# Impacts of Heat and Drought on Gross Primary Productivity in China
## 5 Discussion
### Research Contributions  
First, this study introduced copula functions into the analysis of the impacts of drought and heat on GPP. By constructing a 2D joint distribution of GPP and heat/ drought and a 3D joint distribution of GPP, heat, and drought, ENAG probabilities under different drought levels and heat intensities were obtained. Generally, previous research on the impacts of extreme climate events on GPP has been divided into two methodologies. In the first method, drought or heat events that occurred in a certain period and region were selected with which to monitor dynamic GPP changes under extreme climate conditions in the given period compared with changes in other periods. In the second method, extreme events, including extreme climatic events (heat, heat waves, extreme precipitation, extreme cold, etc.) and extreme GPP events were first identified, and the relationship between extreme climate events and extreme GPP was then analyzed by correlation analysis, regression analysis, or other methods. Neither of the above methods consider interactions between climate variables. The research method utilized in this study analyzed the influence of drought and heat stress on GPP more intuitively from the perspective of probability and considered the combined influence and synergistic effect of these two influences on GPP. This methodology is conducive to understanding the possible results of the distribution of GPP losses under extreme climate conditions and to providing a reference for future research.  
Second, this study reveals the nonlinear impacts of drought and heat on GPP. According to the 2D copula model of GPP and drought/heat, this study found that when the drought level/heat intensity increases, the ENAG probability in each vegetation region increases, and the higher the drought level/heat intensity is, the more the probability increases. According to the 3D copula model, it was determined that the combined impact of drought and heat on vegetation growth is not a simple linear accumulation. When the drought level is low, heat has a big impact on GPP; however, when the drought level is high, the impact of heat on GPP is limited, which is of great significance for future research on the responses of vegetation to heat and drought.  
Third, to study the interaction between vegetation and climate and to evaluate the impact of climate change on vegetation, vegetation models have been rapidly developed. A dynamic global vegetation model is a standard vegetation simulation model that mainly uses climate data and CO\({}_{2}\) concentrations as inputs to simulate the physiological processes of vegetation and to allow for the quantitative understanding of the interaction between vegetation and climate through coupling with climate models [80]. However, the climate data utilized in this vegetation model mostly consist of precipitation and temperature data that are transformed into environmentally limiting factors through functions that eventually become model parameters. This method often ignores interactions between factors, such as between drought and heat, and results in the limiting effect of drought on heat being overlooked, thus causing additional uncertainties in the simulation results if they are considered separately. Therefore, future developments in vegetation simulation models and improvements in simulation accuracy should focus on the synergistic effects and potential nonlinear relationships between different stresses (such as drought and heat).