# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2024-07-26 16:45:30

Jai Ganesh
Registered: 2005-06-28
Posts: 47,358

### Precipitation

Precipitation

Gist

Precipitation is water released from clouds in the form of rain, freezing rain, sleet, snow, or hail. Precipitation is the main way atmospheric water returns to the surface of the Earth.

Summary

Precipitation, all liquid and solid water particles that fall from clouds and reach the ground. These particles include drizzle, rain, snow, snow pellets, ice crystals, and hail.

The essential difference between a precipitation particle and a cloud particle is one of size. An average raindrop has a mass equivalent to about one million cloud droplets. Because of their large size, precipitation particles have significant falling speeds and are able to survive the fall from the cloud to the ground.

The transition from a cloud containing only cloud droplets to one containing a mixture of cloud droplets and precipitation particles involves two basically different steps: the formation of incipient precipitation elements directly from the vapour state and the subsequent growth of those elements through aggregation and collision with cloud droplets. The initial precipitation elements may be either ice crystals or chemical-solution droplets.

Development of precipitation through the growth of ice crystals depends on the fact that cloud droplets can freeze spontaneously at temperatures below about −40 °C, or −40 °F. (The reduction of cloud droplets to temperatures below the normal freezing point is termed supercooling.) Within supercooled clouds, ice crystals may form through sublimation of water vapour on certain atmospheric dust particles known as sublimation nuclei. In natural clouds, ice crystals form at temperatures colder than about −15 °C (+5 °F). The exact temperature of ice crystal formation depends largely on the physical-chemical nature of the sublimation nucleus.

Once ice crystals have formed within a supercooled cloud, they continue to grow as long as their temperature is colder than freezing. The rates of growth depend primarily upon the temperature and degree of vapour saturation of the ambient air. The crystals grow at the expense of the water droplets. In favourable conditions—e.g., in a large, rapidly growing cumulus cloud—an ice crystal will grow to a size of about 0.13 millimetre (0.005 inch) in three to five minutes after formation. At this size, the rate of growth through sublimation slows down, and further growth is largely through aggregation and collision with cloud droplets.

Small solution drops are also important as incipient precipitation particles. The atmosphere contains many small particles of soluble chemical substances. The two most common are sodium chloride swept up from the oceans and sulfate-bearing compounds formed through gaseous reactions in the atmosphere. Such particles, called condensation nuclei, collect water because of their hygroscopic nature and, at relative humidities above about 80 percent, exist as solution droplets. In tropical maritime air masses, the number of condensation nuclei is often very large. Clouds forming in such air may develop a number of large solution droplets long before the tops of the clouds reach temperatures favourable to the formation of ice crystals.

Regardless of whether the initial precipitation particle is an ice crystal or a droplet formed on a condensation nucleus, the bulk of the growth of the precipitation particle is through the mechanisms of collision and coalescence. Because of their larger size, the incipient precipitation elements fall faster than do cloud droplets. As a result, they collide with the droplets lying in their fall path. The rate of growth of a precipitation particle through collision and coalescence is governed by the relative sizes of the particle and the cloud droplets in the fall path that are actually hit by the precipitation particle and the fraction of these droplets that actually coalesce with the particle after collision.

Details

In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls from clouds due to gravitational pull. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail. Precipitation occurs when a portion of the atmosphere becomes saturated with water vapor (reaching 100% relative humidity), so that the water condenses and "precipitates" or falls. Thus, fog and mist are not precipitation; their water vapor does not condense sufficiently to precipitate, so fog and mist do not fall. (Such a non-precipitating combination is a colloid.) Two processes, possibly acting together, can lead to air becoming saturated with water vapor: cooling the air or adding water vapor to the air. Precipitation forms as smaller droplets coalesce via collision with other rain drops or ice crystals within a cloud. Short, intense periods of rain in scattered locations are called showers.

Moisture that is lifted or otherwise forced to rise over a layer of sub-freezing air at the surface may be condensed by the low temperature into clouds and rain. This process is typically active when freezing rain occurs. A stationary front is often present near the area of freezing rain and serves as the focus for forcing moist air to rise. Provided there is necessary and sufficient atmospheric moisture content, the moisture within the rising air will condense into clouds, namely nimbostratus and cumulonimbus if significant precipitation is involved. Eventually, the cloud droplets will grow large enough to form raindrops and descend toward the Earth where they will freeze on contact with exposed objects. Where relatively warm water bodies are present, for example due to water evaporation from lakes, lake-effect snowfall becomes a concern downwind of the warm lakes within the cold cyclonic flow around the backside of extratropical cyclones. Lake-effect snowfall can be locally heavy. Thundersnow is possible within a cyclone's comma head and within lake effect precipitation bands. In mountainous areas, heavy precipitation is possible where upslope flow is maximized within windward sides of the terrain at elevation. On the leeward side of mountains, desert climates can exist due to the dry air caused by compressional heating. Most precipitation occurs within the tropics and is caused by convection. The movement of the monsoon trough, or intertropical convergence zone, brings rainy seasons to savannah regions.

