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Messages - slow wing

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Arctic sea ice / Re: Latest PIOMAS update (February 2020)
« on: February 07, 2020, 05:45:40 AM »
Here are volume and volume-anomaly graphs.

It is getting harder to find a new color for a new year. I am trying a new color scheme that I found here:

Have a look, I am not sure myself yet, comments are welcome.
Hi Wipneus, you asked the same question a year ago and I replied then with a suggested colour palette.

Did you try those colours and, if so, did they work OK?

Arctic sea ice / Re: 2019 sea ice area and extent data
« on: November 08, 2019, 10:57:07 AM »
[ADS NIPR VISHOP (JAXA)] Arctic Sea Ice Extent.

ADS is 45 minutes late on the update.
If someone else can post the new values…
Thank you  :)

Still hasn't updated.

Arctic sea ice / Re: "Stupid" Questions :o
« on: October 23, 2019, 06:24:33 AM »
Thanks for all your interesting & some authoritative responses in this discussion.

I still don't understand, how can you use a very thin slice of a full model to approximate the true situation?

I can do it because a) I am only seeking order-of-magnitude accuracy & b) am considering the limited & somewhat artificial situation where the only heat transport mechanism is thermal conduction.

I think I found a better approximation in this article:

This is comparing apples to oranges. You're showing an amount of heat whereas I calculated a rate of heat transfer. That's a lot of heat but it still has to get to the surface to affect the ice.

Have you all forgot the basics of sea ice formation? RoxTheGeologids, macid, slow wing?

Yes, I'm worried that some of the people here may have forgotten more about that than you or I ever knew.

I hope that the current expedition will show how this happens in real time! It's a really interesting theory.. lets see if the real world works that way.

Yes, an exciting prospect!

Arctic sea ice / Re: "Stupid" Questions :o
« on: October 22, 2019, 02:11:21 PM »
The above discussion suggests a third mechanism whereby incoming storms can retard the start of the refreeze: introducing water vapour to the atmosphere which raises the 'effective temperature' of the sky for long-wave radiation. This lowers the rate of net heat loss from the water and so retards refreeze.

(This 'effective temperature' of the sky is a description I am familiar with from solar water heating applications, and I've also seen it used before in this forum.)

Arctic sea ice / Re: "Stupid" Questions :o
« on: October 22, 2019, 02:01:04 PM »
Good questions, thank you Macid.

Answering your last question first, my thermal conductivity calculation was for an illustrative 'toy model' that might approximate the true situation in some circumstances. The whole point is to get the magnitude of the heat flux for the process of thermal conduction -- which was found to be of order 1/100 W/m^2.

As you point out, this is negligible compared to the other thermal processes effecting the melting or freezing of the ice, which was what the toy model was intended to illustrate.

The background to my post above has been the common narrative on this forum that excess heat gets stored in the water column over the course of the melt season, together with the assertion that the refreeze cannot proceed to any great extent until that excess heat has first been removed by extraction to the atmosphere.

I've never been comfortable with that explanation because, given the situation of relatively calm water, I can't see how that trapped heat -- which I presumed to extend down by at least several meters and probably tens of meters or more, depending on whether it was sourced from ocean currents or direct sunlight -- can get to the surface to influence the refreeze.

So yes, as you point out, in calm conditions then the long-wave radiation to the cold sky should start the refreeze without noticing how much excess heat has been trapped below. Then, once the ice has formed and grown thick enough, there is no chance for wind and waves to start bringing the excess heat up to the surface. So the re-freeze continues and the trapped excess heat below becomes essentially irrelevant.

My suggestion above concerns the converse situation, where there is wind and waves. I'm suggesting that could mix some of the excess heat up to the surface to replace the heat lost to long-wave radiation and so to retard the start of the re-freeze.

Arctic sea ice / Re: "Stupid" Questions :o
« on: October 22, 2019, 12:52:31 PM »
It's certainly relevant to the discussion whether or not it has been windy lately in the Arctic basin.

I do have the impression it has been unusually windy over the past month compared to previous years, but nothing quantitative and based only on looking at the weather maps which appeared to show lots of isobar lines in the basin, indicating strong pressure gradients and therefore strong winds. I might be wrong in this.

Arctic sea ice / Re: The 2019/2020 freezing season
« on: October 22, 2019, 09:22:11 AM »
.... Nevertheless, it would appear that accumulated heat in the Arctic Ocean/system is an important factor.

