## 1 Introduction  
Droughts are among the most complex and costly natural disasters in the world. They are usually divided into meteorological, agricultural, hydrological, and economic droughts [1]. With global climate change and increased human activities, the frequent occurrence of droughs has become a serious challenge [2; 3; 4; 5]. Under future climate change scenarios, the severity of droughs is expected to increase [6]. Since droughs profoundly impact the economy, society, ecology, and environment, they increasingly attract the attention of researchers in different fields. China has suffered a growing number of drought events, including extreme drought episodes, since the 1990s [7; 8]. Droughs in China are highly complex, since they are affected by many factors, such as climate, topography, and human activities [9]. The severity of droughs in the northern region of the country (drought-prone area) has intensified, while their frequency in the southern region is increasing [10; 11]. The impacts of droughs on agriculture and ecology threaten food and ecological security in China, the most populous country in the world. Thus, assessing the temporal and spatial characteristics of droughs, as well as understanding their trends and behaviors, is a crucial task to provide a scientific basis for developing mitigation and adaptation measures to lessen the impact of drought disasters under a changing climate. Drought indices are among the most popular methods for monitoring and evaluating droughs [12]. Many drought indices have been proposed in the literature, but the most commonly used drought indices are the standardized precipitation index (SPI) [13], Palmer drought severity index (PDSI) [14], and standardized precipitation evapotranspiration index (SPEI) [3; 15]. SPI is a widely used drought index using a range of timescales that considers precipitation and ignores other climatic factors, such as temperature and evapotranspiration. On the other hand, PDSI combines the effects of precipitation and evapotranspiration, but with the handicap of having a fixed temporal scale. [PERSON] et al. [15] introduced a multi-scale index based on SPI, with the inclusion of potential evapotranspiration--the SPEI. Using precipitation and evapotranspiration, SPEI not only retains PDSI's evapotranspiration sensitivity to temperature, but also includes SPI's calculation simplicity and suitability for multi-scale and multi-space comparison. Because this index is suitable for monitoring drought characteristics under climate change, it has been widely used worldwide. Moreover, SPEI may be used as a tool to assess the impacts of droughs on different systems (hydroology, agriculture, and ecology) [16]. Vapor pressure deficit (VPD) is the difference between the saturation and actual vapor pressure, and is an important indicator of the degree of air dryness considered as a key factor affecting the physiological function of vegetation [17]. High VPD is one of the main causes of vegetation drought and may inhibit photosynthesis in vegetation [18]. Vegetation is an essential component of terrestrial ecosystems, reflecting an ecosystem's production and carbon sink capacities. However, it is sensitive to climate change, and its growth is strongly affected by droughs [19; 20]. Drought is a vital factor leading to the decline of vegetation productivity [21; 22; 23]. However, the response of different ecosystems to drought varies [24]. Thus, assessing the impact of drought on vegetation has become a crucial scientific issue [25]. Many studies use gross primary productivity (GPP), net primary productivity (NPP), and the normalized difference vegetation index (NDVI) to characterize ecosystem productivity and analyze the productivity response to climate change [26; 27; 28]. Among these, GPP is the number of photosynthetic products, or total organic carbon, fixed by organisms through photosynthesis in a unit of time. It is the largest component and foundation of the carbon cycle of an ecosystem [29].