Thursday, March 31, 2011

Poundings for Florida ending; powerful shortwave next week

As many people have noted recently, the end of March has been unusually cool across much of the northern part of the country, as arctic air has settled in.  Here's this morning's approximate low temperatures across the country:
Fig 1 -- Surface temperature (colors) and pressure (contours) at 11Z, March 31, 2011. From the HOOT website.
Note that 40 degree Fahrenheit lows exteded all the way down to the Gulf coast, with temperatures in the teens and 20s across the upper midwest.  Very winter-like, even though by all measures we have definitely moved into spring.

Of course, as cold air moves south, so does the jet stream.  Remember that the jets above are directly tied to temperature gradients below through the thermal wind relation.  So, as the gradient of temperature between arctic air to the north and warm subtropical air to the south moves south, so do the jet streams above.  Here's this morning's 500mb chart (from College of DuPage--the HOOT site seems to be behind on its graphics).  The yellow contours are isotachs showing wind speed.
Fig 2 -- 500mb geopotential height (blue contours) and winds (yellow dashed contours) for 12Z, March 31, 2011.  From the College of DuPage.
Jet stream winds usually follow the contours of geopotential height since things are roughly (but not quite) in geostrophic balance up there.  We can see that there is a large-scale trough over the eastern half of the US, which corresponds well with the pool of colder air we're seeing at the surface.  One jet streak is analyzed over the central plains with another over the far southeastern US.  As the jet stream shifted south, the jet streaks shifted with it.  Since divergence associated with jet streaks helps drive surface cyclogenesis, the storm track also has shifted south.  As a result, places along the Gulf Coast, particularly Florida, have seen repeated rounds of strong storms as jet streak after jet streak and storm after storm move over them.  Today is no exception.
Fig 3 -- Base reflectivity composite over the southeastern US from 1808Z, March 31, 2011.  From
A tornado watch is in effect for central Florida at the moment.  The past several days have seen multiple mesoscale convective systems move through the state.  This is more than the typical diurnal cycle of convection over Florida...

But the end is in sight!  The European model shows that the broad trough over the eastern US is going to start moving eastward.  Here's the 500mb forecast for Friday morning:
Fig 4 -- ECMWF 24-hour forecast of 500mb winds (colors) and geopotential height (contours) for 12Z, Friday, April 1, 2011.  From the HOOT website.
The trough axis is really sharpening up and has moved further to the east.  There is a cyclonically-curved jet streak forecast in the base of the trough.  Since we expect to see divergence aloft in the exit region of a cyclonically-curved jet streak, we see that the best place for a surface cyclone to be developing is now well off-shore.  The convergent entrance region of the jet streak is forecast to move into the southeast by tomorrow morning, meaning widespread subsidence and generally clearing conditions.

The pattern is forecast to continue to be progressive, with the next shortwave moving through on Sunday into Monday.
Fig 5 -- ECMWF 96-hour forecast of 500mb winds (colors) and geopotential height (contours) for 00Z, Monday, April 4, 2011.  From the HOOT website.
The broad troughing in the eastern US has flattened out by this point and somewhat of a weak ridge has built up across the midwest.  However, there is a clear and rather sharp shortwave forecast to be digging through the four-corners region by this point.  The ECMWF sharpens this shortwave enen more by Monday night.
Fig 6 -- ECMWF 120-hour forecast of 500mb winds (colors) and geopotential height (contours) for 00Z, Tuesday, April 5, 2011.  From the HOOT website.
It will be very interesting to see what happens as this shortave comes through.  Based on this 500mb forecast and following jet streak divergence aloft, we'd expect a surface cyclone to be forming somewhere over, say, western New Mexico on Sunday night. However, the divergent jet streak region has moved all the way up to northern Michigan by Monday night (if we treat the jet streak forecast for Monday night as a straight jet streak).  That seems awfully fast motion to me--from New Mexico up to northern Michigan in 24 hours?  I suspect with this forecast we might end up seeing an occlusion of the first low followed by new cyclogenesis taking place further north. Just a thought.

Models begin to diverge in their long-range outlook past Monday night.  First, the forecast from the ECMWF for 500mb on Tuesday night (00Z, Wednesday):
Fig 7 -- ECMWF 144-hour forecast of 500mb winds (colors) and geopotential height (contours) for 00Z, Wednesday, April 6, 2011.  From the HOOT website.
The trough axis is very well-developed with a coherent jet around it and is beginning to take on a positive tilt across the central Ohio River valley.  The main divergent region is probably over eastern Quebec.  The strong winds in the jet streak on the eastern side of the trough point to what would probably be a rather strong cold front at the surface below.

Now let's take a look at the GFS forecast for the same time:
Fig 8 -- GFS 132-hour forecast of 500mb winds (colors) and geopotential height (contours) for 00Z, Wednesday, April 6, 2011.  From the HOOT website.
The GFS shortwave trough is lagging behind the ECMWF trough quite noticeably.  The trough is more neutrally tilted and is located over Missouri/Arkansas instead of out over the central Ohio River valley.  Also the jet streak pattern is not nearly as well-developed as was seen in the ECMWF model.  Here there is a much smaller jet streak in the lower Ohio River valley, with a divergent region probably over Indiana--vastly different from the eastern Quebec divergent region in the ECMWF.  There are noticeable differences elsewhere, too.  The GFS has a well-developed, cut-off low sitting off the west coast of British Columbia whereas the ECMWF has some kind of crazy combination of shortwaves that isn't as coherent.  Of course, we're looking at several days out here, so our models aren't that trustworthy.  Even in the upper-level features that we are the best at predicting (overall), there is often great disagreement at this range.

