Storm Calculations

C.A.P.E is an indicator of atmospheric instability and hence associated with storms and their strength. In order to calculate the energy to create a storm we approximate the C.A.P.E. using some simple indicators and from that the necessary energy.
==When to use==
C.A.P.E should be used if clouds are created together with a lot of wind. If the C.A.P.E. value is lower than the condensation value, use condensation instead. See Cloud Calculations for details on that. It shouldn't be used if the storm is only moved from one place to another.
==Calculation Method==
The main variable for the calculation is the value for instability.
Using this thread as a reference, our alternatives for instability will be as follows:
*1000 j/kg, - "weak instability"
*2500 j/kg - "moderate instability"
*4000 j/kg - "strong instability"
*5890 j/kg - 1999 Oklahoma Tornado Outbreak
*8000 j/kg - 1990 Plainfield Tornado
In order to make use of the value we chose, we need to calculate the mass of the clouds.
First we need the radius of the cloud. That can be measured using pixel scaling, but for the average cumulonimbus cloud we will be using 20 kilometers or 20000 meters, as that's the viewing distance in clear days.
Then we can find the mass by using this calculator, with the average cumulonimbus cloud having an area of 1,256,637,061.43 square meters, 8000 and 11800 meters being the cloud thickness, and 4000 meters being the usual height of the cloud bottom above sea level.
That get us a cloud with a mass of for a 8000 meters tall cloud, and for a 11800 meters tall cloud.
Multiplying that with the instability value gives us the energy in joules.
==Standard results==
In the following a table of the most common results will be given. For that the following assumptions will remain steady throughout all of the results:
*The storm is cylindrical in shape.
*The clear day viewing distance is the radius the clouds cover (20km).
The variables that will change:
*The thickness of the clouds: The clouds of the storms are assumed to be cumulonimbus clouds and hence about 8000m to 11800m tall.
*Assumed instability in joules.
 	8000m 	11800m
1000 j/kg	5.42*1015 J	6.53*1015 J
2500 j/kg	1.35*1016 J	1.63*1016 J
4000 j/kg	2.16*1016 J	2.61*1016 J
5890 j/kg	3.19*1016 J	3.85*1016 J
8000 j/kg	4.33*1016 J	5.23*1016 J
==Table of Results using CAPE and Different Real-Life Examples==
The values of this table are obtained form using the areas of different countries, continents, oceans, etc., multiplying it by 8000 to 11800 meters to get the volume, using cloud density to find the mass and using CAPE multipliers to get AP values from the storm cloud's mass.
Assumptions:
*The storm covers the entirety of the country/continent/island/ocean/etc. or an area equivalent to its total area and nothing else.
That's about it.
The following calculator is used:
https://jscalc.io/embed/XmzHyrORzxFLum94
With the cloud/air thickness being the same as before (8000 to 11800 meters) and the height of cloud/air bottom above sea level being 4000 meters.
Apart from the cloud thickness, the only value that changes in the calculator is the area of the cloud, with examples shown below.
===Vatican City - 440,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	1.8983620e+12 J	4.7459051e+12 J	7.5934482e+12 J	1.1181352e+13 J	1.5186896e+13 J
11800 m	2.2893020e+12 J	5.7232552e+12 J	9.1572083e+12 J	1.3483989e+13 J	1.8314416e+13 J
===Malta - 316,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	1.3633691e+15 J	3.4084227e+15 J	5.4534764e+15 J	8.0302440e+15 J	1.0906952e+16 J
11800 m	1.6441351e+15 J	4.1103378e+15 J	6.5765405e+15 J	9.6839559e+15 J	1.3153081e+16 J
===New York City - 783,800,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	3.3816731e+15 J	8.4541828e+15 J	1.3526692e+16 J	1.9918054e+16 J	2.7053385e+16 J
11800 m	4.0780795e+15 J	1.0195198e+16 J	1.6312318e+16 J	2.4019888e+16 J	3.2624636e+16 J
===Rhode Island - 4,002,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	1.7266465e+13 J	4.3166164e+16 J	6.9065863e+16 J	1.0169948e+17 J	1.3813172e+17 J
11800 m	2.0822243e+16 J	5.2055607e+16 J	8.3288972e+16 J	1.2264301e+17 J	1.6657794e+17 J
===Hawaii - 28,311,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	1.2214665e+17 J	3.0536663e+17 J	4.8858661e+17 J	7.1944379e+17 J	9.7717323e+17 J
11800 m	1.4730098e+17 J	3.6825245e+17 J	5.8920392e+17 J	8.6760277e+17 J	1.1784078e+18 J
===Japan - 377,930,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	1.6305635e+18 J	4.0764089e+18 J	6.5222542e+18 J	9.6040194e+18 J	1.3044508e+19 J
11800 m	1.9663544e+18 J	4.9158860e+18 J	7.8654176e+18 J	1.1581827e+19 J	1.5730835e+19 J
===California - 423,970,694,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	1.8292042e+18 J	4.5730106e+18 J	7.3168170e+18 J	1.0774013e+19 J	1.4633634e+19 J
11800 m	2.2059022e+18 J	5.5147556e+18 J	8.8236090e+18 J	1.2992764e+19 J	1.7647218e+19 J
