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:
- 1 Kj/kg, - "weak instability"
- 2.5 Kj/kg - "moderate instability"
- 4 Kj/kg - "strong instability"
- 5.89 Kj/kg - 1999 Oklahoma Tornado Outbreak
- 8 Kj/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 volume. That can be calculated as described here. That cloud type to assume for that is cumulonimbus.
Then we get the mass by multiplying the volume with 1.003 kg/m^3.
Multiplying that with the instability value gives us the energy in Kj.
For short the formula is: Volume (in m^3) * 1.003 kg/m^3 * Instability.
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 Kilojoules
| 8000m | 11800m | |
|---|---|---|
| 1 Kj/Kg | 1*1016 J | 1.48*1016 J |
| 2.5 Kj/Kg | 2.5*1016 J | 3.71*1016 J |
| 4 Kj/Kg | 4*1016 J | 5.94*1016 J |
| 5.89 Kj/Kg | 5.93*1016 J | 8.76*1016 J |
| 8 Kj/Kg | 8*1016 J | 1.18*1017 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 formula is used:
(Area of country in m^2 * (8000m or 11800m)) * 1.003 * CAPE
CAPE will be switched out for 1000 j/kg, 2500 j/kg, 4000 j/kg, 5890 j/kg, and 8000 j/kg for different ends.
Vatican City - 440,000 m^2
| 1000 j/kg | 2500 j/kg | 4000 j/kg | 5890 j/kg | 8000 j/kg | |
|---|---|---|---|---|---|
| 8000 m | 3.53056e+12 J | 8.8264e+12 J | 1.412224e+13 J | 2.0794998e+13 J | 2.824448e+13 J |
| 11800 m | 5.207576e+12 J | 1.301894e+13 J | 2.0830304e+13 J | 3.0672623e+13 J | 4.1660608e+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 | 2.535584e+15 J | 6.33896e+15 J | 1.0142336e+16 J | 1.493459e+16 J | 2.0284672e+16 J |
| 11800 m | 3.7399864e+15 J | 9.349966e+15 J | 1.4959946e+16 J | 2.202852e+16 J | 2.9919891e+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 | 6.2892112e+15 J | 1.5723028e+16 J | 2.5156845e+16 J | 3.7043454e+16 J | 5.031369e+16 J |
| 11800 m | 9.2765865e+15 J | 2.3191466e+16 J | 3.7106346e+16 J | 5.4639095e+16 J | 7.4212692e+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 | 3.2112048e+16 J | 8.028012e+16 J | 6.4032e+13 J | 1.2844819e+17 J | 2.5689638e+17 J |
| 11800 m | 4.7365271e+16 J | 1.1841318e+17 J | 1.8946108e+17 J | 2.7898144e+17 J | 3.7892217e+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 | 2.2716746e+17 J | 5.6791866e+17 J | 9.0866986e+17 J | 1.3380164e+18 J | 1.8173397e+18 J |
| 11800 m | 3.3507201e+17 J | 8.3768002e+17 J | 1.340288e+18 J | 1.9735741e+18 J | 2.6805761e+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 | 3.0325103e+18 J | 7.5812758e+18 J | 1.2130041e+19 J | 1.7861486e+19 J | 2.4260083e+19 J |
| 11800 m | 4.4729527e+18 J | 1.1182382e+19 J | 1.7891811e+19 J | 2.6345691e+19 J | 3.5783622e+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 | 3.4019409e+18 J | 8.504852e+18 J | 1.3607763e+19 J | 2.003743e+19 J | 2.7215522e+19 J |
| 11800 m | 5.0178628e+18 J | 1.2544657e+19 J | 2.0071434e+19 J | 2.95552e+19 J | 4.0142888e+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 | 5.5816629e+18 J | 1.3954157e+19 J | 2.2326652e+19 J | 3.2875995e+19 J | 4.4653303e+19 J |
| 11800 m | 8.232951e+18 J | 2.0582382e+19 J | 3.2931812e+19 J | 4.8492091e+19 J | 6.5863622e+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 | 1.378406e+19 J | 3.4460151e+19 J | 5.5136242e+19 J | 8.1188116e+19 J | 1.1027248e+20 J |
| 11800 m | 2.0331472e+19 J | 5.082871e+19 J | 8.1325956e+19 J | 1.1975247e+20 J | 1.6265191e+20 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 | 6.8330514e+19 J | 1.7082629e+20 J | 2.7332205e+20 J | 4.0246673e+20 J | 5.4664403e+20 J |
| 11800 m | 1.0078751e+20 J | 2.5196865e+20 J | 4.0315003e+20 J | 5.9363843e+20 J | 8.0630007e+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 | 1.1222314e+20 J | 2.8055788e+20 J | 4.4889259e+20 J | 6.6099435e+20 J | 8.977851e+20 J |
| 11800 m | 1.6552914e+20 J | 4.1382286e+20 J | 6.6211657e+20 J | 9.7496665e+20 J | 1.324233e+21 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 | 5.6610343e+20 J | 1.4152586e+21 J | 2.2644137e+21 J | 3.3343491e+21 J | 4.5288274e+21 J |
| 11800 m | 8.3500251e+20 J | 2.0875064e+21 J | 3.3400103e+21 J | 4.9181644e+21 J | 6.6800205e+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 | 1.2261418e+21 J | 3.0653546e+21 J | 4.9045673e+21 J | 7.2219751e+21 J | 9.8091346e+21 J |
| 11800 m | 1.8085592e+21 J | 4.5213976e+21 J | 7.2342366e+21 J | 1.0652414e+22 J | 1.4468473e+22 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 | 2.88864e+21 J | 7.2216e+21 J | 1.155456e+22 J | 1.701409e+22 J | 2.310912e+22 J |
| 11800 m | 4.260744e+21 J | 1.065186e+22 J | 1.7042976e+22 J | 2.5095782e+22 J | 3.4085952e+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 | 4.0919892e+21 J | 1.0229971e+22 J | 1.6367954e+22 J | 2.4101809e+22 J | 3.2735908e+22 J |
| 11800 m | 6.0356831e+21 J | 1.5089208e+22 J | 2.4142732e+22 J | 3.5550172e+22 J | 4.8285465e+22 J |