So what does this all mean?  We know that the rounds of storms in Florida look to be coming to a close very shortly.  The flow will begin to flatten out as troughing moves off the east coast this weekend.  Then, a new shortwave is forecast to dig in out of the desert southwest and onto the plains from Sunday into Monday.  From there on out--things get dicey.  Trying to time this shortwave for its impacts on the east coast is very difficult right now. 

Even trying to figure out what kind of precipitation type is going to fall is somewhat of a mystery.  The long-range forecast from the Climate Prediction Center is forecast a "heavy snow event" for the northern plains and upper midwest on Sunday into Monday.
Fig 9 -- CPC precipitation hazards forecast for Apr 2-13, 2011.  As of March 30, 2011.  From the CPC.
They are also calling for a widespread area of heavy precipitation and flooding on the east coast from April 4th-6th (Monday through Wednesday).  These forecasts make more sense given the more southerly track of the shortwave forecast by the GFS model, so I'd guess they're leaning toward that solution.  They're cutting it fine on the precipitation type in the northern plains, though.  The GFS forecast critical thickness lines for Monday evening, which help make a first-guess at precipitation type, are shown below:
Fig 10 -- GFS 4.5 day forecast of critical thickness values for 00Z Tuesday (Monday evening), Apr. 5, 2011.  From the College of DuPage.
In the plot above, I'm guessing based on the scale that the purple shadings are something like relative humidity at some level.  Which level?  I'm not sure.  But regardless, the colored lines are critical thickness forecasts.  Remember with critical thickness that you want to be north of the lines (in the colder air) for snow and south of the lines (in the warmer air) for rain.  Here we see that on Monday night (the end of the CPC's April 3-4th heavy snow swath), the critical thickness lines go right through the region they've outlined.  As such, I don't think we can really make much of a claim for an exclusively heavy snow event in the areas they've outlined.  There definitely is the possibility for snow in the far northern plains based on this forecast solution.  But we need more evidence from more model agreeement before saying that for certain.

And given the disagreements in the models after Monday, it doesn't seem very useful to try and look at any more diagnostics past this point.

So...this weekend will be the test.  Will the models come into better agreement?  Or will we still by guessing by the time Monday rolls around?

Tuesday, March 29, 2011

Heavy Rain for the Pacific Northwest

We currently have relatively weak flow across the Rocky Mountains and central US, so it's a bad time to be looking for lee-side cyclogenesis.  So, in the meantime, I'll turn to more current weather to discuss.

Spring has definitely arrived here in the Pacific Northwest--the trees are blooming, leaves are starting to appear, and high temperatures are consistently in the 50s.  However, with spring comes bouts of heavy rain which continue the feel of winter well into June.

The jet stream is on its way north and with it, lots of moisture.  Here's the water vapor satellite image from this morning:
Fig 1 -- GOES-W WV satellite image at 17Z, March 29, 2011.  From the HOOT website.
That's a lot of upper-level moisture pouring in from the tropics up to Washington and southern British Columbia.  It's interesting to note just how long this particular jet streak happens to be--here's the northern hemispheric analysis of 250mb winds from 12Z this morning:
Fig 2 -- 250mb winds (colors) and geopotential height (contours) at 12Z, March 29, 2011.  From the HOOT website.
 This particular jet streak begins all the way back in eastern China and crosses the entire Pacific before ending over the northwest coast.  This sets the stage for a very long-duration rainfall event as moisture is continually advected into the region.

How much rainfall are we looking at?  Here is this morning's 24-hour rainfall forecast for the end of the day on Wednesday from the 12km UW WRF model.
Fig 3 -- Previous 24-hours of rainfall at 00Z, Thursday, March 31, 2011.  From the UW Modeling page.
The units on these maps are somewhat odd--"cin" stands for "centi-inches" or hundredths of an inch, I believe.  Therefore the black colors in the northern and central Cascades that correspond to "256" on the color bar would actually be 2.56 inches--which is a lot.  You can really see the orographic enhancement of the precipitation like I talked about in my last blog post.  The strongest bands of precipitation are on the windward side of the Cascades and the Bitterroots on the Montana-Idaho border.  On the leeward (eastern) side, the precipitation drops off considerably.  Also note how dry it is over the northern Puget Sound area.  This is a rain shadow behind the Olympic Mountains on the Olympic peninsula.  Rain continues through Thursday as well:
Fig 4 -- Previous 24-hours of rainfall at 00Z, Friday, April 1, 2011.  From the UW Modeling page.
You can tell by comparing Thursday's rainfall totals (figure 4) with Wednesday's rainfall totals (figure 3) that the axis of the jet stream is expected to move further north during the time between.  Oregon and points further south aren't seeing nearly as much precipitation on Thursday as they did on Wednesday.  There's still some black shadings in the North Cascades, though, indicating another 2.5 inches or so on Thursday.  That's over 5 inches total, according to these models.  Will these amounts verify?  The models do tend to over-estimate mountain precipitation in this area, so probably not.  But still--quite a bit of water.

