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Dr. Christopher S. Baird

How does a cloud fill up with water?

Category: Earth Science      Published: February 7, 2014

cloud
Public Domain Image, source: Christopher S. Baird.

Strictly speaking, a cloud does not fill up with water. First of all, a cloud is not a sponge made out of some other material which soaks up water. The water in a cloud is the cloud. More accurately, a cloud consists of very small liquid water drops or ice crystals suspended in air. The water drops and ice crystals that make up a cloud are floating not because they are soaked up by some sponge-like material that is holding them in place. Rather, the water drops and ice crystals that make up a cloud float because they are so small that the air resistance balances out gravity. To be more precise, the water drops and ice crystals that make up a cloud do not actually float motionless in the sky. Rather, they are constantly falling very slowly under the influence of gravity and are occasionally lofted upwards by an updraft of wind. This falling and updrafting motion of the drops/crystals that make up a cloud is so slow, and clouds are so big and far away, that it is hard for a casual human observer on the ground to notice this motion. The book "Cloud Physics" by Louis J. Battan states, "A droplet of 10-micron radius falls at a speed of 1 cm/sec [0.02 mph], while droplets of 50-micron radius fall at a speed of 26 cm/sec [0.6 mph]." When the drops of liquid water or ice that make up a cloud increase in size through collisions and coalescence, they can get so big that the air resistance can no longer counter gravity (when r > 0.1 mm). Such droplets fall down as rain.

Secondly, clouds are not full of water. They are mostly full of air. When we say a bucket is filled with water, we mean that just about every available space in the bucket contains water. In a cloud, every available space definitely does not contain water. The water making up a cloud falls down as rain long before it coalesces enough to fill the entire volume of a cloud. Amazingly, only one billionth of the volume of a cloud consists of water. The rest is air. This means that for every one cubic nanometer of a cloud containing water, there are about a billion cubic nanometers in the cloud that contain just air. The book "Color and Light in Nature" by David K. Lynch and William Charles Livingston states, "Despite their impressive visibility, clouds are tenuous beings. A cumulus may have 1000 droplets per cubic centimeter, but these drops are minute and comparatively widely spaced. Water makes up less than one billionth (10-9) of the cloud's apparent volume and contributes only about one millionth of a gram per cubic centimeter to its density." Clouds are definitely not full of water. They are mostly full of air.

How can clouds be so visually striking when they are mostly invisible air? The key is that light reflects off the surface of objects. The more surface area, the more that light gets reflected. It is the same reason that pure solid ice is mostly clear but snow (which is just ice in small complex shapes) is bright white. While a cloud does not contain a lot of water in terms of total volume, the water it does contain is divided among trillions of small droplets, leading to many reflecting surfaces.

For example, assume for simplicity that a cloud consists of water droplets that are all the same size with radius r and are distributed uniformly. Suppose the total volume of the cloud is fixed at Vcloud and the total volume of the water in this cloud is fixed at Vw. Since the volume of a single spherical drop of water is 4/3 π r3, the number of drops n in the cloud times this drop volume gives us the total water volume in the cloud: Vw = n 4/3 π r3. Similarly, the surface area of one sphere is 4 π r2, so the total droplet surface area in the whole cloud is Atotaln 4 π r2. Solving the volume equation for n and substituting the result into the area equation, we find: Atotal = 3Vw/r. Since the total water volume is fixed, this equation tells us that as the radius of each drop goes down, the total droplet surface area goes up, as shown in the graph below. For small cloud droplet sizes, the total cloud droplet surface area jumps up to very high values. Since the amount of the light reflected by an object depends strongly on its surface area, the large total cloud droplet surface area allows a cloud to be bright despite being mostly air. Note that as an individual drop shrinks in size, its individual surface area of course gets smaller. But for a fixed total volume of water in a cloud, smaller drops means more drops, which means more total surface area.

plot of the total surface area as a function of drop radius in clouds
Assuming that the total volume of a cloud and its total water volume are constant, and that the cloud droplets are all the same size, the total droplet surface area of the cloud is inversely proportional to the drop radius, as shown in this plot. Since the amount of light reflected by an object strongly depends on the surface area of the object, we see that the small drop sizes in a cloud produce a huge surface area which reflects a lot of light. In this way, clouds can be bright despite being so empty. Public Domain Image, source: Christopher S. Baird.

Topics: atmosphere, cloud, condensation, droplet, gravity, ice, temperature, water, weather