5.1: Energy Balance

A Balanced Budget

In Investigation 3, we introduced the concepts of Heat, Radiation, and Absorption. Recall that radiation is either absorbed, reflected, or scattered by Earth’s surface/atmosphere. What is reflected either returns to space, is absorbed by other materials, or is scattered in the atmosphere, producing the beautiful colors we see. We’ll investigate this breakdown a bit more in this investigation, but for the sake of simplicity, we can say that approximately 70% of the sunlight that reaches Earth’s atmosphere is absorbed by the Earth (51% by Land/Ocean/Surface, and 19% by the Atmosphere and Clouds) and 30% is either reflected or scattered by Earth (20% is reflected by clouds and the atmosphere, 4% by land/ocean/surface, and 6% is scattered by atmospheric molecules, producing colors).

All the energy that the Earth absorbs increases its temperature above absolute zero (0 K). According to the Law of Conservation of Energy, energy cannot be created or destroyed, but can be transferred from one form of energy to another. Thus, the energy absorbed by the Earth is converted into other forms of heat, such as conduction, convection, radiation, and latent heat exchanges. We’ll briefly cover those later in this investigation. While the energy budget sounds complicated, you can think about it like a checking account, and you can think about your budget as two main components: Income and Spending.

A balanced budget is achieved when your income and your spending are equal. In this case, what goes in equals what comes out, and the amount of money in your account ends up staying the same. When income is higher than spending, meaning you are earning more money than you are losing, the amount of money in your account should go up. When income is less than spending, meaning you spend more money than you make, the amount of money in your bank account should go down ☹.

Now let’s apply that same concept to temperature:

1. When incoming solar radiation equals the amount of radiation lost by Earth, Earth’s temperature should:
   1. Increase
   2. Decrease
   3. Remain the Same.

Well, let’s throw our budget out of balance. Figure \(\PageIndex{1}\) is a 24-hour graph of incoming (yellow line) vs. outgoing (blue line) radiation and temperature (red line).

Figure \(\PageIndex{1}\): Daily radiation balance and air temperature, highlighting warming when energy in exceeds out and cooling otherwise. (Public Domain; Alicia Mullens). Alternative Description of Image.

From just after sunrise (6 am) until mid-afternoon, incoming solar radiation is larger than outgoing radiation (the blue line). During this time, more heat is going in than coming out. Just like the checking account example before question 1.

2. When incoming solar radiation is greater than outgoing radiation, Earth’s temperature should:
   1. Increase
   2. Decrease
   3. Stay the same

Notice that the warmest time of day, i.e., when the red temperature line is at its peak, occurs a few hours after noon, i.e., when the sun is at its highest in the sky. This is called Temperature Lag. This is because, even though solar radiation declines after noon, it remains greater than outgoing radiation for some time. However, as the Earth continues to warm, it also emits more radiation (as per the Stefan-Boltzmann law from Investigation 3). In the afternoon, incoming radiation begins to decline while outgoing radiation continues to increase. Eventually, the two equal one another, and balance is achieved again. At this moment, the temperature stops rising and levels off, and it is the warmest time of the day. So if you’ve ever wondered why it’s warmer at 3 or 4 pm than it was at noon, it’s because Earth remains in an energy surplus until later in the afternoon.

3. Now let’s go past mid-afternoon. At this point, the sun is lower on the horizon, and the amount of incoming solar radiation is less than the amount leaving Earth. At this point, the air temperature should:
   1. Increase
   2. Decrease
   3. Stay the same

If you’ve ever noticed, especially on those long, sunny summer days, it feels cooler later in the evening (around sunset) than it did earlier in the afternoon. This is because, even though there is still sunlight coming in, it is now much less than the radiation escaping Earth. Once it is nighttime, no sunlight is heating the Earth anymore. But the Earth continues to emit radiation. It is important to note that this is not because of “heat left over from the day.” If the sun never rose again, Earth would still continue emitting radiation for a long period of time because it would still have a temperature above 0 K. So at night, Earth continues cooling until the next morning, when the Sun rises, and the cycle begins all over again.

A quick review before we continue on:

• When incoming heat is greater than outgoing heat, Earth warms
• When incoming heat is less than outgoing heat, Earth cools
• When incoming heat is equal to outgoing heat, Earth’s temperature remains the same.

Energy Balance and Seasons

Let’s apply this same concept to understand our seasons. But before we do, we need to know two important dates for the Northern Hemisphere (these two dates are the opposite for the Southern Hemisphere):

Winter Solstice: December 21st. On this day, the Sun is the furthest south of the equator, and the amount of incoming solar radiation in the Northern Hemisphere is at its lowest.
Summer Solstice: June 21st. On this day, the Sun is the furthest north of the equator, and the amount of incoming solar radiation in the Northern Hemisphere is at its highest.

4. Applying the same logic from questions 2-3 (namely, the warmest time of day is a few hours after the sun is at its peak), the warmest time of the year should be:
   1. Before June 21st
   2. Exactly on June 21st
   3. After June 21st

Let's check our answer. Figure \(\PageIndex{2}\) shows a map of the average warmest day of the year for the continental United States.

Figure \(\PageIndex{2}\): Map of the average warmest day of the year for the United States, including Alaska and Hawaii. (Public Domain; NOAA via Climate.gov). Alternative Description of Image.

5. With the exception of Southern Arizona, New Mexico, and western Texas, most of the continental United States has an average warmest day of the year:
   1. Before June 21st
   2. Exactly on June 21st
   3. After June 21st
6. This ___________ the hypothesis made in question 4.
   1. Can Confirm
   2. Cannot Confirm