# Contents

## Idea

According to Wikipedia:

A cloud is a visible mass of water droplets or frozen ice crystals suspended in the Earth’s atmosphere above the surface of the Earth or other planetary body. Clouds in the Earth’s atmosphere are studied in the nephology or cloud physics branch of meteorology. Two processes, possibly acting together, can lead to air becoming saturated: cooling the air or adding water vapor to the air. Generally, precipitation will fall to the surface; an exception is virga which evaporates before reaching the surface. Clouds can show convective development like cumulus, be in the form of layered sheets such as stratus, or appear in thin fibrous wisps as with cirrus. Prefixes are used in connection with clouds: strato for low cumulus-category clouds that show some stratiform characteristics, nimbo for low to middle stratiform clouds that can produce moderate to heavy precipitation, alto for middle clouds, and cirro for high clouds. Whether or not a cloud is low, middle, or high level depends on how far above the ground its base forms. Some cloud types can form in the low or middle ranges depending on the moisture content of the air. Clouds have Latin names due to the popular adaptation of Luke Howard’s cloud categorization system, which began to spread in popularity during December 1802. Synoptic surface weather observations use code numbers for the types of tropospheric cloud visible at each scheduled observation time based on the height and physical appearance of the clouds. While a majority of clouds form in the Earth’s troposphere, there are occasions where clouds in the stratosphere and mesosphere are observed. Clouds have been observed on other planets and moons within the Solar System, but due to their different temperature characteristics, they are composed of other substances such as methane, ammonia, or sulfuric acid.

## Details

According to Fredric Taylor:

Clouds are, in many ways, the most crucial part of the climate system, because they have a large effect on the energy balance of the atmosphere and surface, but are very variable and difficult to predict.

### Classification and climate effects

This is also from Wikipedia:

The individual genus types result from the physical categories being cross-classified by height range family within the troposphere. These include family A (high), family B (middle), family C1 (low), family C2 (low to middle with some vertical extent), and family D (low to middle with considerable vertical extent). The family designation for a particular genus is determined by the base height of the cloud and its vertical extent. The base height range for each family varies depending on the latitudinal geographical zone. See the figure below:

The role of clouds in regulating weather and climate remains a leading source of uncertainty in projections of global warming. This uncertainty arises because of the delicate balance of processes related to clouds, spanning scales from millimeters to planetary. Hence interactions between the large scale (synoptic meteorology) and clouds becomes difficult to represent in global models. The complexity and diversity of clouds, as outlined above, adds to the problem. On the one hand, white colored cloud tops promote cooling of the Earth’s surface by reflecting shortwave radiation from the Sun. However radiation that makes it to the ground is reflected back in long wavelengths that are easily absorbed by water in the clouds resulting in a net warming at surface level.

High clouds, such as cirrus, particularly show this duality with both shortwave albedo cooling and longwave greenhouse warming effects that nearly cancel or slightly favor net warming with increasing cloud cover. The shortwave effect is dominant with middle and low clouds like altocumulus and stratocumulus which results in a net cooling with almost no longwave effect. Consequently, much research has focused on the response of low clouds to a changing climate. Leading global models can produce quite different results, though, with some showing increasing low-level clouds and other showing decreases.

### Physical Models

From Wikipedia:

Cloud physics is the study of the physical processes that lead to the formation, growth and precipitation of clouds. Clouds are composed of microscopic droplets of liquid water (warm clouds), tiny crystals of ice (cold clouds), or both (mixed phase clouds). Cloud drops initially grow by the condensation of water vapor onto the drop when the supersaturation of an air parcel exceeds a critical value according to Köhler theory. Cloud condensation nuclei (cloud seeds of size less than $1\mu m$) are necessary for cloud drop formation because of the Kelvin effect, which describes the change in saturation vapor pressure due to a curved surface. At small radii, the supersaturation needed for condensation to occur is so large that it does not happen naturally. Raoult’s Law describes how the vapor pressure is dependent on the amount of solute in a solution. At high concentrations, when the cloud drop is small, the supersaturation required is smaller than without the presence of a nucleus.

In warm clouds, larger cloud droplets fall at a higher terminal velocity because the drag force on smaller droplets is larger than on large droplets. The large droplet can then collide with small droplet and combine to form even larger drops. When the drops become large enough so that the acceleration due to gravity is much larger than the acceleration due to drag, the drops can fall to the earth as precipitation. The collision and coalescence is not as important in mixed phase clouds where the Bergeron process dominates. Other important processes that form precipitation are riming, when a supercooled liquid drop collides with a solid snowflake, and aggregation, when two solid snowflakes collide and combine.

