## 4 Discussion
### Drought Impacts on Continental GPP  
Drought may significantly affect terrestrial carbon fluxes through the severely impacted structure and function of terrestrial ecosystems [83; 84; 85]. The factor that primarily regulates vegetative activity affects how GPP reacts to drought. For instance, temperature and radiation are major factors restricting the productivity of terrestrial ecosystems in northern regions of the Northern Hemisphere. [86; 87]. In these areas, drought was typically followed by temperature and radiation increases, which may have contributed to a rise in GPP [88; 89; 90]. In our study, except for some regions in high latitudes in the Northern Hemisphere which showed increased GPP when drought happened, parts of tropical South America also showed an increase in GPP. For these regions, GPP showed a negative correlation with drought, which means that when drought occurs, GPP shows higher values. As indicated by [PERSON] et al., (2003) [86], at high latitudes in the Northern Hemisphere, temperature was the major limitation for vegetative productivity. Decreasing precipitation was typically followed by increasing temperature, which induced increased GPP. Our study is consistent with [30; 91], which showed that GPP has increased in some high latitudes of the Northern Hemisphere. With regard to the Amazon rainforest, radiation is the main factor affecting GPP in South America's tropical regions. [86; 87]. In most cases, the reduction in precipitation happened at the same time as the rise in radiation. As a result, in the Amazon rainforest, GPP increased slightly in drought years compared to normal years. Our study is consistent with [92; 93], which showed that GPP increased in drought years. However, some studies find that the drought has reduced GPP [94; 95]. Therefore, GPP response to drought in rainforests has large uncertainties and needs to be more deeply investigated in the future. The pattern of GPP response to drought in this study is similar to that from the BEPS [96], CABLE, LPJ-wsl, and ORCHIDEE models. This demonstrates that simultaneous assimilation of soil water and CO\({}_{2}\) can effectively reveal the spatial characteristics of drought effects on GPP.  
Drought duration is a key variable for describing the large-scale biospheric drought response [30]. In this study, the optimized CCDAS GPP can reflect the effect of sub-annual drought durations (<9 months) on GPP in most of the world (68%) by adding the assimilation of soil moisture, while for GPP products from other process-based TBMs (TRENDY) as well as the NDVI and SIF derived from remote sensing, they capture longer drought durations (>12 months) in most parts of the world. As previously described, daily scale ESA-CCI soil moisture observations were used to optimize model parameters to produce monthly scale carbon and water fluxes, and this daily scale assimilation is able to capture the seasonal and inter-annual variability of water and thus better reflect the short-term drought (<9 months) impacts on GPP. Many studies have been conducted on the relationship between GPP and drought [97; 98; 99; 100; 101; 102; 103; 104], and the majority of these focused on the outputs of TBMs' simulations or currently available remote sensing products. In this study, we employed multiple sources of observations, including satellite-derived soil moisture and in situ CO\({}_{2}\) concentrations, to efficiently constrain the parameters of the carbon and water cycle processes through data assimilation techniques. Based on the constrained simulated GPP, we then reliably revealed the differences in GPP response to drought duration at the regional scale.