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.

Converting the Flooding Colorado Rain to Snow

The rainfall totals coming out of Colorado over the week have been incredible--upwards of 15" in many places.  One common comparison to "put this into perspective" that I've seen a lot of on TV, online and social media is converting these rainfall totals to equivalent snow depth.  In another blog post, I talked about computing snow ratios--the ratio of snow depth to liquid water precipitation.  One common snow ratio we use for quick, back-of-the-envelope calculations is 10:1--10 inches of snow for every 1 inch of liquid water precipitation.  Thus I've seen a lot of people commenting that the 15" of rain they saw in Boulder would have been 12.5 feet of snow (150")!  While that sounds incredible, could that really happen?  Had this event happened in winter, would this storm really have produced 10 feet of snow in Boulder?

It's extremely unlikely.  There are many factors working against such an event.  First, let's start by looking at the tremendous amounts of moisture associated with this storm.  In my last blog, I talked about how the precipitable water (PWAT) associated with this storm is the highest ever observed in the month of September over Denver.  Here's the annual climatology of average precipitable water values, with the PWAT observed on Thursday evening highlighted.  You can see it was at the maximum observed PWAT value for September.

But what about PWAT values during the winter?  Notice that in December through February, the PWAT values on average are only about 0.25 inches with all-time maxima around 0.5-0.6 inches.  We're currently just about 200% of the normal PWAT for September, so even with the same anomaly in winter that would still work out to be only 0.5 inches.  Certainly a lot for winter, but less than half of the current PWAT.

So why are the PWAT values so much lower in the winter?  Remember that as the temperatures get lower, so do the saturation vapor pressures for water vapor in air.  This means that, by mass, at colder temperatures far less water vapor can be present in air before it starts condensing out.  We often describe this as the air not being able to "hold" as much water at lower temperatures.  You've felt this--even with the relative humidity at 80% on both a hot day and a cold day, the hot day feels far muggier than the cold day.  There's just more water vapor present when the air is warmer.  For snow, we want the temperatures through a good depth of the lower atmosphere to be below freezing, putting more limits on just how high the PWAT values can go.  It's just too cold to have this much water.

Another thing to consider is the matter of what is called precipitation efficiency.  One distinguishing feature of the rain that has been affecting Colorado is that it has had a high precipitation efficiency.  What does precipitation efficiency mean?  It's basically the ratio of how much water is raining out of a storm to how much water is being brought into a storm through advection and evaporation.  If the precipiation efficiency (PE) is 100%, then as much rain is falling out of a storm as is entering it.  If PE is at 0%, then the storm is growing--the cloud is getting bigger--but no precipitation is falling out of it.  PE can theoretically go all the way up to infinite, for a storm that is raining but no longer has any inflow.  Here's a figure from Market et al (2003) showing these different PEs:

These storms in Colorado have had a very high precipitation efficiency--probably close to 100%.  We've had 12+" of rain over 36 hour periods or so in many places with precipitable water values staying very steady around 1.2-1.3 inches over the same period of time.  To get so many inches of rain with these PWAT values the storms have to be very efficient.  One rule of thumb to estimate precipitation efficiency (Scofield et al 2000 and Market et al 2003) is to multiply the average relative humidity from the surface to 500mb by the total precipitable water.  Well, let's look at our Denver sounding from Wednesday evening:

Our dewpoint and temperature are virtually identical up to ~600mb and pretty close above that (aside...we drop below freezing at that point so we have to consider relative humidity with respect to ice...)...so we are more or less saturated (at 100% relative humidity) all the way up through 500 mb.  With precipitable water around 1.3 inches, the rule of thumb would suggest precipitation efficiency of  130%--probably a bit of an overestimate, but still--very efficient.

This high efficiency is typical of warm rain processes--storms where the rain spends little to no time frozen. Throw in cold processes--including ice and snow--and efficiency tends to drop.  There are a lot of microphysical reasons why this is so, but snowing just is not as efficient of a process.  A study by Hindman et al. (1981) (cited in the Market study mentioned above) showed that for mountain winter storms, typical precipitation efficiencies average between 7%-49%.  Much less efficient than warm rain storms.

So, in summary, if it were cold enough to snow we wouldn't have nearly as much water vapor as this week's Colorado rain storms have had.  And even if we did have anomalously high water vapor to work with, ice and snow precipitation does not occur nearly as efficiently as warm rain precipitation.  We wouldn't be able to capitalize on this moisture.  Unfortunately for Colorado, all this rain had to be rain...

Epic rainfall and flash flooding in Colorado

Rainfall over the past several days including some extraordinary rainfall last night has led to a critical situation along the Colorado Front Range today.  Unfortunately the forecast for the next couple of days has more rain on the way.  Let's look at what has been going on.

