# Satellite-Observed Global Terrestrial Vegetation Production in Response to Water Availability
## 1 Introduction
Therefore, determining the corresponding time scale when GPP and SPEI have the highest correlation based upon different time scales is of great significance in understanding the variations in different terrestrial ecosystems' productivity depending upon drought resistance. In addition, we give greater attention here to the way to quantify the probability of varying degrees of damage to vegetation productivity under predictable drought scenarios. Copulas can be used to couple multiple variables and construct their joint probability distribution by considering their correlations [18], which can derive the vegetation productivity loss distributions conditioned on any drought scenario. For example, [PERSON] et al. [19] estimated the probability of drought in agricultural production in Australia based on a copula model, while [PERSON] et al. [20] constructed a bivariate probabilistic framework to assess vegetation vulnerability and map drought-prone ecosystems in China's Loess Plateau. Given ecosystem productivity's key role in affecting the global carbon budget and the supply of ecosystem services, in the context of global warming, the rapid increase in atmospheric carbon dioxide concentration, and increasing human food production and resource demand, estimating ecosystem productivity accurately is important to assess drought's effects on terrestrial ecosystems precisely [21]. Three main methods are used to estimate ecosystems' productivity at the regional and global scales--remote sensing-based light-use efficiency (LUE) models [22], machine learning algorithms [23], and process -based physiological and ecological models [24]. Remote sensing observations can provide information continuously on land surface features that affect ecosystem productivity, such as ecosystem structure, vegetation phenology, biomass, soil moisture, and land cover over a large area. The LUE model relies on remote sensing observation data to estimate ecosystem productivity through the utilization rate of photosynthetically active radiation in the ecosystem [25]. We gave special attention to determining water stress and produced a data set of monthly LUE GPPs at the global scale based on various representations of water stress: Water stress based on vapor-pressure deficit, humidity deficit and root-zone soil-water content separately. Our study had two primary objectives. The first was to determine the seasonal dynamics of global vegetation productivity's response to drought across various climate zones and land biomes, and the second was to quantify the probability of varying degrees of damage to vegetation productivity under predictable drought scenarios. First, we used a LUE model to produce a dataset of global monthly satellite-observed GPPs, which are designed primarily to determinate water stress. Second, we explored vegetation productivity's spatio-temporal evolution of dependence and response time to water availability by correlating monthly GPP series with the multiple timescale SPEIs (1- to 24-months). Finally, we developed an optimal bivariate probabilistic model in each pixel of the globe using the copula method, which was used to derive the vegetation productivity loss probabilities under different drought scenarios.