===Texas - 695,621,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	3.0012284e+18 J	7.5030710e+18 J	1.2004913e+19 J	1.7677235e+19 J	2.4009827e+19 J
11800 m	3.6192877e+18 J	9.0482193e+18 J	1.4477151e+19 J	2.1317604e+19 J	2.8954302e+19 J
===Alaska - 1,717,854,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	7.4116110e+18 J	1.8529027e+19 J	2.9646444e+19 J	4.3654388e+19 J	5.9292888e+19 J
11800 m	8.9379244e+18 J	2.2344811e+19 J	3.5751697e+19 J	5.2644375e+19 J	7.1503395e+19 J
===Brazil - 8,515,767,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	3.6740929e+19 J	9.1852323e+19 J	1.4696371e+20 J	2.1640407e+20 J	2.9392743e+20 J
11800 m	4.4307189e+19 J	1.1076797e+20 J	1.7722875e+20 J	2.6096934e+20 J	3.5445751e+20 J
===Arctic Ocean - 13,985,935,800,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	6.0341749e+19 J	1.5085437e+20 J	2.4136699e+20 J	3.5541290e+20 J	4.8273399e+20 J
11800 m	7.2768254e+19 J	1.8192063e+20 J	2.9107301e+20 J	4.2860502e+20 J	5.8214603e+20 J
===India Ocean - 70,551,276,126,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	3.0439060e+20 J	7.6097650e+20 J	1.2175624e+21 J	1.7928606e+21 J	2.4351248e+21 J
11800 m	3.6707541e+20 J	9.1768854e+20 J	1.4683016e+21 J	2.1620742e+21 J	2.9366033e+21 J
===Pacific Ocean - 152,809,298,510,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	6.5928948e+20 J	1.6482237e+21 J	2.6371579e+21 J	3.8832150e+21 J	5.2743158e+21 J
11800 m	7.9506056e+20 J	1.9876514e+21 J	3.1802422e+21 J	4.6829067e+21 J	6.3604844e+21 J
===All of the earth's oceans - 360,000,000,000,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	1.5532053e+21 J	3.8830132e+21 J	6.2128212e+21 J	9.1483793e+21 J	1.2425642e+22 J
11800 m	1.8730653e+21 J	4.6826633e+21 J	7.4922614e+21 J	1.1032354e+22 J	1.4984522e+22 J
===Surface area of the entire Earth - 509,968,658,925,000 m^2===
 	1000 j/kg 	2500 j/kg 	4000 j/kg 	5890 j/kg 	8000 j/kg
8000 m 	2.2002389e+21 J	5.5005974e+21 J	8.8009559e+21 J	1.2959407e+22 J	1.7601911e+22 J
11800 m	2.6533461e+21 J	6.6333654e+21 J	1.0613384e+22 J	1.5628209e+22 J	2.1226769e+22 J
==Creating a real-life hurricane==
If a character creates a real-life hurricane, or its winds, the following calculation can be used. What is important is that one is reasonably certain that the hurricane in question covers the same gigantic area as a real one typically does. Usually, characters with the ability to manipulate the weather don't necessarily create one of this size, instead of more local phenomena. Hence a convincing argument regarding the size needs to be made. The following calculation was originally made here by Chris Landsea:
Hurricanes can be thought of, to a first approximation, as a heat engine; obtaining its heat input from the warm, humid air over the tropical ocean, and releasing this heat through the condensation of water vapor into water droplets in deep thunderstorms of the eyewall and rainbands, then giving off a cold exhaust in the upper levels of the troposphere (~12 km/8 mi up).
One can look at the energetics of a hurricane in two ways:
#the total amount of energy released by the condensation of water droplets or ...
#the amount of kinetic energy generated to maintain the strong swirling winds of the hurricane. 
It turns out that the vast majority of the heat released in the condensation process is used to cause rising motions in the thunderstorms and only a small portion drives the storm's horizontal winds. 
Method 1) - Total energy released through cloud/rain formation: An average hurricane produces 1.5 cm/day (0.6 inches/day) of rain inside a circle of radius 665 km (360 n.mi). (More rain falls in the inner portion of hurricane around the eyewall, less in the outer rainbands.) Converting this to a volume of rain gives 2.1 x 1016 cm3/day. A cubic cm of rain weighs 1 gm. Using the latent heat of condensation, this amount of rain produced gives 5.2 x 10^19 Joules/day or 6.0 x 10^14 Watts.
Method 2) - Total kinetic energy (wind energy) generated: For a mature hurricane, the amount of kinetic energy generated is equal to that being dissipated due to friction. The dissipation rate per unit area is air density times the drag coefficient times the windspeed cubed. One could either integrate a typical wind profile over a range of radii from the hurricane's center to the outer radius encompassing the storm, or assume an average windspeed for the inner core of the hurricane. Doing the latter and using 40 m/s (90 mph) winds on a scale of radius 60 km (40 n.mi.), one gets a wind dissipation rate (wind generation rate) of 1.3 x 10^17 Joules/day or 1.5 x 10^12 Watts.
Conclusion:
#Energy to create Hurricane Force winds: 1.5e+12 J / 358.508604207 Tons of TNT, Multi-City Block level
#Energy to create a full Hurricane: 6.01e+14 J / 143.642447418938 Kilotons of TNT, Large Town level
==See also==
*Cloud Calculations
*Other Calculation Instructions
Category:Calculation Instructions