It seems to be THE most important factor

Wondering if the record late refreeze may be due, at least in large part, to the Arctic basin having been stormy since the extent minimum?

I have posted my speculation on the importance of storms in the refreeze here on the Stupid Questions thread.

Arctic sea ice / Re: "Stupid" Questions :o
« on: October 22, 2019, 09:19:09 AM »
From the Freezing Season thread...

.... Nevertheless, it would appear that accumulated heat in the Arctic Ocean/system is an important factor.

It seems to be THE most important factor

Wondering if the record late refreeze may be due, at least in part, to the Arctic basin having been stormy since the extent minimum?

Reason: the thermal conductivity of water is terrible, as I illustrated earlier on this Stupid Questions thread.

So I'm guessing that, to a good approximation, it will only be the action of wind & waves stirring up the water that makes the accumulated sub-surface heat available to retard the refreeze.

Also, ice can't easily form in wind & waves.


Arctic sea ice / Re: "Stupid" Questions :o
« on: October 15, 2019, 11:10:14 AM »
I posted this originally in the Mike Horn expedition thread :

But here is a question. Mike mentions he was about 87 N. Should the sun be below the horizon by this date ? I plugged this lattitude into a couple of online solar angle calculators and they are saying max angle is circa -4 degrees ie below the horizon.

To still see the sun you would need to be near 82 N (according to the online calculations).

Or maybe the calculations are not taking into account the flattening at the poles ?

Agree it is puzzling. However, there is some refraction of sunlight in the atmosphere. Wikipedia says that at sunset it is 35.4' -- so more than half a degree. So that accounts for a small part of the discrepancy.

This website, which includes refraction, says there is no direct sunlight but still 4h19 minutes of "civil twilight" at 87N, even now on 15th October, which is two days after the photo.

Arctic sea ice / Re: Latest PIOMAS update (October 2019)
« on: October 06, 2019, 05:35:49 AM »
Thanks Wipneus!

The September monthly volume trend:

Thanks for this plot. There is clearly some year-to-year correlation but, that aside, it seems to me that the Arctic sea ice volume data seems reasonably well described by a linear decline.

Eye-balling, it looks like it reaches zero volume in about 10 years time (and may fluctuate down to that sooner). I wouldn't rule that out!

Arctic sea ice / Re: meaningless freezingseason/melting season chatter.
« on: September 25, 2019, 03:31:06 PM »
🌍🔥  New #IPCC #ClimateChange report released today: "IPCC Special Report on the Ocean and Cryosphere in a Changing Climate" #SROCC

Press release:

Full Report, & Summary for Policy Makers: 🔥🌍

Arctic sea ice / Re: Arctic Ocean salinity, temperature and waves
« on: September 22, 2019, 10:40:24 AM »
It's hard to match the ITP buoys temperature & salinity profiles with their location using the standard plots provided, so I practiced my R and took a stab at it.

Excellent! Much appreciated initiative, MyACIsDying. This is a plot I've wanted to see often.

Arctic sea ice / Re: 2019 sea ice area and extent data
« on: September 21, 2019, 06:12:57 AM »
Juan hasn't posted it yet so if I may...

September 20th, 2019:
     4,054,403 km2, an increase of 44,272 km2.
     2019 is 2nd lowest on record.

Arctic sea ice / Re: The 2019 melting season
« on: September 18, 2019, 09:54:31 AM »
... something I don't really get.

Suggest asking about it in the Stupid Questions thread, as plenty here do get it.

Short answer:

1) Salinity is more important than temperature in determining water density; and

2) The Arctic Ocean at its surface is less saline than the other oceans.

Arctic sea ice / Re: 2019 sea ice area and extent data
« on: September 18, 2019, 05:36:30 AM »
Yes, another JAXA extent drop: to 3,964,239 km2, so down 26,948 km2 from yesterday.

Arctic sea ice / Re: 2019 sea ice area and extent data
« on: September 16, 2019, 05:38:13 AM »
September 15th, 2019:

     4,006,036 km2, a drop of -19,682 km2.
     2019 is 2nd lowest on record for this day.

P.S.: 2019 is now the second lowest year for extent on record, now 11,228 km2 below the 2016 minimum of 4,017,264 km2 and behind only 2012.

Arctic sea ice / Re: "Stupid" Questions :o
« on: September 15, 2019, 08:35:18 AM »
"The 2019 melting season", Reply #6567
... with melt potentially continuing through this next week given the heat anomalies ... last years min was on 21 Sep!

