## 1 Introduction  
The increase rate of CO2 in the 20 th century was faster than any stages during the past 22000 years [1]. According to observed data from Mauna Loa, Hawaii, USA, the mean CO2 concentration reached 408.3 ppm in 2018, which was an increase of 29% compared to the observed value (316.0 ppm) in 1959 and an increase of 45% compared to the value (277 ppm) in the pre-industrial period. Global CO2 emissions are still increasing sharply. The cumulative CO2 emissions from anthropogenic sourcesreached \(615\pm 80\) Pg C between 1870 and 2017; of these emissions, \(425\pm 20\) Pg C was from fossil fuel and industrial processes and \(190\pm 75\) Pg C was from deforestation and other land use changes [2]. Approximately half of these CO\({}_{2}\) emissions remained in the atmosphere over the long term (\(250\pm 5\) Pg C, \(41\%\)); others were sequestered by terrestrial ecosystems (\(190\pm 50\) Pg C, \(31\%\)) and ocean ecosystems (\(150\pm 20\) Pg C, \(4\%\)), while the fate of \(4\%\) (\(25\) Pg C) of CO\({}_{2}\) emissions is unknown. The retention of CO\({}_{2}\) in the atmosphere causes an increase in the CO\({}_{2}\) concentration and has become one of the main drivers for global warming. Net primary productivity (NPP) is the net carbon fixed by plants through photosynthesis. It quantifies the conversion of atmospheric CO\({}_{2}\) into plant biomass, and is identified as a key variable for sustainability [3; 4], biodiversity [5] and environmental degradation (e.g., desertification, deforestation) [6; 7]. In recent years, carbon sequestration in terrestrial ecosystem has an uptrend and great interannual variability [8; 9; 10]. However, there were large uncertainties in the current estimates of terrestrial carbon sinks due to the complexity and diversity of terrestrial ecosystems. The terrestrial carbon sink is the residual of NPP minus heterotrophic respiration. Therefore, accurate estimation of NPP is the prerequisite for constraining the uncertainties in estimated terrestrial carbon sinks. China covers a vast land area, i.e., 9.6 million km\({}^{2}\), and the regional climate is dominated by Asian monsoon, with diverse climate types ranging from tropical to cold-temperate and from humid to extremely dry [11]. China has experienced explosive economic growth in recent decades; this growth has been detrimental to the environment through land-use change, consumption of resources, and pollution. The extensive economy led to the largest annual CO\({}_{2}\) emissions in the world, and a series of policies on climate change and CO\({}_{2}\) emissions, such as adjustments in the energy structure, improvements in the energy efficiency, and reforestation [12], have been implemented to achieve global emission-reduction targets. Therefore, China is one of the most critical and sensitive regions in the global climate system, and studies of NPP and its dynamics in China are helpful for improving our understanding of the carbon balance at both the regional and global scales. A number of studies have been conducted to examine the magnitude and pattern of NPP in China with statistical model [13], light use efficiency models [14; 15; 16; 17; 18], and process-based biogeochemical models [19; 20; 21; 22; 23; 24; 25]. These estimates of total NPP in China range from 1.44 to 4.64 Pg C yr\({}^{-1}\), owing to differences in model structure, parameters, and input data. Large uncertainties were still present in the estimation of the total NPP in China. Total NPP in China presented increasing trend in recent years [11; 19; 24; 26], where the total NPP changed obviously, and the reasons for this are still unclear. In addition, a few studies have been conducted to investigate the response of terrestrial NPP to different future scenarios of climate change and increasing CO\({}_{2}\) in China. Therefore, the assessment of long-term trends in the magnitude and patterns of terrestrial NPP in China was one of the objectives of this study. Climatic extremes, such as droughts and heat waves, have significant impacts on NPP.