Quieting out later this week

Sorry about the delay in updates.  I've been rather busy and went up to Canada over the long weekend, so I'm just now getting back into the swing of things.

Nothing too technical today, just a look at some medium- to long-range model forecasts for the end of this week.  The active weather continues today across the upper midwest with a shortwave trough present over the northern plains:

Fig 1 -- ECMWF analysis of 500mb height (contours) and winds (shading) at 12Z, May 31, 2011.  From the HOOT website.

There looks to be another powerhouse trough digging into the west coast--we might think that this would cause trouble later on this week.  But, it looks like the models are going to keep that cyclone cut off over the west coast, allowing a ridge to build across the east by the end of this week.

Here's the 500mb forecast for Thursday morning.

Fig 2 -- ECMWF 48-hour forecast of 500mb height (contours) and winds (shading) at 12Z, June 2, 2011.  From the HOOT website.

The trough has moved a bit inland and a strong jet streak is noted over the east-central Rockies.  The Storm Prediction Center has a slight risk of severe weather on Thursday for that region, and with this upper-air map it's easy to see why.  However, note the ridge that has started building across the south and up into the northern plains.  This is a powerful ridge--one that looks to be difficult to budge.  By Saturday morning, here's the forecast 500mb chart:

Fig 3 -- ECMWF 96-hour forecast of 500mb height (contours) and winds (shading) at 12Z, June 4, 2011.  From the HOOT website.

The trough over the northwest was re-enforced by another trough moving down from the Gulf of Alaska in this forecast, and even that isn't enough to push the troughs eastward into that large high-pressure/height ridge.  Instead, the cut-off cyclone in the west slides south to just off the central California coast.  What does this mean for our weather in general?  Here's the GFS forecast of surface temperatures around the middle of the day on Saturday:

Fig 2 -- GFS 102-hour forecast of surface temperature (colors), sea-level pressure (contours) and winds (barbs) for 18Z, June 2, 2011.  From the HOOT website.

 That ridge over the central US should keep skies relatively cloud- and rain- free going into the weekend.  This will allow solar heating to take full effect and we see temperatures forecast up into the 90s for much of the south and lower Mississippi River valley.  In contrast, the west coast gets stuck with much cooler weather under that trough--by late morning it's only forecast to be up to around 55 in Los Angeles.  Not very seasonable.  So, the west coast once again sees a delayed start to that summertime heat....

At least with this weather pattern, the tornado and severe weather threat over the hard-hit areas of the country will be virtually non-existent.  This will allow the recovery efforts to continue on.

On another note, tomorrow (June 1st) marks the official beginning of the North Atlantic hurricane season...

After a terrible tornado in Joplin, another risk tomorrow...

As most people are well aware by now, a horribly strong tornado ripped through the heart of Joplin, Missouri on Sunday evening.  With 116 people confirmed as killed so far, this is the deadliest tornado to strike the US since the 1940s.  The photos and videos of the aftermath of this storm are everywhere.

I had a very slight acquaintance with Joplin.  Every time I would drive between my home in northern Illinois and the University of Oklahoma in Norman, I would stop in Joplin, often for lunch and always to get gas.  The gas station at which I always stopped no longer exists.  Their delightful main street with its Route 66 nostalgic decorations is decimated.  I just can't believe the scenes I'm seeing.

And, unfortunately the weather is gearing up for yet another round of severe storms on the southern plains.  The SPC already has a moderate risk out for Tuesday.

Fig 1 -- SPC Day 2 convective outlook as of 1730Z, April 23, 2011.  From the SPC.

Joplin is on the edge of the moderate risk area, but most of Oklahoma and eastern Kansas fill out that risk area.  The SPC is calling tomorrow a "classic" severe weather outbreak scenario.  Since I don't have much time tonight, I'm just going to show the NAM model graphics for 00Z, Wednesday (Tuesday night).

First, the 500mb forecast shows a compact shortwave moving out into the central plains with a small, but still powerful jet streak on the southern side of the trough:

Fig 2 -- NAM 30-hour forecast of 500mb height (contours) and winds (colors) at 00Z, Wednesday (Tuesday night), April 25, 2011. From the HOOT website.

Interestingly enough, it's these very compact shortwaves that can often pack the biggest punch.  We can imagine with this scenario that a surface low with trailing cold front would be located over northern Oklahoma.  Dropping down to 850mb, we can see the beginnings of the nocturnal increase of the low-level jet:

Fig 3 -- NAM 30-hour forecast of 850mb height (contours) and winds (colors) at 00Z, Wednesday (Tuesday night), April 25, 2011. From the HOOT website.

Winds in the 850mb jet are out of the south over Oklahoma, whereas winds at 500mb are out of the west--a fair amount of directional wind shear, favoring strong supercells.  A quick glance at surface moisture (in terms of the dewpoint) shows that there is indeed a lot of energy to work with at the surface:

Fig 4 -- NAM 30-hour forecast of dewpoint temperatures (colors) and winds (barbs) at 00Z, Wednesday (Tuesday night), April 25, 2011. From the HOOT website.

Those are 70 degree dewpoints being forecast for eastern Oklahoma, southeastern Kansas and into Arkansas.  A sharp dryline is visible across western Oklahoma and down into Texas.  With rich moisture and surface convergence along these boundaries, storms are bound to fire.

For another look at all of these ingredients being condensed together in the models, here's a forecast sounding for 21Z on Tuesday afternoon at Norman, OK:

Fig 5 -- NAM 27-hour forecast sounding for Norman, OK, at 21Z, Tuesday, April 24, 2011.  From the HOOT website.

Very steep lapse rates in a virtually uncapped profile. The dewpoint temperature is up in the 70s, but not nearly as high as the forecast surface temperature of around 90.  This implies some lift is going to be needed to get the surface air up to its level of free convection to tap into the convective available potential energy.   But, in the larger-scale environment we saw with divergence aloft and convergence near boundaries at the surface, so this should not be a problem.  Speaking of convective available potential energy, this forecast sounding is suggesting a surface-based CAPE value of 4567 J/kg.  Lots of potential instability.  Notice in the winds that there's also a fair amount of directional shear (like we saw in the 500mb and 850mb maps).  Winds at the surface are out of the south, and they rotate around, becoming more westerly by around 400mb.  The speed shear isn't as strong as I've seen recently, but remember this is at 21Z, which is the middle of the afternoon.  The speed of the low-level winds really picks up right around and after sunset.  That will increase the low-level wind shear and make any storms that exist around that time particularly dangerous.

