From AMS Glossary
(Sometimes called electrical storm.) In general, a local storm, invariably produced by a cumulonimbus cloud and always accompanied by lightning and thunder, usually with strong gusts of wind, heavy rain, and sometimes with hail.
It is usually of short duration, seldom over two hours for any one storm. A thunderstorm is a consequence of atmospheric instability and constitutes, loosely, an overturning of air layers in order to achieve a more stable density stratification. A strong convective updraft is a distinguishing feature of this storm in its early phases. A strong downdraft in a column of precipitation marks its dissipating stages. Thunderstorms often build to altitudes of 40 000–50 000 ft in midlatitudes and to even greater heights in the Tropics; only the great stability of the lower stratosphere limits their upward growth. A unique quality of thunderstorms is their striking electrical activity. The study of thunderstorm electricity includes not only lightning phenomena per se but all of the complexities of thunderstorm charge separation and all charge distribution within the realm of thunderstorm influence. In U.S. weather observing procedure, a thunderstorm is reported whenever thunder is heard at the station; it is reported on regularly scheduled observations if thunder is heard within 15 minutes preceding the observation. Thunderstorms are reported as light, medium, or heavy according to 1) the nature of the lightning and thunder; 2) the type and intensity of the precipitation, if any; 3) the speed and gustiness of the wind; 4) the appearance of the clouds; and 5) the effect upon surface temperature. From the viewpoint of the synoptic meteorologist, thunderstorms may be classified by the nature of the overall weather situation, such as airmass thunderstorm, frontal thunderstorm, and squall-line thunderstorm.
Byers, H. R., and R. R. Braham Jr. 1949. The Thunderstorm. U.S. Government Printing Office, . 287 pp.
Byers, H. R. 1951. Compendium of Meteorology. p. 681.