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Weather Almanac for April 2003
THE ENERGY OF A RAINSHOWER
One required ingredient for both cumulus clouds and shower formation is ascending air which these thermals provide, pushing the moist air to its condensation level where the cumuloform clouds find their base and higher. Ascending air and condensation of water vapour form clouds, but this does not assure that rain will fall from them.
For some of those rising warm thermals, however, the conditions they experience are conducive to climb higher up the precipitation ladder. If precipitation is to fall from a cloud, there must be additional processes within the cloud forming raindrops from the cloud droplet population. A typical raindrop contains the water equivalent of a million cloud droplets, and the raindrops must grow to sizes that can fall to the ground without evaporating if there is to be rain.
Drop growth by collision and coalescence the combining of raindrops and droplets into larger drops is one process for increasing raindrop size. Turbulent currents within the cloud provide the first collisions between droplets. Clouds with strong updraft regions have the best drop-growth environment because the drops and droplets stay in the cloud longer and thus have many more collision opportunities. (For more on the development of clouds and rain, see Making Clouds and Rain.) When the drops grow large enough to overcome the pushing force of the updrafts, or when the updrafts cease, drops fall earthward as rain.
For a few thermals, conditions may be ideal for ascent to high altitudes, and the resulting cloud becomes a cumulonimbus with a few flashes of lightning and low, rumbling thunder: a spring thundershower.
Eventually, raindrops fall through the cloud base and descend earthward. If the raindrops are not large enough to traverse the drier air below, they evaporate back into the air. We see these aborted showers as virga, fuzzy streaks falling out of a cloud which do not reach the surface.
The larger drops reach the surface, however, and strike it with a force dependent on their size. Drizzle drops are typically 1.2 mm (0.05 inches) in diameter the size of a grain of salt and hit sofly. Typical raindrop diameters are 3.0 mm (0.12 inches), while large raindrops 6.0 mm (0.24 inches) in diameter strike with significant force.
How fast do raindrops fall? Assuming the raindrops fall through still air, two forces acting on the drops determine its terminal velocity. First, gravity pulls the raindrop earthward. If the drop fell through an airless environment, the raindrop would accelerate at 9.81 m/s2 until it hit a surface, its speed on contact depending on the fall distance or, alternatively, its fall time. Thus, a raindrop falling from 500 metres (1650 ft) through a vacuum would smash into the ground at nearly 100 metres/second (225 mph). Fortunately, the second force acting on the drop aerodynamic resistance or drag slows the falling drop. When the two forces balance, the drop reaches its terminal velocity. Thereafter, it falls at that terminal speed until it hits the ground.
Small drizzle drops fall at 2 m/s (4.5 mph). A raindrop 2 mm (0.08 inches) in diameter falls at 6.5 m/s (14.5 mph) while a large raindrop measuring 5 mm (0.2 inches) across the size of a small housefly falls at around 9 m/s (20 mph). For comparison, a baseball dropping from a towering pop-up hits the outfielder's glove at a terminal speed of 42.8 m/s (95 mph).
Since the drops are falling within an environment where updrafts and downdrafts are common, they will fall at speeds different from those calculated above. A drop's falling speed can be calculated by adding the speed of the up/downdrafts to its terminal velocity.
Here, we consider the updraft as a negative speed. A drop falling at a terminal speed of 6.5 m/s caught in a 2 m/s updraft, would fall relative to the ground at 4.5 m/s. If the updraft speed is greater than the terminal speed, the drop will rise in altitude rather than fall. That drop fallin in a downdraft of 2 m/s descends at 8.5 m/s.
In a rain shower, a great deal of energy is transferred from the falling drops to atmosphere as it falls through and the earth as it hits. Following the procedure outlined by E.C. Pielou in her book The Energy of Nature, we can calculate the energy in falling rain.
First, let's set the rain shower of an intensity that would dump 1 mm (0.04 in) of rain uniformly over an area of one hectare (10,000 square metres or just under 2.5 acres). The volume of water in the rainfall is depth x area = 0.001 m x 10,000 m2 = 10 m3. The mass of that volume is 10,000 kg (each cubic metre of water weighs 1000 kg).
If that mass fell unimpeded from an average height of 500 metres, the potential energy (mass x acceleration by gravity x fall distance) released when it reaches the ground would be
10,000 kg x 9.81 m/s2 x 500 m = 4.9 x107 Joules
We know, however, that the aerodynamic resistance works against the falling mass. If we assume the rain fell in uniform-size drops of 2-mm diameter falling with a terminal velocity of 6.5 m/s, we can calculate the kinetic energy with which the accumulated drops struck the ground. From basic physics, the kinetic energy of the falling rain is:
½ x mass x velocity squared = ½ x 10,000 kg x (6.5 m/s)2 = 2.1x105 Joules.
Comparing these two numbers shows us that the drag has reduced the potential energy release at the surface by a factor of about 250. This energy has been lost to the atmosphere, dissipated as heat through the drag. (Drag is the same as friction. If you run your hand over a rough surface long enough, you can feel some of the heat energy lost by the motion to friction flowing back into your hand.) Much of the remaining energy is transferred to the surface by the impact.
If our rainfall was instead composed totally of large drops measuring 5 mm (0.2 inches) across and falling at 9 m/s, the kinetic energy of the fall would be about twice as much: 4.0x105 Joules.
The Joule is not a unit of energy for which most of us have a good appreciation. One calorie (gram) is 4.2 Joules; therefore, 1 Joule is about a quarter calorie (0.24 cal). One Joule is also a watt-second. Thus, the small-drop rainfall imparts a total of 50,000 calories of energy to the surface, or enough to light a 100-watt lightbulb for thirty-five minutes.
The shower intensity we chose was fairly light in total rainfall accumulation. What if the shower was a heavy downpour that deluged the hectare with 25 mm of rain (about one inch)? If this does not sound impressive, it takes over 1.2 billion raindrops per square metre (about a square yard) to accumulate this much rain. Distributed over a hectare (2.47 acres), that totals more than a quarter million litres (66,000 gallons) of water weighing 253 tonnes (280 tons).
On the other hand, assuming the deluge all fell as large 5-mm-diameter drops, the total kinetic energy of such a rainfall would be: 107 Joules. Enough energy to light that 100-watt bulb for 28 hours.
Where does all that energy go?
Most of the energy is transferred into the surface it has struck whether rock, soil, water or living matter. Some of that energy deforms both the surface and the drop. The drop may be rent apart, and some of the energy transferred back in a rebound of the drop pieces which then either evaporate into the air or fall again to the surface. Some energy is used to deform the surface, forming drop craters in dirt or sand, causing a splash in a water surface, damaging the substrate perhaps chipping a bit of rock loose or breaking the body of a plant or small animal struck by the drops. A good portion is lost to that universal energy sink: entropy.
And, a fraction of the raindrop energy is transformed into sound, the nature of the resulting sound waves dependent on the energy of the falling drops and the nature of the surface struck. This is the energy that gives us the well known pitter-pat, splat, tip-tap, and the myriad other sounds we associate with falling rain.
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