Precipitation is a major component of the water cycle, and is responsible for depositing fresh water on the planet. Approximately 505,000 cubic kilometres (121,000 cu mi) of water falls as precipitation each year: 398,000 cubic kilometres (95,000 cu mi) over oceans and 107,000 cubic kilometres (26,000 cu mi) over land. Given the Earth's surface area, that means the globally averaged annual precipitation is 990 millimetres (39 in), but over land it is only 715 millimetres (28.1 in). Climate classification systems such as the Köppen climate classification system use average annual rainfall to help differentiate between differing climate regimes. Global warming is already causing changes to weather, increasing precipitation in some geographies, and reducing it in others, resulting in additional extreme weather.

Precipitation may occur on other celestial bodies. Saturn's largest satellite, Titan, hosts methane precipitation as a slow-falling drizzle, which has been observed as Rain puddles at its equator and polar regions.

Types

Precipitation is a major component of the water cycle, and is responsible for depositing most of the fresh water on the planet. Approximately 505,000 {km}^3 (121,000 cu mi) of water falls as precipitation each year, 398,000 {km}^3 (95,000 cu mi) of it over the oceans. Given the Earth's surface area, that means the globally averaged annual precipitation is 990 millimetres (39 in).

Mechanisms of producing precipitation include convective, stratiform, and orographic rainfall. Convective processes involve strong vertical motions that can cause the overturning of the atmosphere in that location within an hour and cause heavy precipitation, while stratiform processes involve weaker upward motions and less intense precipitation. Precipitation can be divided into three categories, based on whether it falls as liquid water, liquid water that freezes on contact with the surface, or ice. Mixtures of different types of precipitation, including types in different categories, can fall simultaneously. Liquid forms of precipitation include rain and drizzle. Rain or drizzle that freezes on contact within a subfreezing air mass is called "freezing rain" or "freezing drizzle". Frozen forms of precipitation include snow, ice needles, ice pellets, hail, and graupel.

Measurement:

Liquid precipitation

Rainfall (including drizzle and rain) is usually measured using a rain gauge and expressed in units of millimeters (mm) of height or depth. Equivalently, it can be expressed as a physical quantity with dimension of volume of water per collection area, in units of liters per square meter (L/m^2); as 1L=1{dm}^3=1mm·m^2, the units of area (m^2) cancel out, resulting in simply "mm". This also corresponds to an area density expressed in kg/m^2, if assuming that 1 liter of water has a mass of 1 kg (water density), which is acceptable for most practical purposes. The corresponding English unit used is usually inches. In Australia before metrication, rainfall was also measured in "points", each of which was defined as one-hundredth of an inch.

Solid precipitation

A snow gauge is usually used to measure the amount of solid precipitation. Snowfall is usually measured in centimeters by letting snow fall into a container and then measure the height. The snow can then optionally be melted to obtain a water equivalent measurement in millimeters like for liquid precipitation. The relationship between snow height and water equivalent depends on the water content of the snow; the water equivalent can thus only provide a rough estimate of snow depth. Other forms of solid precipitation, such as snow pellets and hail or even sleet (rain and snow mixed), can also be melted and measured as their respective water equivalents, usually expressed in millimeters as for liquid precipitation.

Precipitation is any liquid or frozen water that forms in the atmosphere and falls back to the earth. It comes in many forms, like rain, sleet, and snow. Along with evaporation and condensation, precipitation is one of the three major parts of the global water cycle.

Precipitation forms in the clouds when water vapor condenses into bigger and bigger droplets of water. When the drops are heavy enough, they fall to the earth. If a cloud is colder, like it would be at higher altitudes, the water droplets may freeze to form ice. These ice crystals then fall to the earth as snow, hail, or rain, depending on the temperature within the cloud and at Earth’s surface. Most rain actually begins as snow high in the clouds. As the snowflakes fall through warmer air, they become raindrops.

Particles of dust or smoke in the atmosphere are essential for precipitation. These particles, called “condensation nuclei,” provide a surface for water vapor to condense upon. This helps water droplets gather together and become large enough to fall to the earth.

A common misconception is that when raindrops fall, they have a teardrop shape. In fact, smaller raindrops (ones that are approximately one millimeter (0.039 inches) across) are almost perfectly spherical. Larger raindrops (two to three millimeters (0.078-0.118 inches) across) are also round, but with a small indent on their bottom side. They look more like kidney beans when falling. Very large rain drops (larger than 4.5 millimeters (0.177 inches)) have a huge indent and look more like a parachute. These extra-large drops usually end up splitting into two smaller droplets. The indents on raindrops are caused by air resistance.

Precipitation is always fresh water, even when the water originated from the ocean. This is because sea salt does not evaporate with water. However, in some cases, pollutants in the atmosphere can contaminate water droplets before they fall to the ground. The precipitation that results from this is called acid rain. Acid rain does not harm humans directly, but it can make lakes and streams more acidic. This harms aquatic ecosystems because plants and animals often cannot adapt to the acidity.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline