## 1 Introduction  
A compound heatwave-drought (CHD) event refers to the extreme climatic phenomenon when heatwaves and droughts occur simultaneously. Extreme CHD events have become increasingly frequent and severe with the global climate change [1, 2], and this phenomenon is projected to continue in the future [3, 4, 5]. An extreme CHD event can cause greater damages than an individual extreme event does [6, 7, 8], leading to intensified effects on natural and socioeconomic systems [9, 10, 11]. For example, the risk of the reduction in terrestrial photosynthesis under CHD conditions can increase by \(8-9\%\) in comparison to individual dry conditions, and the risk is even enhanced by \(25-42\%\) compared to individual dry conditions. hot conditions [8]. Gross primary production (GPP), the photosynthetic activity of terrestrial ecosystems, is a key component of the carbon cycle and is highly responsive to extreme climatic conditions [12; 13; 14; 15]. Understanding how GPP responds to CHD events is crucial for assessing the resilience of terrestrial ecosystems to these intensifying climate challenges. Numerous studies have investigated the effects of CHD events on GPP and explored the underlying mechanisms. In response to soil moisture deficit caused by drought, plants typically adopt a strategy of reducing stomatal conductance to minimize water loss [16]. However, this adaptive mechanism simultaneously inhibits carbon dioxide absorption, thereby weakening photosynthesis [17]. Prolonged drought can affect aboveground carbon allocation, such as reducing leaf area index, which further decreases GPP [18; 19]. On the other hand, heatwaves not only can reduce photosynthetic capacity by directly damaging plant tissues but also can further suppress carbon fixation by significantly increasing evapotranspiration rates and exacerbating water stress [12; 20]. Additionally, the simultaneous occurrence of high temperatures and droughts often leads to a significant increase in vapor pressure deficit (VPD) [21; 22], which has been emphasized as the critical role in regulating GPP [23; 24; 25]. Overall, these studies indicate that extreme CHD events significantly reduce GPP in terrestrial ecosystems through multiple mechanisms and may have profound implications for the global carbon cycle. However, not all extreme climate events result in significant damage to ecosystem productivity. Vegetation has notable adaptability and resistance to certain levels of climatic stress, and their responses depend on many key factors, such as event intensity and duration [26]. In response to moderate to extreme climate events, vegetation can reduce the decline in GPP by regulating stomatal conductance and other mechanisms [27]. However, there is still limited understanding and quantification of these adaptive mechanisms and how GPP responds to CHD events of different intensities. Addressing this limitation is essential for predicting future ecosystem responses under intensifying climate extremes and for developing targeted mitigation and adaptation strategies. Moreover, different vegetation types show varying levels of resilience to extreme CHD events due to their differences in leaf characteristics, root systems, and canopy structures [28; 29]. Generally, forests are more resistant than grasses or shrubs to short-term droughts due to their deeper root systems [30; 31]. For forests specifically, evergreen forests and deciduous forests may also exhibit significant differences in GPP responses to extreme climate events. For instance, [PERSON] et al. (2024) analyzed tower observations and found that evergreen forests showed larger GPP reductions than deciduous forests in 2022 compared to 2021, with relative amplitudes of \(-21.0\%\) and \(-3.4\%\), respectively [32]. However, the different GPP responses across vegetation types to CHD events of varying intensities remain insufficiently explored. This gap may hinder the efficient identification of terrestrial sensitivity to extreme events and limit our understanding of vegetation adaptation mechanisms.