Such extended rainfall events being forecast often raises the specter of flooding in the mountain rivers.  The Northwest River Forecast Center (NWRFC) runs many hydrologic models using the input from atmospheric models (like the ones we've been looking at) to try and predict how much water will enter each river basin.  They can use this information to try and forecast river height.  Here's a chart from the NWRFC showing the observed and predicted levels of the Snoqualmie River near the city of Snoqualmie east of Seattle.
Fig 5 -- Observed (blue line), model forecast (green line) and extended trend (cyan line) of river stage level for the Snoqualmie River near Snoqualmie, WA.  From the NWRFC.
On the above chart, the current time (late Tuesday morning) is shown by the vertical purple line.  Flood stage is shown by the horizontal red line.  You can see that for the past several days river levels have remained relatively constant at around 5 feet.  However, with rains expected to begin Tuesday afternoon and continue through Thursday, the level of the river is forecast to rise sharply, peaking around 17 feet on Thursday, which is 4-5 feet above flood stage.  However, the river is also forecast to quickly drain out, dropping below flood stage once again by the weekend.  I'm curious as to the timing of this rise--I'd expect the peak to occur on Friday or so, after the rain had stopped.  Granted, the plot above was made around 9Z this morning, before the new 12Z model data had come in.  So maybe this forecast will be amended in the near future.  Regardless, flood watches have been posted for a lot of the central and northern Cascades.

It's going to be a wet week in Seattle.

Sunday, March 27, 2011

Some Basics of Mountain Flow

It's been a week since my last blog post and that's mostly because I've been away on spring break this past week.  But I am back now, so I should start posting things regularly again.

A few people have asked me recently about the dynamics behind mountain flow--why we get this "rain shadow" effect among other things.  There are several excellent resources out there that explain this, but I'll do my best here to try and describe what's happening--and why flow over mountains becomes very, very complicated.

So, let's set the stage.  We'll assume we have a north-south running mountain chain (like the Rockies, the Sierras or the Cascades) and prevailing west to east flow (like usual).  The air in the lower parts of the atmosphere tends to have much more moisture than the air above it.  This is because the sources of water vapor are all near the ground--the oceans, lakes, evaporation from plants and so on.  The dotted line at the top of the figure below represents the stable tropopause layer.
(Click to enlarge this or any image)
So what happens when this air reaches the mountains?  Air in the lower levels will be forced up to rise over the mountains.  It can't go down because the ground is below (or, there's more air below that's also being forced up).  Therefore this lower-level air gets lifted over the mountains.
Remember that the low-level air is moister than the air above.  As this low-level air is forced upward, it cools.  Anyone who has ever climbed a mountain knows that it gets colder the further up you go.  As the air cools, it soon reaches its dewpoint temperature and the moisture in that air condenses into clouds and eventually rain.  This is why we see the heaviest rain on the windward slopes of mountains.  More on that later.

Anyhow, the air continues to move over the mountain range.  All that upward motion from below pushes on the air above it, forcing upward motion in the air above further downstream.  This causes a sort of  translation of upward motion up through the atmosphere--which will become important later.  In the meantime, eventually most of the moisture in the lower-level air is condensed out into precipitation as the air is forced up and over the mountains.  This air becomes significantly drier.
By the time the air reaches the far side (the leeward side--away from the direction of the prevailing wind) of the mountain, there's now a sort of "vacuum" below--as the terrain slopes down and away, the air rushes down the slopes of the mountain to fill in all that space.

In the meantime, that upward motion that has been translating up through the atmosphere has run into the tropopause.  Remember that the tropopause layer is very stable and tends to resist vertical motion.  We'll get back to what happens there later.  But now as the air rushes down the leeward side of the mountain, its pressure increases and it warms up.  What little moisture there was left in the air is now nowhere near saturation--as the air warms, the difference between the dewpoint of the air (the temperature at which it becomes saturated) and the actual temperature of the air will increase.  This makes the air feel very, very dry.

This dryness on the lee-ward side of the mountains is what gives rise to the "rain shadow" effect--all the precipitation tends to fall on the windward side of the mountains where lift is being forced by the terrain.  By the time the air has gotten over the mountains, not only has it lost much of its moisture, but the combination of downward motion and the air heating up (bringing the air further and further away from saturation) makes the leeward side of the mountains a poor place for any precipitation to develop at all.  This is starkly evident if we look at a map of annual precipitation in the western US:
Average annual precipitation in the western United States from 1961 to 1990.  From the Oregon State PRISM group.
The effects of major mountain ranges dictate where we see precipitation maxima.  I tried to annotate roughly where the crests of several mountain ranges are.  Note how particularly well they correspond with the edges between precipitation maxima (the blues and purples) and minima (the reds and yellows).  Particularly striking are the effect of the Cascades in the northwestern US and the Sierra Nevada in northern and eastern California.  To the west of these ranges there is heavy precipitation --80-100 inches of rainfall each year.  But just to the east of them, there are enhanced areas of dryness--only 5 or 6 inches of precipitation per year in some areas.  We see similar, but less intense separations over some of the mountain ranges further east like the Bitterroots in Montana and even the Wasatch in northern Utah.  There's still a maximum to the west of the mountain crest and a minimum to the east.

By the time we get to the high peaks of the Front Range of Colorado, though, there really isn't that much of a stark divide in precipitation--you can see hints of one, but its not nearly as obvious as it was further west. Why is that?  Each time air is forced over a mountain range, it loses more moisture to precipitation on the windward side of the mountains.  The most moist air is out over the Pacific Ocean--naturally.  Most of the moisture in that air is immediately lost when it hits the Coast Ranges, the Cascades or the Sierras in the far west.  The low-level air still retains some moisture, but not nearly as much by the time it crosses all those high mountains.  So by the time it is forced up and over ranges further east like the Bitterroots and the Wasatch, we still see some precipitation enhancement, but there was much less moisture to begin with.  And by the time the air finally reaches the Front Range of Colorado, it has very, very little moisture left in it--all the moisture has been "wrung out" by precipitation over multiple mountain ranges.  Thus we really don't see nearly as much of an enhancement in precipitation on the windward side of those far eastern ranges.  We do see a little, but not much.

