## 1 Introduction
However, this approach of diagnosing health by detecting disturbance events only focuses on a single dimension (short-term changes) of the ecosystem and ignores long-term trend changes in vegetation (such as gradual changes in vegetation growth that are due to slow acting climate and land degradation) [27]; therefore, it does not provide a comprehensive evaluation analysis of ecosystem health. Long-term trend analysis is considered an effective way to understand vegetation dynamics. A number of studies use trend detection techniques [28; 29; 30] to explore the long-term trend changes of vegetation to reveal the ecosystem health [31]. However, some time series analysis only consider monotonic trends, assuming that vegetation trends maintain their rate of change throughout the study period [32]. When using simple linear models to characterize vegetation trends, important breakpoint and potential trend reversals can be masked (i.e., browning in greening trends of NDVI time series). Therefore, some segmented linear trend analysis methods have been proposed which can detect significant breakpoint and multiple trend types to obtain richer vegetation health dynamic information [32; 33; 34]. In conclusion, the segmented linear trend analysis can determine whether the health status of vegetation is improved or degraded, and the causes of change can be analyzed according to the information of breakpoints. In addition to change detection algorithms, health detection indicators are also very important. There are different challenges in vegetation monitoring in arid and semi-arid regions compared with those in suitable temperature regions: low signal-to-noise ratio of vegetation and high background reflectance of soil. GPP can directly characterize vegetation photosynthesis and is not affected by vegetation coverage and soil background reflectivity. On the other hand, vegetation in arid and semi-arid areas is susceptible to climatic conditions, and water is the main constraint factor for plant productivity. Underdrought stress, vegetation and soil functions decline, but vegetation may still appear a healthy green in early stages [35]. Ec can represent the response of vegetation to water conditions and is an important health indicator in semi-arid regions. At the same time, as important parameters of ecosystem carbon and water cycle, GPP and Ec play an important role in regional and global carbon and water balance as well as energy flow. Considering that previous studies have not evaluated the ecosystem health of the CLP in multiple dimensions, more comprehensive and accurate ecological health evaluation results may be lacking. This study aims to: (1) propose a multi-dimensional (overall dimension and local dimension) ecosystem health assessment method based on BFAST and BFAST01 algorithms; (2) extract health assessment indexes according to short-term and long-term changes of ecological function-oriented metrics (GPP and Ec) and characterize the spatiotemporal variations of the CLP ecosystem health. The study should improve our understanding of the health of the CLP under ecological restoration projects and provide a new theory and method for regional health evaluation.