The Bering Sea: A Puzzle of Wind Speed
The 12Z surface analysis over the North Pacific basin caught my eye yesterday morning (January 20). That's because there was a 1055 mb high centered just to the north of Wrangle Island over the Arctic Ocean (between the Chukchi Sea and East Siberian Sea) and two lows, a 973-mb cyclone over the Bering Sea and a 965-mb low centered over the northern Gulf of Alaska. Check out the cropped 12Z surface analysis below; here's a political map to get your bearings (I circled the general region of interest).
A portion of the 12Z surface analysis over the North Pacific basin on January 20, 2013. Alaska is on the right. Full analysis. Courtesy of the Ocean Prediction Center.
Needless to say, there was an impressive pressure gradient across the region, particularly over the Bering Sea. Before I show you the wind analyses over this region, check out the GFS model analysis of mean sea-level isobars on a North-Pole view (a different map projection than the OPC surface analysis above). I hope that you agree that the GFS had a fairly good handle of the pressure pattern over the region at 12Z.
I decided to look at the wind analyses at 100 meters, an altitude where friction is a bit less important compared to the earth's surface. At any rate, the 12Z GFS analysis of isotachs and streamlines at 100 meters (below; larger image) shows that easterly winds had speeds greater than 50 knots (but less than 60 knots) over the Bering Sea. This observation might be a bit surprising, given the impressive pressure gradient over the Bering Sea and the fact that there were stronger winds father south on the back side of the 965-mb low over the Gulf of Alaska, where the pressure gradient was not quite as large (revisit the 12Z GFS model analysis of MSL isobars).
The 12Z GFS model analysis of isotachs (color-filled in knots) and streamlines at 100 meters. Larger image. Courtesy of Penn State.
What's up with that? Let's assume that, at 100 meters, friction is not as important...so let's neglect it (as a general rule, the effects of friction typically vanish by 500 mb, where the standard height is 5500 meters). Our assumption of neglecting friction means that there are essentially two forces at work here: the pressure gradient and the Coriolis forces.
I'll write a blog about the Coriolis force (Coriolis effect) one day, but, for now, I'll just emphasize that it acts 90 degrees to the right of a moving air parcel in the Northern Hemisphere. Moreover, the magnitude of the Coriolis force depends on latitude (more precisely, the sine of latitude) and the speed at which an air parcel is moving (mathematical representation).
I'll bet you never thought you'd see math in a Weather Underground blog, but meteorology is a science, and mathematics is the language of science.
Okay, after the initial shock has worn off, check out this idealized set-up in the east-west direction (I'll keep this as simple as I can, but I'd also have to tackle the north-south direction in order to complete the analysis). The black curve represents a portion of the local isobar (or height contour). The pressure-gradient force is indicated by the blue vector pointing to your left (toward lower pressure...the red "L"), and its magnitude depends on density (the Greek letter rho) as well as the variation of pressure, p, in the east-west direction (along the x axis). The blue vector pointing to the right represents the Coriolis force. Along the x axis, its magnitude depends on the north-south component of the geostrophic wind (note the subscript, g), which is the idealized wind that results from the balance of the pressure-gradient and Coriolis forces).
Now let's apply what we've learned to yesterday's 12Z surface analysis over the Bering Sea and northern Gulf of Alaska. Why were wind speeds at 100 meters over the Bering Sea, where there was a dramatically tight packing of isobars (large pressure-gradient force) noticeably lower than the wind speeds in the wake of the low-pressure system over the northern Gulf of Alaska (where the pressure-gradient force was a bit weaker)?
Recall that the magnitude of the Coriolis force depends on the sine of the latitude, which increases with increasing latitude. Specifically, the sine of latitude is larger over the Bering Sea than it is over the northern Gulf of Alaska. Thus, even though the pressure gradient is larger over the Bering Sea, the larger value of the sine of latitude over the Bering Sea allows the magnitude of the Coriolis force to balance the pressure-gradient force at a somewhat lower wind speed. I'm not saying that the 50-knot wind over the Bering Sea (as shown on the GFS model analysis) is nothing to sneeze at, but it's perhaps not as fast as you might initially think after looking at the pressure gradient. Indeed, if you look closely at OPC's 12Z surface analysis, you can see wind speeds that belie the locally strong pressure gradient (I can make out two observations of 20 knots and 25 knots).
Here endeth the lesson.
Lee
Reader Comments
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I learned the word geostrophic, too. I am not quite understanding why wind should follow parallel to an isobar. Is that ONLY if you get the exact balance of pressure gradient effect and Coriolis effect? The absolute simplest situation I can think of is the wind just pointing at right angles to the local isobars, although I now realize I never see that. I can't believe I haven't thought this through before, even though I've explained how the Coriolis effect creates the spinning effect in a hurricane.