Even some medium-scale models are explicitly forecasting some major storms.  Here's the OWL/WRF model at the University of Oklahoma and its forecast for simulated composite radar reflectivity at 00Z on Tuesday evening:

Fig 6 -- 48-hour OWL/WRF forecast of simulated composite reflectivity valid 00Z, Wednesday (Tuesday evening),  May 25, 2011.  From the HOOT website.

This is showing storms at around 7PM CDT (just before sunset) in northern Kansas and also in northern Oklahoma.  I should note, this is a 48-hour simulation--this does NOT mean that there will be storms in these places.  What these kinds of forecasts can hint at, though, is the timing of when storms will start going up and also what kind of mode they will be in.  Individual cells?  A line of storms along the front?  Here we still are seeing individual cells.

We can also simulate an infrared satellite image from the model output.  Here's the simulated infrared satellite image from the same model at the same time:

Fig 9 -- 48-hour OWL/WRF forecast of simulated infrared temperature at top of atmosphere, valid 00Z, Wednesday (Tuesday evening),  May 25, 2011.  From the HOOT website.

I think this sort of image does a better job at showing those modes of convection as opposed to the simulated composite reflectivity.  Here you can see some explosions of clouds that are developing storms down into southern Oklahoma and the Dallas/Fort Worth area.  This shows developing storms that haven't shown up on the composite reflectivity yet. So...even at 48 hours out models are hinting that we're could see discrete storms on Tuesday.  Discrete storms in a high shear environment with surface dewpoints in the 70s--a recipe for supercells, large hail and tornadoes.  Unfortunately, Joplin is not out of the woods yet.

Seeing ground clutter on radar

This evening there are severe weather watches across several parts of the central US, including a tornado watch across eastern Oklahoma.  Early this evening, a few storms fired to the east of the I-35 corridor--including a couple tornadic ones.  Here's the radar image from 0103Z.  I noted the locations of the tornadic storms with white arrows.

Fig 1 -- 0.5 degree base reflectivity from KOUN at 0103Z, May 22, 2011.

Now, the large spike off to the southeast of the radar is NOT a sun spike like I talked about the other day.  It's actually a blockage return from a large water tower that sits just to the southeast of the radar (this is the KOUN testbed radar in Norman).  Most of the radar energy emitted in that direction bounces off the water tower and comes right back to the radar, which the radar interprets as continuous returns from all ranges in that direction.  But I want to focus on all of those returns to the west of the radar.  It looks like a whole bunch of storms are firing up to the west.  But...there's actually nothing there.

So what are those returns?  It's something called ground clutter.  Here's what happens.  Sometimes the vertical density profile of the air in the lower atmosphere arranges itself in such a way that radar beams emitted into the air get bent in odd directions.  With the right conditions, sometimes the beams can get bent into the ground.

When an emitted radar pulse hits the ground, it bounces back and returns mostly along the same path upon which it traveled out.  As such, the radar interprets this as a very strong return at the range where the radar beam hit the ground.  This sort of phenomenon is more common in coastal areas and also when there are strong inversions in the low levels of the atmosphere.  So all of those chaotic (but still strong looking!) returns west of the radar are actually ground clutter--areas where the lowest radar beam is hitting the ground.

If you spend a lot of time looking at radar images, ground clutter is often easy to spot.  For one, it moves chaotically and not uniformly like precipitation does, and often wildly fluctuates in the strength of the returns.  So seeing all these random strong returns dance around in a radar animation is usually strong evidence that you're seeing ground clutter.  But there's another way to check for ground clutter--look at the accompanying radar velocity image.  Here's the velocity image from the same time as the reflectivity image above.

Fig 2 -- 0.5 degree base velocity from KOUN at 0103Z, May 22, 2011.

Notice how the storms to the east have very nice, colorful velocity fields.  You can even see some couplets in the velocity images indicating rotation in those storms.  But what about the velocities from all the ground clutter out to the west?  They're all gray--indicating zero velocity!

That makes perfect sense, though.  There is no Doppler shift when the radar beam hits the ground.  After all--the ground isn't moving, so why would it have a velocity value?  Any strong thunderstorms are most certainly going to have some pretty strong velocities associated with them.  So strong radar returns with zero velocities associated with them are almost certainly not precipitation.  They're almost always some sort of clutter.

In fact, the NEXRAD radars have built in algorithms that look for just this combination--strong reflectivity returns in areas of zero velocity--to remove clutter from the radar.  So, it's not as common to see this kind of clutter on radars as it used to be. However, the radar I'm showing in the images above (KOUN) is an experimental testbed radar used by the Radar Operations Center, so sometimes they don't have all the algorithms enabled.  As such, it's kind of fun to watch it once in a while to see all these random radar phenomena that we never get to see on other radars.

If the right environmental conditions persist, ground clutter can also hang around for a while.  Here's the reflectivity image from half an hour later:

Fig 3 -- 0.5 degree base reflectivity from KOUN at 0133Z, May 22, 2011.

Those two tornadic storms that were to the southeast of the radar have actually merged into one storm--which has an even more pronounced hook echo than either of the two storms had before.  The dynamics of merging supercell thunderstorms are not well understood and that's an area of ongoing research.  In the meantime, you can see some kind of a weak boundary running roughly north to south-southwest just west of the radar.  You can often see boundaries between different air masses on radar--but that's a subject for another blog.  All those now-weaker returns to the west of the radar are still ground clutter.  Often the patterns of ground clutter will take the shape of the local topography, following hilltops and ridgelines (since those are the first places to get hit by the radar beam).  Looking at the corresponding velocity image...

Fig 4 -- 0.5 degree base velocity from KOUN at 0133Z, May 22, 2011.

The strong velocity couplet in the tornadic supercell is pretty obvious in this image.  But, as expected, the velocities are still zero in the ground clutter to the west.  So, I'm afraid it looks like no storms for Norman tonight...

A reminder of what we're really looking at...

This will be a short post today.  I recently had to install Unidata's Integrated Data Viewer program on a computer and thought I'd use some of the program's capabilities to remind  us what we're actually looking at when we look at upper-level height charts.

Take the 300mb chart for instance.  I often will show charts like this:

Fig 1 -- NAM 6 hour forecast of 300mb height (contours) and winds (colors) at 18Z, May 18, 2011.

