Today's classic case of isentropic lift

An incredible band of snow and rain currently stretches across the eastern  half of the country, as seen here on the radar composite from around 0100 UTC tonight:

Widespread precipitation from Texas all the way up through New York.  You'll notice in the middle of that band there is an area of relatively strong reflectivity.  This doesn't necessarily mean it is precipitating heavier in that area; rather it's a symptom of what we call the "bright band" effect that occurs when the radar is sampling mixed-phase precipitation.  It turns out that melting snow is more reflective to our WSR-88D radar beams than either pure snow or pure rain.  Usually this effect is somewhat localized and doesn't always show up well on radar composites, but here we have a very clear "bright band" that shows the separation between all snow to the north and all rain to the south.

You'll also notice that the character of the reflectivity changes across the band.  To the north the reflectivity looks a lot smoother and the northern edge of the precipitation looks almost "wispy".  That's a good indication that the radar is seeing snow.  This is opposed to the precipitation to the south which is much more "blobby" and irregular---characteristic of the radar seeing rain.  A striking example of how valuable our network of radars can be for determining precipitation types (even without looking at dual-pol products!)

But there's a bit more I wanted to talk about with respect to this band.  And it's going to get a little technical, so stop now if you just want to enjoy the fun radar images.  Here we overlay the Storm Prediction Center's mesoanalysis for 0100 UTC:

There's a lot going on on this map, but I want to focus on the surface temperature contours (the red solid and blue dashed lines).  You can see where the strong temperature gradient associated with a frontal zone is located--the temperature contours are really "squashed" together in a band from central Mississippi through northern Alabama and eastern Tennessee.  But notice that the precipitation itself is actually well behind the surface front---it doesn't begin in earnest until central Tennessee into eastern Kentucky.  Why the separation?  Why is the "lift" so far behind the surface front?

This is a classic case of what we call isentropic lift.   The surface front is only the leading edge of a dome of colder air.  This edge slopes back to the north and rises in height the further north you go.  Let's draw a cross-section through an analysis of what's going on now.  Below is a cross section (from the College of DuPage site) from New Orleans, Louisiana (on the left) to Green Bay, WI (on the right):

The red lines you see there are called "isentropes", lines of equal potential temperature.  You can see that there is a "wedge" of colder potential temperatures, and this wedge slopes up to the right (to the north).  That's describing the structure of the dome-like cold air mass sitting to the north.  If you look at the wind barbs in this dome of cold air (particularly between the surface and 850 hPa), you'll notice that they all have a strong northerly component (note: even though in this cross section "north" is technically to the right, with wind barbs "north" is still oriented "up").  This makes sense---cold air advecting out of the north.  If we look on the left end of the diagram outside of the cold air (down near New Orleans) the winds have a strong southerly component---warm air advecting out of the south.

It turns out that, as long as air remains unsaturated, as it is advected along it will maintain the same potential temperature.  In other words, if air starts at a potential temperature, it will follow that same potential temperature line wherever it goes.  So let's take air just above the ground at New Orleans.  It has a potential temperature on that map of just under 300 K. As that air moves northward, it is going to stay on the 300 K isentrope.  As we said before, all the isentropes are tilted upwards as we head north.  So,  warm air moving in from the south will be forced to rise following its isentropes as it moves northward.

The air that rises will keep following the isentrope until it's saturated.  We can see from the radar images that the air must be lifted for quite a ways before it hits saturation, as the precipitation band is so far behind the surface front.  But it's all laid out for us in that cross-section!  You can even see in the cross section above that the moist air (to the south; green contours are moisture) has a lobe lifted up and over the cold air, just like we'd expect if this were happening!

We can also look at a single isentrope and see what is happening along that particular isentrope.  Let's look at the 296 K isentrope.  We see in the cross section above that the height of that isentrope above the ground changes quite a bit as you move around horizontally.  We can make a map showing the height of that isentrope above the ground, and the moisture and winds along that isentrope.  Here is such a map, again from College of DuPage:

The heights are the black contours on this map and they are given in pressure levels.  Remember that pressure decreases with actual height.  So, we see lower pressures to the north (some of the black contours get below 400 hPa up in Canada) and higher pressures to the south (around 850 hPa in Louisiana).  This agrees with that cross section---as we go north, the 296K isentrope gets higher above the ground.  Notice the winds on this map; they are mostly southerly over the southern US. Combine this with the fact that this surface is higher off the ground as you move north and we can again conclude that the air moving northward will be rising along with this isentropic surface.  We also see how much moisture is being brought northward with this air---relative humidities over 85% for much of that region! So we have moist air being forced to rise by this flow, a classic isentropic lift setup.

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...