Cloud Calculations

Due to being virtually always present clouds are one of the most common objects affected by the attacks or powers of characters. As such how to calculate feats involving the creation, destruction or movement of clouds is of common interest.

## Cloud Size

The first step necessary for any cloud calculation is determining how much of a certain cloud was affected (created, destroyed or moved). Pixel scaling is the most reliable way to do so and the first thing one should try to do. However, in case of clouds there often is nothing one could scale from. Hence other practices are often relevant.

### Viewing Distance

If all clouds visible in the sky are affected and the view to the horizon is not obstructed by obstacles, through for example buildings or trees, one can use the maximum viewing distance to figure out the radius in which the clouds are affected.
There are two things that limit how far one can see. One is the curvature of earth, that is the horizon, and the other is the visibility, that is how much fog, air pollution and similar limit the maximum viewing distance.

In practice the limit is almost always determined by the visibility, as clouds, due to being high up in the sky, are usually in the line of sight for over a hundred kilometers beyond the horizon.

On clear days (no rain, fog or snow) the visibility is about 20km. On very clear days it can be around 50km and on exceptionally clear days even 280km. On slightly hazy days it can also just be 10km.

The standard value to use is hence 20km. Higher or lower values can be used if there is a reason for it.

### Base Area

The base area is the area on the underside of the affected part of the cloud or, roughly speaking, the area of the land that the affected part floats above.

One can either scale that directly or one can work with the viewing distance. In the latter case the base area is given by pi\*(viewing distance)^2.

### Characteristic Cloud Thickness

Different types of clouds have a characteristic thickness to them. The thickness is the distance from the lower border to the upper border of the clouds. If clouds can't be directly scaled this is usually the only way to figure out the height to use for the calculation of the affected cloud volume.

### Cloud Height

The cloud height is in this context the distance between sea-level and the lower edge of the affected clouds. The most reliable way to get this value is via pixel scaling, but that frequently is not an option. In such cases one can make an educated guess based on the cloud type.

 stratus
 cumulus
 stratocumulus
 Nimbostratus
 cumulonimbus

### Volume

Using the values from above one can approximate the volume of the clouds.
A simple acceptable approximation is given by (base area)\*(cloud thickness).
There are better, but more complicated, formula model the clouds as the intersection of a spherical shell and a spherical sector. However, usage of those usually isn't necessary with the normal distances.

## Cloud Mass

When determining the mass of the cloud, there are two different things one could consider its mass.

1. The mass of the water in the cloud.
2. The mass of the water and air that make up the the cloud together.

Which to use depends on which way the cloud was affected. Chemical changes, like vaporization or condensation of water use the first mass, while movement changes like the creation of instabilities or changing the clouds position or shape use the second mass.

The density of just the water in the cloud is the liquid water content. The liquid water content depends on the cloud type. Following values can be used as orientation:

 fog
 stratus
 cumulus
 stratocumulus
 Nimbostratus

In order to calculate the mass of water in the cloud one simply needs to multiply the volume of the cloud with the liquid water content.

Determining the mass of the air in the cloud with the water is more difficult, as air density changes depending on height. A decent approximation can be archieved by integrating the barometric formula (in its density form) over the cloud volume.

To make that easier this calculator can be used. The "Area above which the cloud/air floats" is the base area, "Cloud/air thickness" is the cloud thickness and the "Height of cloud/air bottom above sea level" is the cloud height. The result is then the mass in kg. Note that this only is correct if the cloud's volume can be calculated as base area times cloud height.

For more complicated cloud shapes, where the calculator is not applicable, one can do a low-end approximation by simply multiplying the cloud's volume by the air density at the upper edge of the cloud.

## Energy

In order to get the final result you need to find out which method was used to affect the clouds. There are 3 methods that are typical:

1. Condensation, for creation, or vaporization, for destruction, of clouds. This should be used if clouds are created or destroyed, by condensing / vaporizing the water that makes up the cloud. If the cloud creation includes the creation of great amounts of natural winds, in other words storms, CAPE should be used instead.
2. Kinetic Energy for moving of clouds. Should only be used if clouds are moved from one place to another.
3. Convective available potential energy (CAPE) for creation of storms. Should be used if clouds are created together with a lot of wind. If the CAPE value is lower than the condensation value, use condensation instead.