Those black contours are the height of the 300mb surface above ground, and we use them to diagnose where there are troughs (generally low heights) and ridges (generally high heights).  We could color-shade the contours of height (instead of wind) to get a better sense of the topography of the 300mb surface:

Fig 2 -- Color-shaded version of figure 1 in IDV.

This is the exact same map as I showed above, only I removed the winds and color-shaded the height contours instead.  Cool colors indicate lower heights and warmer colors indicate higher heights.  You can see that the deep trough over the Pacific northwest and the shortwave trough over the middle Atlantic states clearly stand out as locally low heights (intrusions of blue colors into areas of warmer colors).

But remember--these are heights above the ground.  When we look at height contours of a particular pressure surface, we're actually looking at a topographical map of the elevation of that surface above the ground.  As such, if we were to consider a three-dimensional map of the 300mb surface, it would look something like this:

Fig 3 -- Same as figure 2, only tilted.

I've used the 3-d rendering capabilities of the IDV program to change our three-dimensional angle of viewing the 300mb surface.  Now you can really start to see how these contours show the "topography" of the surface.  Where we saw troughs indicated above, the height of the surface is lower.  In fact, if we were to look at this surface from the side (looking straight north) at a cross section, it would look like this:

Fig 4 -- Side view of figures 2/3 looking north.

Those 300mb troughs really are "troughs" in that they dig down beneath the mean height of the 300mb surface.  That Pacific northwest trough is the downward bulge on in the middle-left side of the image while the relatively shallower mid-Atlantic trough is the smaller bulge just to the east of it.  Note in the background you see what looks like extended troughing across the back.  That's just an artifact of this perspective--the 300mb height surface naturally decreases in elevation as you head toward the poles.  The anomalies in the 300mb height are the bulges in the foreground--the troughs that make our weather happen.

Now, the 300mb surface doesn't actually vary as much as these figures imply.  I've greatly exaggerated the vertical scale on these to show the features.  If I decrease the exaggeration, the horizontal cross section in figure 4 quickly turns to this:

Fig 5 -- Figure 4 at a much smaller vertical exaggeration.

The cross-section quickly reduces to looking like a horizontal line.  The troughs and ridges are still there--believe me.  They're just so small over such large horizontal scales.  The actual height of the 300mb surface maybe varies by 500-800m from its mean height, at most.  That's less than a kilometer.  The US is several thousand kilometers across.  That means the scale of the vertical perturbations is actually very small compared to their horizontal extent.  But, incredibly, even these tiny perturbations in height are enough to cause all the powerful weather we experience.  Pretty amazing.

Also, the troposphere isn't nearly as thick as that outline box implies. The tropopause is usually at 10-15 km above the ground.  Once again, compared to horizontal scales of thousands of kilometers, the troposphere is a very, very thin layer.  It would be hard to even see it if we looked at a cross section over the US at actual scale.  So, we exaggerate it vertically quite a bit to show these small contrasts.

Anyhow, I just wanted to use this kind of 3-d visualization to remind people that all these flat, horizontal maps we look at are representations of a three-dimensional atmosphere.  The troughs and ridges on an upper-air map really are troughs and ridges in the height of that surface.  It's a great topography that's constantly changing.  And, even though these changes may seem small in scale, they make all the difference when it comes to our weather.

Radar Spikes are Not a Government Conspiracy

Recently I've read a few claims by people online that something funny is going on with our NEXRAD Doppler radars.

What is this strangeness?  Apparently some people believe that the appearance of certain "spikes" on the national radar mosaics are evidence of a government-led weather modification program.  They believe that the radars are picking up high-energy pulses from some secret government device designed to covertly modify our weather.

So...are these spikes real?  They certainly are.  Here's a loop from the other day of the radar mosaic of the western United States.  If you look carefully (particularly across the northern half of the image), you'll see several spikes pointing from the centers of the radars out to the northwest that sweep across the country from right to left.  It's mostly in the first two frames of the loop, so it happens fast...

Fig 1 -- NEXRAD Radar Mosaic at 0318Z, May 13, 2011.

And here's the actual image from the lowest (0.5 degree) tilt of the Seattle radar at the time the spike appeared there.

Fig 2 -- KATX 0.5 degree base reflectivity at 332Z, May 13, 2011.

So are these mysterious spikes evidence of some government conspiracy?  Absolutely not.

Their cause is actually quite simple--it's just the sun.  And I can prove it.

To explain, we have to remember that our NEXRAD radars are very sensitive instruments in many ways.  First, they are highly directional--the big parabolic dish surrounding their antenna and transmitter assembly focuses the transmitted and received radar beam so that the radar can only send and receive energy in and very close to the direction in which it is pointed.  This has to be so, otherwise the radar would only tell us that something was out there--and not where that something is.  So the radar is very sensitive to the direction in which it is pointed.

The NEXRAD radars also transmit and receive radiation at a very specific wavelength.  They are what is known as S-band radars, meaning they emit electromagnetic radiation at a wavelength of 10 centimeters.  The radar is also programmed only to detect radiation at those wavelengths too--it assumes that the radar itself is the only source of EM radiation at 10cm, so any 10cm wavelength radiation it detects must have come from the radar.

However, it turns out that even in the microwave 10cm band, there is another source of radiation--the sun.  The 10cm band is by no means the peak solar emission band--it turns out that the peak of the sun's emissions actually lie in the visible light region.  In fact, this is why many evolutionary biologists believe that we see light in the the "visible" range--that's where most of the sun's energy is emitted.  But, the sun emits energy across a wide variety of wavelengths--including some at the 10cm band the radar emits and sees.

So what does this mean?  It means that if the radar happens to be pointed directly at the sun, it will receive some additional radiation in the 10cm band that it did not send out.  However, the radar doesn't know that this radiation wasn't radiation that it emitted.  So it interprets it as just normal signal bouncing back.  Since the emission from the sun is continuous, the return is interpreted as a continuous beam stretching out from the radar in the direction of the sun.  And that is where those spikes come from.

Actually, radar engineers have known about this phenomenon for a long time and have designed ways to take advantage of it.  In the NEXRAD system, every so often the radar is programmed to interrupt its scanning cycle and point in the direction of the sun.  Since the sun's emission spectrum is relatively constant (or, at least we can measure it with good accuracy), the radar can  use the amount of radiation it detects coming from the sun to calibrate itself by comparing this to what the value should actually be.  So, we actually use the radar spike phenomenon to calibrate our radars.  Pretty amazing.

