## 1 Introduction  
The CLP plays a critical and irreplaceable role in maintaining regional sustainable development and ensuring national food security [1; 2; 3]. With increasing food demand, it is urgent to explore CLP dynamics spatially and temporally at national and regional scales [4]. However, many studies have been conducted to research the spatial distribution of CLP [5; 6], such as land productivity potential assessment [7] and soil quality evaluation [8]. In the context of increased soil erosion and climate change [9], compared with spatial assessment studies, understanding the temporal trend and future sustainability of CLP has become the key to regional sustainable development [10; 11]. It is also essential for improving the level of CLP and developing cultivated land protection policies to control land and environmental degradation [12]. The research and development of temporal changes of CLP are limited, mainly for the follow reasons. The first is that it is difficult to find an indicator of CLP which characterizes the combined effect of various factors over many years [13]. The other reason is that the trend and amplitude of temporal change are difficult to quantify. Furthermore, how to determine future sustainability is also a problem [14]. Therefore, some related research had been carried out to address these problems. Cultivated land is a complex system that combines natural and human factors [15]. At present, studies on the indicators for monitoring and estimating CLP include the normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), GPP which reflects crop growth based on remote sensing (RS) [16; 17; 18]. These indicators have a high correlation with crop yield. As far as the comprehensiveness of these indicators is concerned, the effect of temperature and precipitation on crop growth are considered in the GPP calculation, which has a higher accuracy of simulated production [19]. The GPP is the capacity of the vegetation to capture carbon and energy by photosynthesis over a unit of time [20]. It is a comprehensive indicator formed by the interaction of various factors, such as climate, topography, soil, plant and microbial characteristics, disturbances and human influences. Hence, GPP is considered one of the major indicators in agricultural ecosystems for monitoring and assessing the variations in productivity [21; 22]. The models that estimate the GPP of terrestrial ecosystems have been grouped into three categories [23]: process-based models, regression statistical models and satellite-based drive models. The advantage of the satellite-based drive model compared to other models is that it uses simple parameters and large-scale inversion. RS technology, with long temporal series and high spatial coverage, has developed into an indispensable and useful method for monitoring land surface dynamics and changes [24]. VPM, a satellite-based drive model of GPP estimation, is developed from RS data and flux observations, with the advantage of simple input parameters and equal accuracy with process-based models. The most important merit is that the C\({}_{3}\) and C\({}_{4}\) crops of different photosynthesis processes are considered separately. Since 2004, model validation studies have been carried out in 10 types of ecosystems at 21 field sites [25]. The VPM was used as an important basis for GPP time trend extraction based on RS data [26]. The studies of monitoring and analyzing trend changes with long-term RS data have mainly focused on the dynamic monitoring of inter-annual vegetation [27]. Time-series statistical methods, such as Theil-Sen median trend analysis and MK test, T-test, linear regression analysis, Cusum test, Pearson correlation coefficient, Spearman's rho test, Wald-Wolfowitz test and the Hurst exponent [28], were used to extract dynamic information.