Thursday, September 26, 2013

Sea-level pressure is horribly complicated

Yes, it's going to rain a lot this weekend in the Pacific Northwest.  Let's get that out of the way first.  If you want more details on that, see Cliff Mass's blog here.  I may post more on that event this weekend as it unfolds.

Right now I want to talk about pressure.  Atmospheric pressure.  This is the first part of a two-part blog series I'm writing on surface pressure observations and how you can help make surface pressure observations better if you own a weather station.  Yes, you.  But to talk about that, we need to get some basics out of the way first.

Atmospheric pressure is one of the more vital observations that we make in meteorology.  We usually think of pressure as the "weight" of all the air in a column above a certain point.  This makes pressure unique among our surface weather observations in that it is strongly connected with the entire depth of the atmosphere.  By observing changes in surface pressure, we're looking at the sum of changes throughout the depth of air above your head.  This makes pressure really valuable--and it shows.  Mariners closely watch their barometers--they know that falling pressure often signals approaching stormy weather while rising pressure indicates clearing skies.  What other single surface observation can so thoroughly describe the changes in the weather?

Mariners have an advantage, though.  They're all on boats at sea-level.  Changes in elevation mean changes in surface pressure.  Here's an example.  This is a map of the raw surface pressure analyzed over the Pacific Northwest:

Pressure values are given in a variety of ways.  The international standard in meteorology is to use a unit called hectoPascals (hPa), which is hundreds of Pascals.  Fortunately, another unit we're more familiar with in the US--the millibar--is exactly equivalent to the hectoPascal.  So, a pressure of 1000 mb is also a pressure of 1000 hPa. Another unit you may be familiar with if you're a pilot or you watch the evening news a lot is "inches of mercury".  I don't use that unit a lot, but it's common among non-meteorologists.  Standard pressure at sea-level is about 1013 mb/hPa or 29.92 in. of mercury. We'll talk more about pressure units in a later blog.

Anyhow, does that surface pressure map above look vaguely familar?  For comparison, here's a map of the land surface elevation over the same area:
The surface pressure pattern looks nearly identical to the elevation map.  By far, the most dominant signal in surface pressure is the signal of terrain.  As you go up higher in the atmosphere, there's less air above you, so the "weight" of the air decreases and the pressure at these higher altitudes is lower.  This poses a bit of a problem for trying to find the weather signal from surface pressures.  The difference between high and low pressure centers in the weather can be on the order of  only a few millibars...maybe tens of millibars for deep lows and strong highs.  Yet we see on the surface pressure map that the pressure change just from going from sea-level to the peaks of the mountains is on the order of hundreds of millibars!  This swamps our weather signal.

So what is a meteorologist to do? We try to filter out the signal of the terrain in some way.  One of the most common ways is to compute the mean sea-level pressure (MSLP), also called "reducing" the pressure to sea-level.  To compute this, we have to make assumptions about the lower atmosphere.  It turns out that the rate at which pressure decreases with height is very predictable, provided that you know the temperature as you go up in height.  If we knew the temperature in the atmosphere between the top of the mountains and sea-level, we could extrapolate what the pressure would be at sea-level if we filled the mountains with air.

The problem is--there is no atmosphere underneath the mountains.  So we can't know what the "air" temperature is between the top of the mountains and sea-level because all we have there is rock.  So how do we get around this?  There are a number of ways.  Some ways involve guessing what the temperature profile would be by using the temperatures along the slopes of the mountains.  Other ways use nearby weather balloon observations launched from lower elevations to help guess what the temperature profile would be.

The most common method, however, is to use an idealized atmosphere.  A long time ago, most of the international community agreed upon a standard "averaged" atmospheric temperature profile to tackle this very problem.  Well, most of the international community.  There are two basic forms: the US Standard Atmosphere  and the International Standard Atmosphere.  From Wikipedia, here's what the US Standard Atmosphere looks like:

The temperature curve is the red line in the middle of the diagram, and you can see how the standard atmosphere changes with altitude. You'll note that for the lower part of the atmosphere there is a constant "lapse rate"--the rate at which temperature decreases with height.  This is about 6 degrees Celsius per kilometer.  Using that, if we know the temperature at the surface of the terrain, we can just keep adding 6 degrees Celsius for every kilometer we go down in elevation until we reach sea-level.  This lets us extrapolate the "average" temperature profile from the terrain elevation to sea-level to let us get our reduced pressure value.