Want more proof that these spikes are caused by the radar pointing at the sun?  We can compute exactly when the spike will occur.  Here's how:

 The sun's path through the sky is very predictable given some knowledge about the time of year and the latitude and longitude of the point you're at.  We often talk about the sun's position in the sky in terms of what is called the solar zenith angle.  This is the angle the sun is in the sky relative to its position at local noon.  In terms of the solar zenith angle, 0 degrees is when the sun is at its highest point in the sky--local noon.  +90 degrees is when the sun is setting on the western horizon and -90 degrees is when the sun in rising on the eastern horizon.  Here's a diagram to help:

We know that at some point the sun will be at an angle such that the radar is pointing directly at it.  The lowest elevation tilt on the NEXRAD radar systems (as of right now) is 0.5 degrees above horizontal.  The lowest tilt is what's used to make all of those composite images and is the same as the radar image from Seattle I showed above.  So, the question is--what will the solar zenith angle be such that a radar beam pointed at 0.5 degrees above horizontal will be pointed directly at the sun?  Here's a modified (and slightly exaggerated--0.5 degrees is a rather small angle...) diagram to show how we can reason this out:

We know that if the radar was pointed at an elevation of zero degrees, it would be pointing straight horizontal.  But that corresponds to a solar zenith angle of 90 degrees--right at sunset.  If the radar is tilted 0.5 degrees above that, the corresponding solar zenith angle would be (90 degrees - 0.5 degrees) = 89.5 degrees.  So we want to figure out at what time during the day the solar zenith angle will be 89.5 degrees.  This should tell us exactly what time we expect the spike to appear on the radar.

There's a well-established formula to calculate the solar zenith angle in terms of some other quantities:

Where theta is the solar zenith angle, phi (the trident-sort of symbol) is the latitude, delta (the curly d) is something called the "solar declination angle" and h is the "local hour angle".

Well, latitude makes sense--we understand that one.  The solar declination angle is the latitude at which the sun is directly overhead at noon on the day of interest.  Because the earth is tilted this latitude changes throughout the year.  On the equinoxes, the solar declination angle is zero degrees--the sun is directly overhead at noon on the equator (zero degrees latitude) on the equinoxes.  But what about the rest of the year?  There are several formulas to calculate the solar declination angle, making various degrees as approximations.  If we assume that the earth's orbit is circular (which it isn't exactly, but it's very close...) then a commonly used-formula is:

Where the only thing you have to plug in is N, which is the ordinal day of the year.  Some people call this the "Julian Day", but technically that's not correct.  This is simply the day of the year you're on if you started counting at 1 for January 1st and kept counting all the way up to 365 (or 366 if it's a leap year) on December 31.  For instance, on May 12th of this year (when I grabbed those radar images above), it was the 132nd day of the year, so N=132.  (Side note: the equation above actually makes a lot of sense if you know that the maximum solar declination angle (on the summer and winter solstices) is 23.44 degrees (which is also the tilt of the Earth's axis) and for every 365 days the earth makes one full 360 degree circle around the sun--hence the 360/365 fraction.  I have no real explanation for the +10, though...).  Anyhow, this formula makes that solar declination angle easy to figure out.

Finally, the hour angle h.  This is what we're trying to solve for, actually.  So, we can re-arrange the equation for the solar zenith angle above to solve for h:

Remember, we're trying to find the time at which the radar beam will be pointed at the sun.  This is the time when the solar zenith angle (theta) equals 89.5 degrees.  We can compute the solar declination angle (delta) for whatever day we want using the above formula.  So, we can plug those into this formula, take the arc-cos of the result and we have h--this "hour angle".

 But what is h?  It's the local time in an "angle" format.  If you think of the day as a full circle, every 24 hours we make a 360 degree circle in time. So the hour angle just tells you want part of the time circle during the day you're in, in terms of degrees instead of hours.  The full expression for the hour angle is:

Like I said, there's that factor of 360 degrees every 24 hours showing up.  The time in UTC (the Z time I always quote--it's Greenwich mean time) is obviously t_UTC, and lambda (the last term) is the degrees of longitude of the point you're interested in.  Since locally we're not in UTC/Greenwich mean time, the actual time at which we reach this 89.5 degree zenith angle will be offset by a certain amount depending on how far we are from the prime meridian (on which UTC/Greenwich mean time is based).  We use the longitude to measure how far we are away from the prime meridian and add it to our hour angle to account for this displacement.

Anyhow, so we know h (the hour angle) now.  Using h and the last equation I gave, we can solve for t_UTC--the time in UTC time at which the sun will be at the 89.5 degree zenith angle and at which we would expect to see the radar spike.

Here's a sample calculation.  The Seattle radar is located at 48.19 degrees N latitude and -122.49 degrees longitude.  On May 12th (the day my radar pictures above are from), it was the 132nd day of the year.  Knowing that, we can plug in N=132 to the equation for delta to find that the solar declination angle on that day was  17.97 degrees.

Knowing the solar declination angle, and that our latitude is 48.19 degrees, and that we want to know when the solar zenith angle (theta) is 89.5 degrees, we can plug all that in to solve for the hour angle h.  We find that h = 69.58 degrees.

Now, using the very last formula, we can solve for t_UTC knowing h=69.58 degrees and our longitude (lambda) is -122.49 degrees.  We get t_UTC (in hours) is -3.5273 hours (it's negative because we switched over a day in the time difference between the prime meridian and Seattle).  3.5273 hours is 3 hours and 31.6 minutes.  So based on this prediction, the spike would appear on the radar between 331Z and 332Z.

Check the time on the Seattle radar image above in the upper right corner of the image--332Z (and 44 seconds).  Pretty much right on--off by less than a minute.

It's difficult to get an exact match, however.  It takes the radar between 5-10 minutes to complete a full scan, so the time they give doesn't match up exactly with the time the radar was pointed at the sun--it was sometime in the 5-10 minutes before the time given on the radar image.  Also, this calculation assumes that the sun is a single point in the sky and that the radar beam is also a single line with no width.  In reality, the sun does take up a certain area of the sky and the radar beam spreads out as it leaves the radar.  So there are actually several minutes when the radar beam could feasibly be pointed at the sun.  Sometimes we'll see the spike on two or three successive radar scans because of this.  This time prediction, then, should be the time of the most direct pointing at the sun.

