Raking Leaves and Basic Concepts in Meteorology

By: 24hourprof , 6:35 PM GMT on October 03, 2013

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I was raking leaves yesterday afternoon as temperatures flirted with 80 degrees Fahrenheit here in central Pennsylvania. It's been quite a run of warm days and cool nights during late September and early October. I think about weather all the time, so you shouldn't be surprised that the mindless job of raking allowed me to come up with a good idea to blog about basic principles in meteorology.

After I finished raking, I started looking at data (you know me). The recent spell of cool nights in central Pennsylvania came courtesy of light winds, a clear sky, relatively low dew points, and increasingly longer nights. The high-pressure systems responsible for this early-autumn weather came from the west, and so I expanded my purview to include the northern-tier states east of the Rockies. I eventually found these classic plots (below) of upwelling infrared radiation (top) and air temperature (bottom) at Sioux Falls, South Dakota, on September 21, 2013. Let's learn some basic meteorology from this case...here's the corresponding meteogram that I'll refer to along the way. The meteogram spans from 00Z (6 P.M. CDT) on September 21 to 00Z on September 22).


The plots of upwelling infrared radiation (top) and air temperature (bottom) at Sioux Falls, South Dakota, from 00Z (6 P.M. CDT) on September 21 to 00Z on September 22, 2013. Units of upwelling radiation and air temperature are watts per square meter and degrees Celsius, respectively. Courtesy of Earth System Research Laboratory.

For the record, upwelling infrared radiation is the component of IR energy that's emitted upward by the earth's surface. Quantitatively, upwelling infrared radiation from the earth's surface is proportional to the fourth power of its absolute temperature (expressed in Kelvins). This relationship is often referred to as the Stefan-Boltzmann Law.

To get your bearings for these two plots, the units (vertical axes) for upwelling IR radiation and air temperature are watts per square meter and degrees Celsius, respectively. I note here that, although upwelling IR was calculated using values of absolute temperature, we're using degrees Celsius on the bottom graph because these units are more intuitive than Kelvins. Last but not least, the horizontal axes designate time...00Z (6 P.M. CDT) on September 21 (left) to 00Z (6 P.M. CDT) on September 22 on the right.

On this clear, mostly calm night at Sioux Falls (revisit the meteogram to verify weather conditions), the values of upwelling infrared radiation fell "in-step" with the decrease in air temperature. With no change in air mass on this night (check out the 06Z surface analysis), air temperatures decreased simply because the ground steadily cooled, emitting more infrared radiation (upwelling IR) than it received from the cloudless nighttime atmosphere. Put another way, the ground ran a negative energy budget at Sioux Falls during the night. The bottom line is that you can readily see the Stefan-Boltzmann Law at work...upwelling IR decreases with decreasing ground temperature (I'm using the air temperature as a proxy for ground temperature).


The 06Z surface analysis on September 21, 2013. Courtesy of WPC.

During the daytime hours, the increase in upwelling infrared radiation nicely mirrored the rise in air temperatures, which was attributable to solar heating (revisit the meteogram...there was no change in air mass as the 18Z surface analysis indicates and the sky was sunny).

If you look really closely at the data on the top graph around the time of the daytime maximum air temperature (between 21Z and 22Z...3 P.M. and 4 P.M.), upwelling infrared radiation has already started to decrease even though air temperature continues to increase slightly. What's up with that? As I stated earlier, the air temperature is only a proxy for the ground temperature (with regard to the Stefan-Boltzmann Law, upwelling IR depends on the temperature of the ground, not the air, but the two temperatures are pretty much in sync). Also keep in mind that the air temperature is measured two meters above the ground. So there's a bit of a lag between these two temperatures, which explains the slight "out-of-step" we observed around the time of maximum air temperature.


(Top) The plot of net infrared radiation at Sioux Falls, SD, from 00Z (6 P.M. CDT) on September 21 to 00Z (6 P.M. CDT) on September 22, 2013. Units are Watts per square meter. (Bottom) The corresponding plot of air temperature, in degrees Celsius. Courtesy of Earth System Research Laboratory.

