I've likened energy budgets to your bank account, and we'll use that idea to diagnose surface temperature trends. In banking, if you deposit more money in your account than you withdraw, your account balance will grow. But if you withdraw more than you deposit, your account balance will shrink.
Using radiation to construct an energy budget is similar. If an object absorbs more radiation than it emits, then its temperature will increase. It will warm up because more radiation is coming in than is going out. On the other hand, if an object absorbs less radiation than it emits, its temperature will decrease. It will cool because more radiation is going out than is coming in and being absorbed.
So to figure out if you have a net gain or loss of radiation, you take the difference between your incoming radiation and outgoing radiation. For the earth's surface we use this equation. We have downwelling solar and downwelling infrared as our sources of incoming absorbed radiation, and upwelling infrared radiation as outgoing emitted radiation. A positive result means a net gain in radiation and the earth's surface warms up. A negative result means a net loss of radiation, and the earth's surface cools.
Let's look at an example from Penn State University on May 8, 2017. To get our bearings on the graph, the red curve shows downwelling solar radiation, which is coming to the ground and being absorbed. The blue curve shows downwelling infrared radiation, which is radiation coming to the earth from clouds and air molecules in the atmosphere. The green curve shows upwelling infrared radiation, which is radiation that's being emitted from the earth.
To get a sense of what's going on here, let's start by looking at the solar curve. It's flat at zero watts per square meter until just after 10Z, which is 6:00 AM local time at Penn State on May 8, because Daylight Saving Time is in effect. After sunrise around that time, the amount of downwelling solar increases. And the curve is mostly smooth except for a few wiggles, which is telling us that skies were mostly clear.
Then after 17Z, the solar curve jumps around quite a bit, and there are some really big decreases because of clouds scattering some incoming solar radiation back to space. We also see some small upward bumps in the downwelling infrared curve, because the clouds were emitting some additional IR radiation to the ground, too.
So what if we want to calculate a net gain or loss of radiation at local noon? That's 16Z on May 8 at Penn State. And we just have to read our values off the graph and plug them into our equation.
It looks like incoming solar would be about 1,000 watts per square meter at 16Z, and we just have to plug that into our equation. Downwelling infrared radiation looks to be about 250 watts per square meter. So those are our two sources of incoming radiation at the surface.
Our upwelling infrared is our emitted radiation, marked by the green curve. And it would be about 400 watts per square meter. So we have to subtract 400 in our equation.
Crunch the numbers and we end up with a positive result of 850 watts per square meter. The ground was warming up at local noon because we had a net gain in radiation at that time. More radiation was coming in and being absorbed than was being emitted. In reality other factors impact temperature, too, but we're going to ignore those for now and just focus on the impacts of radiation on temperature trends.
If we wanted to do a calculation at nighttime, we could do that too. Let's do one before dawn at 9Z. That's 5:00 AM local time at Penn State on May 8. Note the little bump up in downwelling infrared at this time, suggesting some cloudiness. Again, we just have to read the values off the graph and put them into our equation.
There's obviously no contributions from the sun at 9Z because it's before the sun comes up. So downwelling solar is zero watts per square meter. Downwelling infrared is about 300 watts per square meter, and upwelling infrared is about 320 watts per square meter. So we take 300 and we subtract 320. And we get a result of negative 20 watts per square meter. That's a small negative result. And the ground would be cooling very slightly, since we have a small net loss of radiation. A little more radiation is leaving than is coming in and being absorbed.
So clouds acting as space heaters at this time were able to boost downwelling infrared radiation almost enough to erase the radiation deficit and nearly stop the nighttime decrease in temperature at this time.