Also, there are other concerns if your radar is on top of a mountain or something--then looking at the horizon means looking down instead of horizontal and your solar zenith angle will be different.  But still--this estimate is very, very good.

Hopefully, with all that math, this seals the case for radar spikes being simple artifacts of the sun and NOT part of any government conspiracy of weather modification.  Just using knowledge of how the sun moves in the sky, I can predict when the spike will appear every time, for any radar, on any day.  Hardly a secret.

I should note that the spike doesn't always show up, though.  If there's a mountain range to the west of the radar or thick clouds blocking the sunlight, then you won't see a spike.  But on most clear days, its very noticeable.

Here are my predictions for when the maximum spike will appear on the Seattle and Chicago radars at sunset for the next three days.  Conspiracy?  No.  It's science.

KATX (Seattle) Spike Appearance

May 14 -- 334Z

May 15 -- 335Z

May 16 -- 337Z

KLOT (Chicago) Spike Appearance

May 14 -- 0058Z

May 15 -- 0059Z

May 16 -- 0100Z

Poor Convective Timing and Cold Pools

Many people I know were discussing the moderate risk of severe weather that the Storm Prediction Center had issued last night for today in western Oklahoma:

Fig 1 -- SPC Day 1 convective outlook as of 12Z, May 11, 2011. From the SPC.

However, by mid-morning, that moderate risk had gone away (and the slight risk had expanded considerably further north)...

Fig 2 -- SPC Day 1 convective outlook as of 1630Z, May 11, 2011.  From the SPC.

So what happened?  Why did the severe potential decrease over that area from what we were expecting?

The answer lies in the timing of convection with this surface low--and what convection in the early morning does for the next day.

Take a look at Norman, Oklahoma's sounding from 12Z this morning:

Fig 3 -- KOUN sounding from 12Z, May 11, 2011. From the SPC.

This is a pretty good sounding in terms of its thermodynamics if we're looking for severe weather.  There's high CAPE values and a capping inversion is present (the winds are another story, however).  Remember that the capping inversion is what keeps a "lid" on the convection during the day.  We see that capping inversion as the abrupt warming with height shown in the red temperature line right at 850mb in the above diagram.  Now, often we talk about the capping inversion being "bad" for convective development because it prevents storms from forming.  However, to get severe storms, particularly supercells, you want there to be some sort of capping inversion in place.  This allows two things:

1. By having a capping inversion, it ensures that storms can't just fire off everywhere--only in unique places where there is enough lift to overcome the capping inversion can storms form.
2. Having the capping inversion in place allows the surface to heat up (and possible more moisture to advect in) throughout the day, creating an even more unstable environment so that if that instability is released in the late afternoon, the convective development is particularly explosive.  With no capping inversion in place, as soon as the surface started heating at the beginning of the day things would quickly become unstable and storms would fire off without taking advanatage of a full-day's worth of heating.

So, for severe, supercellular storms, we do want there to be a capping inversion, particularly in the morning to mid-afternoon hours.

Also, in the above sounding, notice that I drew a yellow circle around the layer right at and above the capping inversion.  Notice how dry the air is right here--the dewpoint temperature (shown by the green line) is much less than the actual air temperature, indicating dry air here.  Now, this can be a good thing for severe thunderstorm formation as dry air aloft tends to contribute to stronger downdrafts and more damaging winds at the surface (but that's for another blog post).  But, for now, just keep this feature in mind.

This morning, as the sun came up, the visible satellite image showed this:

Fig 4 -- GOES-E visible satellite image from 1316Z, May 11, 2011.  From the HOOT website.

You can see the nice, comma-shaped curl of the low-pressure cyclone over eastern Colorado.  But notice what we have in western Kansas and western Oklahoma--lots of clouds!  It turns out that there was enough lift and enough low-level moisture early this morning to cause showers to form over western Oklahoma and western Kansas.  So what does this mean?

Mid-level winds this morning were generally out of the southwest, as shown in this GFS analysis from 12Z this morning:

Fig 5 -- GFS analysis of 700mb winds (colors) and height (contours) for 12Z, May 11, 2011.

 So what would these winds do?  They brought the clouds (and their moisture) northeastward and into the moderate-risk corridor that the SPC had outlined.  How significant was this moisture?  Here's the special sounding launced at Norman five hours later at 17Z:

Fig 6 -- KOUN sounding from 17Z, May 11, 2011.  From the SPC.

Notice how much the dewpoint has increased in the area I had circled-- the air is no longer very dry there--it's nearly saturated (i.e., the air temperature and the dewpoint temperature are about the same).  So what happened when those clouds moved in?  Remember that at 12Z this layer of air was rather dry over Norman.  So, as clouds and their liquid water droplets moved in, the liquid water in those clouds started evaporating into the much drier air.  In one of my previous blog posts, I talked about how condensation (going from water vapor to liquid water) releases a lot of energy, which in turn warms the air.  When the opposite happens--when liquid water evaporates into water vapor--it consumes a lot of energy, which in turn cools the air.  This is a phenomenon called evaporative cooling.

You can see in the sounding above that that's exactly what happened--not only has that circled layer become moister, but the temperatures have cooled down considerably.  In fact, they've cooled so much that the capping inversion (which was a layer where temperatures warmed considerably with height) is no longer visible--the cooling due to the cloud water has removed the cap!

Now remember what I said before--to get supercellular types of storms, you want the capping inversion to linger throughout the day, at least into the middle of the afternoon, to allow instability to build and to prevent storms from firing up everywhere.  But now it's late morning and the cap seems to have completely disappeared over Norman due to this cloud intrusion.  The result?  Here's the radar two hours later at 1938Z:

Fig 7 -- NEXRAD base reflectivity radar mosaic for 1938Z, May 11, 2011.  From the NWS.

Storms basically just fired up everywhere.  As a result, though there was and still is a risk of severe weather, the potential for isolated supercells and strong tornadoes has gone away.  The cap just eroded too early.  The wind shear also wasn't that great yet anyhow--we needed a strengthening of the winds aloft forecast for later in the day to get the kind of shear necessary to support strong rotation.  So, things were just timed poorly.