I remember when I first started blogging at Wunderground (many thanks, Jeff Masters), and I wrote that a cloudless nighttime atmosphere emits infrared radiation toward the ground (downwelling IR). A typical radiating temperature of a clear nighttime sky is 250 Kelvins. To get a sense for infrared emissions from a clear atmosphere, check out (above) the corresponding plots of net infrared radiation at the ground and air temperature at Sioux Falls on September 21. By "net" I mean, "emitted IR by the ground (outgoing) minus IR from the nighttime sky absorbed by the ground)." Note that the net loss of infrared radiation at the ground was greatest around the time of maximum air temperature (during the mid-to-late afternoon).

In summary, radiational cooling (which I define as the net loss of infrared radiation at the ground) was greatest at Sioux Falls around the time of the maximum temperature of the ground (between 3 and 4 P.M. CDT on September 21). Earlier in the afternoon, the ground's temperature had been increasing because the ground absorbed more solar radiation than the infrared radiation it emitted. The lagging air temperature (measured at two meters) followed the lead of the ground temperature, lending credence to our observation that the maximum air temperature occurs around the time the net loss of infrared radiation from the ground is greatest. I know it's not intuitive, but that's the real deal here.


(Top) The plot of net solar (red) and net infrared (blue) at Sioux Falls, SD, from 00Z (6 P.M. CDT) on September 21 to 00Z (6 P.M. CDT) on September 22, 2013. Units are Watts per square meter. (Bottom) The corresponding plot of air temperature, in degrees Celsius. Courtesy of Earth System Research Laboratory.

To better visualize the individual roles of solar and infrared radiation, check out the plot (above) of net solar (red) and net IR (blue) and air temperature at Sioux Falls, South Dakota, on September 21. Note that the vertical axis (watts per square meter) has a more extensive scale to account for the large values of net solar radiation. By the way, net solar radiation means "Downwelling Solar" (incoming) minus "Upwelling Solar" (reflected).

I know I'm repeating myself, but the basic meteorology here is important...even though radiational cooling of the ground (net IR loss) was greatest at the time of the ground's maximum temperature (Stefan Boltzmann at work), the ground temperature was still relatively high because net solar gain was so much larger than the net IR loss. And the air temperature, which lags the temperature at the ground a bit, followed suit in fairly quick fashion..

What else can we learn from this case? Below, I inserted the Sioux Falls' meteogram so I can refer to them more easily. Okay, sometimes you'll here forecasters talk about the dew point being a rough lower bound for the expected nighttime low temperature on clear, calm nights. Focus your attention on the top rectangle of data and note how the temperature (the magenta plot) gradually decreases toward the dew-point plot (green), the two eventually "merging" around 12Z (6 A.M. CDT)...about the time when the low temperature of 36 degrees was measured. You can read the hourly temperatures off the scale shown on the left in the top rectangle of data. As it turned out, the low occurred between hourly observations during the six-hour period ending at 12Z (see the "T6NF" line of data).


The meteogram at Sioux Falls, South Dakota (KFSD), from 00Z on September 21 to 00Z on September 22, 2013. Courtesy of the University of Wyoming.

Another basic but interesting observation comes from the dew-point plot (green in the top rectangle of data). During the period from 00Z on September 21 to 00Z on September 22, the dew point at Sioux Falls, South Dakota, was pretty steady, vacillating only slightly around 40 degrees during the period (again, read temperatures and dew points off the scale shown on the left of the top rectangle of data). But once the sun rose and air temperatures started to climb (around 13Z or 7 A.M. CDT), the relative humidity, which was close to 100% during the wee hours of the morning, abruptly decreased after 13Z in tandem with the sudden increase in temperature after sunrise. To get your bearings, relative humidity is the blue plot in the top rectangle of data...you can read percents off the scale shown on the right of the top rectangle of data).

At any rate, my point here is that, even though the dew point (and the amount of water vapor) remained relatively steady, the relative humidity changed dramatically in response to changing temperature. The sensitivity of relative humidity to temperature is the primary reason I never showed relative humidity whenever I was on-air during my 20-year stint on public television.

