## 1 Introduction  
Climate change is an important factor affecting forest growth. Therefore, approaching the impacts of climate change on forest ecosystems is of great significance to ameliorate degraded land and support forestry development. Gross primary productivity (GPP) refers to the amount of organic carbon fixed by organisms, mainly by green plants, through photosynthesis in a unit of time, also known as total primary productivity [1; 2; 3; 4]. The GPP determines the initial amounts of material and energy entering the terrestrial ecosystem [5; 6; 7; 8]. Climate is the main factor that determines the distribution of forests and other species. Temperature and precipitation are the two most significant climate factors that affect the characteristics and distribution of forest ecosystems [6; 7; 8; 9; 10; 11]. Forest resources in the Altay Mountains are the key component of the Xinjiang terrestrial ecosystem and are a green reservoir for regulating and conserving water resources [12; 13; 14]. Therefore, revealing the internal relationship between climate change and vegetation productivity in the Altay Mountains has important practical significance for improving the quality and productivity of forest land in the Altay Mountains, improving the management level of forest land, and promoting the healthy development of forest land [15; 16]. Due to the close relationship between forests and climate, climate change will inevitably have a certain impact on forests [17; 18; 19]. The accurate estimation of the gross primary production of vegetation is vital for understanding the global carbon cycle and predicting future climate change. Multiple GPP products are currently available based on different methods and research tools, but their performances vary substantially when validated against GPP estimates from eddy covariance data. Measuring or estimating vegetation productivity mainly includes direct harvesting, volume conversion, and biomass equation methods. The harvesting method was developed first, where the biomass of each component is directly obtained by cutting and weighing all trees or estimating the biomass by directly measuring the biomass of the standard trees [20]. Direct harvesting requires a lot of human and material resources while causing unavoidable damage to the forest and the environment. The volume conversion method can be conducted due to the significant correlation between the stand volume and biomass. Nevertheless, the output of this model cannot provide an accurate estimation of forest biomass as it is related to forest density, age and site conditions. Biomass growth models can describe changes in an individual tree or stand size over time. Although these methods are widely used to connect individual trees and stand levels [21; 22], the errors in estimating the stand biomass using the individual tree biomass growth combined with the stand structure are almost not quantified. Compared with other research tools, the MODIS data can effectively reflect the landscape information on a regional scale. The MODIS-GPP product (MOD-17) is a global GPP product using remote sensing data developed according to the light-use efficiency principle. The GPP product has been widely used in appraisal and application research on various vegetation productions [23]. Research on the impact of climate change on forest ecosystems began in 1990 in China. However, most of this research work focused mainly on the variation of the forest ecosystem and its response to the annual average change in climate indicators, and little or no consideration was given to the relationship between seasonal changes in meteorological factors and vegetation productivity [23; 24; 25]. [PERSON] et al. analyzed the vegetation vitality in northern Eurasia and northern North America by using satellite data from 1981 to 1999; the analysis indicated that the vegetation vitality increased significantly and the growth period was prolonged [26].