How the program began:

During 1942 and 1943, the Weather Bureau cooperated with the
military in setting up volunteer storm spotter networks to protect
military installations and recognized the value of first hand, real time
information. The primary concern was for lightning near ordnance plants, but the program grew substantially during the war, and the spotter mission expanded to  include other hazardous weather,
including tornadoes. After WWII, spotter networks were maintained for military installations. 

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On May 25, 1955, a tornado in Udall, Kansas killed 80 people and injured 273.

The Weather Bureau decided to train severe weather
spotters to provide real time data.

The Weather Bureau decided to recruit severe weather spotters to help obtain real time severe weather
information in order to help extend lead time and increase accuracy of severe weather forecasts.

On March 8, 1959, the Weather Bureau held the first training course in Wellington, Kansas for 225 severe weather spotters.

In 1965, the Natural Disaster Warning System (NADWARN) was established to coordinate the natural
disaster-related emergency functions of various Federal agencies. A special, tornado-specific plan called SKYWARN was created, under the guidance of the United States Weather Bureau.

The SKYWARN Program today:

SKYWARN consists of a network of
all-hazard weather spotters (not just
tornadoes). NWS has over 167,000 trained all-hazard weather spotters in the SKYWARN program. These spotters work with the Warning Coordination Meteorologists (WCMs) at the 122 NWS offices throughout the United States. Some WFOs offer
additional classes in winter storm watch, hurricane watch, floods, thunderstorms,
tornadoes, use of radar, and amateur radio networking.