If you're not interested in further technical details about forcings and responses in the atmosphere around mountains, then you can just stop here and enjoy seeing rain shadows across the US...

But now I want to go back to the schematics I've been drawing to look at a slightly more complicated question of what's causing what in this case.  The atmosphere is full of forcings and responses to forcings.  Mountains are particularly fun cases to look at.

First, what is the most direct effect the introduction of a mountain to our simple eastward-moving air?  If you put a mountain into the flow, the air is going to crash into the mountain on the windward side and there's going to be kind of a hole left in the flow (that "vacuum") on the leeward side.  If we look at this in terms of pressure, we would see higher pressure being caused by the air crashing into the mountain on the windward side, and lower pressure in that vacuum on the leeward, eastward side.  We'll consider this the "forcing" of the mountain.
Now the question becomes--what does the atmosphere do to respond to this forcing?  Well, it wants to evacuate air from the area of higher pressure and bring air in to fill the area of lower pressure.  So we see the response in terms of vertical motion--the atmosphere tries to remove air from the higher pressure are by drawing it up vertically (it can't pull down air because the side of the mountain is right there--and that's what's causing the higher pressure in the first place).  The atmosphere also tries to fill the low pressure area by pulling air down into it from above to increase the pressure.
This makes perfect sense because that's what we intuitively think of happening with the flow over a mountain--air generally rises on the windward side and falls on the leeward side--it goes up, over the mountain, then comes back down.  Furthermore, this agrees with how we think of precipitation--we almost always associate precipitation with rising motion, and that's exactly where we see it.

But it gets slightly more complicated in real life.  Usually the air is relatively stable while this is going on.  Up near the tropopause it's particularly stable.  Remember how that upward motion was being translated upward in the atmosphere?  Eventually that will reach the tropopause, usually just downstream of the mountains.  The very stable tropopause is not conducive to rising motion--it's very difficult to force air to move vertically beyond that height.  So with all this air moving upward toward the tropopause, the air will have to start diverging there because it can no longer move upward.

So now we see sustainable upward motion, supported by divergence aloft, directly over the area of downward motion trying to fill in the low pressure area on the downwind side of the mountains.

The net result is that some of the downward motion on the leeward side of the mountains is effectively "cancelled out" by the upward motion supported by divergence aloft at the tropopause.  This means that the atmosphere cannot "fill" the low pressure on the leeward side of the mountain--the downward motion that would do so is being somewhat cancelled out by the upward motion supported by the divergence aloft.  Thus, with this kind of flow pattern, there will always be an area of lower pressure on the leeward side of the mountains.  This is the "lee-side low" or the "downslope low" and its formation is referred to as lee-side cyclogenesis.

That's a pretty complicated system of forcings and responses.  There are two things going on--the direct response to the mountain being there and the indirect response of the atmosphere aloft to the presence of the mountain.  I'll try to summarize what happens in a list here:

  1. The presence of the mountain creates a partial vacuum or area of lower pressure on the downwind side of the mountain.
  2. Air moving over the mountain top rushes downward to fill that low pressure center.
  3. In the meantime, upward motion caused by the air rising on the windward side of the mountain translates upward and eastward, eventually reaching the very stable tropopause usually just down-wind of the mountain.
  4. When this upward-moving air reaches the stable tropopause, it can't move up anymore and spreads out instead, creating divergence aloft.
  5. This rising air and divergence aloft somewhat "cancels out" the sinking air trying to fill the low on the east side of the mountain.
  6. As a result, the low pressure center never can get filled in and a lee-side low persists.

I hope that description helps some of you understand the dynamics around mountains and why this flow is very complicated.  These lee-side lows actually form the basis for a lot of the storm systems we see across the central United States.  Some time soon I'll look at how we can see these lee-side lows in our observations.

As always, if you have any questions, email me at the address on the upper-right part of my blog page.  I always enjoy hearing from my readers...

Sunday, March 20, 2011

Progressive Pattern This Week

It's been a while since I actually looked at a week-long forecast of what's up in the weather, so I thought I'd begin the week by taking a quick look at that.

A look at tonight's 00Z 300mb analysis shows the upper-air pattern:
Fig 1 -- 300mb objective analysis valid 00Z, March 21, 2011.  From the HOOT website.
Features of note include the rather deep trough just off the California coast, with smaller shortwaves over eastern Montana and the Dakotas and also just off the northeast coast.  In examining the wind pattern, it seems that the jet streaks really aren't that organized--there's lots of wind maxima floating around out there.  It should be no surprise, then, that the surface map tonight looks just as disorganized.
Fig 2 -- Surface objective analysis of temperatures (colors) mean sea-level pressure (contours) and winds (barbs)  at 00Z, March 21, 2011.  From the HOOT website.
There are a few scattered low-pressure centers that don't seem to be doing much.  There's a low up in northern Minnesota that seems to be associated with the leading edge of those shortwaves coming out of the Dakotas that I mentioned before.  Another surface low is analyzed in central Colorado--but is there really much upper-air support for that one?  The same goes for the low pressure center off the northwest Oregon coast--that looks to be right under the middle of the upper-level trough--a bad place to be if you're a low since you're away from the jet streaks and divergence aloft.  So based on the upper-air and surface analyses given, I'm really not seeing too much in terms of low-pressure centers strengthening and becoming big concerns--for now.

