Session 2: Energy Balance

Part 4:
Energy Balance

How much radiation does the earth's surface absorb? What causes the air to warm during the day? How does the temperature change over the course of a day? We will try to answer these questions in this section.

The Solar Constant

As mentioned earlier, almost all the energy we see and feel comes from the sun. Scientists have determined a standard value for that amount of energy, which is called the solar constant. It is the average amount of energy that reaches the top of the atmosphere, on a plane perpendicular to the sun's rays, at an average distance from the sun. This value is approximately 1370 watts per square meter (W/m²). We say approximately because the sun's energy output does change slightly with time, due to sun spots and other phenomena, which we'll save for the astronomers. There are two key points, however. First, the sun's energy output is relatively constant, and there is essentially no interference (obstructions) with that radiation until it enters the atmosphere.

Earth's Energy Balance

The Earth's average temperature remains fairly constant from year to year. There are long term trends (like the ice ages), but no evidence of any dramatic temperature change from one year to the next. Therefore, the Earth must be releasing into space the same amount of energy that it receives from the sun. If this did not occur, the atmosphere would measurably warm or cool, depending on the amount of heat lost to space. So what happens to solar radiation once it enters the atmosphere, and how does energy get radiated into space? Well, we can think of the incoming solar radiation as being broken up into parts. The diagram below shows the average break down of solar radiation as it enters the atmosphere.

The Average Break Down of Solar Radation as it enters the Atmosphere

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When we combine the break down of incoming radiation with the break down of outgoing radiation, we have the earth-atmosphere energy balance. The chart below displays the average break down of energy lost and gained at the earth's surface. The units used are relative to the amount of incoming radiation. Notice that the total energy lost at the earth's surface (lower left hand corner) is equal to the amount gained at the surface (lower right hand corner).

The Average Break Down of Energy Lost and Gained at the Earth's Surface

(Click image to view in separate window)

The net energy at the earth's surface can be thought of as the sum of the incoming energy minus the energy required to heat the air minus the energy to evaporate water. This simple equation is known as the energy budget equation. The energy used to heat the air is directed upward, away from the surface, and so is considered a subtraction. The same is true for the energy required to evaporate water. This energy, however, is in the form of a heat we can't feel. It is known as latent heat.

Latent Heat

When you touch a hot stove, the heat you feel is called sensible heat (because your sense of feel is able to react to it). Latent heat is not really heat you can feel, but energy required to break the molecular bonds that keep molecules in a single phase. For example, it is latent heat that is used when you boil water and form steam. Latent heat is absorbed from the surroundings to melt ice and evaporate water. This makes sense because water molecules vibrate faster than ice molecules (as any liquid has more energy than its corresponding solid state). Latent heat is released when you go the other direction: freezing water and condensing vapor. The concept of latent heat is crucial to understanding why clouds develop. As the water vapor in the air cools, it condenses, releasing huge amounts of energy that allow the cloud to develop further by decreasing stability. We will discuss stability in greater depth in Session 6.

Bowen Ratio

The comparison between the amount of sensible heat and the amount of latent heat is often important when determining energy balance. As a quick method to compare the amount of sensible heat energy to the amount of latent heat energy, the Bowen Ratio was developed. It has the following form:

where B is the Bowen Ratio value, H_S is the sensible heat, and H_L is the latent heat. In situations where there is little moisture available, the H_L value will be small, and the Bowen Ratio will be greater than one. In situations where it is very humid, the H_L value will be large, and the Bowen Ratio will be less than one. In situations where the amount of sensible heat energy is near the amount of latent heat energy, the Bowen Ratio will be approximately one.

During the night, there is no incoming solar radiation, so the amount of sensible heat energy becomes minimal or even negative (loss of heat energy) . In these situations, the Bowen Ratio will be very small or even negative, as latent heat is not as dependent on incoming solar radiation.

Daily Temperature Variations

Let's look at the energy balance in terms of the daily variations in temperature. Incoming solar energy is a maximum when the sun is highest in the sky. But the surface of the earth warms continuously from the time the sun rises to the time it sets. Therefore, the earth radiates its maximum amount at sunset, and does not begin to slow down until the sun sets (no more incoming radiation). The earth is releasing the least amount of energy early in the morning, before the sun rises. The net energy at the surface is therefore the difference in the incoming radiation (shortwave) and the radiation emitted from the earth (longwave). The chart demonstrates further. Here, the energy surplus area means that more energy is entering the earth than is leaving it. The deficit area is just the opposite -- more energy is lost by the Earth than gained (due to the absence of sunlight). Remember, the total amount of net energy gained is zero -- there is an energy balance. The surplus area on the chart is showing the daily replenishment of energy into the Earth-atmosphere system necessary to maintain that balance.

One important item to notice is that the earth's maximum emission of heat is skewed to the right (toward sunset) of the maximum incoming energy . Another key observation is that the earth emits and absorbs radiation much more efficiently than the atmosphere. That is why the late afternoon is often much warmer than at noon, when the incoming shortwave radiation is a maximum. That's also why the early morning is the coolest time of day. The atmosphere warms and cools slowly, but the ground warms and cools much more quickly. The next time you're outside, feel the ground with your hand. If it is mid-day, it will feel significantly warmer than the air. If it is late night, it will feel significantly cooler. Differences in the rate of radiation absorption and release are a major factor influencing energy balance. This, and other factors, are discussed in the next section.

On to Focus on Air Quality

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Part 4: Energy Balance