Big earth science data offers the scientific community great opportunities. Many more studies at large-scales, over long-terms and at high resolution can now be conducted using the rich information collected by remote sensing satellites, ground-based sensor networks, and even social media input. However, the hundreds of terabytes of information collected and compiled on an hourly basis by NASA and other government agencies present a significant challenge for atmospheric scientists seeking to improve the understanding of the Earth atmospheric system. These challenges include effective discovery, organization, analysis and visualization of large amounts of data. This paper reports the outcomes of an NSF-funded project that developed a geospatial cyberinfrastructure -- the A2CI (Atmospheric Analysis Cyberinfrastructure) -- to support atmospheric research. We first introduce the service-oriented system framework then describe in detail the implementation of the data discovery module, data management module, data integration module, data analysis and visualization modules following the cloud computing principles-Data-as-a-Service, Software-as-a-Service, Platform-as-a-Service and Infrastructure-as-a-Service. We demonstrate the graphic user interface by performing an analysis between Sea Surface Temperature and the intensity of tropical storms in the North Atlantic and Pacific oceans. We expect this work to contribute to the technical advancement of cyberinfrastructure research as well as to the development of an online, collaborative scientific analysis system for atmospheric science.