## 1 Introduction  
CO\({}_{2}\) emissions have kept increasing due to large-scale use of fossil fuels and have attracted global attention [1]; and recent human-induced emissions of greenhouse gases are reaching the highest levels in history [2]. Increasing human-induced CO\({}_{2}\) emissions may affect climate change and limit the sustainable development of human society and economy [3]. In order to study the trend and affecting factors of CO\({}_{2}\) emissions in different production sectors and to promote the green economic development, many researchers have used the evaluation methods of carbon footprint (CF) in different research fields [4; 5; 6]. China is a country with a long history of agricultural civilization. Because of the population increase, economic development, improvement of living standards, and limitation of agricultural land resources, the modern agricultural production mainly depends on agrochemicals and fossil fuels both in the economically developed and underdeveloped regions in China [7]. In order to combat serious ecological degradation in its economically underdeveloped regions, China has launched a few key ecological and agricultural policies or projects. Large-scale policies or projects have strongly affected the agrochemical and energy inputs. Previous studies have paid more attention to human-induced CO\({}_{2}\) emissions for agricultural production, their potential risks to the environment, and ways of reducing agricultural carbon emission by using CF evaluation in economically developed regions [8; 9; 10; 11]; yet, relatively few studies have focused on the change in CF for agricultural production in its ecologically vulnerable and economically underdeveloped regions, which have also been strongly affected by the rapid development of the economy in China. Human-induced CO\({}_{2}\) emissions for agricultural production and their potential risks to the environment are closely related to the area and location of agricultural land and the agrochemical and energy inputs. As a type of highly intensive agricultural land, cropland sometimes decreases due to the change of cropland into construction land for regional economic development and the change of low quality cropland to forest or grassland for ecological security, but sometimes it increases because of the change of grassland or forest to cropland for food security in the ecologically vulnerable regions in China [12; 13; 14]. The Chinese government always tries to keep a balance between decreasing the ecological degradation and increasing the agricultural efficiency. In order to reduce the adverse effects of ecological and agricultural policies on agricultural production and to support and benefit farmers, the Chinese government has launched some preferential agricultural policies after the Grain for Green Policy (GFGP) [15]. For example, focusing on \"agriculture, rural areas, and farmers\", 12 consecutive \"Central First Documents\" were released from 2004 to 2015 [16]. The implementation of the mentioned agricultural policies has effectively changed the agricultural land use structure and input structure in China, especially in the GFGP implementation area since the early 1990s. Thus, it is necessary to study the total carbon footprint (TCF) trend and its potential risks to the environment in its ecologically vulnerable and economically underdeveloped regions. The above-mentioned ecologically vulnerable and economically underdeveloped regions are mainly located in western China, with physical geographical characteristics of the obvious change in altitude, more mountain and plateau landscapes, great daily or seasonal range of temperature, and frequently occurring droughts, floods, and strong storms [17]. The GFGP has mainly launched in western China, which mainly covers five topographic regions. Some studies have paid attention to the CO\({}_{2}\) emissions for agricultural production and their potential risks to the environment in northwest China [18], Loess Plateau [19], Sichuan Basin [20], and Yunnan-Guizhou Plateau [21].