## 1 Introduction  
Carbon use efficiency (CUE) is a pivotal metric, defined as the ratio of net primary production (NPP, g C m\({}^{-1}\) yr\({}^{-1}\)) to gross primary production (GPP, g C m\({}^{-1}\) yr\({}^{-1}\)). It exemplifies the capacity of plants to transform atmospheric carbon [1; 2; 3; 4]. The global carbon cycle remains of paramount concern [5; 6], with vegetation CUE playing a pivotal role in determining the rates of carbon cycling and turnover in terrestrial ecosystems [7; 8]. Nevertheless, the quantitative assessment of the impact of climate change and anthropogenic activities on vegetation CUE is fraught with difficulties [9; 10; 11]. Ecological engineering represents a pivotal methodology for the restoration of regional ecological functions through human intervention. It is, therefore, crucial to quantify the responses of vegetation CUE to ecological engineering and climate-driven factors in order to enhance our understanding of carbon sequestration dynamics. In previous studies, methodological challenges in calculating vegetation CUE have often led to it being perceived as a constant parameter, obscuring inherent variation [2; 12; 13; 14; 15; 16]. However, as research has progressed, a growing number of factors have been identified that influence the CUE of vegetation. There is evidence that vegetation CUE is influenced by a variety of factors, including climatic conditions, geographic location, altitude, vegetation type, CO\({}_{2}\) concentration, soil fertility, and stand age [4; 16; 17; 18; 19; 20; 21; 22]. At present, research on CUE has produced extensive findings at both regional and global scales. However, studies specifically addressing CUE at the local scale remain limited [21]. Previous research has mainly examined the spatiotemporal patterns of CUE at regional or global scales [23; 24], focusing on the driving factors of precipitation and temperature. Few studies have examined the effects of ecosystem types and water stress on CUE [22]. Globally, CUE shows a pronounced latitudinal gradient, with higher values at higher latitudes. It shows a non-linear decrease with increasing temperature but is relatively stable with increasing precipitation [25]. There is also a strong latitudinal gradient in CUE in China. However, there are slight variations in the response of CUE to temperature and precipitation, with both factors decreasing CUE as they increase [22]. In particular, the response of CUE to temperature and precipitation in Ningxia Province in northern China shows some deviations from global observations [26]. Evapotranspiration is crucial to the life activities of vegetation, regulating both photosynthesis and autotrophic respiration [27; 28], and is, therefore, a key factor influencing CUE. In China, ecological engineering included reforestation, farmland reclamation, and water conservation. These measures were aimed at halting ecological degradation. They also aimed to improve regional vegetation conditions and restore the ecological environment [29]. Previous research has often overlooked the effects of evapotranspiration and ecological engineering on CUE, resulting in significant gaps in our understanding of this issue. To address these gaps, dynamic evapotranspiration data were integrated, and the effects of ecological engineering were considered. This integration was essential for a more comprehensive understanding of the factors driving changes in vegetation CUE under varying environmental conditions. The Three Rivers Source region encompasses the headquarters of the Yangtze, Yellow, and Lancang Rivers. It is located in the heartland of the Qinghai-Tibet Plateau. This region is often referred to as the \"Water Tower of China\" [29]. Since 1978, the Three Rivers Source region has experienced significant ecological degradation and a drastic decline in ecosystem services. These changes have largely been attributed to intensified human activities and unsustainable resource exploitation. Recognizing this ecological crisis, various stakeholders have emphasized its importance.