# Clouds

Clouds have dimensions, shape, structure, and texture, which are influenced by the kind of air movements that result in their formation and growth, and by the properties of the cloud particles. In settled weather, clouds are well scattered and small and their horizontal and vertical dimensions are only a kilometer or two. In disturbed weather, they cover a large part of the sky, and individual clouds may tower as high as 10 kilometers or more. Growing clouds are sustained by upward air currents, which may vary in strength from a few cm/s to several m/s. Considerable growth of the cloud droplets, with falling speeds of only about one cm/s, leads to their fall through the cloud and reaching the ground as drizzle or rain. Four principal classes are recognized when clouds are classified according to the kind of air motions that produce them:

• 1. Layer clouds formed by the widespread regular ascent of air
• 2. Layer clouds formed by widespread irregular stirring or turbulence
• 3. Cumuliform clouds formed by penetrative convection
• 4. Orographic clouds formed by ascent of air over hills and mountains

We do not discuss how such kinds of clouds are created, because it is part of meteorology. Interested readers can find information in References 1—8.

There have been several proposed alternative mathematical formulations for the probability distribution of sky cover, as an observer’s view of the sky dome. Each of them uses the variable x ranging from zero (for clear conditions) to 1.0 (for overcast). There are four cloud cover models: (1) the first cloud cover model; (2) the second cloud cover model; (3) the third cloud cover model; and (4) the ceiling cloud model. We do not enter into discussions on each of these models because this is out of scope of the present monograph, and we refer the reader to the excellent works [4,6—8].

We only will note that in all cloud models a distinction between cloud cover and sky cover was not explained, and therefore should be briefly explained here. Sky cover is an observer’s view of cover of the sky dome, whereas cloud cover can be used to describe areas that are smaller or larger than the floor space of the sky dome. It follows from numerous observations that in clouds and fog the drops are always smaller than 0.1 mm, and the theory for the small size scatters is applicable [7,20—24]. This gives for the attenuation coefficient

where A is the wavelength measured in centimeters, and q is the water content measured in grams per cubic meter. For visibility of 600, 120, and 30 m, the water content in fog or cloud is 0.032, 0.32, and 2.3 g/m3, respectively. The calculations show that the attenuation, in a moderately strong fog or cloud, does not exceed the attenuation due to rain with a rainfall rate of 6 mm/h.

Due to lack of data, a semiheuristic approach is presented here. Specifically, we assume that the thickness of the cloud layer is wc = 1 km, and the lower boundary of the layer is located at a height of hc = 2 km. The water content of clouds has a yearly measured percentage of [7]

where pc is the probability of cloudy weather (%).

We should notice that although the attenuation in clouds is less than in rain, the percentage of clouds can be much more essential than that of the rain events. Thus, the additional path loss due to clouds can be estimated as 2 and 5 dB for 350 km path and h2 = 6 km, and for the time availability of 95% and 99%, respectively.

# Snow

Snow is the solid form of water that crystallizes in the atmosphere and, falling to the Earth, covers permanently or temporarily about 23% of the Earth’s surface. Snow falls at sea level poleward of latitude 35°N and 35°S, though on the west coast of continents it generally falls only at higher latitudes. Close to the equator, snowfall occurs exclusively in mountain regions, at elevations of 4900 m or higher. The size and shape of the crystals depend mainly on the temperature and the amount of water vapor available as they develop. In colder and drier air, the particles remain smaller and compact. Frozen precipitation has been classified into seven forms of snow crystals and three types of particles: graupel, that is, granular snow pellets, also called soft hail, sleet, that is, partly frozen ice pellets, and hail, for example, hard spheres of ice (see details in References 1—4, 6—9).