7:48 PM GMT on January 21, 2013
Love the excitement! Yes, the balance between the two forces above the altitude where friction acts yields the geostrophic wind. The atmosphere is never truly geostrophic (you can't fly a kite in the geostrophic wind), but it's often so close that model analyses like today's 12Z NAM plot of 500-mb heights and winds (below; larger image) look like the real McCoy.
Isn't it the top of the PBL (1 - 1.5 km AGL)
where friction is no longer a factor in the balance between the PGF and Coriolis?
12:46 AM GMT on January 22, 2013
I think you misunderstood what I was trying to say...I was taking into account the West and other mountainous regions, where well-mixed PBL can extend to 500 mb. See skew-T below.
See what I mean? I reworded it slightly to make it more palatable.
12:50 AM GMT on January 22, 2013
Many thanks!
With respect, I'm not convinced of this explanation yet. You seem to be saying that the wind speed associated with a pressure gradient naturally decreases with increasing latitude. I do not see how this is possible.
You say that:
"Specifically, the sine of latitude is larger over the Bering Sea than it is over the northern Gulf of Alaska. Thus, even though the pressure gradient is larger over the Bering Sea, the larger value of the sine of latitude over the Bering Sea allows the magnitude of the Coriolis force to balance the pressure-gradient force at a somewhat lower wind speed."
It seems to me that the Coriolis force, being fictitious due to our rotating reference frame, only describes how quickly the path of an air parcel departs from a straight line in this reference frame. In the tropics, it takes longer for a large-scale flow to become rotational and tangential to a circle. In the polar regions, it happens quicker because the magnitude of the Coriolis force is larger. In essence, the near-balance between the PGF and Coriolis force occurs "faster," as you mentioned in your post.
How is it, exactly, that this balance happening quicker limits the maximum wind speed?
After typing this, I am now curious whether the air flow, being bent parallel to the isobars quicker at high latitudes, has a lower speed because it spent less time being accelerated along the pressure gradient? In other words, as the air leaves the "point source" (high or low), it gets accelerated by the PGF, but quickly gets turned perpendicular to the pressure gradient, and integrating through the time taken for this to happen, the resulting magnitude of the velocity is less than it would have been if it had taken more time for the flow to become perpendicular to the PGF?
However, I am still pondering how the maximum speed, and thus kinetic energy of the air flow can be reduced just because the ground beneath is rotating at a faster rate.
Just trying to understand. Chances are I'm missing something basic. Things like this get me all the time.
12:00 PM GMT on January 22, 2013
First, I'm NOT saying that wind speed increases with increasing latitude.
Your question goes to the heart of educational philosophy. In higher education, there are some that shun mathematics for inadequate and sometimes incorrect conceptual explanations. Writing a blog limits me somewhat because my readers are not all mathematically ready. So what you're missing is the mathematics that support this concept.
Here is a copy of the PPT slide that I show my synoptic class. Whether you accept it or not, it's up to you. It sets up the force diagram that paves the way for the geostrophic wind.
Here's the geostrophic-wind equation (pressure-gradient force on the left, Coriolis on the right side of the equation):
If the Coriolis parameter, f, increases (latitude increases), then V sub g, the geostrophic wind, must decrease.
So, for a FIXED pressure-gradient force, the geostrophic wind decreases with increasing latitude. NOT necessarily the observed wind (other forces are likely at work...friction, etc.).
Mathematics is the language of science. Until you're able to support your arguments with mathematics, you will not be able to find scientific truth.
Hope this helps.
12:41 PM GMT on January 22, 2013
Here's a more realistic example at Albuquerque, New Mexico, at 00Z on June 1, 2012. A very, very deep boundary layer extending to almost 500 mb.
So, you see, just a blanket "1-1.5 PBL" is NOT a universal rule for the depth of a boundary layer. It depends on latitude, season, prevailing weather conditions, time of day, etc.
Hope this helps.
1:50 PM GMT on January 22, 2013
Yes. It occurs in a well-mixed boundary layer bereft of baroclinicity (away from fronts and horizontal temperature gradients).
For example, check out the 00Z surface analysis on April 10, 2011 (below), and note that Jackson, Mississippi, lay in the warm sector of a warm sector of a mid-latitude cyclone. Warm sectors are typically mT air masses, so there really isn't any baroclinicity in warm sectors. Neither is there any warm advection (oh, yes, there might be a little warm advection closer to the fronts around the edges of a warm sector, but, by and large, warm advection in the warm sector is zero or small at best (contrary to popular belief).