Here endeth a lesson on basic principles in meteorology.

Lee

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21. WunderAlertBot (Admin)
9:01 PM GMT on October 07, 2013
24hourprof has created a new entry.
20. georgevandenberghe
1:09 PM GMT on October 07, 2013
Quoting 19. georgevandenberghe:


Growing old beats the alternative. But do everything you can to protect your health now.


The other piece of unsolicited advice I toss out from time to time to students is to make getting enough sleep a very high priority. Otherwise you will retain much less of your education even if you do pass the tests. I made this mistake in graduate school and have lost more than I should have of that learning. It's ultimately what you learn and can apply, more than your final grades that matters a decade post graduation.
Member Since: February 1, 2012 Posts: 17 Comments: 1373
19. georgevandenberghe
1:01 PM GMT on October 07, 2013
Quoting 16. Astrometeor:
Good evening Lee, I don't wanna grow old! I give my back enough grief as it is, really.

Took the SAT test yesterday for a second time. I was unhappy with my first test, had a 620 on my math, hoping for that to go up this time around.


Growing old beats the alternative. But do everything you can to protect your health now.
Member Since: February 1, 2012 Posts: 17 Comments: 1373
18. 24hourprof
11:21 AM GMT on October 07, 2013
Quoting 16. Astrometeor:
Good evening Lee, I don't wanna grow old! I give my back enough grief as it is, really.

Took the SAT test yesterday for a second time. I was unhappy with my first test, had a 620 on my math, hoping for that to go up this time around.


620 is very, very, good. Congratulations.

Mathematics is the language of science, so the best meteorologists are the ones who can couple experience, insight, and observation with mathematical underpinning.

Good for you!

Best,

Lee
Member Since: October 24, 2012 Posts: 88 Comments: 793
17. 24hourprof
11:19 AM GMT on October 07, 2013
Quoting 15. rpointwx:


Thank you to both of you. One pesky weed removed. Let the gardening continue.


Any time.

I am always open to questions from scientifically curious folks like you who are eager to learn. It makes this job fun for me.

Best,

Lee
Member Since: October 24, 2012 Posts: 88 Comments: 793
16. Astrometeor
1:31 AM GMT on October 07, 2013
Good evening Lee, I don't wanna grow old! I give my back enough grief as it is, really.

Took the SAT test yesterday for a second time. I was unhappy with my first test, had a 620 on my math, hoping for that to go up this time around.
Member Since: July 2, 2012 Posts: 79 Comments: 8246
15. rpointwx
12:35 AM GMT on October 07, 2013
Quoting 14. 24hourprof:


Good job, George. Thanks!

Lee


Thank you to both of you. One pesky weed removed. Let the gardening continue.
Member Since: December 27, 2009 Posts: 0 Comments: 10
14. 24hourprof
12:28 PM GMT on October 06, 2013
Quoting 13. georgevandenberghe:


I'll expand a little on this. The atmosphere is almost transparent to visible light and is not heated much by it. The heating is from below as Lee says from conduction, convection and IR radiation which is absorbed by water vapor and C02. The first two terms dominate during the day. One consequence of this is that there is almost no diurnal temperature variation above the top of the boundary layer which is around 1000 meters above the surface in winter and 2000 meters above in late spring and summer (higher when the airmass is cold and the sun is strong)
One of the rules of thumb for this top (abbreviated
ROT by John Dutton at PSU) is the 850mb pressure surface around 1500 meters for regions near sea level but it's breached in spring and not reached in late fall and winter.

Ok I've gotten too wordy. Basically visible sun does not heat the atmosphere directly. Conduction from the ground does it, convection carries the heat up and IR radiation from the ground contributes. THere is little diurnal temperature variation more than 2000 meters above the surface.


Good job, George. Thanks!

Lee
Member Since: October 24, 2012 Posts: 88 Comments: 793
13. georgevandenberghe
12:14 PM GMT on October 06, 2013
Quoting 12. 24hourprof:


Dear fellow gardener, :-) LOL!

A clear atmosphere radiates infrared energy as a 250 Kelvin blackbody (a body with the property that the spectrum of their emissions depend only on temperature). The earth's surface radiates infrared energy as a warmer blackbody most of the time. Hence, the net IR at the ground is usually negative (the ground emits more IR than it receives from a clear atmosphere). All bets are off when clouds are in the picture, especially low clouds (low clouds radiate as a fairly warm blackbody).

You are correct. The earth's surface warms the atmosphere by conduction, convection, and radiation. The atmosphere absorbs some incoming solar radiation, but the earth's surface is the primary "warmer" of the atmosphere.

Master Gardener Grenci. :-)



I'll expand a little on this. The atmosphere is almost transparent to visible light and is not heated much by it. The heating is from below as Lee says from conduction, convection and IR radiation which is absorbed by water vapor and C02. The first two terms dominate during the day. One consequence of this is that there is almost no diurnal temperature variation above the top of the boundary layer which is around 1000 meters above the surface in winter and 2000 meters above in late spring and summer (higher when the airmass is cold and the sun is strong)
One of the rules of thumb for this top (abbreviated
ROT by John Dutton at PSU) is the 850mb pressure surface around 1500 meters for regions near sea level but it's breached in spring and not reached in late fall and winter.

Ok I've gotten too wordy. Basically visible sun does not heat the atmosphere directly. Conduction from the ground does it, convection carries the heat up and IR radiation from the ground contributes. THere is little diurnal temperature variation more than 2000 meters above the surface.
Member Since: February 1, 2012 Posts: 17 Comments: 1373
12. 24hourprof
7:02 PM GMT on October 04, 2013
Quoting 11. rpointwx:
I have what is probably a few silly questions but nonetheless I would like to do a little "weeding".

Could you explain why the the net IR always appears negative? Does this have to do with the ground being able to emit energy more readily than the atmosphere?

Also I know that the temperature is the average kinetic energy and the net radiation is positive due to incoming solar radiation but could you explain why the incoming solar radiation (UV, visible) cause the temperature to increase when I thought that the atmosphere warms via the ground emitting infrared. To put it another way it is my understanding that the atmosphere doesn't absorb energy well at the visible or UV wavelength so if the net IR is negative how does the temperature increase. I know its probably a silly question but I am here to weed.


Dear fellow gardener, :-) LOL!

A clear atmosphere radiates infrared energy as a 250 Kelvin blackbody (a body with the property that the spectrum of their emissions depend only on temperature). The earth's surface radiates infrared energy as a warmer blackbody most of the time. Hence, the net IR at the ground is usually negative (the ground emits more IR than it receives from a clear atmosphere). All bets are off when clouds are in the picture, especially low clouds (low clouds radiate as a fairly warm blackbody).

You are correct. The earth's surface warms the atmosphere by conduction, convection, and radiation. The atmosphere absorbs some incoming solar radiation, but the earth's surface is the primary "warmer" of the atmosphere.

Master Gardener Grenci. :-)

Member Since: October 24, 2012 Posts: 88 Comments: 793
11. rpointwx
4:09 PM GMT on October 04, 2013
I have what is probably a few silly questions but nonetheless I would like to do a little "weeding".

Could you explain why the the net IR always appears negative? Does this have to do with the ground being able to emit energy more readily than the atmosphere?

Also I know that the temperature is the average kinetic energy and the net radiation is positive due to incoming solar radiation but could you explain why the incoming solar radiation (UV, visible) cause the temperature to increase when I thought that the atmosphere warms via the ground emitting infrared. To put it another way it is my understanding that the atmosphere doesn't absorb energy well at the visible or UV wavelength so if the net IR is negative how does the temperature increase. I know its probably a silly question but I am here to weed.
Member Since: December 27, 2009 Posts: 0 Comments: 10
10. georgevandenberghe
3:13 PM GMT on October 04, 2013
This requote was a mistake when I tried to correct my previous comment. OOPs

Quoting 9. georgevandenberghe:


I learned the heat capacity concepts in middle school. Radiative transfer concepts were in the physics majors' first course at VPI where, as a Virgina resident, I did my first two year of undergraduate work 1976-78 but it took solid root because I'm interested in these concepts. The interest in radiative cooling at night comes from being a gardener. Paradoxically, the gardener's nighttime cooling problem is more relevant for a longer season in Tallahassee.

My research at FSU was underwhelming and was on monsoon/midlatitude interactions. Had I gone on, my interests were in general circulation issues. All of my published work (not very much) is in the HPC or numerical analysis literature (A 1989 paper in the Journal of Mathematics and Applied Computation, and a 2006 HPC conference proceedings entry at ECMWF [ the powerpoint presentation that was ancestor to that paper is at
http://www.ecmwf.int/newsevents/meetings/workshop s/2006/high_performance_computing-12th/pdf/George_ Vandenberghe.pdf ] ). I did more work in the late 80s and early 90s that I regret not publishing.
Member Since: February 1, 2012 Posts: 17 Comments: 1373
9. georgevandenberghe
1:45 PM GMT on October 04, 2013
Quoting 8. 24hourprof:


Good stuff, George. Was your research in the area of radiative transfer? You have a really strong handle on this kind of science.

Lee


I learned the heat capacity concepts in middle school. Radiative transfer concepts were in the physics majors' first course at VPI where, as a Virgina resident, I did my first two year of undergraduate work 1976-78 but it took solid root because I'm interested in these concepts. The interest in radiative cooling at night comes from being a gardener. Paradoxically, the gardener's nighttime cooling problem is more relevant for a longer season in Tallahassee.

My research at FSU was underwhelming and was on monsoon/midlatitude interactions. Had I gone on, my interests were in general circulation problems, esp. short term temporal variability. All of my published work (not very much) is in the HPC or numerical analysis literature (A 1989 paper in the Journal of Mathematics and Applied Computation, and a 2006 HPC conference proceedings entry at ECMWF [ the powerpoint presentation that was ancestor to that paper is at
http://www.ecmwf.int/newsevents/meetings/workshop s/2006/high_performance_computing-12th/pdf/George_ Vandenberghe.pdf ] ). I did more HPC work in the late 80s and early 90s that I regret not publishing.
Member Since: February 1, 2012 Posts: 17 Comments: 1373
8. 24hourprof
1:31 PM GMT on October 04, 2013
Quoting 6. georgevandenberghe:


Outgoing radiation at a ground temperature of 273K is 314W/m**2. Incoming radiation from a 250K sky is 224W/m**2. I'm assuming blackbody emissivity radiation which is close for infrared. THe net radiative cooling is about 90W/m**2. A typical radiation inversion is 200 meters deep and most of the cooling at night happens under it. Heat capacity of the column is around 200,000 J/kelvin. The top 10 cm of soil would be that order, 200,000 J/kelvin. Cooling rate then is a little less than 1K/hour which seems reasonable and consistent with what I see on calm clear dry nights in spring and fall. More later


Good stuff, George. Was your research in the area of radiative transfer? You have a really strong handle on this kind of science.

Lee
Member Since: October 24, 2012 Posts: 88 Comments: 793
7. 24hourprof
1:30 PM GMT on October 04, 2013
Quoting 5. georgevandenberghe:


I posted on a neighborhood listserv about the loss of the American Chestnut in the 30s and 40s. Someone answered about Chinese chestnuts in leaf piles where kids jump in and get spiked. And the debate went on.

Have you considered a small portable backpack leaf blower?

By the way early October seems early for leaves even in State College. I remember mid to late October for peak color and early November for leaf fall there. But as has happened in other cases (all of those 70 degree nights in 1979 in State College that NEVER HAPPENED) my memory may be faulty.



Thanks George. I should, of course, do what you suggest. I'm just stubborn and too old-fashioned, I guess.

Lee
Member Since: October 24, 2012 Posts: 88 Comments: 793
6. georgevandenberghe
1:22 PM GMT on October 04, 2013
Quoting 4. 24hourprof:


Hi George,

I've used an infrared thermometer and that's a reasonable number, I think (if I recall, I did the experiment during fall).