There has been a highly amplified upper-air pattern over the continental US over the past few days. Here's yesterday morning's 500mb analysis from the HOOT site:

 

 You can see a large, cut-off low centered over the Great Basin region.  Notice where there are lots of height lines (the black contours) close together--off in the upper Midwest and the Canadian Prairies.  That's where the main jet stream is located--the strong, west-east flow that helps guide storms across the country.  The jet stream is well to the north of this low--in fact, the low is comfortably tucked under a very high-amplitude ridge that goes well up into Canada and is centered over the Pacific Northwest.  Here in Seattle this ridge has given us clear skies and record-breaking warmth of the past few days.  Unfortunately that same ridge is keeping the steering flow away from the low over Colorado, leaving it in place.

The green colors in that analysis image show relative humidity at the 500mb level.  There has been a steady stream of moisture being pulled up from the south around this low over the high plains and eastern Rockies.  This moisture can also be monitored in real-time using satellite-derived water-vapor imagery, like this image from last night:

The brighter whites, purples and blues indicate lots of moisture in the upper troposphere.  The CIMSS Satellite blog has an excellent loop of water vapor imagery for this event at their post here.  Water vapor imagery often isn't very good for showing us the low-level moisture; what you're seeing above is mostly moisture aloft.  Checking last night's sounding from Denver we can see that there was far more moisture in the lower levels of the atmosphere:

The dewpoint and temperature profiles are almost right on top of each other from the surface up to around 600mb--that's a very deep layer for the atmosphere to be saturated.  A lot of people have been commenting on how unusually moist this is for Colorado.  One way we estimate the amount of water vapor throughout the entire depth of the atmosphere is through a measure called Precipitable Water (PWAT).  This basically says that if all of the water vapor in the air above your head were to immediately condense into liquid water and fall down as rain, this is how much rain would fall.  On the sounding above, in the lower right corner you'll see the PWAT value calculated as 33.16 mm.  That's 1.3 inches of precipitable water.  For comparison, here is a climatology of the average precipitable water values in Denver throughout the year from the NWS Rapid City page:

You can see in September that the average precipitable water (the 50th percentile) is only about 0.55 in.  Where does 1.3 inches fall?  Above the maximum value (1.25 in.) for September! An extraordinary amount of moisture.

Another thing you'll note on the sounding above is that near-surface winds are out of the southeast.  This promotes upslope flow--easterly winds forced to rise when they meet the mountains.  This constant rising motion in very moist air produces continuous condensation, clouds and rain.  You can see how steady the rainfall was last night in looking at this timeseries of observations from the NCAR Foothills lab on the northeast side of Boulder.

The rain gauge reset itself to zero this morning (hence the big drop in precip down to zero again), but you can see that over just last evening over 6 in. of rain had fallen.  In one evening.  The rainfall was also quite steady over this entire period--no big spurts or jumps in the precipitation that you'd expect if this was due to strong convection.  In fact, not much lightning was reported with this rain (though there was some).  There have been several reports of particular locations in the foothills getting over 8" of rain so far.  This also shows an interesting feature of this event.  Remember our precipitable water above?  It was only 1.3 inches.  If that was the total precipitable water, how could we be getting 6-8 inches of rain?  Remember that there is that stream of moisture constantly being brought up on the south--we saw it on the water vapor imagery.  This keeps replenishing the water vapor in the atmosphere, bringing in more and more moisture as the current moisture rains out.  Still--too get the much rain with these precipitable water values, these clouds have been very efficient at their rain production.

The rainfall overnight consisted of broad areas of stratiform precipitation in some locations, but also (particularly near Boulder) a series of more intense precipitation cells, probably somewhat convective, that repeatedly formed east of town and then moved west over the foothills.  Here's an example radar image from last night:

So what are the consequences of so much water over such a short period of time?  Flash flooding.  Here's the stream gauge data for Boulder Creek at Broadway in downtown Boulder:

There were extreme rises in the stream level overnight.  You'll note that the typical river stage is only a little over 1 foot.  From 6 PM Wednesday through about 3 AM MDT, the creek rose rapidly to just over 7 feet--moderate flood stage.  There was a drop off early this morning as the rain eased a bit, but more rain is developing today and you can see the stream flow on the rise again.  Basically all of the canyons along the northern Front Range hit at least minor flood stage last night and into today.  Here's the gauge data for St. Vrain Creek near Lyons--approaching record levels.  There was also a dam failure last night upstream from Lyons, prompting extensive evacuations.

There continue to be problems with managing this massive amount of water.  Pretty much every road going into the mountains is closed due to flooding or mudslides at this time.  Many streets in Boulder itself are impassible due to high water.  There are evacuations underway in the Big Thompson River canyon (the location of an infamous flood in 1976--which had distinctly different meteorological origin, being due to a parked convective storm as opposed to widespread, more stratiform rain).

Unfortunately it doesn't look like it's time to take a breath just yet.  The rain died down a little overnight, but it's forecast to pick up again today.  We're already seeing that throughout the region.  Here's the latest High-Resolution Rapid Refresh model's forecast for total accumulated precipitation through tonight.

It's predicting another 1-2 inches over the northern Front Range.  It's also alarming to note the 3-5 inch accumulations suggested for the mountains behind Colorado Springs and Pueblo, suggesting an additional flash flooding threat further south.