## 1 Introduction
The advantage of Copula functions is their ability to flexibly handle dependency structures between multiple variables, especially in cases of nonlinear relationships or tail dependencies [30]. This method allows researchers to more accurately quantify the probability of GPP loss under different combinations of extreme events, leading to a better assessment of CDHEs' impacts on ecosystems. Despite the increasing number of studies on the impact of CDHEs on GPP [31; 32; 33], research focusing on tropical forests remains insufficient. This is mainly because the species diversity, structural complexity, and environmental heterogeneity of tropical forests make such studies challenging. In this context, rubber plantations, as a type of artificial tropical forest ecosystem, can serve as a unique entry point for research. Compared to natural tropical forests, rubber plantations are often even-aged monocultures with simpler structures. This makes the effects of CDHEs easier to observe and quantify, showing distinct response characteristics. Rubber trees exhibit clear physiological responses to CDHEs. Heatwave promotes leaf transpiration, leading to stomatal closure, which limits CO2 absorption and reduces photosynthetic rates. It also decreases the efficiency of photosynthetic enzymes, further reducing GPP. Under drought conditions, water uptake by roots is restricted, affecting nutrient absorption and transport. As water is a key component in photosynthesis, its shortage also limits GPP. Due to their unique latex production physiology, rubber trees are sensitive to water stress. The effects of cutting rubber activities and the tropical water pump phenomenon intensify drought stress [34]. Due to the systemic effects of compound factors, heatwave accelerates water evaporation, increasing drought severity. Drought leads to a decrease in the overall specific heat of the ecosystem, exacerbating the severity and duration of hot weather. Hainan Island, ranking as the second-largest natural rubber planting area in China, is located at the northern edge of the tropics. With frequent heatwave and drought events [35; 36], it provides an ideal natural setting for studying the impacts of CDHEs. Given the relative lack of research on the impact of CDHEs on tropical forest GPP, this study uses rubber plantations on Hainan Island as a starting point. It aims to diagnose the mechanisms by which CDHEs affect rubber tree GPP and to quantify the productivity response to compound drought and heatwave events. The objectives of this study were (1) to identify the optimal combination of drought and heatwave indices by calculating Pearson and Spearman correlation coefficients between the Standardized Temperature Index at 1-month time scale (STI-1) (heatwave index) and multiple drought indices (Standardized Precipitation Evapotranspiration Index (SPEI), Standardized Precipitation Index (SPI), Standardized Relative Humidity Index (SRHI), and Standardized Soil Moisture Index (SSMI)) at 1-, 3-, 6-, 9-, and 12-month time scales, where the optimal combination was defined as the drought index and time scale that showed the strongest and most significant negative correlation with STI-1, indicating a higher likelihood of co-occurrence and providing a robust basis for constructing the CDHI; (2) to construct a CDHI using Copula functions based on the selected optimal index combination, to capture the characteristics of CDHEs experienced by rubber plantations; and (3) to construct a Bayes-Copula conditional probability model between the CDHI and rubber plantation ecosystem GPP to quantitatively assess the impact of CDHEs on rubber plantation GPP and reveal potential losses. This study combines the quantification of CDHEs with probability assessment of GPP responses, providing a methodological framework for studying CDHEs impact on tropical forests. The results help improve our understanding of how tropical forest ecosystems respond to climate change and provide scientific evidence for developing regional climate change strategies.