## 1 Introduction  
In recent decades, driven by intensive human activity and climate change, the function of terrestrial ecosystem has been disturbed and continuously degraded on regional and global scales. The increasing levels of atmospheric CO\({}_{2}\) concentrations and climate change have highlighted the need for a better understanding of terrestrial carbon cycling and its responses to climate change. Gross primary production (GPP) represents the capacity of the plants in an ecosystem to capture energy and carbon [1]. Net Primary Productivity (NPP) is defined as the amount of atmospheric carbon that is captured by plantsand transformed into biomass [2]. The GPP is the sum of NPP and autotrophic respiration (Ra), and Ra plus heterotrophic respiration (Rh) comprises ecosystem respiration. GPP, NPP and Ra are the most important and highly related constituents of carbon cycling. The carbon fixed by photosynthesis is allocated to a variety of usages in plants, including growth and maintenance respirations and biomass accumulation [3]. About 50-70% of the carbon fixation is returned to the environment through Ra [4; 5]. Carbon allocation among plant processes (e.g., respiration, biomass production) and organs (e.g., leaves, stem) is a key process in the carbon cycle because it determines the residence time and location of carbon in the ecosystem [6; 7]. For example, the residence times of the carbon used for maintenance respiration and the carbon allocated to the structural biomass of organs are drastically different, ranging from a few hours to a few years [6]. Therefore, the allocation process of carbon is highly relevant to understanding ecosystem carbon stock and carbon cycles [6]. Carbon use efficiency (CUE) is defined as the ratio of NPP to GPP, which indicates the ecosystem capacity in transferring CO\({}_{2}\) into biomass and carbon sequestration [8]. CUE is an important functional parameter of ecosystems and can be used for comparing carbon cycle differences in various ecosystems [9]. The index is intuitive and easy to compare between different vegetation types, and to apply to different time scales [7]. A higher CUE indicates a higher growth transfer per unit of carbon sequestration. In practice, GPP usually represents the total amount of carbon captured through photosynthesis, and NPP is the net carbon stored in plant after the reduction of GPP through by plant respiration [1]. CUE is also a measure of how GPP is partitioned into NPP and Ra [7]. Less Ra may result in larger carbon reserve accumulation. Hence, CUE is related to photosynthetic process, and it is also regarded as an important indicator for characterizing ecosystem functions. How efficiently an ecosystem is able to convert GPP into plant and soil storage greatly determines the carbon sequestration of terrestrial ecosystems, so CUE changes strongly affect ecosystem carbon budgets [10]. Quantitative analysis of spatial-temporal changes of CUE and its influencing factors will help better understand the effects of climate change on carbon processes of ecosystems [11]. Satellite remote sensing provides critical information for investigating large-scale and long-term variability of ecosystem CUE. [PERSON] et al. [12] demonstrated that CUE of different vegetation differed greatly from the south temperate to the tropic ecoregions based on a global forest C-flux database, and found that the spatial patterns of forest annual Ra at the global scale were largely controlled by temperature. [PERSON] et al. [1] reported that CUE exhibited a pattern depending on the climatic characteristics-based upon Moderate-Resolution Imaging Spectroradiometer (MODIS)-derived NPP and GPP data. [PERSON] et al. [13] investigated spatial variations in CUE from different models and analyzed the responses of CUE to precipitation and temperature. [PERSON] et al. [3] established a global database of site-year CUE based on field observations for five ecosystem types and diagnosed the spatial variability of CUE with climate and other environmental factors (e.g., soil variables).