One interesting facet of these storms is how they have fired and propagated ahead of the convergence along the main dryline/front.  Here's the surface analysis from the SPC around the time of the radar image above:

Fig 8 -- SPC surface analysis of dewpoint temperature (color shadings), temperature (red contours), mean sea-level pressure (black contours) and wind (barbs) for 19Z, May 11, 2011.

Some features stand out.  Note the surface low (pressure is in the black contours) is analyzed in extreme southeastern Colorado near the Oklahoma panhandle.  The dryline is clearly visible as the strong gradient of moisture extending along a north-south line across far western Oklahoma.  It's the area where the dewpoint temperature (the colored shadings) drop from greens down through blues to nothing--indicating dewpoints to the west of the dryline are below 56 degrees Fahrehnheit while to the east they are in the upper 60s.  Also notice in the wind barbs how there is convergence along the dryline--winds to the west of the dryline are out of the west whereas winds to the east of the dryline are out of the south-southeast.

However, the storms at that time were more in west-central Oklahoma--slightly ahead of the dryline.  Look at the the temperature contours (the red lines) in western Oklahoma.  See how underneath the storms it's much colder than it is elsewhere?  In fact, while temperatures are in the mid-80s in eastern Oklahoma, underneath the storms it gets down into the mid-60s.  This is a result of all that cold, downdraft air falling with the rain underneath the storms.  This zone of colder temperatures underneath the storms is often referred to as the "cold pool". 

Here's a map from the Oklahoma Mesonet from one hour later.  The storms have moved further east, and you can see that there's a wide swath of colder temperatures underneath them:

Fig 9 -- Air temperature at 2m from the Oklahoma Mesonet at 5:25PM CDT, May 11, 2011.  From the Oklahoma Mesonet.

Notice that both in front of and behind the storms the temperatures are in the 70s, whereas underneath the storms, the temperatures drop to the low 60s.  This is a very well-defined cold pool.

One interesting thing about cold pools is that they can provide a lifting mechanism for storms to propagate into areas even when there is a capping inversion present.  Think about the leading edge of the storms and their cold pool--it's like a miniature cold front.  Downdraft air from the thunderstorms can blast out in front of the storms and provide convergence and lift as it runs along.  This allows storms to keep going as they track along with the leading edge of their cold pool. So, if a bunch of storms can establish a decent cold pool, they don't need to have a front or other convergence around to provide lift--the leading edge of their cold pool can provide them with their own lift.  It's a lot like the squall-line and bow-echo dynamics I discussed in a previous blog post--convergence along the leading edge of their cold pools are what keep them going.


So...even though the moderate risk got cancelled, there still have been a lot of severe storms today, including in the convergent zone along a warm frontal boundary in the upper midwest.  This slow-moving cyclone will continue to track across the country over the next day or two, bringing even more chances of severe weather.

A weak trough with conditional severe threat early this week

Back to a general synopsis of the weather conditions to expect in the coming week...

The SPC has a slight risk of severe weather out for various isolated spots in the upper midwest with even more conditional possibilities of severe weather in the southern plains over the next few days.

So, let's look at the overall setup.  Here's Sunday morning's 12Z 300mb upper air analysis:

Fig 1 -- 300mb analysis of winds (colors) and heights (contours) for 12Z, Sunday, May 8, 2011. 

Not the most amplified pattern at all--there is generally zonal (west to east) flow across the country with no deep troughs or ridges.  There is a shortwave trough entering the Pacific northwest, however, and this trough going to end up causing the severe weather chances throughout this week.

However, this isn't a typical kind of trough, at least according to the model forecasts.  Here's the GFS forecast down at 500mb on Monday morning.

Fig 2 -- GFS 18 hour forecast of 500mb heights (contours) and winds (colors) for 12Z, Monday, May 9, 2011.

That trough is forecast to deepen awfully quickly (though we're also looking at a lower level of the atmosphere in this image, but still...).  This seems like a rapid transition from a relatively flat, zonal pattern to an amplified trough-ridge pattern.  When such changes happen, we usually expect active weather.  With the curved jet streak visible on the southern side of the trough, we'd expect divergence in the exit region of the jet streak over the four-corners area and into southern Colorado.  With divergence aloft there, we might guess that there would be a surface low there...

Fig 3 -- GFS 18 hour forecast of surface temperature (colors) mean sea-level pressure (contours) and winds (barbs) for 12Z, Monday, May 9, 2011.

...but no! At least, not according to the GFS.  It has a pronounced surface low analyzed much further north over the Dakotas.  This doesn't seem to be very coherent--a low pressure center can't sustain itself without divergence aloft.  Therefore we'd expect that low to be weakening and we're still looking for a low to form under the area of divergence aloft.  Fortunately, the GFS model has these known physical relationships built into it, and by Monday evening the surface pattern seems to have corrected itself:

Fig 4 -- GFS 30 hour forecast of surface temperature (colors) mean sea-level pressure (contours) and winds (barbs) for 00Z, Tuesday (Monday evening), May 10, 2011.

The GFS has brought the center of the low back down further southwest.  But notice what has happened in the meantime.  In figure 3 (on Monday morning), there seemed to be a weak cold front trailing behind the low to the southwest.  However, with divergence aloft over southern Colorado, the strongest pressure falls at the surface were also in the southern Colorado area.  These pressure falls caused the surface winds across the southern plains and the southwest to back slightly, becoming more southeasterly rather than straight southerly as air rushed toward the region where pressure was falling.  This, combined with lots of daytime heating, seems to have caused warm air to surge westward, effectively wiping out that weak cold front we saw Monday morning.  As such, the GFS really doesn't have much of a cold front shown by Monday evening.

Of course, remember from the thermal wind arguments that I've talked about frequently in these blog posts that the upper-air winds, particularly the upper air jets, are dictated by temperature gradients below.  By effectively erasing that weak cold frontal boundary, the temperature gradient there has been erased too.  Without that temperature gradient, the jet aloft should tend to weaken.  Here's the GFS 500mb forecast for Monday night:

Fig 5 -- GFS 30 hour forecast of 500mb heights (contours) and winds (colors) for 00Z, Tuesday, (Monday night), May 10, 2011. 

It's rather subtle, but you can begin to see that the jet streak seems to be further retreating to the west around the base of the trough.  Now the exit region seems to be over eastern Arizona or western New Mexico.  It's still not in the best position to be supporting that surface low over eastern Colorado.

