Storm Calculations

Convective Available Potential Energy (CAPE) is a meteorological term used to describe the amount of energy available in the atmosphere for the development of convective storms, such as thunderstorms. CAPE is a measure of the potential for upward vertical motion of air and the resulting development of strong updrafts within a storm.

## When to use

* Severe Weather Prediction: Meteorologists use CAPE as a critical parameter for predicting the potential for severe weather, especially thunderstorms. High CAPE values suggest a favorable environment for strong updrafts, which can lead to the formation of severe thunderstorms, including supercells capable of producing large hail, damaging winds, and tornadoes.

* Forecasting Thunderstorms: CAPE is often included in weather forecasts to help predict the likelihood of thunderstorm development. High CAPE values indicate an atmosphere with a strong potential for vertical instability and the possibility of vigorous convection.

* Storm Chase Planning: Storm chasers and meteorologists who study severe weather patterns use CAPE values to identify regions where conditions are favorable for the formation of intense thunderstorms. High CAPE values can be an indicator of areas with increased storm potential.

* Air Mass Analysis: CAPE is also used in air mass analysis to understand the vertical stability of the atmosphere. It helps meteorologists categorize air masses as stable or unstable, which is crucial for predicting weather patterns.
* Research and Studies: Meteorologists and atmospheric researchers use CAPE values to analyze historical weather data, study atmospheric instability, and investigate the factors that contribute to severe weather events.
* Model Input for Numerical Weather Prediction: Numerical weather prediction models use CAPE values as inputs to simulate atmospheric conditions and predict future weather patterns. Incorporating CAPE data into these models enhances their accuracy in predicting thunderstorm development and associated severe weather.

* 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 5,421,709,348,262.685 kilograms for a 8000 meters tall cloud, and 6,538,231,495,882.477 kilograms 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.

 2500 j/kg
 4000 j/kg
 5890 j/kg
 8000 j/kg

## 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.

## 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:

1. the total amount of energy released by the condensation of water droplets or ...
2. 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:**

1. **Energy to create Hurricane Force winds:** 1.5e+12 J / 358.508604207 Tons of TNT, Multi-City Block level
2. **Energy to create a full Hurricane:** 6.01e+14 J / 143.642447418938 Kilotons of TNT, Large Town level