# Satellite-Observed Global Terrestrial Vegetation Production in Response to Water Availability
## 1 Introduction  
The Intergovernmental Panel on Climate Change (IPCC) report shows that the world will continue to warm in the 21 st century [1]. This indicates that as the future temperature rises, the occurrence and frequency of extreme weather and climate, such as heatwaves and droughts, will increase rapidly [2]. This trend and its associated adverse effects on natural and social ecosystems are expected to increase further [3]. Terrestrial ecosystems' gross primary productivity (GPP) is the largest component of global terrestrial carbon flux, and slight fluctuations in GPP have a significant influence on atmospheric CO\({}_{2}\) concentration [4]. On a global scale, particularly in arid and semiarid regions, water stress is the primary environmental factor that limits terrestrial ecosystems' productivity [5]. Hence, studying drought's effects on their productivity has become an important priority in global change research. The terrestrial ecosystem's productivity characterizes its quality, it is the key to controlling the ecosystem's carbon, water, energy and nutrient cycles, and plays a decisive role in regulating its function and controlling its carbon source and sink [6]. At the same time, ecosystem productivity is also the basis of a variety of ecosystem services [7] and is the source of food, fiber, wood, livestock grains and biofuels in human society [8]. As the main outcome and important manifestation of global climate change, drought not only affects photosynthesis and ecosystem productivity directly [9], but it can also affect terrestrial ecosystem productivity in directly by changing the intensity and frequency of other forms of disturbance, such as increasing the frequency and intensity of fires, plant mortality and the occurrence of pests and diseases [10]. In recent years, many studies have investigated drought's effects on terrestrial ecosystems' productivity at different spatio-temporal scales based on long-term observations from ecological research sites, field experiments, eddy covariance measurements, large-scale satellite measurements and model simulations [11; 12; 13]. Satellites data used commonly to evaluate vegetation productivity include primarily the Moderate Resolution Imaging Spectroradiometer-Fraction of Photosynthetically Active Radiation (MODIS-FPAR) and the Global Inventory Modeling and Mapping Studies-Fraction of Photosynthetically Active Radiation (AVHRR GIMMS-FPAR), remotely-sensed data for atmosphere state, MODIS Enhanced Vegetation Index, leaf area index, spatially distributed CO\({}_{2}\) concentrations, and canopy information. For example, [PERSON] et al. [11] found that the drought stress in Europe in summer 2003 caused the reduction of ecosystem productivity by jointing flux tower, remote sensing (including MODIS and AVHRR-GIMMS FPAR) and modelling datasets. [PERSON] et al. [14] emphasized that the drought in Southwestern China in spring 2010 reduced primary productivity by using primary productivity products derived from MODIS. [PERSON] et al. [15] used four remote sensing data-driven models and demonstrated that drought's effects on terrestrial primary production were underestimated. Previous studies have shown that different vegetation types and environmental conditions (such as climate and soil factors) largely determine biological communities' resistance and ability to recover from drought stress [16]. Although there is increasing recognition of drought's adverse effects on terrestrial vegetation productivity, few studies have focused on the seasonal dynamics in global productivity in response to drought across various climate zones and land biomes. Moreover, studies of drought's lag effect on terrestrial vegetation productivity and vegetation's responses to drought at various time-scales on a global scale are scare. The Standardized Precipitation Evaportranspiration Index (SPEI) quantifies different drought types based on the water balance, and is used widely on global and regional scales because of its multiple time scales and spatial comparability [17].