## 1 Introduction  
Understanding the interactions between terrestrial ecosystem and atmospheric CO\({}_{2}\) column is significant to understand the variations of greenhouse gases in our atmosphere. The terrestrial biosphere is a large and persistent carbon sink [1]. Every year about 1/3 of the anthropogenic CO\({}_{2}\) emission from fossil fuels combustion, cement production, and land-use change is absorbed by the terrestrial ecosystems [2]. The CO\({}_{2}\) uptake and release induced by terrestrial biosphere activities essentially contribute to the seasonal cycle of atmospheric CO\({}_{2}\) column [3], which is, however, weakly related to fossil emission [2] and ocean fluxes [4]. The CO\({}_{2}\) seasonal cycle amplitude (SCA) is mainly determined by the difference between the dominant CO\({}_{2}\) uptake during the growing seasons and CO\({}_{2}\) release during the autumn and winter seasons [5,6]. To understand the underlying mechanisms, surface measurements and satellite observations have been widely used in analyzing the seasonality of atmospheric CO\({}_{2}\)[7, 8, 9, 10, 11, 12, 13]. CO\({}_{2}\) data from current surface monitoring networks have been crucial in gaining important insights of the mechanisms of CO\({}_{2}\) seasonal variations [7, 8, 9, 10]. Seasonal cycle of CO\({}_{2}\) at high northern hemisphere (NH) latitudes has been found to be dominantly induced by terrestrial activities, especially within tundra and boreal forest biomes using data from long-term surface measurements and atmosphere transport models [10]. Variations in the strength of carbon sinks over North America can be well monitored by measurements from ground sites [7]. An enhanced strength of the seasonal exchange of CO\({}_{2}\), which is substantially larger than current model simulations in northern extratropical land ecosystems, especially in boreal forest, can be found from ground-based and aircraft-based observations [9]. Climate-vegetation-carbon cycle feedback at high latitudes and the latitudinal gradient of the increasing CO\({}_{2}\) SCA can be precisely observed by a total carbon column-observing network (TCCON) [8]. However, in global scale, it is still difficult to capture the full picture with detailed variations of biosphere-atmospheric CO\({}_{2}\) interaction by current ground measurement networks. With the advantages of global coverage and high-density measurements, satellite observations have the potential to improve our understandings in both global and local scales. Results from validation with TCCON measurements show that XCO\({}_{2}\) retrievals from the Greenhouse gases Observing SATellite (GOSAT) well capture the XCO\({}_{2}\) seasonal cycle [14]. Spatial distributions of SCA, derived from gridded data over 10\({}^{\circ}\) by 10\({}^{\circ}\) in space, are consistent among satellite observations from GOSAT and the Scanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) and model simulations from Monitoring Atmospheric Composition and Climate (MACC 13.1) and CarbonTracker (CT2013b) at the global scale [15]. In addition, the latitudinal gradient of biosphere-atmosphere CO\({}_{2}\) interactions has been revealed with satellite observations [11, 13, 16]. However, geographic distribution of the magnitude of biosphere-atmospheric CO\({}_{2}\) exchange, which drives the atmospheric CO\({}_{2}\) seasonal cycle, and its underlying mechanisms are still highly uncertain [17, 18]. Analysis at finer scale of the interaction using biophysical parameters and XCO\({}_{2}\) retrievals from satellite observations is still lacking. One of the challenges is the irregular distribution and gaps of the XCO\({}_{2}\) retrievals in space and time, which result from certain constraints, such as cloud coverage and satellite observation modes [7].