# Bergeron process

The Wegener–Bergeron–Findeisen process (after Alfred Wegener, Tor Bergeron and W. Findeisen), (or "cold-rain process") is a process of ice crystal growth that occurs in mixed phase clouds (containing a mixture of supercooled water and ice) in regions where the ambient vapor pressure falls between the saturation vapor pressure over water and the saturation vapor pressure over ice. The saturation vapor pressure over water is greater than the saturation vapor pressure over ice (at the same temperature) creating a subsaturated environment for liquid water but a supersaturated environment for ice. This results in rapid evaporation of liquid water and rapid ice crystal growth through vapor deposition. If the number density of ice is small compared to liquid water, the ice crystals can grow large enough to fall out of the cloud, melting into rain drops if lower level temperatures are warm enough.

## History

The principle of ice growth through vapor deposition on ice crystals at the expense of liquid water was first theorized by the German scientist Alfred Wegener in 1911 while studying hoarfrost formation. Wegener theorized that if this process happened in clouds and the crystals grew large enough to fall out, that it could be a viable precipitation mechanism. While his work with ice crystal growth attracted some attention, it would take another 10 years before its application to precipitation would be recognized.[1]

In the winter of 1922, Tor Bergeron made a curious observation while walking through the woods. He noticed that on days when the temperature was below freezing, the stratus deck that typically covered the hillside stopped at the top of the canopy instead of extending to the ground as it did on days when the temperature was above freezing. Being familiar with Wegener's earlier work, Bergeron theorized that ice crystals on the tree branches were scavenging vapor from the supercooled stratus cloud, preventing it from reaching the ground.

In 1933, Bergeron was selected to attend the International Union of Geodesy and Geophysics meeting in Lisbon, Portugal where he presented his ice crystal theory. In his paper, he stated that if the ice crystal population was significantly small compared to the liquid water droplets, that the ice crystals could grow large enough to fall out (Wegener's original hypothesis). Bergeron theorized that this process could be responsible for all rain, even in tropical climates; a statement that caused quite a bit of disagreement between tropical and mid-latitude scientists. In the late 1930s, German meteorologist Walter Findeisen extended and refined Bergeron's work through both theoretical and experimental work.

## Required Conditions

It is often assumed that the Bergeron process is the dominant process in all mixed phase clouds, but this is not necessarily the case. At subfreezing temperatures, $e_s$ is always greater than $e_i$, but the ambient vapor pressure ($e$) is not bounded to a particular range. This results in the three possible scenarios:

\begin{align} (1) ~~~e > e_s > e_i \\ (2) ~~~e_s > e > e_i \\ (3) ~~~e_s > e_i > e \\ \end{align}

Of these three scenarios, only the second describes the Bergeron process. It is worth noting that in the absence of evolving supersaturation, a population of ice and liquid particles in region 1 will eventually transition into region 2 before reaching equilibrium. Both ice and water particles will grow until the ambient vapor pressure falls into equilibrium with respect to liquid water, at which point droplets will cease to grow. During this process, both liquid water and ice are competing for vapor, limiting the growth rate of both species. With the liquid water in equilibrium, the environment is still supersaturated with respect to ice, which will allow ice crystals to continue to grow, moving the population into region 2. The ice crystals will continue to grow under the Bergeron process until all liquid water has evaporated and they come into equilibrium with the vapor field. During this phase of growth, the role of liquid water is reversed; instead of competing with ice for vapor, it serves as an additional source, enhancing the growth rate. Once in equilibrium, the ice crystals will remain in this state until the equilibrium is externally perturbed.

In an adiabatic updraft, expansion of the parcel results in a direct decrease in the vapor pressure as well as a decrease in temperature which in turn decreases the saturation vapor pressure. The saturation vapor pressure decreases more rapidly than the vapor pressure, resulting in a supersaturated condition. The strength of the supersaturation is a function of the rate of production of excess vapor (a function of updraft speed) and the rate of vapor depletion (a function of particle phase, size and number density).

Using these relations, Korolev and Mazin [2] derived expressions for critical updraft speeds that represent the boundaries between regions one, two and three:

$u^{*}_{z} = \frac{e_s - e_i}{e_i} \eta N_i \bar{r_i} \,$

(1)

$u^{0}_{z} = \frac{e_i - e_s}{e_s} \chi N_w \bar{r_w} \,$

(2)

where,

• $u^{*}_{z}$ is the critical updraft speed separating region 1 and 2
• $u^{*}_{0}$ is the critical downdraft speed separating region 2 and 3
• η and χ are coefficients dependent on temperature and pressure
• $N_i$ and $N_w$ are the number densities of ice and liquid particles (respectively)
• $\bar{r_i}$ and $\bar{r_w}$ are the mean radius of ice and liquid particles (respectively)

For values of $N_i \bar{r_i}$ typical of clouds, $u^{*}_{z}$ ranges from a few cm/s to a few m/s. These velocities can be easily produced by convection, waves or turbulence, indicating that it is not uncommon for both liquid water and ice to grow simultaneously. In comparison, for typical values of $N_w \bar{r_w}$, downdraft velocities in excess of a few $m s^{-1}$ are required for both liquid and ice to shrink simultaneously.[3] These velocities are common in convective downdrafts, but are not typical for stratus clouds.

## Formation of ice crystals

The most common way to form an ice crystal, starts with an ice nucleus in the cloud. Ice crystals can form from heterogeneous deposition, contact, immersion, or freezing after condensation. In heterogeneous deposition, an ice nucleus is simply coated with water. For contact, ice nuclei will collide with water droplets that freeze upon impact. During immersion, an ice nucleus will hit a water droplet and instantly freeze it. Water can also condense onto ice nuclei and then freeze.

Water will freeze at different temperatures depending upon the type of ice nuclei present. Ice nuclei cause water to freeze at higher temperatures than it would spontaneously. For pure water to freeze spontaneously, called homogeneous nucleation, cloud temperatures would have to be -42 degrees Celsius.[4] Here are some examples of ice nuclei:

Ice Nuclei Temperature to Freeze (degrees C)
Bacteria -2.6
Kaolinite -4
Silver Iodide -7
Vaterite -9

## Ice Multiplication

Different ice crystals present together in a cloud.

As the ice crystals grow, they can bump into each other and splinter and fracture, resulting in many new ice crystals. There are many shapes of ice crystals to bump into each other. These shapes include hexagons, cubes, columns, and dendrites. This process is referred to as "Ice Enhancement" by Atmospheric Physicists and Chemists.[5]

## Aggregation

The process of ice crystals sticking together is called aggregation. This happens when ice crystals are slick or sticky at temperatures of -5 degrees Celsius and above, because of a coating of water surrounding the crystal. The different sizes and shapes of ice crystals fall at different terminal velocities and commonly collide and stick.

## Accretion

When an ice crystal collides with supercooled water its called accretion (or riming). Droplets freeze upon impact and can form graupel. If the graupel formed is reintroduced into the cloud by wind, it may continue to grow larger and more dense, eventually forming hail.[5]

## Precipitation

Eventually this ice crystal will grow large enough to fall. It may even collide with other ice crystals and grow larger still through collision coalescence, aggregation, or accretion.

The Bergeron Process often results in precipitation. As the crystals grow and fall, they pass through the base of the cloud, which may be above freezing. This causes the crystals to melt and fall as rain. There also may be a layer of air below freezing below the cloud base, causing the precipitation to refreeze in the form of ice pellets. Similarly, the layer of air below freezing may be at the surface, causing the precipitation to fall as freezing rain. The process may also result in no precipitation, evaporating before it reaches the ground, in the case of forming virga.