Rapidly Melting Snow

By: 24hourprof , 3:52 PM GMT on January 13, 2013

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While watching the local evening news last week, I winced when I heard expectations for a rapidly disappearing snowpack in central Pennsylvania. That's because these medium-range forecasts were based "solely" on sunshine and temperatures in the 40s during the first half of this week (January 7-10). There wasn't any mention of dew points, which, as you will soon learn, play a pivotal role in the melting of snow.

To get a sense for weather conditions in State College during the first half of the week, check out (below) the meteogram at University Park's Airport, which shows plenty of sunshine on Tuesday, the 8th, and the daytime start on Wednesday, the 9th. In fairness, there was some melting, but our snowpack here in State College hung pretty darn tough through Thursday (January 10).

Early Friday morning (January 11), in anticipation of the snowpack rapidly melting, I took a number of measurements in my side and back yards just before light rain started to fall. The snow depth in my yard varied from two to four inches, so I decided that three inches was reasonably representative of the snowpack in my neighborhood.


The meteogram at the University Park Airport, PA, from 11Z on January 8, 2013, to 12Z on January 9, 2013. Courtesy of the University of Wyoming.

The snowpack in State College went pretty quickly this weekend (see the Web Cam at Penn State's Arborteum farther down on the page). So why didn't sunshine and temperatures in the 40s rapidly melt the snowpack in State College during the first part of the week? Well, dew points were relatively low through Thursday, a factor that sometimes gets overlooked (obviously). Now here's the $64000 question: Why do low dew points typically suppress the rapid melting of a snowpack? And if you want more food for thought, consider that a warm rain, at temperatures and dew points above the melting point of ice, is much more effective when it comes to rapidly melting a snowpack...of course, the higher the temperature and dew point, the more rapid the melting (stay tuned).

I'll go one step further. Are you sitting down? Here goes. During a warm rain, invisible water vapor rapidly melts most of the snow, not the visible raindrops. I realize that this statement flies in the face of the popular notion that a warm rain is directly responsible for rapidly melting snow. As you will soon learn, it's not so. Intrigued yet? Read on.

To explain why invisible water vapor is a rapid melter of snow (and visible raindrops are not), let's start with some basic concepts (after my last blog on sudden stratospheric warming probably gave you a headache, I feel obliged to tackle some fundamentals here). For starters, let's talk about sublimation. To keep things simple, suppose that there isn't any melting. Furthermore, let's assume that there isn't any net condensation onto the snowpack, which is a reasonable assumption when dew points are low. I'll also assume that there's no settling (compaction) of the snow cover. Nonetheless, the depth of the snow cover would still decrease due to sublimation. In this situation, ice goes directly to the vapor phase (do not pass go; do not collect $200). In other words, sublimation results in the relatively slow ablation of snowpacks (ablation is the general term for the reduction of snow or ice from the earth's surface).

When a warm rain falls over a snowpack, surface dew points increase and there's net condensation on the snowpack. In other words, water vapor condenses onto the cold snowpack (keep in mind that the snow is relatively cold compared to the overlying air because the temperature of the snowpack stays at 0 degrees Celsius). For the record, net condensation means that the rate of condensation is greater than the rate of evaporation.


The Arboretum At Penn State on Sunday morning, January 13. Officially, there's a trace of snow cover. Courtesy of The Arboretum at Penn State.

As a result of net condensation, condensational heating occurs, providing heat energy that melts the snow. Over the years, people have asked me for a simple demonstration of condensational heating. Alas, I've not come up with a good one. Its inverse, evaporative cooling, is easy to demonstrate (simply lick the back of your hand and blow on it). In my view, however, the rapid disappearance of the snowpack in my yard this weekend is testimony to the impact of condensational heating.

Of course, I haven't shown you that "warm raindrops" are not largely responsible for the rapid meting of a snowpack. If you're interested, check out this paper (pdf file) written by Craig Bohren, a professor emeritus at Penn State. It's mathematical, which is why I didn't address it here.

