## 1 Introduction  
Irregular changes of environmental factors caused by climate change have significant impacts on the change of surface vegetation growth, resulting in erratic carbon exchange between terrestrial ecosystem and the atmosphere [1]. Grasslands are a potentially important sink for carbon in the terrestrial biosphere because of the high levels of carbon accrual and sequestration below ground in the soil, and up to 90% of grassland biomass is below ground. The levels of soil carbon are higher in grasslands than in forests, agroecosystems, or other ecosystems [2, 3]. Carbon cycling within grasslands is sensitive to climatic factors [4] and vulnerable to climate change [5, 6, 7]. As climate change intensifies, it is crucial to understand the response of vegetation greenness or carbon exchange within grassland to environment factors' dynamics. Normally, the carbon exchange between terrestrial ecosystem and the atmosphere is quantified by gross primary productivity (GPP) and ecosystem respiration (RE) [8, 9]. The solar-induced chlorophyll fluorescence (SIF), which is an optical signal emitted in the spectral range 650-850 nm from the chlorophyll a molecule in vegetation [10], demonstrates a tight relationship with photosynthesis at the ecosystem scale through ground-based and airborne hyperspectral measurements [11; 12; 13]. The global SIF observations from satellites have become available in recent years, which has led to tremendous developments in monitoring terrestrial photosynthesis and ecosystem productivity (i.e., GPP) at various spatial and temporal scales, which caused SIF to be increasingly used as a proxy for GPP on large scales [14; 15; 16]. Additionally, SIF was utilized to characterize vegetation greenness [17], determine the vegetation growing season [18], estimate evapotranspiration [19], and the like. Climatic factors, such as precipitation, temperature, solar radiation, transpiration, evaporation, soil moisture, etc., influence land-atmosphere carbon exchange through their impact on vegetation growth and greenness. Precipitation is the primary connection in the water cycle that provides for the delivery of atmospheric water to the Earth, and it controls ecosystem dynamics and drives biological processes [20; 21]. The appropriate temperature and solar radiation, which are usually used as input variables in the calculation of some indices, are the elements that ensure the normal growth of vegetation [22]. The vapor pressure deficit (VPD) is calculated from the near-surface temperature and relative humidity, which can characterize the water stress in the air [23; 24]. The soil moisture provides available water to vegetation roots and represents the water stress from the soil [25; 26]. Evaptranspiration is the sum of transpiration from vegetation and the evaporation from the soil and land surface, and the important connection in the water cycle between the atmosphere and the land [27; 28; 29]. A clear understanding of the responses of vegetation productivity or ecosystem carbon uptake to the above climatic factors is helpful to extreme events monitoring, mechanism model establishment, etc. Previous studies evaluated the vegetation response to changes in air temperature [30; 31], precipitation [32; 33; 34], and solar radiation [35; 36], but fewer climatic variables were involved. However, since the response periods of vegetation to different climatic factors are diverse, it is also necessary to concurrently consider the relationships between grasslands and multiple climatic factors [37]. Here, we used SIF, precipitation (P), VPD, evaporative stress (ES), and root-zone soil moisture (RSM) derived from remote sensing, reanalysis, and assimilation datasets, to explore the responses of vegetation growth and productivity to climatic factors over the Eurasian Steppe.