However, there's a lot of other things going on in the surface map above that I am interested in.  Note that even though there are no strong low pressure centers, there are decently strong gradients of pressure--particularly across the southern plains and up into the Ohio River valley.  These pressure gradients are helping to drive those strong, southerly winds we see in the surface analysis.  Those winds are helping to advect warm, moist air up from the Gulf of Mexico.  You can see in the surface analysis how far that warm air has moved up already.  In fact, there even looks to be a front stretching across the central plains, through northern Illinois and along the Ohio River.

But, that "front" doesn't seem to be associated with any low-pressure center.  You could argue that it's associated with that low in Colorado or maybe even the remnants of an occluding low over Minnesota.  But these look pretty iffy...

Without a low-pressure center really driving this front along, we'd expect this to be a stationary front--one that's not going to move much until the winds start organizing themselves better.  To do that they're going to need upper-level divergence to come in and start spinning up a surface low.  What would do that?  How about that trough moving in from the west coast?  Here's the GFS forecast for Monday:
Fig 3 -- GFS 24-hour forecast of 300mb  winds (shaded) and heights (contours) for 00Z, Tuesday (Monday evening) March 22, 2011.  From the HOOT website.
That deep trough from the west coast is forecast to move in with an organized, strong jet streak on its leading side.  The exit region of that jet streak (we could get finicky with the details and say the left-exit region, but that's more difficult to pin down...and besides, the area between a trough and a ridge is generally a divergent region aloft...) should bring some healthy divergence aloft to the central Rockies.  And, just like that, surface pressures are forecast to fall in that region...
Figure 4 -- GFS 24-hour forecast of surface temperature (colors), mean sea-level pressure (contours),  and winds (barbs) for 00Z, Tuesday (Monday evening) March 22, 2011.  From the HOOT website.
There's an area of forecast lowering pressures extending from Montana down through eastern Colorado, corresponding to the exit region of that jet streak.  Note how in 24-hours the GFS has not moved that frontal boundary at all--without a surface low to organize the wind field, that boundary won't move.

However, there is a curiosity (at least to me) that I can't fully explain.  We have that stationary front sitting there for some 24+ hours over the central United States.  It has a pretty good temperature gradient across it--mid-60s to the south of the front and 30s north of the front.  Since our winds aloft are connected to the temperature gradients below (via the thermal wind relation), I would have expected the upper-level winds to have picked up a bit over the frontal boundary.  Yes--they do pick up a little bit in this GFS forecast over the front in the 300mb image above, but not in a very organized way directly over the frontal boundary.  This puzzles me a bit, and makes me slightly suspicious of the upper-air forecast from the model.  Just a curiosity.

Anyhow, by Tuesday morning, the GFS (if it is to be believed) moves the upper-level trough out over the plains with a strong jet streak on its eastern side.
Fig 5 -- GFS 36-hour forecast of 300mb  winds (shaded) and heights (contours) for 12Z, Tuesday, March 22, 2011.  From the HOOT website.
However, notice that the "tilt" of the trough axis is changing.  In the first (and to some extent the second) upper-air maps shown above, if we were to draw a trough axis through the trough, it would be oriented roughly straight north-south.  This is called having a "neutral" tilt.  Now in the image above on Tuesday morning, if we were to draw the same axis, it would be tilted, going from northwest to southeast.  This is called being "negatively" tilted.  As the tilt of a trough axis changes, so do the locations all the forcings associated with it (i.e. the jet streaks).  At the time above, however, we see a nice, cyclonically-curved jet streak and would expect a strong surface low to be forming underneath the divergent exit region, somewhere over the central plains.  And that's exactly what the GFS is doing...
Figure 6 -- GFS 36-hour forecast of surface temperature (colors), mean sea-level pressure (contours),  and winds (barbs) for 18Z, Tuesday,  March 22, 2011.  From the HOOT website.
Now that stationary front that is STILL sitting across the central plains and across the Ohio River valley finally has a low-pressure center that can take over its dynamics and start advecting it around.  Or will it?  Regardless, the wind field is now being profoundly directed by the surface low.  This is enhancing convergence along that pre-existing front and also along a dryline and cold front in western Texas and New Mexico, respectively.  Aloft we know that a divergent region of a jet streak is moving overhead, particularly in the eastern and southern plains area.  With convergence below and divergence aloft, the stage is set for thunderstorms to start firing up on Tuesday.

One interesting aspect of this potential severe weather event on Tuesday is that the stationary front has been sitting there for over 48 hours now.  This low-pressure center did not have to do a whole lot of work to advect warmth (and moisture) north from the Gulf of Mexico--it's just sitting there already.  Thus we'd expect thunderstorms to be rather widespread as such a large area will have had time to bring moisture and warmth northward.

In accordance with this pattern, the SPC has a day-three slight risk out from the southern plains up into the southern Great Lakes:
Fig 7 -- SPC three-day convective outlook valid for 12Z Tuesday through 12Z Wednesday.  From the SPC website.
And, we now see, at least on the large scale, why they have this region highlighted.  Though I highly encourage you to read their discussion for an excellent description of what they're looking at.