So what is most important to the rapid melting of snow is that net condensation occurs. For the record, the rate of evaporation of meltwater on the surface of the snowpack (at 0 degrees Celsius) is pretty much set in stone. So the amount of net condensation onto the snowpack depends pretty much on the rate of condensation, which is a function of dew point and temperature. As the dew point increases above a snowpack, the number density of water vapor also increases. If rapid melting by condensational heating is the goal, a relatively high number density of water vapor is crucial (that's why low dew points don't typically promote rapid melting, despite sunshine). Moreover, as the temperature of the water vapor increases, the rate of condensation also increases. So higher dew points and temperatures mean that there's greater net condensation, and, ultimately, greater condensational heating. Bye, bye, snow!

I should point out that the wind can accelerate the loss of snowpack during a warm rain. Here's the story. There is a very thin, stagnant boundary layer that separates the snowpack and the overlying air. This boundary layer acts as a barrier to the net transport of water vapor onto the surface of the snowpack during a warm rain. As the wind speed increases, the thickness of the boundary later decreases, thereby promoting a greater net transport of water vapor to the snow surface. That means a greater degree of net condensation and greater condensational heating.

As a caveat to this discussion, rain doesn't have to be present for dew points to increase over a snowpack. Indeed, moist (and warm) advection also increases surface dew points over a snowpack.

If you walk away from reading this blog with the understanding that a warm rain does not directly melt snow (to any significant degree) and that it's the net condensation of invisible water vapor onto the snowpack that ultimately matters, then I've done my job. In deference to the role of a warm rain, it does provide ideal conditions for the dew points to increase, paving the way for greater condensational heating and the rapid melting of snow.

Lee

Many thanks to Craig Bohren for his observations and input.

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21. rpointwx
6:07 PM GMT on September 14, 2013
I know this is an old post but I have a question. Could you incorporate the argument using vapor pressure gradients as well? If you were to have a day where the temperature is relatively warm but the air is dry wouldn't there be a stronger vapor pressure gradient and therefore more melting/evaporating? I assume the layer directly above the snow has more water than the above layer of air. Would this not also promote more evaporation? Is it just that the air is still relatively dry and cool enough to melt less than the heat of condensation could?
Member Since: December 27, 2009 Posts: 0 Comments: 10
20. WunderAlertBot (Admin)
4:46 PM GMT on January 16, 2013
24hourprof has created a new entry.
19. georgevandenberghe
9:43 PM GMT on January 15, 2013
Quoting 24hourprof:


Looks like you'll get it by 180 hours as the 510-dekameter thickness is headed your way. Here's the 00Z NAM run from last evening...run your cursor over the forecast times along the top.

Now that's a high-amplitude pattern!!!!!


It's high amplitude but I've seen higher. 12Z GFS brings -20 at 850
to my region which over bare previously warm ground would probably fully mix in the afternoon and translate to about -4C at the surface. That's 25F for a high, and respectably cold for this area. If it verifies the cold will kill a lot of garden bugs that normally don't overwinter here but might have survived conditions we've had so far. Several of the past cycles have also brought in an arctic outbreak and I'm starting to buy in.

I normally (but not this year so far) overwinter my citrus trees in my unheated garage at refrigerator temperatures. Long duration cold periods are a concern and it looks like one might be in the cards for days 8-15. It's far from the worst I've dealt with; the 1994 outbreak was a garage evacuation event and I lost some trees in 2004.
The experimental information was worth it.

Member Since: February 1, 2012 Posts: 17 Comments: 1625
18. DelWeather
6:16 PM GMT on January 15, 2013
Quoting georgevandenberghe:
If I can dig up my notes (in storage right now) I'll see if I can find a way to reduce the radiative transfer calculations to analytic formulas using meteorologically valid simplifications for temperature and moisture distributions so that they can be expressed as analytic functions of pressure and I can integrate emissivity and absorption through the layers.


If you can't reduce this to analytical functions, does the data exist at a level of detail to do layer-by-layer numerical integration? That is, consider each, say, 50 m of atmosphere as a separate layer and figure out the radiative transfer into and out of that layer, then sum over the layers. Sounds fun, if the data can be found in a format easy to convert to a .cvs file or something similarly easy to call into a program. Figuring out the transfer equations from layer to layer is then the trick.
Member Since: October 9, 2012 Posts: 0 Comments: 50
17. 24hourprof
11:52 AM GMT on January 15, 2013
Quoting georgevandenberghe:
It should be possible to estimate the condensational heating term by taking a large area core sample at the beginning of the period of interest, measuring the mass and then leaving it in a side closed open top white container until it is melted and measuring the mass again and subtracting the mass increase from any rain (measured separately) that falls. The residual will be the amount of water that condensed from which the condensational heating contribution can be calculated, I agree likely large. This measurement will be contaminated by dew points significantly below freezing however.

