Budgets and Composition

Read...

Understanding the global climate system often involves thinking in terms of “budgets.” Traditionally, we've used the analogy of a checkbook to explain budgets, but in today's digital age, online bank accounts serve as a more relevant comparison. Imagine you have a certain amount of money saved up, let's say $1,000, in your bank account; this is your account balance. Now, there are two crucial aspects we need to consider: inflows and outflows. Inflows represent money being added to the bank account, while outflows represent money being withdrawn from it – a logical concept. To maintain a constant balance, your net inflow and net outflow should be equal, in other words, money in should equal money out.

The energy within the Earth’s climate system follows a similar principle. It's essential to remember that temperature is strongly connected to energy. Over the years, we've noticed that the average weather experienced in any given location on Earth remains relatively consistent in the long term – this is what we call climate. This consistency suggests that, to maintain global energy balance, the Earth must radiate longwave energy to space at the same rate that it receives shortwave energy from the sun!

Remember, the Stefan-Boltzmann Law tells us that *any* body with a temperature greater than zero must be emitting some energy. Given this, we can estimate Earth's global temperature using the information about solar radiation from the previous section and the Stefan-Boltzmann law within this straightforward in = out framework. Most of the energy entering the Earth's system comes from the sun. We've defined a solar constant ($1370 W / m^2$) and explained that, in reality, this number gets divided by a factor of 4 when it's distributed across the entire surface of the Earth. Additionally, we've determined that Earth's albedo, representing the reflected energy, is approximately 30%. This means that only about 70% of the incoming radiation is absorbed by the planet, while the rest is reflected back into space. So, let's perform a simple calculation:

$$1370 W / m^2/ 4 = 340 W / m^2\ast 70.2 \mathrm{\%} = 239 W / m^2$$

Therefore, when we average this value across the entire Earth, every square meter of the planet absorbs 239 Joules every second from the sun. That's a substantial amount of energy! A Tesla can go about 350 miles with about 8,000 W – think about this, if we managed to cover the playing field at Beaver Stadium (18,000 square meters) with perfect solar panels that took every bit of incoming solar energy and converted it to electricity, we could fully charge over 32,000 Teslas every single minute! This hopefully gives some indication why solar energy is considered such a promising renewable energy source.

This represents our energy input, but we also need to account for energy output. As mentioned earlier, the Stefan-Boltzmann Law relates the energy radiated from a black body in space to its temperature. To offset the incoming solar energy, Earth must radiate $239 W / m^2$ back into space. Without delving into too many details, we can use a simple equation to calculate this – don’t worry, I won’t make you solve it! The mathematical expression of Stefan-Boltzmann's law is as follows:

$$E = \sigma T^4$$

Here, E represents the emitted energy, T denotes the temperature, and σ is a constant (interestingly named the Stefan-Boltzmann constant). One thing it tells us is that as T goes up, E must also go up by some amount – we’ve already discussed that before. But if we rearrange the equation and solve for T, we can estimate the temperature Earth needs to have in order to radiate at $239 W / m 2$ and achieve our in = out balance. This is referred to as Earth's “emission temperature,” or in simpler terms, what an alien observer in outer space would measure with a thermometer pointed at Earth. If you're interested, feel free to use your calculators to verify, but the temperature comes out to be around 255 Kelvin. In more familiar units, this is equivalent to -18 °C or 0 °F. Quite chilly! We have satellites in space, and they corroborate this temperature as the overall emission temperature for Earth – fascinating, isn't it?

However, 0 °F is exceptionally cold! While certain regions on Earth can experience such cold temperatures occasionally, the average surface temperature of our planet is significantly warmer. Observations indicate that our global mean surface temperature is closer to 290 K (16.8 °C or 62 °F). This apparent disparity raises a crucial question: why is our planet's surface warmer than its emission temperature of longwave radiation to space? The answer lies in our atmosphere, which envelops our planet and makes the surface much more hospitable, given the input of solar energy. Continue reading to unravel this fascinating phenomenon.

Atmospheric composition

Before we explain why the Earth’s surface temperature is what it is, we need to briefly discuss the composition of the atmosphere. Obviously, the air we breathe is critical for our survival, but it's actually a mixture of many different types of molecules. Some of the gases are “permanent,” meaning that their concentrations are basically constant. Other gases are “variable,” meaning that their concentrations vary from time to time and place to place. I've summarized the gases that comprise our atmosphere and their concentrations in the table below:

What are the big takeaways? First of all, even though we need to breathe oxygen to survive, oxygen is not the most abundant gas in the atmosphere. Nitrogen is, by far. There's nearly four times as much nitrogen as there is oxygen. However, nitrogen and oxygen, combined, account for roughly 99% of “dry air” in the atmosphere, so they're the “big two” in terms of total concentration. For every million molecules of air you breathe in, 990,000 of them are nitrogen and oxygen.

Of course, air isn't perfectly “dry.” Water vapor also exists in our atmosphere, but note that the concentration of water vapor is rather small and is variable (it varies from 0 to 4 percent). Furthermore, while you might hear a lot about carbon dioxide in the news because of its connection to climate change, it only accounts for about 0.041 percent of the atmosphere. Surprised? Give me a second, because we’ll talk about why it’s still important in a minute.