## 1 Introduction  
Northern Shaanxi is located in the north center of the Loess Plateau, with a semiarid to subhumid climate and a vulnerable ecosystem. This region is sensitive to global changes and was heavily affected by human activities during past decades. Due to overcultivation of the sloping lands, the region suffered from serious soil erosion. To alleviate this land degradation problem, the Chinese government implemented the Grain for Green (GFG) program in 1999 by supplying grain or money as a subsidy to help farmers convert sloping farmlands into forestland/grassland, plant trees on degraded land, and reduce grazing on grassland. Many studies indicated that this program has stimulated a positive change in vegetation [1, 2, 3, 4], land use / land cover [5], soil erosion [6, 7], and carbon sequestration [8, 9]. This program has also yielded obvious changes in crop production [10, 11] and farmer household livehoods [12, 13]. The impact of GFG has had strong support in Northern Shaanxi [14]. One of the most important results of GFG is the promotion of vegetation, which can improve soil erosion in this area. Thus, in order to determine the response of the ecosystem to GFG, it is critical to find the changes in vegetation, including the quantity and, especially, the quality. Gross primary productivity (GPP) is the rate of carbon fixation or gross assimilation per unit of ground surface area [15] and is a measure of photosynthesis representing the primary conduit of carbon flux from the atmosphere to the land [16]. GPP changes can represent the activity of the vegetation to some extent, so such changes provide a good indicator to determine variation in vegetation quality.  
With progress in remote sensing technology, it has become common practice to utilize imagery data to estimate GPP at large scales [17]. Many models have been developed for this purpose, including CASA [18], GLO-PEM [19], C-Fix [20], MODIS-PSN [21], VPM [22], EC-LUE [23], TG [24], and VI [25]. Of these models, the eco-process model CASA is more widely used than others but remains constrained by difficulties in obtaining data for the complex driving variables [26; 27]. In contrast, the vegetation photosynthesis model (VPM) developed by [PERSON] et al. [22] has the lowest requirements for observational data. This model uses an improved EVI (enhanced vegetation index) to estimate the absorbed fraction of photosynthetically active radiation via green (photosynthetically active) vegetation and LSWI (land surface water index) to estimate water stress on light use efficiency. This model has been applied to estimate the GPPs of various vegetation types, including forests, grasslands, and maize crops and has been validated using CO\({}_{2}\) flux tower data [28; 29; 30] in several areas, including northern China.  
The aim of this study is to quantitatively identify the magnitude of GPP changes and GFG contributions, taking the hilly region of Northern Shaanxi as a case area. With this aim, the annual GPP was first estimated for 2000 to 2012 using the VPM model with MODIS imagery and climate data; then, the change trend and magnitude were detected using a Mann-Kendall test and Sen's slope estimator. Finally, the contribution of GFG to GPP variation was determined using linear regressions. In this way, we determined the response of the ecosystem to GFG in Northern Shaanxi.