However, the dynamics start changing by Wednesday.  Remember how the trough was becoming more negatively tilted?  The GFS forecasts it to continue to do so on Wednesday:
Fig 8 -- GFS 60-hour forecast of 300mb  winds (shaded) and heights (contours) for 12Z, Wednesday, March 23, 2011.  From the HOOT website.
This has the effect of what I call "flat-lining" the jet streak (that's not a technical term--just something I use) and making the winds more zonal (more west-east).  Our once-curved jet streak becomes a more straight jet streak, with divergence assumed in the left exit region, or over the southern Great Lakes.  Since we connect the winds aloft with temperature gradients below, we might expect another west-east oriented pseudo-stationary front to have set up underneath and parallel to the jet streak.  Here's the GFS forecast for the surface at that time:
Figure 9 -- GFS 60-hour forecast of surface temperature (colors), mean sea-level pressure (contours),  and winds (barbs) for 12Z, Wednesday,  March 23, 2011.  From the HOOT website.
We see the surface low right where we would expect it to be--in the southern Great Lakes region underneath the divergent exit region of the jet.  We don't exactly see a west-east oriented frontal boundary (yet...).  We do see that the cold front is not a very strong one at all--the temperature and wind gradients across it are very weak.  It also is sharply tilted and not parallel to the jet aloft--the thermal wind response may be trying to pull the front more horizontal to be in line with the jet streak aloft.  Furthermore, the cold front doesn't even really extend up to the surface low anymore.  This hints that the low is occluding and dying.  As the trough aloft becomes so negatively titled, it more or less loses its identity as a trough and, with it, the ability to direct the upper-air pattern in a way favorable to the surface low.  So, the surface low starts dying off...

Just to show how nicely (at least in this case) the thermal wind response can work (at least in the model), here is the GFS forecast for the surface pattern by Wednesday evening.
Figure 10 -- GFS 72-hour forecast of surface temperature (colors), mean sea-level pressure (contours),  and winds (barbs) for 00Z, Thursday (Wednesday evening),  March 24, 2011.  From the HOOT website.
 The surface low has drifted off to the east but remains diffuse and unorganized.  The frontal boundary has also become diffuse but it is now once again oriented in a west-east direction--in agreement with the jet aloft. Such is the power of the thermal wind adjustment.  Of course, if the temperature gradient continues to weaken (which, judging by the winds, it looks like it will...), that will feed back and in turn weaken the jet aloft.  It's all one big dynamic give and take.

So that's my take on the large-scale dynamics for the first half of this week.  Lots to look forward to...

Wednesday, March 16, 2011

Inferring the Upper-Air Pattern from a Single Sentence

In reviewing all the weather blogs I read this morning, I noticed this line in WGN-Chicago's Weather Blog:

"...Powerful southwest winds predicted to gust to 35 mph Thursday afternoon combined with jet stream-induced warming produced as air sinks and compresses beneath the nose of powerhouse 170 mph upper winds should more than compensate for the reduction of sunshine and allow warming to proceed."
--WGN Weather Blog, March 16, 2011.

Hmm...this looks like something we can explore with our knowledge of jet streak dynamics.

Assuming the statement above is correct (and it was written by Tom Skilling, who is one of my favorite and most trusted TV meteorologists, so I have no doubt that it is correct...), we can start making some inferences about what the weather pattern must look like without even looking at a map and just using our knowledge of what dynamics are necessary to produce the kinds of effects described.

First, we can consider the statement about the jet-stream winds.  Tom Skilling states that air will be "sinking" beneath the "nose" of the upper-level winds.  Now, the "nose" of a jet is just a colloquial term used in the meteorology community to refer to the exit region of the jet streak--the leading edge of it on a map.  Since he's talking about sinking motion under the exit region (the "nose") of the jet, we're looking for some jet streak structure that allows for sinking motion under the exit region.  Convergence aloft leads to sinking motion throughout the lower atmosphere, so we're looking for a jet streak pattern that has convergence in the exit region.   We can consider curved jet streaks or straight jet streaks.

Let's consider curved jet streaks first.  Remember my diagram for curved jet streaks from an eariler blog post:
Fig 1--Schematic of divergence and convergence in cyclonically-curved (lower left) and anti-cyclonically curved (upper right) jet streaks.
 We saw that in cyclonically curved jet streaks (like on the lower-left part of the above image) there was convergence in the entrance region and divergence in the exit region.  Well, that's not what's being described above--we wanted convergence in the exit region since the motion below it is described as "sinking".  However, in the anti-cyclonically curved jet streak above (the upper-right side), we see that in such a jet streak, we do expect convergence in the exit region of the jet.  So here's one possibility--there could be an anti-cyclonically curved jet aloft.

But what about a straight jet streak?  Here's a schematic of divergence and convergence associated with a straight jet streak:
Fig 2 -- Divergence and convergence associated with a straight jet streak.
We see in the diagram above that it is possible to have convergence in the exit region of a straight jet streak, albeit the right exit region.  There would be implied divergence in the left exit region.  But still--if the jet streak were to the north of Illinois, Chicago would still be under the convergent region of the jet and we'd see sinking motion and warming like the description above says.  So, this too is a possibility.

So which is it?  Are we expecting a straight or a curved jet streak?  Well, we can also infer that the jet streak must be rather straight.  How?  By the first part of the statement above:

"...Powerful southwest winds expected to gust to 35 mph..."

That's a description of what's going on at the surface.  So we're expecting strong winds.  How do we get strong winds at the surface?  We need a low-pressure center at the surface somewhere to provide the pressure gradient necessary to generate such strong winds.  Where would this low-pressure center be?  The wind direction tells us that.  Remember that winds tend to blow roughly counter-clockwise (cyclonically) around a low pressure center.  Therefore, to get winds out of the southwest, the low pressure center must be off to the north or northwest somewhere.