But I'm still waiting for -8C to do the supercooling experiment :-)


Looks like you'll get it by 180 hours as the 510-dekameter thickness is headed your way. Here's the 00Z NAM run from last evening...run your cursor over the forecast times along the top.

Now that's a high-amplitude pattern!!!!!
Member Since: October 24, 2012 Posts: 90 Comments: 798
16. 24hourprof
11:47 AM GMT on January 15, 2013
Quoting georgevandenberghe:
If I can dig up my notes (in storage right now) I'll see if I can find a way to reduce the radiative transfer calculations to analytic formulas using meteorologically valid simplifications for temperature and moisture distributions so that they can be expressed as analytic functions of pressure and I can integrate emissivity and absorption through the layers. A lot of my calculus has survived thirty five years of decay.

I'm not going to be able to do this fast but I remember finding it borderline tractable before in 1980 when I last looked at it.
I'm thinking about three weeks to either do it or give up.


It's a good problem, George. No hurry.
Member Since: October 24, 2012 Posts: 90 Comments: 798
15. 24hourprof
11:46 AM GMT on January 15, 2013
Quoting georgevandenberghe:


And you're right. I need to proof my thinking more. I missed the well mixed assumption which is not an assumption one can generally make esp at night.



No worries, George. I enjoy reading your comments.
Member Since: October 24, 2012 Posts: 90 Comments: 798
14. georgevandenberghe
2:15 AM GMT on January 15, 2013
It should be possible to estimate the condensational heating term by taking a large area core sample at the beginning of the period of interest, measuring the mass and then leaving it in a side closed open top white container until it is melted and measuring the mass again and subtracting the mass increase from any rain (measured separately) that falls. The residual will be the amount of water that condensed from which the condensational heating contribution can be calculated, I agree likely large. This measurement will be contaminated by dew points significantly below freezing however.

But I'm still waiting for -8C to do the supercooling experiment :-)
Member Since: February 1, 2012 Posts: 17 Comments: 1625
13. georgevandenberghe
8:59 PM GMT on January 14, 2013
Or maybe I should go to the library and find the works on radiative transfer written before 1960 when computing these numbers became feasible. It's worth the effort just to exercise decaying skills anyway.
Member Since: February 1, 2012 Posts: 17 Comments: 1625
12. georgevandenberghe
8:57 PM GMT on January 14, 2013
If I can dig up my notes (in storage right now) I'll see if I can find a way to reduce the radiative transfer calculations to analytic formulas using meteorologically valid simplifications for temperature and moisture distributions so that they can be expressed as analytic functions of pressure and I can integrate emissivity and absorption through the layers. A lot of my calculus has survived thirty five years of decay.

I'm not going to be able to do this fast but I remember finding it borderline tractable before in 1980 when I last looked at it.
I'm thinking about three weeks to either do it or give up.
Member Since: February 1, 2012 Posts: 17 Comments: 1625
11. georgevandenberghe
2:23 PM GMT on January 14, 2013
Quoting 24hourprof:


That's not true, George. Only if the boundary layer is well mixed. Just a quick search of recent archives gave me this skew-t from Yellowstone Park, Wyoming... it shows that surface dew points are not highly correlated to dew points in the lowest 100 mb. So I respectfully but strongly disagree.



And you're right. I need to proof my thinking more. I missed the well mixed assumption which is not an assumption one can generally make esp at night.

Member Since: February 1, 2012 Posts: 17 Comments: 1625
10. 24hourprof
2:15 PM GMT on January 14, 2013
Quoting georgevandenberghe:



Surface dewpoint is highly correlated with dewpoints in the bottom 100mb of the atmosphere (about 3000 feet).


That's not true, George. Only if the boundary layer is well mixed. Just a quick search of recent archives gave me this 12Z skew-t from Yellowstone Park, Wyoming... it shows that surface dew points are not highly correlated to dew points in the lowest 100 mb. So I respectfully but strongly disagree.

