Illinois Institute of Technology, which, combined with taking courses there cost-free, broadened her scientific education. During the summers she would pursue her research at Woods Hole. She received her doctorate in 1949, the first woman to have done so, and moved to Woods Hole in 1951.
While at Woods Hole (1951–1960), she developed the first numerical model of a cloud, which was developed and validated using data from an instrumented patrol bomber (PBY) aircraft on loan from the U.S. Navy. Although the Navy did not want her to fly on the airplane, the Woods Hole director and the Office of Naval Research said that they did not want the airplane if she did not fly on it. Indeed, she was instrumental in breaking barriers for women in subsequent field programs.
Simpson’s conceptual model of cumulus clouds differed from that espoused by Richard Scorer and Frank Ludlam of Imperial College, leading to sharp exchanges both in the literature and in person and then to a visit to Imperial College in 1954. There, based on laboratory experiments, theory, and observations of glider pilots, she and Scorer developed the first finite-difference model of a cumulus cloud, which was envisioned as a buoyant bubble entraining air from the environment, which, thanks to Rossby, was run on a computer in Stockholm, Sweden, in 1955.
She subsequently collaborated with Riehl on seminal papers (1958, 1979) on the role of “hot towers” or convective clouds in maintaining the trade wind circulation, providing the solution to an apparent paradox. As every school child knows, air in the trade-wind belts converge near the Equator, where it rises and carries the excess heat energy aloft and then poleward into both hemispheres. However, observations in the early to mid-1950s showed a minimum in energy at midlevels separating high-energy values near the surface and aloft. Clearly this was not possible for a broad rising updraft. With Riehl she showed that the energy exchange could be explained by updrafts in convective clouds carrying high-energy air through midlevels. Occupying only a small fraction of the area, these “hot tower” clouds were missed in observed energy profiles.