So we'd expect a surface low to be someplace off to the north-northwest or so.  It's also probably a pretty deep low to be generating 35 mph winds and it also can't be too far away.  But to support such a strong low-pressure center at the surface, what must be happening aloft?  We have to be seeing divergence aloft--it's the same argument we always would use for finding areas of strong vertical motion underneath jets.  Divergence aloft leads to rising motion which in turn causes the pressure at the surface to fall as all that air is lifting away.

So now we can tie this back into our upper air pattern.  We see our jet aloft most be able to satisfy two conditions to fit this story:
  1. There has to be a region of convergence aloft over northern Illinois to be producing the downward motion (and warming) that are being advertised.
  2. There has to be a region of divergence aloft somewhere to the north or northwest of Illinois to support a surface low-pressure center off to the north or northwest.  We know there is probably a low-pressure center there because the winds in northern Illinois are forecast to be strong and out of the southwest.
An anti-cyclonically curved jet streak doesn't really fit the bill--it doesn't really allow for an area of divergence off to the north or northwest.  However, a straight jet streak does allow this--we can position a straight jet streak just north of Illinois to satisfy all of these criteria:

So now we have a good guess as to what the upper-air pattern (and, also from this line of reasoning, the surface pressure map as well) should roughly look like.

So how does this compare to the models?  Here's the GFS forecast for mid-day Thursday up at 250mb:
Fig 5 -- GFS 30 hour forecast of 250mb height (contours) and winds (shaded) at 18Z, Thursday, March 17, 2011.  From the HOOT website.
Not too bad at all for a rough guess.  The jet streak itself is rather straight with a slight anti-cyclonic bend to it.  The shading can kind of throw you off when trying to find entrance and exit regions.  If we just shaded the stronger wind speeds  in the core of the jet (like, the yellows, oranges and reds in the above image) we do see a broad exit region of the jet extending through the Dakotas and into Minnesota.  Because this jet doesn't seem to have a very focused exit region in the model, we'd expect the surface pressures related to it to also be kind of broad.  Here's the GFS forecast for the surface at that time:
Fig 6 -- GFS 30 hour forecast of surface pressures (contours), temperatures (shaded) and winds (barbs) at 18Z, Thursday, March 17, 2011.  From the HOOT website.
It's a very broad area of low pressure, but it is generally located to the north-northwest of Illinois like we expected.  Also the winds are strong out of the southwest, accordingly.  It all agrees rather well.

It's pretty fun to be able to pull together a full synoptic pattern from just that one sentence...

Friday, March 11, 2011

How does a Tsunami work?

Usually I talk about the weather in this blog.  The fact is, a lot of the dynamics of weather are derived from basic fluid dynamics which apply not only to air, but to water as well.  We talk about waves in the atmosphere all the time--short waves, long waves, buoyant waves, etc.--and the same mechanics describe water waves.  So today I'm going to give a brief look at some of the simple mathematics behind tsunami-like waves.

Of course, the motivation for this is the tsunami generated by the very powerful earthquake that occurred last night in Japan.  How powerful was it?  According to the USGS, a magnitude 8.9-9.0 earthquake.  According to the list of strongest earthquakes on Wikipedia, this places it as the fifth most powerful earthquake ever recorded (in terms of magnitude).

It was so strong that even short-range seismographs around the world were able to pick up on the tremor.  Here's the seismograph from a small seismomenter on the Mount Augustine volcano in southern Alaska from the past 24 hours.  The earthquake is clearly visible just before 630Z in the upper right part of the trace:
Fig 1 -- Helicorder seismograph on the Mount Augustine Volcano in Alaska from 20Z March 10, 2011 to 20Z, March 11, 2011.
In fact, almost every single volcanic seismomenter in Alaska picked up the earthquake signal.  The lower 48 seismometers picked it up to--here's a similar plot from the Black Mountain, California, seismometer.  Once again, the quake shows up just before 630Z:
Fig 2 -- Seismograph from Black Mountain, California, from 2315Z, March 10, 2011 to 2315Z, March 11, 2011.
An earthquake of this magnitude can (and did) generate a tsunami--a very powerful ocean wave that swamps inland.  There are a plethora of videos now of the tsunami impacting Japan--and the horrible destruction brought with it.  This wave had so much energy in it that it easily transversed the Pacific Ocean.  One of NOAA's DART buoy's off the coast of Hawaii showed the interruption of the normal tidal cycle as the tsunami went through:
Fig 3 -- Water Column height from NOAA DART buoy 51047 off the coast of Hawaii from 00Z, March 7, 2011 to 20Z, March 11, 2011.
Note that for the past few days, the height of the water column rose and fell very periodically--these are the normal tides we see on a daily basis.  However, there was a sudden jump early this morning (around 11-12Z) where the cycle was interrupted by a powerful wave.  The switch to green colors indicates a change from 15 minute data collection to one minute data collection.  You can see that, at least at this buoy (which is some distance out to sea), the actual change in the height of the water column wasn't even as much as the change we usually see in height due to the normal tidal cycle.  But this was way out to sea--tsunamis move and behave differently when they get close to land.  How does that work?