Member Since: October 24, 2012 Posts: 90 Comments: 798
9. georgevandenberghe
1:38 PM GMT on January 14, 2013
Quoting 24hourprof:


P.S.

I agree, in principle, that more water vapor will increase the downwelling IR (all else being equal). But we have to keep in mind that the downward IR is a consequence of radiation by the entire atmosphere, not just the atmosphere near the surface. I think that one could calculate the downward IR contributed by everything from the surface to 10 meters, to 100 meters, to 1000 meters, and so on for a given temperature and water vapor profile. This would require a radiative transfer code. I do not believe that it could be done by back-of-the-envelope calculations.

My gut feeling is that changing the dew point near the surface will not contribute very much to
the downward IR.



Surface dewpoint is highly correlated with dewpoints in the bottom 100mb of the atmosphere (about 3000 feet). If that layer is moist and fairly warm and the rest of the atmosphere is very dry, I suspect downward IR will still be high although you're right it would take a radiative transfer code to validate my hunch. The moist boundary layer, bone dry above is fairly common in summer in the centers of stationary high pressure systems where subsidence persists for several days and dry air does not mix through the inversion (summer height of such an inversion is higher, between 850 and 700mb (5500-10000 feet).

My family would probably be displeased if I pumped water into our summertime house air. However I think I can do the experiment with ice suspended in air in a breeze on dry (15C) dewpoint days and moist (23C) dewpoint days with the same air temperature (32C). These conditions are common in summer in DC. (actually I'm disturbingly close to 15C dewpoints outside right now but the sensible temperature is also 15C and for midwinter that's VERY moist here)

[ modification.. to make things constant the breeze would have to be provided by a fan and the experiment area would have to be shaded] Also I should have used clearer language on "hot and dry" V.S. "humid" with temperature unspecified.

Radiative flux divergence also determines the cooling rate of a layer and needs to be forecast well in fog formation situations like what we've dealt with in DC the past two days. Our temperature issues outside were dominated by fog and low cloud and marine layer presence. We actually didn't get into the warm air until last night. I was busy doing other things Saturday and Sunday (3 kids.. activities ..)
but it looked like we had less low cloud and fog than forecast Saturday and much more Sunday. The actual temperature issues in this area this weekend though were VERY complex and I haven't thoroughly looked at them yet. In particular regions to our southwest did not clear out Saturday and were much cooler, a fairly rare outcome with marine layers where the northeast is usually colder.

I'm expecting the cold front to finally ooze through today and warned the kids to take their coats even though it is warm and humid outside this AM.

Member Since: February 1, 2012 Posts: 17 Comments: 1625
8. 24hourprof
1:04 PM GMT on January 14, 2013
Quoting georgevandenberghe:
The other term that increases with high dewpoints is downward IR radiation. I haven't done the math to determine how much of the melting is due to this and how much is due to condensational heating and sensible heating.

The DC area sometimes gets the combination of deep snowpack and +60F dewpoints. One striking example was in 1996 about two weeks after the January blizzard. This destroyed a 12" dense snowpack in a day and the associated several inches of rain caused severe river flooding. The streamers of dense fog coming off surviving snow ridges and patches were dramatic.

A dramatic demonstration of condensational heating occurs when you buy an ice cream cone on a hot humid breezy day and bring it outside. Melting rates are higher than on hot dry days and on humid days the cone will be destroyed in about ten minutes. Comparing the melting rates of popsicles under these different conditions is probably a better way to demonstrate it.

If you ever have the misfortune to have flesh contact steam you will get a much more malevolent demonstration of condensational heating.


P.S.

I agree, in principle, that more water vapor will increase the downwelling IR (all else being equal). But we have to keep in mind that the downward IR is a consequence of radiation by the entire atmosphere, not just the atmosphere near the surface. I think that one could calculate the downward IR contributed by everything from the surface to 10 meters, to 100 meters, to 1000 meters, and so on for a given temperature and water vapor profile. This would require a radiative transfer code. I do not believe that it could be done by back-of-the-envelope calculations.