#### Cloud Formation and Growth

This part follows the presentation in Taylor. The Kelvin equation which gives the criteria for cloud droplet stability, can be re-written as

$p(r)= p_0\e^{\frac{2\sigma M}{r\rho RT}}$

where $p(r)$ is the pressure as a function of radius $r$, $p_0$ the saturated pressure, $\sigma$ surface tension, $M$ the molar mass, $\rho$ density and $R$ is the molar gas constant. We can rewrite this to get the radius at which growth is initiated:

$r^* =\frac{2\sigma M}{\rho RT\ln(S)}$

where $S=\frac{p(r)}{p_0}$ is the saturation ratio. The chance that a droplet reaches this size by itself is small, so typically the condensation happens more often is eg salts and natural and anthropogenic aerosol particles. Some researchers believe that, the latter aerosol already is the major seeder of clouds. The annual release of sulfur to the atmosphere is around $10^14$ gram.

Using Raoult’s law, that the saturated vapor pressure is like the concentration $S(r)\sim \frac{n_0}{n_0 + n}$, with $n$ is the quantity of molecules of solute and $n_0$ for water. Let $a=\frac{2\sigma M}{\rho RT}$ in Kelvins equation, then we can rewrite it as $S=e^\frac{a}{r}$.

$n$ is constant, say $b$ and $n_0$ is proportional to $r^3$. Rewrite Rauoult’s law as:

$S(r)= \left (1+\frac{b}{r^3}\right )^{-1}$

Then we get the saturated vapor pressure:

$S(r)=e^\frac{a}{r}\left (1+\frac{b}{r^3}\right )^{-1}$

The last Kohler equation is shown below (it has diameter instead of radius on the x-axis):

The equation has a maximum at $r^*$. Here we can see that the critical radius depends on the amount of solute, eg salt. and will only happen for saturation over 100 %.

If we have a cloud droplet in the right radius and saturation it will grow slowly by vapor diffusion and some other processes; coagulation and freezing.

## References

Abstract: A new computational approach, CRCP, is proposed in which both the large-scale (LS) tropical dynamics and cloud-scale (CS) dynamics are captured explicitly. The leading idea is to represent subgrid scales of the LS model by imbedding a 2D CS model in each column of the 3D LS model – the approach tailored for distributed memory architectures. The overall

philosophy underlying CRCP is the reinvestment of efforts from large-eddy simulation to elaborate yet ‘embarrassingly parallel’ turbulence models. Similar as in the traditional ‘convection parametrization’, the LS model provides ‘ambient forcings’ for the CS model imbedded inside each LS column, and the CS model feeds back a ‘convective response’ for every column of the LS model. Furthermore, availability of the cloud-scale data allows for explicit coupling of moist convection with radiative and surface processes. Following our experience with cloud-resolving modeling of the tropical convection, the CS model is oriented along the E–W direction inside each LS model column. A simple strategy for the coupling the LS and CS models derives from physical understanding of interactions between LS ﬂow and moist tropical convection. Theoretical considerations are illustrated with an example of application to observational data fromthe Phase III of the GlobalAtmospheric Research Programme Atlantic Tropical Experiment (GATE).

Abstract: Traditionally, the effects of clouds in GCMs have been represented by semiempirical parameterizations. Recently, a cloud-resolving model (CRM) was embedded into each grid column of a realistic GCM, the NCAR Community Atmosphere Model (CAM), to serve as a superparameterization (SP) of clouds. Results of the standard CAM and the SP-CAM are contrasted, both using T42 resolution (2.8° × 2.8° grid), 26 vertical levels, and up to a 500-day-long simulation. The SP was based on a two-dimensional (2D) CRM with 64 grid columns and 24 levels collocated with the 24 lowest levels of CAM. In terms of the mean state, the SP-CAM produces quite reasonable geographical distributions of precipitation, precipitable water, top-of-the-atmosphere radiative fluxes, cloud radiative forcing, and high-cloud fraction for both December–January–February and June–July–August. The most notable and persistent precipitation bias in the western Pacific, during the Northern Hemisphere summer of all the SP-CAM runs with 2D SP, seems to go away through the use of a small-domain three-dimensional (3D) SP with the same number of grid columns as the 2D SP, but arranged in an 8 × 8 square with identical horizontal resolution of 4 km. Two runs with the 3D SP have been carried out, with and without explicit large-scale momentum transport by convection. Interestingly, the double ITCZ feature seems to go away in the run that includes momentum transport.

The SP improves the diurnal variability of nondrizzle precipitation frequency over the standard model by precipitating most frequently during late afternoon hours over the land, as observed, while the standard model maximizes its precipitation frequency around local solar noon. Over the ocean, both models precipitate most frequently in the early morning hours as observed. The SP model also reproduces the observed global distribution of the percentage of days with nondrizzle precipitation rather well. In contrast, the standard model tends to precipitate more frequently, on average by about 20%–30%. The SP model seems to improve the convective intraseasonal variability over the standard model. Preliminary results suggest that the SP produces more realistic variability of such fields as 200-mb wind and OLR, relative to the control, including the often poorly simulated Madden-Julian oscillation (MJO).