After completing a bachelor's degree at the City College of New York in 1857 Abbe studied astronomy at Ann Arbor, Michigan, and obtained the master's degree in 1860. From 1860 to 1864 he assisted the US Coast and Geodetic Survey in Cambridge, Massachussets and spent the next two years as a guest at Pulkovo Astronomical Observatory near Leningrad in Russia. The years 1867-1868 were spent at the US Naval Observatory, after which he served as director of Cincinnati Observatory from 1869 to 1870. He then joined the weather service of the US Signal Service as meteorologist. In 1891 this service developed into the US Weather Bureau, and in the same year Abbe was awarded the PhD degree.
Abbe is regarded as the first official weather forecaster of the US government. He edited the Monthly Weather Review for many years, was professor of meteorology at the forerunner of George Washington University (1886-1905), and also lectured in meteorology at Johns Hopkins University. His publications in astronomy include a report on the solar eclipse of 29 July 1878, and a report on standard time in 1879 which helped to promote the introduction of standard time zones. His numerous publications in meteorology dealt with a variety of topics, such as instuments and methods, weather prediction, the physics of the earth's atmosphere, and long term forecasting.
From October 1889 to May 1990 Abbe served as meteorologist on the United States Scientific Expedition to West Africa. The expedition visited the Cape, where Abbe made meteorological observations while E D Preston, with the support of HM Astronomer at the Cape, David Gill, made magnetic and gravity observations. Abbe compiled detailed maps of an unusually heavy south-easter during his visit. He also obtained from A G Howard maps illustrating the heavy north-westerly storm of July 1889, based on data collected by the Meteorological Commission. On 29 January 1890 he read a paper on "The modern weather bureau" to the South African Philosophical Society in Cape Town (Transactions, Vol. 6, pp. 17-30), dealing mainly with the development of the weather service in the United States. Towards the end of his paper he drew attention to the advances made by A G Howard in establishing a proper forecast service in South Africa, and used Howard's storm maps to illustrate the possibility of issuing storm warnings. Years later, in 1907, he again turned his attention to South Africa in article on "Long range seasonal forecasts for South Africa" in the (US) Monthly Weather Review (Vol. 85, pp. 166-177). This is a discussion of the theory of long range forecasts and solar cycles proposed in South Africa by D E Hutchins.