My gut feeling is that changing the dew point near the surface will not contribute very much to
the downward IR.
Member Since: October 24, 2012 Posts: 90 Comments: 798
7. 24hourprof
1:01 PM GMT on January 14, 2013
Quoting georgevandenberghe:
The other term that increases with high dewpoints is downward IR radiation. I haven't done the math to determine how much of the melting is due to this and how much is due to condensational heating and sensible heating.

The DC area sometimes gets the combination of deep snowpack and +60F dewpoints. One striking example was in 1996 about two weeks after the January blizzard. This destroyed a 12" dense snowpack in a day and the associated several inches of rain caused severe river flooding. The streamers of dense fog coming off surviving snow ridges and patches were dramatic.

A dramatic demonstration of condensational heating occurs when you buy an ice cream cone on a hot humid breezy day and bring it outside. Melting rates are higher than on hot dry days and on humid days the cone will be destroyed in about ten minutes. Comparing the melting rates of popsicles under these different conditions is probably a better way to demonstrate it.

If you ever have the misfortune to have flesh contact steam you will get a much more malevolent demonstration of condensational heating.


George,

You always make me think. That's good! Thanks.

I noted that you wrote "hot dry days", then "humid days" without any qualification about temperature or anything else.

You would have to make the observations (which are qualitative) under conditions of equal solar illumination (or in the shade), equal infrared (sky temperature) equal temperature, but different dew points, and equal wind speeds.

The energy transfer to the ice cream is composed of many components, only one of which is condensational heating. I don't think you can separate them.

So this is a problem with too many variables, in my view.

You might be able to do an experiment indoors, fixed the temperature, and vary the dew point (with a humidifier). Then you would have to carefully observe how long it takes for a fixed mass of ice to melt as a function of dew point.

Hope this makes sense.
Member Since: October 24, 2012 Posts: 90 Comments: 798
6. georgevandenberghe
1:15 AM GMT on January 14, 2013
On a REALLY warm humid day with dewpoints over 80F, you can get a feeling of condensational heating if you step out of your car with the AC on full blast having blown over your arm. Water will condense out on it faster than sweat could possibly appear and you will feel very rapid warming of the cool skin surface.

In DC you may have to wait a few summers to get a day that absolutely humid (over 80F dewpoint) although sad to say we've had several in the past two summers.
Member Since: February 1, 2012 Posts: 17 Comments: 1625
5. georgevandenberghe
1:07 AM GMT on January 14, 2013
A warning to sleep deprived college students. If you don't get enough sleep you will lose what you learned MUCH more quickly or it will never get learned at all. If you are surviving sleep deprived you will do better (thrive) if you get enough sleep. If you can''t make it without cheating on your sleep you risk a downward spiral of learning less hence having to work harder, sleep less.. ..

This didn't happen to me in college but did in graduate school. I survived but do not retain as much as I would have if I had gotten more sleep and thus focused better during the day.

For what it's worth I am father of twins in 1998 and the sleep deprivation incurred taking care of them was worse than what I dealt with in grad school. That is just a part of life.. fortunately not concurrent with a period of enormous learning like grad school. (and yet some graduate student parents do this and survive!)

I'll state again, sleep deprivation is a really pernicious trap in college or grad school and should be avoided if at all possible.
Member Since: February 1, 2012 Posts: 17 Comments: 1625
4. DelWeather
11:54 PM GMT on January 13, 2013
Quoting 24hourprof:


Thanks.

Perhaps you misunderstood my main point here. I'm talking about condensational heating, not cooling. Or am I misunderstanding your point?



You misunderstood because I made a mistake (which I've now fixed). I said "cooling" at a crucial point when I meant to say "warming." The rest of the analysis is correct, I believe. I'm saying the energy that WAS kinetic energy of a gaseous molecule gets deposited into the solid (ice) molecules when the molecule condenses. Hence the thing that the water condenses on (the snow) gains energy (warms) as the vapor loses energy (by condensing).
Member Since: October 9, 2012 Posts: 0 Comments: 50
3. 24hourprof
10:51 PM GMT on January 13, 2013
Quoting DelWeather:


In college (hence, when sleep-deprived), I once reached over the wrong side of my bed to shut off my alarm and instead clapped my hand over my vaporizer... this was before the days of cool, ultrasonic vaporizers. Ugh. Not a physics experiment I was happy about having done.

