonal variations while achieving higher computational efficiency [26]. Drought indices are effective tools for assessing drought severity [27]. Among these, the Palmer Drought Severity Index (PDSI) [28], standardised precipitation index (SPI) [29], and standardised precipitation evapotranspiration index (SPEI) [30] are considered superior methods for evaluating drought conditions. However, the PDSI and SPI are limited to regions with complex climates and frequent droughts. Specifically, the PDSI integrates the moisture deficit but has high data requirements and fixed timescales. In contrast, the SPI encompasses various timescales and exclusively focuses on the effects of precipitation shortages on drought [31].