If it can not be said, within reasonable certainty, which of the three methods applies to the created clouds all three can be calculated and the lowest result used.

### Condensation / Vaporization

To calculate the energy necessary to create/destroy the clouds via condensation/vaporisation simply take the mass of the clouds (water mass, without air), in kilogram, and multiply it by the latent heat of vaporization for water, which is 2264705 J/kg. An even better result can be reached if one estimates the temperature and uses the formula here to get the latent heat of condensation for water in clouds and multiplies that with the mass of the clouds (in gram).

### Kinetic Energy

To calculate the energy via kinetic energy one needs to additionally know the speed at which the clouds were moved. Since speed is distance over time, one needs to somehow figure out these two values. If that it done it can simply be calculated through the formula "kinetic energy = 0.5 \* cloud mass \* (Speed of cloud movement)2". The cloud mass is here the mass with the air.

One should keep in mind that not all clouds in a cloud movement feat necessarily move with the same speed. In such cases one has to calculate the kinetic energy with the different speeds of the different parts in mind. An example of this would be creating clouds and spreading them omnidirectionally around a center point. In that case the speed with which the clouds move may increase the further from the center they are. In the case of such an omnidirectional expansion one could use the formula "kinetic energy = 0.25 \* cloud mass \* (Speed of cloud movement)2" to account for the different speeds involved.

For pulling in clouds omnidirectional towards a center point, or dispersing them from a center point, the formula "kinetic energy = 1/12 \* cloud mass \* (Speed of cloud movement)2" can be used.

### Common Results

The following values assume that the clouds in question cover a radius of 20km and are cumulonimbus clouds and hence 8000m thick and have a liquid water content of at least 1 g/m^3. For the kinetic energy values it is assumed that the storms are pulled from 20km so that in the end the sky is completely covered within 1 minute. That means this values should not be used, if the timeframe might be longer, the viewing distance is limited to below 20km or the clouds in question are not cumulonimbus clouds. Cloud Height is assumed to be 4000m.

 Kinetic Energy

Common results for CAPE can be found on the Storm Calculations page.

## See also

* Storm Calculations
* Other Calculation Instructions

## References

1. ↑ wikipedia:Cirrus cloud#Description
2. ↑ https://www.sciencedirect.com/topics/earth-and-planetary-sciences/stratus-clouds
3. ↑ http://www.ias.sdsmt.edu/dept/clouds-intro.htm
4. ↑ http://www.ias.sdsmt.edu/dept/clouds-intro.htm
5. ↑ wikipedia:de:Cumulus
6. ↑ https://www.sciencedirect.com/topics/earth-and-planetary-sciences/stratus-clouds
7. ↑ http://www.ias.sdsmt.edu/dept/clouds-intro.htm
8. ↑ https://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%281950%29007%3C0054%3AVALWCI%3E2.0.CO%3B2
9. ↑ wikipedia:Nimbostratus cloud
10. ↑ wikipedia:Cumulonimbus cloud
11. ↑ http://www.ias.sdsmt.edu/dept/clouds-intro.htm
12. ↑ https://www.weather.gov/key/high\_clouds#:~:text=Cirrus%20clouds%20form%20very%20high,like%20feathers%20or%20horse%20tails.
13. ↑ http://www.cas.manchester.ac.uk/resactivities/cloudphysics/background/classification/
14. ↑ https://www.climate-policy-watcher.org/global-climate-2/clouds-stratus.html
15. ↑ http://www.cas.manchester.ac.uk/resactivities/cloudphysics/background/classification/#:~:text=below%206%2C500ft-,Cumulus,may%20occasionally%20produce%20light%20showers.
16. ↑ http://www.cas.manchester.ac.uk/resactivities/cloudphysics/background/classification/#:~:text=Stratocumulus,obscure%20the%20sun%20or%20moon.
17. ↑ https://www.metoffice.gov.uk/weather/learn-about/weather/types-of-weather/clouds/mid-level-clouds/nimbostratus
18. ↑ https://www.epfl.ch/labs/lapi/wp-content/uploads/2020/03/Clouds.pdf
19. ↑ https://en.wikipedia.org/wiki/Cumulonimbus\_cloud
20. ↑ http://pernerscontacts.upce.cz/24\_2011/Krollova.pdf