Anyway, this is a really neat post. I read Dr. Bohren's piece that was linked to the article. After chuckling through the short diatribe against the misuse of the word heat (in fact, advocating a complete abandonment of the term! Perhaps I was not bold enough over on the Climate Change blog), I found the paper easy to understand. It was published in The Physics Teacher, after all!

To explain condensational cooling, I would appeal to a molecular level view of water vapor and condensed water. Water molecules in the gaseous state have much more kinetic energy than those in the liquid state. That's why they are flying around instead of rolling over each other like puppies. To condense a water molecule, you must remove enough kinetic energy from that molecule... where does that energy go? It might be transferred to a gaseous molecule, but it is much more likely that the energy would be transferred to a nearby molecule in the solid state, for there are many more of these about. Thus, to condense a water molecule, the substrate molecules much take on a lot of energy which used to be the condensing molecule's kinetic energy.

It turns out that not much kinetic energy needs to be pulled out of liquid state molecules in order to cool the liquid down to 0 degrees C, but a whole heck of a lot of kinetic energy needs to be pulled out out of gaseous state molecules so that they will slow down and hang out in the liquid.


Thanks.

Perhaps you misunderstood my main point here. I'm talking about condensational heating, not cooling. Or am I misunderstanding your point?

At any rate, we certainly can talk about things happening on a molecular level, but it's not an easy and simple demonstration on par with licking the back of your hand and blowing on it to demonstrate evaporational cooling. See what I mean? Difficult to demonstrate molecules.

Thanks.
Member Since: October 24, 2012 Posts: 90 Comments: 798
2. DelWeather
8:05 PM GMT on January 13, 2013
Quoting georgevandenberghe:
If you ever have the misfortune to have flesh contact steam you will get a much more malevolent demonstration of condensational heating.


In college (hence, when sleep-deprived), I once reached over the wrong side of my bed to shut off my alarm and instead clapped my hand over my vaporizer... this was before the days of cool, ultrasonic vaporizers. Ugh. Not a physics experiment I was happy about having done.

Anyway, this is a really neat post. I read Dr. Bohren's piece that was linked to the article. After chuckling through the short diatribe against the misuse of the word heat (in fact, advocating a complete abandonment of the term! Perhaps I was not bold enough over on the Climate Change blog), I found the paper easy to understand. It was published in The Physics Teacher, after all!

To explain condensational warming, I would appeal to a molecular level view of water vapor and condensed water. Water molecules in the gaseous state have much more kinetic energy than those in the liquid state. That's why they are flying around instead of rolling over each other like puppies. To condense a water molecule, you must remove enough kinetic energy from that molecule... where does that energy go? It might be transferred to a gaseous molecule, but it is much more likely that the energy would be transferred to a nearby molecule in the solid state, for there are many more of these about. Thus, to condense a water molecule, the substrate molecules much take on a lot of energy which used to be the condensing molecule's kinetic energy.

It turns out that not much kinetic energy needs to be pulled out of liquid state molecules in order to cool the liquid down to 0 degrees C, but a whole heck of a lot of kinetic energy needs to be pulled out out of gaseous state molecules so that they will slow down and hang out in the liquid.
Member Since: October 9, 2012 Posts: 0 Comments: 50
1. georgevandenberghe
5:39 PM GMT on January 13, 2013
The other term that increases with high dewpoints is downward IR radiation. I haven't done the math to determine how much of the melting is due to this and how much is due to condensational heating and sensible heating.

The DC area sometimes gets the combination of deep snowpack and +60F dewpoints. One striking example was in 1996 about two weeks after the January blizzard. This destroyed a 12" dense snowpack in a day and the associated several inches of rain caused severe river flooding. The streamers of dense fog coming off surviving snow ridges and patches were dramatic.

A dramatic demonstration of condensational heating occurs when you buy an ice cream cone on a hot humid breezy day and bring it outside. Melting rates are higher than on hot dry days and on humid days the cone will be destroyed in about ten minutes. Comparing the melting rates of popsicles under these different conditions is probably a better way to demonstrate it.

If you ever have the misfortune to have flesh contact steam you will get a much more malevolent demonstration of condensational heating.
Member Since: February 1, 2012 Posts: 17 Comments: 1625

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

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