## 1 Introduction  
In terrestrial ecosystems, vegetation controls the cycling of water and energy between the soil and the atmosphere and provides ecosystem services on which humans depend [1]. The structure and function of vegetation are influenced by climate factors (e.g., temperature, precipitation, and sunshine) and non-climate factors (vegetation itself and land use changes) [2; 3; 4]. To maintain the health and function of the ecosystem, we need to determine what factors affect vegetation growth [5; 6]. Many studies have focused on the vegetation dynamics, resulting from climate variation [7; 8]. For instance, temperature controls the high-latitude vegetation growth in the northern hemisphere [9]. Vegetation greening is primarily affected by solar radiation in tropical rainforest areas [10], while in arid and semiarid areas, the limiting factor of vegetation growth is precipitation [11; 12]. However, the response of vegetation to climate factors is complex and delayed [13]. For example, there is about a 3-month lag between temperature change and vegetation activity in China [14]. The lag effect of the same type of vegetation to different climate factors is different, and the lag effect of different types of vegetation to the same climate factors is also different [15]. In drought areas, the vegetation dynamic is most sensitive to climate factors in the current and previous month [16]. These observations suggest that vegetation dynamics may be influenced not only by the current climate conditions but also by earlier climate conditions. Therefore, the time-lag effects of climate should be considered when exploring the mechanism of vegetation-climate interaction. Besides climate factors, vegetation dynamics are also influenced by its past states [17; 18]. The biological cycles of vegetation consist of many successive growth periods that are tightly connected to the past and present [19], implying that the present growth state of plants will influence subsequent growth. This phenomenon has been defined as vegetation growth carryover [17]. For example, vegetation carryover has an important impact on the daily net carbon exchange in dry-land ecosystems [20], which allows plants to send greening signals by increasing carbon uptake, resulting in more substantial leaves and roots [1]. Such structural changes in vegetation may enhance its resistance to external disturbance unless the change in external environmental conditions exceeds the tolerance of plant growth [17]. The key question is how substantial the role of the carryover effect is, especially when compared with the immediate and lagged impacts of climate factors. Previous researchers analyzed the VGC effect on vegetation growth at hemispheric or global scales [17; 18]. However, processes that dominate at large scales are not necessarily dominant at small scales. Another important question to answer is how does the VGC affect the vegetation growth in ecologically fragile areas? Here, we focus on the Yellow River basin (YRB). The YRB spans the arid, semiarid, and semi-humid areas in China [4]. Droughts occur frequently in the YRB with increasing duration and intensity [21]. Moreover, problems, such as soil erosion and reduced biodiversity, are also prominent in the basin [22], which makes the YRB vulnerable to environmental change [23]. The upper and middle reaches of the YRB account for 91% of the total area of the YRB [4]. There are a large number of tributaries flowing into the main stream in the upper reaches of the Yellow River, which is the main source of runoff in the basin [24]. The loss of the soil and water is serious in the middle reaches, which is the main source area of sediment in the basin [25]. Therefore, our research area is the upper and middle reaches of the YRB, which is very important to the development of the lower reaches and the whole basin. Previous studies on vegetation dynamics in the upper and middle reaches of the YRB have focused on the growing season or annual time scale [4; 6; 21].