Craig Bohren also cites this number on Page 79 of his terrific book, Clouds in a Glass of Beer.

Best,

Lee


Outgoing radiation at a ground temperature of 273K is 314W/m**2. Incoming radiation from a 250K sky is 224W/m**2. I'm assuming blackbody emissivity radiation which is close for infrared. THe net radiative cooling is about 90W/m**2. A typical radiation inversion is 200 meters deep and most of the cooling at night happens under it. Heat capacity of the column is around 200,000 J/kelvin. The top 10 cm of soil would be that order, 200,000 J/kelvin. Cooling rate then is a little less than 1K/hour which seems reasonable and consistent with what I see on calm clear dry nights in spring and fall. More later
Member Since: February 1, 2012 Posts: 17 Comments: 1373
5. georgevandenberghe
1:07 PM GMT on October 04, 2013
Quoting 3. 24hourprof:


Wait until you're 66, Nathan! Raking leaves literally wrecks my lower back. Oh well...it's gotta be done!

Thanks for your kind words.

Lee


I posted on a neighborhood listserv about the loss of the American Chestnut in the 30s and 40s. Someone answered about Chinese chestnuts in leaf piles where kids jump in and get spiked. And the debate went on.

Have you considered a small portable backpack leaf blower?

By the way early October seems early for leaves even in State College. I remember mid to late October for peak color and early November for leaf fall there. But as has happened in other cases (all of those 70 degree nights in 1979 in State College that NEVER HAPPENED) my memory may be faulty.

Member Since: February 1, 2012 Posts: 17 Comments: 1373
4. 24hourprof
12:10 PM GMT on October 04, 2013
Quoting 1. georgevandenberghe:
Thanksgiving is the traditional rake 'em up weekend in the DC area. It's basically green here in DC this first week of October with only a few leaves falling from drought. This is typical in early fall. Looking forward to rain early next week, maybe and maybe a lot.

250K seems cold for a radiative sky temperature during the growing season, even the end of it and I'll see if I can dig up a climatology or at least a point timeseries of this statistic. With a 250K sky and dry air I'd feel exposed to nighttime ground freeze even in a warm air mass.


Hi George,

I've used an infrared thermometer and that's a reasonable number, I think (if I recall, I did the experiment during fall).

Craig Bohren also cites this number on Page 79 of his terrific book, Clouds in a Glass of Beer.

Best,

Lee
Member Since: October 24, 2012 Posts: 88 Comments: 793
3. 24hourprof
12:07 PM GMT on October 04, 2013
Quoting 2. Astrometeor:
Maybe it's just me being a young guy, but I think of jumping into my leaf piles when I rake my leaves.

Good blog Lee, thank you!

-Nathan


Wait until you're 66, Nathan! Raking leaves literally wrecks my lower back. Oh well...it's gotta be done!

Thanks for your kind words.

Lee
Member Since: October 24, 2012 Posts: 88 Comments: 793
2. Astrometeor
10:04 PM GMT on October 03, 2013
Maybe it's just me being a young guy, but I think of jumping into my leaf piles when I rake my leaves.

Good blog Lee, thank you!

-Nathan
Member Since: July 2, 2012 Posts: 79 Comments: 8246
1. georgevandenberghe
8:38 PM GMT on October 03, 2013
Thanksgiving is the traditional rake 'em up weekend in the DC area. It's basically green here in DC this first week of October with only a few leaves falling from drought. This is typical in early fall. Looking forward to rain early next week, maybe and maybe a lot.

250K seems cold for a radiative sky temperature during the growing season, even the end of it and I'll see if I can dig up a climatology or at least a point timeseries of this statistic. With a 250K sky and dry air I'd feel exposed to nighttime ground freeze even in a warm air mass.
Member Since: February 1, 2012 Posts: 17 Comments: 1373

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About 24hourprof

Retired senior lecturer in the Department of Meteorology at Penn State, where he was lead faculty for PSU's online certificate in forecasting.