Three questions I have been wondering about that relate to this melt season:

1) Are the yearly extent minima getting later?

2) Has the Arctic basin been carrying more moisture in the atmosphere at this time of year than in past decades? (Iirc there was an identified step change relating to an extreme weather event in December 2016, was it the 27th? Also, there is more open water in recent years. So this question could include a part 2b: why?)

3) If 'yes' to both 1 & 2, could 2 be at least partially the reason for 1 due to increased moisture in the atmosphere over Arctic basin retarding the loss of heat by long wave radiation?

Have any scientists been watching this and can answer one or more of those questions? Thanks.

Arctic sea ice / Re: The 2019 melting season
« on: September 14, 2019, 05:54:20 AM »
13 September is another of the dates on Neven's excellent year-to-year sea ice map comparison

It's easy to see that 2019 is one of the years with the lowest ice extent although that's qualitative.
(I have to admit that 2007 looks about as low as 2012 to me at a first glance, although we know 2012 is actually far lower.)

Arctic sea ice / Re: 2019 sea ice area and extent data
« on: September 12, 2019, 06:00:43 AM »
September 11th, 2019:
     4,110,564 km2, a drop of -39,332 km2.
     2019 is now 2nd lowest on record.
     (2007, 2012 & 2016 highlighted).

Thanks Juan, always appreciated.

The forecast winds are so favourable for compaction of the ice pack that extent may well drop all the way below 4 million km2 over the course of the next several days, and before freeze-up finally takes hold.

That is so even though 4 million km2 has at times been below the predicted range obtained from extrapolating using the progressions to the minima from the previous years on record -- see the plots that gerontocrat has been posting. (After today's drop though, 4 million km2 is presumably back within the range from those projections.)

The significance of that, of course, is that 2019 would become only the second year to drop below the 4 million km2 marker and it would reach the second lowest minimum extent in the record, below all years except 2012 (all the way down at 3.18 million km2).

Arctic sea ice / Re: The 2019 melting season
« on: September 08, 2019, 02:35:57 PM »
The models at Tropical Tidbits are coming into consensus on a high pressure system forming towards the Canadian side of the central Arctic basin by about 4 days from now and then intensifying.

That could potentially bring some compaction of the ice pack and a relatively late minimum extent date for this year.

To illustrate with an example, here is the latest NAVGEM 96h forecast:

Arctic sea ice / Re: The 2019 melting season
« on: September 08, 2019, 07:44:07 AM »
7 September is a date displayed in Neven's fine year-to-year comparison of sea ice extent & concentration - here.

2019 is shown at bottom right, along with 7 previous years that Neven has chosen as some of the worst for minimum extent. (Further years are displayed further down on the webpage - not seen in the figure below.)

As expected, 2019 looks like it belongs with the previous worst years.

Arctic sea ice / Re: The 2019 melting season
« on: September 06, 2019, 01:16:08 AM »
The weakest ice under full (90° Angle) attack

Windspeeds around 50km/h at a bit of a distance to the "Eye"

Some compaction will be the least impacting extent numbers, some melt still ongoing could
keep area drops in line with extent losses, despite higher concentration.

That's a low pressure system so it causes dispersion -- the opposite of compaction.

On your figure, I suggest you redraw your arrows at 45 degrees to the right of the actual wind directions displayed -- which is the direction the ice goes (Coriolis) -- and then you will see the dispersion.

Arctic sea ice / Re: Latest PIOMAS update (September 2019)
« on: September 04, 2019, 09:07:39 AM »
Thanks Wipneus!

Looking at the graph I think 2019 is now guaranteed a 2nd place finish?

Yes, at least. 2nd or 1st.

Arctic sea ice / Re: Icesat 2 data now available
« on: September 01, 2019, 10:37:01 PM »
Excellent news, thanks!  :)

Arctic sea ice / Re: The 2019 melting season
« on: August 28, 2019, 05:54:38 AM »
Yesterday I compared 2012 ice cover with this year on the same date. This tool makes it easy to compare both years, and I don't see any way how we could catch up to 2012 without an apocalyptic storm.

2012 vs 2019

Wow! That's a great display -- thanks to you and, especially, NASA.

Also convincing that 2019 won't catch 2012 for extent at minimum, barring something extraordinary.

