Cleveland Abbe completed a bachelor's degree at the City College of New York in 1857 and then studied astronomy at Ann Arbor, Michigan, obtaining a 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, 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 degree Doctor of Philosophy (PhD).
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 included An account of progress in meteorology and allied subjects..., comprising four book-length reviews covering the years 1879-1884 (Washington, 1883-1885); The aims and methods of meteorological work... (Baltimore, 1899, 110p); The mechanics of the earth's atmosphere: A collection of translations (Washington, 1891, 1910); and a large number of papers dealing 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 1890 Abbe served as meteorologist of the United States Scientific Expedition to West Africa. The expedition visited the Cape of Good Hope, 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 of the Cape of Good Hope. On 29 January 1890 he read a paper on "The modern weather bureau" before 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 Howard in establishing a forecast service in South Africa, and used Howard's storm maps to illustrate the possibility of issuing storm warnings. Years later he again turned his attention to South Africa in an article on "Long range seasonal forecasts for South Africa" in the (US) Monthly Weather Review (1907). In this paper he discussed the theory of long range forecasts and the effects of solar cycles, as proposed in South Africa by D E Hutchins*.