The Secret Law of Storms states:
At a given wind speed, the marginal rate of increase of sustained wind speed is directly proportional to the marginal rate of pressure fall
Secret Law of Storms expressed in mathematical terms:
where v is the wind speed in km/h, and p is the central pressure in hPa or mb
Storm growth requires an increase in the sustained wind speed given by the acceleration term
and this is driven by
the rate of pressure fall in the Equation 1.
Rule for Thunderstorms
We will now apply the Secret Law of Storms to obtain the Rule for Thunderstorms. Consider the barometric pressure falling from 1009 hPa at a rate of 1 hPa per hour for three hours.
The results are summarised below:
Central Pressure phPa 
Rate of fall (hPa/ h) (dp/dt) 
Increase in wind speed dv/dt (km/h^{2}) 
wind speed v (km / h) 
1009 


9.8 

1 
6.3 

1008 


16.1 

1 
4.8 

1007 


20.9 

1 
4.2 

1006 


25.1 
The result is in agreement Wind Threshold Rule for Thunderstorms:
The wind speed threshold for a thunderstorm is 25 km/h (or 15 mph)
Therefore: A minimum of 3 hPa fall in barometric pressure over 3 hours will produce a thunderstorm
A 4 hPa fall in barometric pressure over 3 hours can be used so as to provide a margin of comfort for prediction purposes. A storm also typically requires the barometric pressure to be less than 1009 hPa (or mb).
Weather Bomb
We will now apply the Secret Law of Storms to the Weather Bomb. By definition a Weather Bomb occurs when the central pressure of a depression at 60˚ latitude decreases by 24 hPa or more in 24 hours. Consider the barometric pressure falling from 1009 hPa at a rate of 1 hPa per hour for 24 hours. It will fall to 986 hPa and applying the Secret Law of Storms the resultant wind speed will be 77.1 km/h. This example shows that even the smallest Weather Bomb will produce a wind of Gale Force strength.
Rule for a Gale
We will now apply the Secret Law of Storms to obtain the Rule for a Gale. Let's calculate the sustained wind speed when the central pressure decreases by 10 hPa over 3 hours. Consider the barometric pressure falling from 1002 hPa at a rate of 10 hPa in 3 hours. It will fall to 992 hPa and applying the Secret Law of Storms the resultant wind speed will be 64.2 km/h.
Therefore, a minimum of 10 hPa fall in barometric pressure over 3 hours will produce a Gale. The Rule for a Gale applies to a rise or fall in pressure.
A minimum of 10 hPa fall in barometric pressure over 3 hours will produce a storm and Gale
Rule for a Severe Thunderstorm
A
severe thunderstorm produces one or more of the following:
 wind gusts of 90 km/h (56 mph) or greater; or
 hail of 2 cm (3/4 inch) diameter or greater; or
 flash floods;
 or tornadoes.
A severe thunderstorm requires:
 barometric pressure of 1005 mb or less; and
 last 3 hours pressure fall of 4 mb or more; and
 last 12 hours pressure fall of 8 mb or more.
Even though the pressure fall can be spread over 12 hours, a severe thunderstorm will still have a 3hour interval where there will be at least a 4 mb fall in pressure
Applying the Secret Law of Storms gives a sustainable wind speed for a severe storm of 56 km/h (or 35 mph). Severe thunderstorms often generate strong wind gusts when rain and hail drag down the surrounding air. Evaporation further cools it accelerating the downdraft. Gusts of at least 90 km/h (56 mph) are produced.
Tropical Revolving Storms are referred to as cyclones in the Indian Ocean and South Pacific, typhoons in the Western Pacific and hurricanes in the Western Atlantic and Eastern Pacific Oceans. A Tropical Revolving Storm satisfies the Barometer Rule for a Severe Thunderstorm and so does a Tropical Storm.
Similarly, it can be shown that a minimum of 6 hPa fall in barometric pressure over 3 hours will increase the wind speed to 54.2 km/h or 29.3 knots. Therefore, a minimum of 6 hPa fall in barometric pressure over 3 hours will produce a Strong Wind. The Rule for a Strong Wind applies to a rise or fall in pressure.
Barometer Rules Summary:
Last 3 hours 
▲10 mb 
Gale Warning (34 – 47 knots) 
▲6 mb 
Strong Wind Warning (26 – 33) 
▼4 mb 
storm ( < 1009 mb or hPa) 
▼6 mb 
storm with a Strong Wind Warning ( < 1009 mb) 
▼10 mb 
storm and a Gale Warning ( < 1009 mb) 
Severe Thunderstorm Warning 
Last 3 hours ▼4 mb Last 12 hours ▼8 mb
(Pressure < 1005 mb)

The above Barometer Rules can be incorporated more generally, for example:
My Barometer Rules Short Guide:
with rules for thunderstorms, Strong Winds and Gales from the Secret Law of Storms Last 3 hours 
▲10 mb 
Gale Warning (34 – 47 knots) 
▲6 mb 
Strong Wind Warning (26 – 33) 
▲1.12.7 
poorer weather to come ( > 1015 mb) 
▼1.12.7 
rain & wind ( < 1009 mb) 
▼4 mb 
storm ( < 1009 mb) rain & wind (1009  1023 mb) 
▼6 mb 
storm with a Strong Wind Warning ( <1009 mb) 
▼7 mb 
firestorm conditions if fire exists & ( < 990 mb) & ( > 40℃) sustained 
▼10 mb 
storm with a Gale Warning ( < 1009 mb) 
Severe Thunderstorm Warning 
Last 3 hours ▼4 mb Last 12 hours ▼8 mb
(Pressure < 1005 mb)

Anytime in Storm Season (Tropics) 
steady 
Tropical Cyclone Early Warning if continuously steady for 6 hours 
▼5 mb 
tropical revolving storm (for fall below tropical seasonal average) 
Stormy Sea Watcher app on Google Play Store
• App provides early warning of storms and gales at sea using alarms.
• It will operate far out at sea as the app itself does not require an internet, WiFi or mobile phone connection to function.
• You can learn how to predict storms, gales and tropical cyclones with the onscreen barometer rules.
Try Storm Sea Watcher app: