## 1 Introduction  
With the intensification of global warming, compound drought and heatwave events (CDHEs) are becoming increasingly frequent and intense on a global scale [1, 2], causing severe impacts on ecosystems and human societies [3]. Global economic losses caused by droughs and heatwaves show a significant upward trend. Drought losses alone increased from USD 17.3 billion in 1980-2009 to USD 23.1 billion in 2010-2017 [4]. Meanwhile, losses due to heatwaves between 1992 and 2013 were estimated to reach as high as USD 1.6-5.0 trillion [5]. Compared to single drought or heatwave events, CDHEs cause even more severe economic losses. For example, three CDHEs in the United States from 2011 to 2013 resulted in losses of about USD 60 billion [6]. Similarly, a CDHE in Europe in 2018 caused economic losses of approximately EUR 3.3 billion [7]. Even tropical forests with the richest biodiversity and authenticity are not immune to these impacts and may even be more severely affected [8]. In order to address these increasing losses, it has become crucial to study how to effectively reduce and mitigate the impacts of droughts and heatwaves. Particularly for tropical forests, a deep understanding of the mechanisms by which CDHEs affect them not only helps reveal the response and adaptation processes of ecosystems to extreme climate events but also aids in better understanding the dynamic role of tropical forests in global carbon balance. This provides key parameters for improving ecosystem models and predicting climate change scenarios [9; 10]. There is now some consensus on the definition and quantification methods for CDHEs. The IPCC's SREX (the Intergovernmental Panel on Climate Change, Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation) report proposed three definitions for compound events [11]: (1) two or more extreme events occurring simultaneously or successively; (2) combinations of extreme events with underlying conditions that amplify their impact; or (3) combinations of events that are not themselves extremes but lead to an extreme event or impact when combined. Most current CDHEs studies are primarily based on definition (1), viewing them as events where droughts and heatwaves occur simultaneously or successively [12; 13; 14]. Based on this consensus, researchers mainly use two approaches to identify and quantify CDHEs. One is the threshold method [15; 16; 17; 18; 19], and the other is constructing a comprehensive Compound Drought Heatwave Index (CDHI) using drought indices and heatwave indices [20; 21]. Regarding the impact of CDHEs on vegetation, some studies mainly used the Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), or Gross Primary Productivity (GPP) as evaluation indicators [22; 23]. Among them, GPP is the core driving force of ecosystem material cycling and energy flow, capable of rapidly and effectively reflecting ecosystem responses to environmental disturbances, and is a key indicator for assessing ecosystem health [24; 25]. Due to its relatively mature monitoring and assessment methods, GPP has become an ideal choice for studying the impacts of CDHEs. However, traditional analysis methods, such as calculating Pearson correlation coefficients between drought indices, heatwave indices, and GPP, struggle to accurately capture the tail dependency between extreme events and GPP [26]. Even when the overall correlation between two variables is not significant, they may still have strong associations in extreme cases. This is an important consideration when studying extreme events [27; 28]. In order to overcome this limitation, researchers have begun using more complex statistical methods to capture the actual impact of extreme events on GPP. For example, using Copula functions to construct models for assessing the probability of GPP loss under droughts, heatwaves, and CDHEs can better evaluate the impacts of different types of extreme events [29].