However, the temperature at the surface of the terrain can be influenced by a lot of things--local ground cover, instrument siting, etc.  It seems foolhardy to use the instantaneous temperature measurement at a point to begin this computation. Temperature is a very local phenomenon--it varies drastically over very short distances. Furthermore, temperature varies widely throughout the day right at the surface--it gets cold at night and warm during the day--simply because the land surface is right there.  Yet, once you get above the ground, these wild variations in temperature rapidly die off.  So our temperature we use should be more like the temperature we'd expect at that location if the ground were not right beneath it. Frustration! So now what do we do?

The National Weather Service standard used for airport observations across the country is to take the 12-hour mean temperature at the location and use that for the surface temperature.  This doesn't get rid of any temperature bias due to the instrument's location, but it does help eliminate the wild swings in temperature throughout the day.  The long mean provides a smoother temperature that is a bit more reliable.  They take this 12-hour temperature mean and use the US Standard Atmosphere lapse rate to estimate what the "theoretical" temperature of the atmosphere would be all the way down to sea-level. Knowing this, they then correct the raw surface station pressure reading to a mean sea-level value.  After all this work...finally we get a map that looks like this:

You'll notice that a lot of the terrain is filtered out now.  There are still some hints of it, since all the assumptions made were not perfect.  In particular, you'll notice that over the high terrain of Montana and Idaho there is still an area of lower pressure that seems a bit suspicious.  Those locations have a very high elevation.  The higher elevation means we have a longer distance over which we make all these crazy assumptions about the temperature profile.  Thus, there's a greater chance our assumptions won't work very well.  So, even with this methodology, there's still a lot of problems with mean sea-level pressure over areas of very high terrain. But at least now we can get an idea that there's high pressure off the coast...

Another way of filtering out the terrain is to use a variable called the altimeter setting.  This is commonly used by pilots and all airport observations should give the altimeter setting at their location.  The idea behind altimeter setting is to take the assumptions made in the sea-level pressure reduction one step further--and eliminate the temperature component.  Basically they take the average amount you need to adjust the pressure as a function of the elevation of the station regardless of the temperature, and apply this same correction every time.  No worries about temperature or anything like that.  Different countries use different altimeter equations (surprisingly), but the commonly used one that we use in the US goes something like this:

Altimeter Setting = ((Psfc - 0.3)^(0.190284) + 8.4228807x10^(-5) * Elevation) ^ (1/0.190284)

If we map our altimeter settings, we get a map that looks like this:

Notice that it looks rather similar to the mean sea-level pressure map that we had before--but we didn't have to do any of the fancy temperature estimation.  You just plug the surface pressure and the elevation into the above formula and out comes the altimeter setting.  Because this gets us close to sea-level pressure without the added complication of dealing with temperature, this is the pressure variable I prefer to use in my work.

So there you go--pressure is a powerful variable.  But, trying to get the weather pressure signal separated from the terrain pressure signal is complicated.  In a later blog, I'll talk about how people who have their own personal weather stations need to be aware of surface pressure, sea-level pressure and altimeter setting to be sure their station is working well.


  1. Nice write-up, but the "standard" pressure reading used by National Weather Service (and the radio & TV stations) is the "normalized" (for altitude, temperature, and dewpoint) Sea Level Pressure (SLP), NOT altimeter pressure. Granted the two values are usually "close enough...(for government work)..." but they are, nevertheless, NOT the same. A "standard" is a standard for a reason--so everybody (well, most) is using the SAME pressure numbers. Pilots and airports use Altitude Settings because their specific needs are totally different, ie: everybody knowing (and using) the proper flight altitudes, so planes don't fly into one another.

  2. I never claimed that the "standard" pressure reading used by the NWS was the altimeter setting. The National Weather Service uses both sea-level pressure and altimeter setting for different applications, like you describe. The sea-level pressure reading used by the National Weather Service is what I described in my post above, as seen in the NOAA glossary and the ASOS pressure algorithm description:

    Surprisingly, moisture (dewpoint) actually does not play a role in this calculation; it's far more difficult to estimate the effects of moisture throughout a column of air than it is to estimate temperature.

    Altimeter setting and sea-level pressure are NOT the same thing, which is why I describe them as separate things. However, they are designed to accomplish the same task--standardize surface pressure readings along varying terrain.