Thursday, February 19, 2015

Winter Storms and a Simple Math Exercise

I love hearing someone make the same lame jokes about winter storms and global warming. They think they're being cute, but the reality is they are simply showing they don't understand what is going on. They ignore the fact that we will still have winter even with global warming. This is because winter is caused by the way Earth is tilted on its axis.

Every year, on about September 21, the North Pole experiences its one and only sunset of the year. Gradually, over the next three months, the part of the Arctic region experiencing 24-hour nighttime will increase until, on about December 21, everything north of the Arctic Circle has a 24-hour nighttime. Then, that amount will gradually decrease until the North Pole experiences its one and only sunrise on about March 21. What this means is by January and February, there are parts of the Arctic region that have been sitting in dark for 2-4 months. That is going to make those areas cold. Take a look at this current temperature graphic:

Source: Polar Portal
It is no-kidding cold up there. So, it is no wonder we still have winter storms. If that mass of air moves down into our area we are going to feel it, even with global warming. But, it takes energy to move that mass. Lot's of energy.

So, let's do a simple exercise to see for ourselves.

First, take a look at this graphic showing the cold air mass moving into the the eastern U.S. today:

Source: Climate Reanalyzer
I'm sure I don't need to tell the people under that purple area that it is no-kidding cold there, too. That mass of air moved down from the Arctic and is now moving across the country. But, it didn't just happen by itself. It took energy to get there. Let's do a back of the envelope calculation and get an idea of how much.

We want the mass of that blob. To do that, we can find the surface area under the purple region and multiply the area by the pressure (weight per area) and then convert from weight to mass. If we approximate the cold air region as a circle we can calculate the area as pi*r^2. We can estimate the purple blob is about 1000 miles across. A mile has 5280 feet, so it is about 5.3 x 10^6 feet across. Dividing our diameter by two, we get the area is:

Area = pi*([5.3 x 10^6]/2 feet)^2 = about 2.2 x 10^13 square feet

A square foot has 144 square inches, so our area, in square inches, is

2.2 x 10^13 square feet x 144 square inches/square feet = about 3.15 x 10^15 square inches.

Atmospheric pressure is about 14.7 pounds per square inch, giving us a total weight of

3.15 x 10^15 square inches x 14.7 pounds per square inch = about 4.6 x 10^16 pounds.

That is the approximate weight of that big purple air mass over the eastern U.S., but we want mass, preferably in the metric system. There are 2.2 pounds to a kilogram (on the surface of Earth), so the mass of this air, in kilograms, is about:

4.6 x 10^16 pounds x 1 kilogram/2.2 pounds = about 2.1 x 10^16 kilograms.

The amount of energy this mass has can be found by calculating its kinetic energy, the energy of movement. That means we need a speed. I have read winds speeds of up to hurricane strength, but we won't go that high. We can estimate an average speed of about 44 miles per hour and that equates to 20 meters per second. Using that speed, we can estimate the amount of energy as:

Kinetic Energy = 1/2 * m * v^2
                         = .5 * 2.1 x 10^16 kilograms * (20 meters per second)^2 = about 4.2 x 10^18 joules.

How much energy is that? In comparison, the entire planet generates about 6 x 10^20 joules of energy per year. In other words, by our simple exercise, we can see it would take the entire planet about 2.3 days to generate the amount of energy consumed in moving this one single air mass. And, our calculation is actually very low. We did not include friction, interior fluid dynamics, the work required to move the air in front of our air mass out of the way, the work required to move air in behind the air mass, the expansion and compression of gases, etc. There is, in fact, a whole lot more work involved than just getting the mass up to speed.

So, where did that huge amount of energy come from? Well, obviously, it came from the atmosphere. But, where did the atmosphere get it? Simple. It came from the greenhouse effect. If there was no greenhouse effect, energy coming in as sunlight would be reradiated and reflected back out to space and there wouldn't be anything left over to do any work. Some of it must be stored in the atmosphere to be used later on. Most of that is being done through the natural greenhouse effect that has always been there. But, has that greenhouse effect been enhanced by manmade emissions? We can check the frequency of storms to see. If the number of winter storms has been increasing, we can conclude the energy is coming from some other source than naturally stored energy, i.e., AGW.

NSIDC lists the top 57 storms to hit the U.S. These figures show 20 of those storms occurred since 2010 (inclusive). That is an average of 3.33 storms per year. Nine storms occurred in 2000 - 2009, an average of .9 storms per year. Five storms occurred in the 1990s, an average of .5 storms per year. Five storms also occurred in the 1980s, an average of .5 storms per year. Four storms occurred in the 1970s, an average of .4 storms per year. Eleven storms occurred in the 1960s, 1.1 storms per year. There were three storms listed for the 1950s (.3 storms per year) but it doesn't indicate if that means there were only three storms or they didn't list them for years prior to 1956, so we'll leave that figure out of our discussion.

Listing them in order, from the 1960s to the 2010s, we see the average number of severe winter storms per year went from 1.1, .4, .5, .5, .9 and 3.33. After the 60s, there is a definite trend of an increasing number of severe storms per year. This is exactly what we would expect to see if the amount of energy in the atmosphere was increasing. And, we would expect to see the amount of energy in the atmosphere to be increasing if AGW was real.

So, this simple math exercise and this data supports the conclusion that AGW is real and is changing our climate. Is this conclusive? No. There are two significant omissions in this calculation that are important. The storm activity I listed was for severe storms only. What about non-severe storms? How do they factor in? Also, this activity was for the U.S. only. What about the rest of the world? What was going on there?

I could not find data listing all winter storms, so I will leave the focus on severe storms only and I think that is adequate for the question we want to answer - are the number of storms increasing, decreasing or staying about the same.

Wikipedia has a list of windstorms to hit Europe. Going through and picking only the storms to hit in the winter months, I get five storms hit in the 1960s, four in the 1970s, six in the 1980s, ten in the 1990s, 16 in the 2000s and 17 in the 2010s (through Feb 2015). The yearly averages come out to: .5, .4, .6, 1.0, 1.6 and 3.6. The data for Europe is very consistent with what we saw for the U.S. and we see the number of storms for Europe have also been increasing in recent decades at an accelerating rate.

So, our simple exercise shows why we have winter storms, even with global warming. And, it also happens to provide additional evidence AGW is real and getting worse.

So, yes, winter storms really can be the result of global warming.

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