Now look at the 00Z skew-T at Jackson, Mississippi (below) on April 10, 2011. Note that the boundary layer is well mixed (dry adiabatic lapse rate) and, more to your question, that winds veer with height in the boundary layer. This veering is essentially caused by the decrease in the magnitude of friction above the earth's surface. Any such veering with height, in the absence of baroclinicity, is an example of an Ekman spiral.
I've heard people recite the mantra "winds veer with height so there's warm advection." That's hogwash, as my example clearly shows.
Now, if geostrophic winds veer with height, then you can equate this veering with height to warm advection. But there's a big difference between the geostrophic wind and the observed wind in a well-mixed boundary layer. So you have to be careful.
Hope this helps.
3:58 PM GMT on January 22, 2013
P.S. I don't like the word, fictitious, in the context of the Coriolis force (I prefer "apparent"). If the Coriolis force is so "fictitious," why doesn't the 500-mb wind blow directly from high to low 500-mb heights instead of blowing nearly parallel to height lines.
You can't have it both ways.
I vote to take it easy on the undergrad, because (s)he probably heard "fictitious force" from a physics prof! I agree that it is an unfortunate term, though!
Changes in momentum imply interactions. If you find there is no interaction that can be identified as resulting in an apparent change in momentum, you must suspect that you are in a non-inertial frame of reference (that is, your frame is accelerating). Then those "changes in momentum" are actually just "momentum staying the same" in disguise. So the "forces" that appear to have caused the apparent changes are... well here we are... apparent forces! Good term!
Sadly we physicists refer to these as "fictitious" forces which is rather pejorative, when, in fact, it can be very, very handy to just admit you are in an non-inertial frame but going to treat it as an inertial frame nonetheless. Experienced physicists do this all the time, but they cringe when the youthful, inexperienced types try it, because the method is fraught with peril for the uninitiated. So we scare them away with the word "fictitious!"
Of course General Relativity seems to imply that gravitation itself is an apparent force, too. But, as far as I understand, the jury is still out on that, since we haven't been able to quantize GR theory.
7:16 PM GMT on January 22, 2013
Agreed on all counts. Many thanks.
I confess that I tend to be old school (after all, I'm 65) with regard to language.
For example, I absolutely despise the term, "pop-up" thunderstorms. Just hate it. It mistakenly conveys that thunderstorms are random. They are not random. Indeed, thunderstorms are initiated on the meso-beta scale in places where low-level convergence can be 100 or 1000 times greater than convergence on the synoptic scale. So there are real reasons why thunderstorms develop in the places they do. They might seem random, but they are not fundamentally random. I'm not sure where the term originated, but I hear it often used on TWC. Drives me nuts.
At any rate, thanks for the reminder to take it easy on the undergrad. Hopefully, he or she learned something from my explanation.
What would happen to the Coriolis force if the Earth was tidally locked with the sun as our moon is with our Earth? How would this change our weather and ocean currents?
See, I knew it was basic. Yes, I have seen the geostrophic model before, and now I see that the geostrophic wind speed and Coriolis parameter are inversely proportional. Nobody has pointed that out to me before. I'm surprised I didn't catch that. Thanks for reminding me.
My problem is not necessarily with the math, which I have seen before, but rather with making sense of it physically. The math can prove things to me all day long, but until they make sense to me intuitively and conceptually, I remain shaky. I do not like being able to explain concepts to people using only math. I must have a deeper understanding. My "thinking out loud" paragraph in my original query about the air parcel being accelerated for a shorter time along the pressure gradient vector was an attempt at coming up with physical reasoning for explaining this phenomenon.
Yes sir. The word "apparent" actually occurred to me as I posted my original query, but I didn't think to interchange the two. I have heard both words used extensively, and I agree that the latter seems better. The force exists, of course, but not in an inertial reference frame.
12:12 AM GMT on January 23, 2013
You're inquisitive. You're going to make a GREAT meteorologist. And, yes, trying to connect the math to physical conceptual models is something we do all our professional lives. At 65, I'm still learning and revising the way I think about things.
So I think you're well on your way. Keep asking questions and keep trying to connect the math to the conceptual models. You're going to be just fine.
Levi32 is very sharp and will do very well. May the inquisitive nature of his youth remain with him throughout his entire life. After all, everyday life is a lesson, if you remain inquisitive enough to seek what you do not yet know.
10:40 PM GMT on January 23, 2013
You're quite welcome. My pleasure.
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