## 1 Introduction  
Soil moisture, a critical ecological factor, is essential for maintaining ecosystem stability [1, 2]. It directly influences vegetation growth and productivity and indirectly affects ecosystem functions and stability by modulating soil microbial activity, nutrient cycling, and soil physical properties [3]. Global warming and altered precipitation patterns have significantly impacted the spatial and temporal distribution and availability of soil moisture, thereby increasing ecosystem vulnerability [4]. Thus, understanding how ecosystem stability responds to changes in soil moisture is crucial for predicting future climate change impacts on ecosystems [3].  
Ecosystem stability is defined as the ability of an ecosystem to maintain its structure and function relatively stably when facing external disturbances such as climate change and human activities [5]. It reflects the capacity of an ecosystem to maintain its own balance and resilience in dynamic changes and is an important indicator for measuring the health and sustainability of ecosystems [6]. The Enhanced Vegetation Index (EVI) and Gross Primary Productivity (GPP) are commonly used indicators to characterize ecosystem stability. EVI reflects the growth status and cover of vegetation through remote sensing data and can intuitively show the response of vegetation to environmental changes [7]. GPP directly reflects the photosynthetic efficiency and productivity level of vegetation and is the basis for energy flow and material cycling in ecosystems [8]. These two indicators, from the perspectives of vegetation growth and productivity, can effectively reflect the stability and health status of ecosystems and are, therefore, widely used in ecosystem stability research. However, most current studies focus on a single indicator of EVI or GPP, while relatively few studies integrate the two for comprehensive research.  
China's vast territory encompasses a wide array of ecosystem types, and soil moisture conditions exhibit substantial spatial variability across different regions, which has a profound impact on ecosystem stability. Exploring the effects of soil moisture at varying depths on the Enhanced Vegetation Index (EVI) and Gross Primary Productivity (GPP) could potentially uncover the underlying mechanisms linking soil moisture to ecosystem stability. Previous studies have extensively investigated the impact of soil moisture on ecosystem stability in specific regions or particular ecosystem types [9, 10, 11, 12, 13]. However, these studies have predominantly concentrated on specific regions or particular ecosystem types, and there is a lack of a comprehensive investigation into the diverse ecosystem types in China under a wide range of soil moisture conditions at various depths. Moreover, the majority of studies have focused on the impact of shallow soil moisture on ecosystem stability, with limited exploration into the influence mechanisms of the vertical distribution of soil moisture on ecosystem stability.  
To address these knowledge gaps, this study investigates the responses of key indicators of ecosystem stability in China--specifically, the Enhanced Vegetation Index (EVI) and Gross Primary Productivity (GPP)--to soil moisture at four depths (0-50 cm, 50-100 cm, 100-150 cm, and 150-200 cm). The research objectives include (1) examining the spatiotemporal variation characteristics of EVI and GPP across different climatic zones and land cover types; (2) analyzing the spatial auto-correlation characteristics of EVI and GPP using global and local Moran's I; (3) investigating the spatiotemporal variation characteristics of soil moisture at different depths across different climatic zones and land cover types; and (4) conducting correlation analyses between EVI, GPP, and soil moisture at different depths across different climatic zones and land cover types. These research objectives will enhanceour understanding of the mechanisms by which soil moisture affects ecosystem functions in China.