## 1 Introduction  
Asia, which is characterized by a rapidly growing economy, human-induced disturbances, and climate changes, is an important region for understanding global terrestrial carbon cycles [1, 2, 3]. Siberian regions have experienced a 1.0-2.0 \({}^{\circ}\)C increase in temperature from 1961 to 2004 [4]. China and India have recently experienced rapid economic growth and a large increase in CO\({}_{2}\) emissions. For example, CO\({}_{2}\) emissions in China and India accounted for 28% and 7%, respectively, of the global CO\({}_{2}\) emissions in 2011 [5]. In addition, many regions, for example, China, Southeast Asia, and South Asia, have experienced land-use changes, including changes in the use of cropland and forest areas [6, 7]. Terrestrial gross primary productivity (GPP) is the largest atmosphere-land carbon flux, driving terrestrial carbon cycles as a primary input for vegetation carbon. An accurate estimate of the magnitude of temporal GPP changes is required to quantify and predict terrestrial carbon budgets. Numerous approaches have been used to analyze GPP at both global and regional scales, which include analyzing satellite-based remote sensing data as an indicator of GPP [8, 9, 10, 11], using empirical upscaling with machine learning techniques [12, 13, 14, 15], and assembling diagnostic [16, 17, 18] and prognostic [19, 20] terrestrial biosphere model simulations. These approaches have also been used to analyze spatio-temporal GPP variations in Asia. For example, numerous studies have analyzed satellite-based time-series data, including data that from the Advanced Very High Resolution Radiometer (AVHRR) onboard the National Oceanic and Atmospheric Administration (NOAA) satellite series, to infer GPP variations in relation to environmental changes. Analyses of NOAA AVHRR data have revealed that vegetation productivity is increasing and the growing season has lengthened in boreal and Arctic regions [8, 9, 21]. In East Asia, including China, several studies have revealed that the vegetation greenness has increased over the last 20-30 years [22, 23, 24, 25, 26]. In Southeast Asia, interannual variations in vegetation indices were found to be largely determined by the El Nino Southern Oscillation [27]. Furthermore, vegetation greenness was found to have increased in India because irrigated areas and fertilization use increased [28]. However, this increase in vegetation greenness has stagnated in recent years [29]. Terrestrial biosphere models and empirical models have also been used to analyze GPP variations in many regions in Asia. Empirically upscaled estimates of GPP in East Asia revealed a significant reduction in the summer of 2003 in response to meteorological anomalies [30]. Increased GPP has also been identified using diagnostic terrestrial biosphere models in China [31] and India [28]. Further analyses could utilize a combined application of satellite-based observations and terrestrial biosphere models. Moreover, satellite-based observation data can be used for model evaluation. Once the model output successfully reproduces the satellite-based observations, mechanisms from the observed results can be analyzed with process-based models using sensitivity experiments. Recent vegetation greening trends in northern high-latitude regions have been analyzed using the satellite-based leaf area index (LAI) and a terrestrial biosphere model; increases in temperature were related to the vegetation greening trend [32]. The combined use of remote sensing data and terrestrial biosphere models have helped explain the observed changes in the Normalized Difference Vegetation Index (NDVI) in the Amazon from 1984 to 1999. In this region, increased solar radiation has been found to enhance the terrestrial net primary productivity [33]. Vegetation growth in the Northern Hemisphere (\(>\)25\({}^{\circ}\)N) has been explained by a process-based terrestrial biosphere model and has been found to have resulted from changes in atmospheric CO\({}_{2}\), temperature, and precipitation [34].