It turns out that tsunamis can be reasonably well explained by a set of equations called the shallow-water equations.  They are some of the simplest equations to describe wave flow on the free surface of a fluid.  They basically related the change in the height of the surface with time to the slope of the surface at a given time.   If we assume something called the shallow water limit,  which means that we assume that the wavelength between wave crests is on about the same scale as the depth of the fluid (the waves are about as far apart as the water is deep), we can ignore vertical perturbations and get one simple differential equation:
Where the Greek letter eta (the lowercase 'h' looking thing) represents the height of the free surface of the water, H represents the mean depth of the water, and g is the acceleration due to gravity.  I know...I know...looks complicated.  But if you've taken some basic calculus, it's actually pretty easy to sort through this.  Basically, we know we're looking for a WAVE as an answer to this, right?  So why not just assume that our free surface height is a simple sine wave:
We'll just assume our free surface looks like a wave of amplitude A that varies in space (x) and time (t).  The wavelength of the wave is given by lambda and the frequency of the wave is given by sigma.  Just a simple wave.  Now we can plug that wave equation in for eta in the first equation--take the second derivative with respect to time and then take the second derivative with respect to position x.  After some cancelling, we're left with this expression:
This is actually something called the dispersion relation  for this wave--it tells you how frequency (sigma) and wavelength (lamda) are related.  We can rearrange this equation to get:
Now, how do we find the speed of a (non-dispersive) wave?  The speed of such a wave is given by the frequency (in units of seconds^-1 (per second)) multiplied by the wave length (given in meters).  Put those units together and you get...meters per second.  The speed of the wave.  Well, the frequency times the wavelength is just sigma times lambda:
So we can just solve our expression above for sigma times lambda:
And there we go!  We've solved for the speed of shallow water gravity waves.  It's just the square root of the mean depth of the water (H) multiplied by gravity (9.81 meters per second squared).


I find that result fascinating--the speed of waves in this shallow water wave approximation just depends on the depth of the fluid and gravity--that's it.  Amazing.

So it turns out that tsunamis moving through the ocean can be well-approximated by this shallow wave limit.  That seems kind of counter-intuitive--after all, they're moving through the deep ocean--how is that "shallow water"?  Remember the definition of "shallow water" above--it says that the wavelength between the wave crests is about the same as the depth of the fluid.  The Pacific Ocean is around 4 kilometers deep on average.  So when you think about it that way, the wave crests of the tsunami only need to be about 4 kilometers apart to be considered in the "shallow water" limit.  It makes more sense that way.  It really makes sense when you think of how big the Pacific Ocean is--

It's almost 20,000 kilometers across at its widest point from east to west--but only 4 kilometers deep on average.  That's a very "shallow" pool of water given its size...

Anyhow, if we know that the average depth of the ocean is 4 km (4000m) we can compute the speed of a wave moving through it:
So a wave moving through the deep ocean (in the shallow water limit...ha!) would be moving at about 443 miles per hour, on average.  That's amazingly fast!  This explains how the earthquake could have happened late in the night on the west coast of the US and the tsunami wave was already there by the next morning.  At that speed, the wave would have covered the 4800 or so miles from Tokyo to Seattle in about 10 hours.  Which is right on the ball for the time it actually took.

But what happens when the wave reaches shore?  There's really no strong signal of the wave amplitude in the deep ocean, like in the buoy trace above where there was definitely a strong interruption to the tidal cycle, but its amplitude was much smaller than even the normal tidal cycle. But when a tsunami reaches shore, the height of the wave increases dramatically.  What's going on there?

It has to do with several things--one is the slope of the ocean floor.  As the ocean floor goes upward as we approach the coast, the mean depth of the fluid gets shallower, forcing the water to pile up higher.  At the same time, notice our equation for the speed of the wave above--if the mean depth of the water (H) is decreasing, the speed of the wave will also decrease. (Actually, the depth will decrease enough that the shallow-water limit is no longer applicable and we have to consider the deep-water limit--which is completely different and makes less sense, but approximation...).  So the wave is slowing down as it approaches the coast too.  This is why, though we see a wall of water moving toward the shore, that wall of water is definitely not moving at 443 miles per hour--that would be some devastation.  No...the waves do slow down somewhat.

But then we have to consider the conservation of energy.  Remember in classical mechanics, energy comes in two forms--kinetic energy (the energy of motion) and potential energy (based generally on how high off the ground you are).  If you hold a ball high in the air, it has a lot of potential energy--it has the potential to fall due to gravity.  Once you let that ball go, it starts falling--it loses that potential to fall by converting that energy to the kinetic energy of it falling.  It's basic mechanics.

So if the wave is slowing down as it's approaching shore, it's losing kinetic energy--it's no longer moving as fast.  But total energy has to be conserved--that lost energy has to go somewhere.  What does it do?  It converts into potential energy by raising the wave higher.  So the kinetic energy of the fast-moving wave transfers into the potential energy of a much higher (taller) wave as it approaches the coast.  Here's my quick sketch describing this:
So we see that the structure of the tsunami is described by this give-and-take between its kinetic energy (its speed) and its potential energy (its height).  Over the open ocean, the kinetic energy dominates (it moves much faster).  As the wave approaches land, it loses kinetic energy as that converts to potential energy (it slows down, but its amplitude increases).  

Of course, some of that energy is also lost to friction and other dispersive forces as the wave travels.  So generally, the further you are from the source of the wave, the weaker the resulting tsunami.

Anyhow, I think that's enough for one night.  I hope you found at least some of this enlightening as to how tsunami waves actually propagate through the ocean and why they become taller as they approach land.  I don't usually throw a lot of math into these blog posts, but I like to once in a while just to show where things come from.  If you didn't follow that, that's ok.  It's the concept that really counts.