What difference does elevation make for air pressure?

What difference does elevation make for air pressure?

Saturday, my wife and I took a few kids we go to church with up to Mount Rose and Lake Tahoe while their mom had a work meeting in Reno. After spending some time playing in the snow where Highway 431 crosses the mountain (elevation 8,911), we drove down to Kings Beach for some hot chocolate. As we descended to the side of the lake, the oldest kid we were watching was unable to make her ears pop despite several different attempts to do so. She eventually gave up, and just suffered until we got back down to Reno.

Most folks know that the higher you get, the less air there is (and if you didn’t, now you do and can just pretend you always knew it). Saturday’s experience got me thinking, though – how much of a difference does elevation actually make? The product of that wondering is this blog post.

The relationship between elevation and air pressure is not linear but exponential. Instead of changing constantly as you gain elevation, it starts off dropping fast and slows down the higher you get. There are a couple really ugly mathematical formulas to figure out the relationship, but as I don’t like math we’ll rely on a calculator.

The relationship between air pressure and elevation. (Source: University of Illinois Urbana-Champaign)

The “standard” air pressure at sea level is 1013.25 millibars (mb). Of course, weather events cause variations in this. The standard is what it would be if there were no weather events and everything around the planet was exactly the same. At this air pressure, the force the earth’s atmosphere exerts can be rounded to 14.7 pounds per square inch (psi). We’ll talk about individual storms more in-depth later on.

Bringing it back to our situation yesterday, we started off where we all live in Fernley (elevation 4,150), drove through Reno (elevation 4,506), up to Mount Rose (elevation 8,911) and then down to Kings Beach on the north shore of Lake Tahoe (elevation 6,224) before doing that all in reverse. Throughout the day our elevation range (the difference between Fernley and Mount Rose) ended up being 4,761 feet. The following are the “standard” air pressures of everywhere listed:

So, by having internet applications do all the math for us we discover that between Fernley and Mt. Rose there is a near 19% decrease in the amount of air in the atmosphere. For me, 19% seems like a small change – and then I remember that my ears even pop when I drive over the Horse Heaven Hills between Kennewick, Washington, and Hermiston, Oregon. The air pressure difference between Kennewick and the top of that small pass is less than 5%, so my trip yesterday accounted for about four times that difference.

Of course, it is important to remember that everybody’s bodies are different. While my ears pop with a less than 5% difference, your “threshold” might be higher or lower than mine. I am by no means claiming a 5% change in air pressure as the “single true and correct number” for everyone.

This lack of air up in the mountains made running around while playing a snowy game of hide and seek a massive pain in the rear. This wasn’t as bad as the one time my dad ran around and did pushups on top of Pike’s Peak near Colorado Springs at 14,114 feet above sea level (the pressure up there is 592.53 mb, or 58% of what he was used to). It’s also why many Olympians train in places like Colorado Springs, which is over 7,000 feet above sea level. If you can acclimate your body to such low supplies of oxygen, when it’s time to go to the Olympics at a much lower elevation, your body will be able to use that extra oxygen more efficiently.

Air pressure changes so much, that if your smartphone has a barometer in it (list of smartphones here), you should even be able to see a difference in air pressure as you walk up or down stairs or take an elevator.

I’ve never seen air pressures as low as you said, even for the mountains.

While the “standard” air pressure at Reno is well below the lowest pressure ever recorded in a hurricane, you’ll never see a weather report that says that. To ensure uniformity and to make tracking weather systems easier, meteorologists calculate the “sea level pressure” instead of using “ambient pressure” readings. As of the time of writing, the sea level pressure at Reno-Tahoe International Airport was 1036.5 mb, with the ambient pressure (marked as “station pressure” on the National Weather Service’s website) is 880.1 mb. You can thank McRidge for the unusually high reading.

U.S. surface analysis for Sunday morning. (Source: Weather Prediction Center)

Imagine how obnoxiously hard to read weather maps would be if we didn’t convert ambient pressure to sea level pressure for weather reports. There would be consistent low-pressure systems in the Yellowstone area as well as in the Four Corners Region, and putting lines to show the air pressure would be completely useless because of the terrain differences found in the West and in the Appalachians.

What’s the point of ambient pressure?

There are two main places where ambient pressure is used. The first is in altimeters (which is why many smartphones have them). For those who don’t know, altimeters are devices that show your elevation. They have programmed in them the relationship between altitude and air pressure to display a decent estimate of your elevation. This can be useful for a variety of purposes, such as by pilots, folks who jump out of planes, and wilderness backpackers.

The second is in the world of weather. Instead of determining weather events in the upper atmosphere by feet or meters above sea level, meteorologists often use a certain pressure reading (such as 925, 700, or 500 mb). This then helps meteorologists determine where upper-level low- or high-pressure systems may be located as well as the jet stream. On top of this, using pressure levels instead of elevations makes the mathematical formulas used much simpler, and I’m all for making math simple.

Just as the actual air pressure varies from the standard when we are talking about specific elevations, the same is true for high up. Here’s a chart I swiped from the PDX WX Analysis group (though I can’t remember for the life of me who actually made it) that shows the general idea of where these different levels are:

One example of the usefulness of using air pressure instead of elevation is in finding the 500 mb height, which can be used (along with many other variables) to predict where snow might fall.

This 500 mb height is estimated in several ways. One of those ways is by looking at temperature and air pressure data on the ground. Another is done by sending balloons into the atmosphere and using pressure measurements taken by instruments on that balloon to determine where 500 mb is.

GFS chart showing 500 mb and thickness. (Source: Pivotal Weather)

The lines on the above map show different heights of the 500 mb line in dekameters above sea level (one dekameter is 10 meters). In the West, a large area is marked by ‘582,’ which means the 500 mb line is 5820 meters above sea level. This unusually high number is also a product of McRidge.

Air pressure in storms.

Map showing the size of Typhoon Tip compared to the United States. (Source: Wikimedia Commons)

Like has been mentioned before, variations in weather patterns make it so that the air pressure is not exactly the same around the globe. As of the time of writing, the sea level pressure at the center of McRidge is 1049 mb. The lowest ever recorded in a tropical cyclone was 870 mb (in Typhoon Tip).

It takes a lot of energy to get the air pressure as low as it gets in some storms. Let’s take a look at a few storms and what an altimeter would read if it was calibrated to the “standard” instead of taking into consideration the storm conditions.

Side note real quick – all of these calculations I have listed are assuming a temperature of 15ºC (59ºF) which, of course, isn’t the case in probably any of those storms. This is important because the air pressure will also vary based on temperature. This isn’t a new concept, of course. When things heat up, we know they expand. Conversely, when things cool down they contract. That expansion causes pressure to increase.

Note: Calculations will vary depending on the formula used.

Think about a vacuum cleaner. I am in no way prepared to say what pressure your home vacuum cleaner creates, but think for a second about what kind of energy it needs to decrease the pressure enough to suck up dust and whatnot. Now take that energy, and multiply it enough to decrease the atmospheric pressure over an area 9.3 miles wide to have the same air pressure as I do here in the high desert of northern Nevada.

Beyond decreasing the air pressure in that 9-mile area, Typhoon Tip was 1,380 miles wide. There was an area dozens of miles wide below 900 mb, an area even bigger below 925 mb and so on. If you ever have a desire to really appreciate just how much energy a particular storm has, go take a look at its central air pressure and compare that to the “standard” pressure at a particular elevation.

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