Definition of a thunderstorm
The WMO (World Meteorological Organisation) definition used by all Met services around the world including the UK.
'One or more sudden electrical discharges, manifested by a flash of light (lightning) and a sharp or rumbling sound (thunder)'
Ref Geneva, WMO International Cloud Atlas, Vol 1, Geneva WMO 1956, p76
A local calendar day on which thunder is heard.
A thunderstorm does not have to have precipitation, nor does one have to see lightning, just hear the thunder. Its obviously a fairly complex decision but ask any professional observer or consult any official text book.
The meteorological synoptic chart has 99 different weather symbols of which these below show the various types of thunderstorm and their definition.
95 Thunderstorm, slight or moderate, without hail but with rain and or snow at time of observation.
96 Thunderstorm, slight or moderate, with hail at time of observation.
97 Thunderstorm, heavy, without hail but with rain and or snow at time of observation.
98 Thunderstorm combined with duststorm or sandstorm at time of observation.
99 Thunderstorm, heavy, with hail at time of observation.
Another number, 17, is allocated to thunder heard at the reporting station:
17 Thunderstorm, but no precipitation at the time of observation.
Its that which can cause some complication. Its unusual for it not to become one of the 95-99 variety but present weather 17, 'thunder heard' at the reporting station does constitute an 'official' thunderstorm day.