## 1 Introduction  
The carbon dioxide fixed through photosynthesis at the ecosystem level, known as gross primary productivity (GPP), along with the carbon dioxide released via ecosystem respiration (ER), directly governs the global carbon budge balance [1, 2, 3, 4]. GPP and ER demonstrate an intertwined and complementary relationship in the ecosystem, showcasing unique dynamic characteristics despite their close interconnection [5, 6, 7, 8]. Numerous studies have demonstrated that GPP is predominantly driven by climatic factors, resulting in significant interannual variability [9, 10, 11, 12]. Regarding ER, studies have primarily focused on the effects of temperature [13, 14, 15], which may be attributed to the inclusion of soil respiration [16, 17]. Conversely, ER exhibited a positive relationship with vegetation photosynthetic capacity [13, 18, 19], suggesting the influence of available carbon substrates on both plant and soil respiration [20]. The sensitivity (\(S\)) of ecosystem carbon flux, specifically GPP and ER, to climate change can be understood as the magnitude of its response to these changes [21]. For vegetation productivity, \(S\) is generally considered to be an intrinsic characteristic [22, 23], with spatial variability primarily driven by differences in ecosystems and local environmental conditions [23, 24]. Existing studies have demonstrated that \(S\) can also vary in response to various environmental factors, such as drought, heatwaves, and changes in precipitation patterns [11, 25, 26]. In the context of ER, research has predominantly focused on the temperature sensitivity of soil respiration (\(Q_{10}\)), exploring its relationships with climate drivers [27, 28] and soil microbial communities [29, 30]. Soil respiration exhibits a non-linear relationship with soil temperature, with CO\({}_{2}\) efflux increasing up to a peak (28-30 \({}^{\circ}\)C) and decreasing at higher temperatures (>30 \({}^{\circ}\)C). Therefore, \(Q_{10}\) can accurately represent the temperature dependence of soil respiration for temperatures below 26-28 \({}^{\circ}\)C [31].  
Precipitation serves as a pivotal environmental driver influencing both GPP and ER. However, their sensitivities to variations in precipitation (\(S_{\text{GPP}}\) and \(S_{\text{ER}}\)) can differ markedly [32, 33], highlighting the complex interactions within the ecosystems. Numerous studies have investigated the sensitivity of vegetation productivity to precipitation [23, 24, 25], yielding a consensus conclusion: \(S_{\text{GPP}}\) is greater in arid regions and smaller in mesic regions [11, 25]. However, there remains a notable gap in the research regarding the spatiotemporal differences between \(S_{\text{GPP}}\) and \(S_{\text{ER}}\), which may be attributed to the intricate nature of ER, involving various underlying processes and factors. For instance, under optimal soil moisture conditions, the respiration of soil microbes and roots is stimulated, whereas excessive water leading to anaerobic conditions can suppress root respiration [31, 34, 35].  
This study directly explores the similarities and differences in the sensitivity of \(S_{\text{GPP}}\) and \(S_{\text{ER}}\), along with their main environmental drivers, using the FLUXNET2015 dataset. The dataset follows a standardized methodology for data processing, which includes rigorous quality control, filtering, the interpolation of meteorological data, and accurate partitioning of flux data [36]. Specifically, the objectives of this study were to (i) examine the spatial distribution and differences of \(S_{\text{GPP}}\) and \(S_{\text{ER}}\); and (ii) elucidate the temporal trends and variations in \(S_{\text{GPP}}\) and \(S_{\text{ER}}\).