However, on Tuesday, the surface low and the upper-air trough finally seem to be getting their act together.  Cold air from eastern Montana seems to sneak in behind the surface low and re-establish a weak, but strengthening cold front.

Fig 6 --  GFS 48 hour forecast of surface temperature (colors) mean sea-level pressure (contours) and winds (barbs) for 18Z, Tuesday, May 10, 2011.

There's a feedback mechanism at work here--as cold air sneaks in behind the surface low and strengthens the temperature gradient, the upper-level winds increase along the temperature gradient.  This will strengthen the jet streak aloft and bring it further north, finally putting it in a position where its exit region (and associated divergence) is over the surface low and can support it to continue deepening.  But, a strengthening surface low is going to advect more cold air in behind it, further sharpening the cold front.  This strengthens the jet streak even more...and so on.  This is part of a phenomenon called baroclinic instability--an instability driven by temperature gradients.  Here's the 500mb map for Tuesday afternoon showing how the jet streak is forecast to move northward over the strengthening cold front.

Fig 7 -- GFS 48 hour forecast of 500mb heights (contours) and winds (colors) for 18Z, Tuesday,  May 10, 2011. 

Ironically, the GFS then forecasts the whole setup to weaken again after that--but that's already getting pretty far out in model time.

So what's the consequence of this slow-developing cyclone?  As you can see, over much of the central part of the country there will be southerly winds and lots of warm air advection from the south at the surface.  This will bring very warm air pretty far north--notice that high temperatures will probably get into the low 80s as far north as Iowa and northern Illinois.  Furthermore, this southerly advection will bring in more moisture, too. Here's the dewpoint forecast at the surface for Tuesday afternoon:

Fig 8 -- GFS 48 hour forecast of surface dewpoint temperature (colors) for 18Z, Tuesday, May 10, 2011.

That forecast is showing an area of over 70 degree dewpoints on Tuesday afternoon across much of the central Mississippi River valley.  That's a lot of moisture.  With warm, very moist air at the low levels, we're obviously looking at a lot of potential instability across a large swath of the country.

But remember--instability isn't everything.  First we'd have to check if the atmosphere was capped at all.  Here's a different way of looking at potential capping inversions.  This is the GFS forecast for 850mb temperatures on Tuesday afternoon:

Fig 9 -- GFS 48-hour forecast of 850mb temperatures (colors) and height (contours) for 18Z Tuesday, May 10, 2011.

 The temperatures are in Celsius, but you can see that at 850mb the temperatures are in the low-to-mid 20 Celsius range right over our area of 70 degree dewpoints.  That works out to around 70-77 degrees Fahrenheit.  But at the surface high temperature were forecast to be in the upper 70s to low 80s.  This does not represent significant cooling with height if the temperature only drops a few degrees from the surface to 850mb.  Thus, we can conclude that there's probably a fairly strong capping inversion in place over the region of warm, moist air at the surface.

With a capping inversion in place, we're going to need some sort of forcing mechanism to get storms going.  But what forcing mechanism?  We've already seen that the cold front is being washed out or weakly present way out west over the high plains--far removed from our area of greatest moisture and heating.  Furthermore, there's no wide-spread upper-air support.  That upper-level jet at 500mb is just barely keeping the low pressure center going--with no divergence at all suggested over the area of warm temperatures and high dewpoints. As such, there's nothing really to support thunderstorms except the warm moist air at the surface.

So, the chances for severe weather will be highly conditional over the next few days.  Yes, it's going to get warm and sticky over the central part of the country.  And there are a few areas where there seems to be some convergence of winds at the surface.  There looks to be a dryline forming in Oklahoma and Texas by mid-week.  There also will probably be a warm or stationary frontal boundary stretching across the upper midwest at the leading edge of all that warm air as this low tries to organize itself.  The Storm Prediction Center is focusing on any convergence along that warm/stationary front as the best chance for severe weather over the next couple of days.  However, there will be a possibility for thunderstorms anywhere that there happens to be enough convergence near the surface to cause lift that can overcome the capping inversion.  And with such warm, moist air to draw upon, any storms that form will have a high probability of becoming severe.

Furthermore, with how chaotically the GFS seems to be handling this low pressure center's development and the upper-air response, this is a highly uncertain forecast--bound to change as the week goes on.  So...we'll have to be alert.

Why is it so difficult to cool below the dewpoint?

One of the first rules of thumb that novice weather forecasters learn (or, at least, one of the first rules of thumb that I learned) was that when forecasting the overnight low temperature, it should never be more than a degree or two cooler than the dewpoint temperature.  This rule of thumb applies very broadly--it's very hard to cool temperatures down below the dewpoint temperature.  Why is this?

Let's go back to what the dewpoint temperature actually represents.  In a basic sense, it's the temperature that air with a given water vapor content would have to cool to before it becomes saturated.  What does it mean for air to become "saturated"?

Saturation is often described in terms of the amount of water vapor that the air can "hold" at a given temperature and pressure.  While this serves as a fairly good analogy, it's not exactly the way things work.  Air can "hold" as much water vapor as it needs to--it's the rates of evaporation and condensation that define saturation.

In a given parcel of air, there's always evaporation and condensation going on concurrently.  When a parcel of air is not yet saturated (it's temperature is greater than the dewpoint temperature), the rate of evaporation of water into the parcel is greater than the rate of condensation of water out of the parcel.  As such, there is the possibility of a net gain of water vapor into the parcel, assuming that there is water present to evaporate into the parcel.  If there's no real liquid water around to evaporate into the parcel of air, then obviously it won't be constantly gaining water vapor.  But if the parcel is unsaturated, then the potential exists for more water to be evaporated into the parcel than would condense out.

As the parcel comes close to this "saturation" level (for example, by the temperature cooling to the dewpoint temperature), the rate of condensation out of the parcel increases.  Think of it this way--the more water molecules we're adding to the parcel, the greater the probability than molecules will condense out of the vapor phase to form liquid.  When we reach the saturation level, the rate of evaporation into the parcel exactly equals the rate of condensation out of the parcel.  This is why we think of saturation as a "limit" describing how much water the parcel can "hold"--once it reaches saturation, there is no net gain of water vapor into (or out of) the parcel. The evaporation into the parcel and the condensation out of the parcel are equal.

