## 1 Introduction  
Gross Primary Productivity (GPP) of a terrestrial ecosystem refers to the amounts of organic compounds accumulated by green vegetations through assimilating carbon dioxide from the atmosphere via photosynthesis and a series of internal physiological processes [1, 2, 3]. GPP can partially offset anthropogenic CO\({}_{2}\) emissions [3, 4, 5, 6], so that vegetation plays a critical role in the global carbon balance. Statically, vegetation can store about 500 Gt of carbon, which accounts for 20% of all carbon in the terrestrial biosphere [7]. To date, studies [8, 9], using leaf area index (LAI) as a reference, found a significant global vegetation greening; however, the question of whether the vegetation productivity and ecosystem function varies under the obvious vegetation greening has yet to be unraveled. Compared with widely discussed leaf area (LAI or some vegetation indexes)variation, the variation of vegetation productivity is of more practical significance, because it can not only illustrate the variation of vegetation growth but also reflect vegetation's feedback to the carbon cycle. Satellite-based vegetation productivity inversion generally employ Production Efficiency Models (PEMs), which are based on the [PERSON]'s light use efficiency (LUE) theory [10; 11]. There are a lot of different GPP products for a great amount of satellite datasets existing nowadays, e.g., using the SEVIRI/MSG satellite products to derive daily GPP [12]. Till now, the Moderate Resolution Imaging Spectroradiometer (MODIS) GPP product (MOD17) [13] is widely used [14; 15]; however, the MOD17 can only provide GPP products since 2000, which is not long enough for analyzing the spatiotemporal interaction between vegetation and ecosystem. The Global LAnd Surface Satellite (GLASS) program provides GPP product covering with the longest time period (1982-2015), and it has been verified at 54 eddy covariance sites covering six major terrestrial biomes: deciduous broadleaf forests, mixed forests, evergreen needleleaf forests, grasslands, savannas, and croplands [16; 17], providing a reliable and useful data source for the evaluation of terrestrial ecosystems carbon storage capacity. The Northeast China (NEC) is a crucial zone in regional, even global carbon balance because there are abundant vegetation resources: there distributes one-third of forests in China, with boreal forests distributing in the north and southeast NEC, moreover, the boreal forests in the NEC are characterized with high carbon density, high carbon storage, and slow decomposition [18] and are revealed as an important carbon sink in China with 3.44-4.63 Pg carbon storage [19]. Additionally, the NEC is one of the most important agricultural bases in China, providing about one-third of the national grain over the last three decades [20]. What's more, as a transition region from middle to high latitude as well as one of the most climate-sensitive areas in China, the average air temperature in the NEC has increased by 0.38 \({}^{\circ}\)C per decade over the past five decades [21], increasing more significantly since the 1980s [22]. This kind of warming has greatly changed vegetation growth in national or global scale due to response of plant respiration, photosynthesis, and evapotranspiration to climate change [23; 24; 25; 26]. For instance, [PERSON] et al. [8] found that rising temperatures have resulted in greening of the high latitudes and the Tibetan Plateau, while [PERSON] et al. [27] revealed a turning point in late 1990s of global vegetation productivity from increasing to decreasing due to a sharp increase in VPD (Vapor Pressure Deficit). All in all, under the circumstance of obvious climate change, the NEC is a representative place for analyzing regional feedback of vegetation productivity to global warming. A majority of studies focusing on vegetation dynamics in the NEC use LAI or vegetation index (e.g., NDVI) as indicators [28; 29; 30; 31; 32; 33].