Finally, if we were to somehow get beyond this saturation level ("supersaturation"), by, for example, somehow cooling the parcel below its dewpoint, then the rate of condensation out of the parcel would become greater than the rate of evaporation into the parcel.  There is a net loss of water vapor from the parcel until enough water vapor has been lost so that the rates of evaporation and condensation are once again equal (we lose water until we get back to saturation).

I tried to sum up these three situations in the diagram below.

So what does this have to do with cooling below the dewpoint temperature?  A lot. It turns out that when water condenses from water vapor into liquid water, it releases a large amount of heat.  In fact, experimentally we know that water releases 2.5x10^6 Joules of heat energy for every kilogram that condenses from vapor to liquid.  This is called the Latent Heat of Vaporization (or Condensation).  Think about it this way--water vapor molecules are in a gaseous phase--they move around much more quickly than water molecules in their liquid phase.  So, to transition from fast-moving gas molecules to slower-moving liquid molecules, some energy has to be lost.  This energy is lost in the form of radiating heat.

So let's do a simple experiment here.  Let's say that it's a cool spring evening and we've cooled down overnight until our temperature has reached the dewpoint temperature which happens to be 10 degrees Celsius (50 degrees Fahrenheit).  Since we've cooled to our dewpoint temperature, we know that the air is saturated.  So, any further cooling is going to make the air supersaturated, and condensation out will dominate over evaporation into the air until enough water vapor has been lost to bring the air back to saturation.

We can use a thermodynamic chart to find just what mass of water vapor air at that temperature has in it at saturation.  We'll assume that our pressure is 1000mb (a rather typical surface pressure).  I apologize for the poor quality of these charts--it's hard to find a high-resolution thermodynamic diagram online.  I've exaggerated the drawing a bit so it's hard to match up the saturation mixing ratio lines (which tell us the mass of water vapor in the air).  You'll have to trust my numbers here...

Stuve thermodynamic diagram showing the initial pressure, temperature and mixing ratio of water vapor.  The blue vertical lines are temperature contours, the horizontal blue lines are pressure contours (the red dot is on the 1000mb line) and the brown, dashed, tilted lines are mixing ratio contours.  The red dot lies between the 5.0 and 10.0 mixing ratio contours at a value of about 8 g/kg.

We can see that at 1000 mb and 10 degrees Celsius, the "saturation mixing ratio" is about 8 grams per kilogram.  That means, if the air is saturated at 10 degrees Celsius and 1000 mb, then there are 10 grams of water vapor per every kilogram of air.

Now, let's say that we try to cool the air by 2 degrees to 8 degrees Celsius (about 46 degrees Fahrenheit).  If we cool the air, the saturation mixing ratio is going to change.  Let's return to the chart...

Same as previous diagram, but now showing the new position of the cooled air.  The pressure line is the same (1000mb), but the temperature has dropped from 10 Celsius to 8 Celsius and consequently the saturation mixing ratio has dropped from 8 g/kg to 7 g/kg.

We see that at 8 degrees Celsius, the saturation mixing ratio has dropped to 7 grams per kilogram.  Remember, if we cool the parcel below its dewpoint, it becomes supersaturated, which means condensation dominates.  That condensation will continue to dominate until it has removed enough water vapor to bring the air back into saturation again.  In this case, the amount of water that will have to be condensed out to return to saturation is 8 - 7 = 1 gram of water (per kilogram of air).  So if we try to cool the air two degrees Celsius below its dewpoint, we'll condense out 1 gram of water vapor (per kilogram of air).

But, as I mentioned before, when water vapor changes from gas to liquid phase it releases latent heat.  We can calculate how many Joules of heat evaporating one gram of water will release (1 gram = .001 kilograms) by using that latent heat of vaporization (Lv) that I mentioned earlier.

So just evaporating that one gram of water releases some 2,500 Joules of heat.  That heat energy is going to go toward warming the air around the condensing water.  We can use a form of the first law of thermodynamics to calculate just how much the air will warm.

We'll assume here that the second term on the right hand side involving changes in pressure (delta-P) equals zero.  All that's saying is that we're assuming all of the released heat goes to warming the air and none of it does work on the air by changing its pressure and volume.  Remember on our thermodynamic diagram we stayed at the same pressure when we tried to cool the air--so the change in pressure (delta-P) was zero.

The Cp in this equation is the specific heat capacity of air.  For perfectly dry air this works out to about 1004 Joules per kilogram of air per degree Kelvin (Celsius).  Since this isn't perfectly dry air (it has 10 g/kg of water vapor in it, after all...), that number is actually adjusted a bit--it works out to be around 1012 Joules per kilogram of air per degree Kelvin (Celsius).  We know the amount of heat added (delta-Q) on the left hand side--that's the 2,500 Joules we're getting from the condensation of the water vapor.  We also know that since our mixing ratios were defined as grams per kilogram of air, the mass of air we're concerned with is just 1kg.  Knowing all this, we can solve for the change in temperature (delta-T):

Our change in temperature works out to be about 2.5 degrees Celsius of warming.  But remember--we only cooled the parcel by 2 degrees from its dewpoint!  So, the evaporation of the excess water vapor generated by cooling the air 2 degrees actually releases enough heat to warm the air up by 2.5 degrees--that's a net warming of the air!

It should hopefully be clear now why it is so difficult to cool the air below its dewpoint.  As soon as you cool below the dewpoint, water vapor condenses out faster than it is evaporated in.  This excess condensation releases latent heat into the air, which in turn warms the air enough to compensate for the cooling you tried to do in the first place.  It's pretty much a hopeless endeavour--you try to cool, but the condensation that results cancels out all cooling.  This is why the temperature rarely drops more than a degree or two below the dewpoint.

This is a handy tool to have when trying to make a forecast for the low temperature overnight.  Its more or less an absolute minimum possible temperature that could happen (assuming no fronts come through or there are other radical changes to the air mass).  Of course, if you do reach the dewpoint, all that condensation of water vapor as the air keeps trying to cool results in lots of little water droplets--and you get fog.  In fact, on mornings if you wake up and there's fog outside, you know that the air cooled to the dewpoint overnight--and is still at the dewpoint right then.

Looking even more into what this means, note how just a small amount of water vapor--just one gram in a whole kilogram of air--released enough energy to warm the air by 2.5 degrees Celsius.  This is why warm, moist air is so important when looking at the formation of thunderstorms.  The heat capacity of water is pretty incredible, and it provides that extra fuel that makes storms so violent.