The current weather pattern -- shown below -- should continue to disperse the ice pack. The pattern -- a dipole of a low pressure centre inside the pack, towards the Beaufort sector, and high pressure outside the pack, in the ESS -- is predicted to continue at least over the next couple of days.

That might continue the slowdown of extent losses. But the flip side is that the ice movement and the increasing gaps in the ice should both help with melt. So the actual ice volume is presumably going down faster than usual for this time of year.

While 2019 is unlikely to catch 2012 for extent, or even area, the comparison of minimum sea ice volumes should be more of a contest.

  (Parenthetically, the reason the current weather pattern disperses the pack is because low pressure systems tend to disperse the ice away from their low pressure centres as the ice rotates in the CCW winds, while the CW winds of high pressure systems draw the ice towards their centres (in this case, outside the ice pack). This is a consequence of the Coriolis effect -- the ice is pushed in a direction to the right of the wind direction -- by about 45 degrees, I'm told. Qualitatively, winds from the East/West oppose/enhance the ice's velocity from the CCW-rotating Earth, so slowing/speeding it and so it drifts towards/away from the North Pole.)

Arctic sea ice / Re: The 2019 melting season
« on: August 25, 2019, 12:24:43 PM »
The arctic/ice has been so (cuss word)ing cloudy for the last several weeks that I have no idea what's actually unfolding beneath... Lord Vader mentioned already, the north Atlantic/Svalbard area will be the focus for melt/movement now as models are suggesting a quite long period of S or SE winds there.

NASA Worldview is finally showing some clear skies over the Atlantic side. The Laptev sector has been windy since the beginning of August and we see now that it has taken quite a hit.

Interestingly, there is a fringe of more solid ice at the Atlantic edge which -- as I seem to recall from the ice age plot -- contains some multi-year ice. But the ice inside it in the Laptev sector looks to be slush at least up to the northern cloud edge at around 5 degrees from the Pole.

Arctic sea ice / Re: The 2019 melting season
« on: August 20, 2019, 12:36:41 PM »
19 August is another of the dates displayed in Neven's excellent year-to-year comparison of the U. Bremen false colour AMSR2 Arctic sea ice concentration plots, as shown below.

On this date, this year looks roughly comparable to arguably the three worst previous years for the ice: 2007, 2012, and 2016.

The ice coverage on this date probably looked most tenuous in 2016. However, a lot of the ice in the Laptev sector went on to survive the melt season and so 2012 easily retained the record.

Arctic sea ice / Re: The 2019 melting season
« on: August 15, 2019, 06:49:42 AM »
May I ask where I can get that ice concentration map?

I get today's map from here:

A bit later it gets posted to the archive, which also has the previous maps from this month:

 (Edit the month and year to get the analogous archived maps from prior to this month.)

Arctic sea ice / Re: The 2019 melting season
« on: August 14, 2019, 01:49:26 AM »
Ascat with NSIDC ice age overlaid at 20% transparent, mar21-aug12.
Thanks for your great animations, Uniquorn. Really interesting to see this one and it shows that some of the outlying ice has a multi-year component.

Arctic sea ice / Re: Error in "2019 melting season" thread - HTML 500
« on: August 13, 2019, 08:09:29 AM »
It didn't work for me but then I hit "Reload" and it worked.

Arctic sea ice / Re: September predictions challenge 2019
« on: August 10, 2019, 05:37:50 AM »
JAXA:     3.50 to 4.00,  medium (minimum day extent)
NSIDC:   4.00 to 4.50,  medium (September average extent)

"Between 4.00 and 4.50 million km^2"

This is just half a million km^2 more than my estimate for the daily minimum.

"Between 3.50 and 4.00 million km^2"

Sneaked in just before closing and raised my estimate by half a bin...  :P

I didn't see any 'surprises' that would take out much extra ice.

True, there's currently that high pressure system in the ESS that's also acting in a dipole configuration to blow hot air from Russia into the Laptev sector, where the ice already has holes.

But it still takes a lot of energy to melt ice. By mid-August, sun and hot air can only do so much. It's the heat in the water that can still make a real difference. So, yes, wind can help by stirring things up and exposing the ice to more of that heat. Uniquorn also showed a great map of warmer currents expanding in the Beaufort Sea and also near and under the ice edge just north of Svalbard. So I expect more melting there.

But more overall melting to come than in other years? I don't see that there is particularly more vulnerable ice. Average melt would leave around 3.8 million km^2 at minimum, according to the helpful posts in the "2019 sea ice area and extent data".

So that's around the bin center for my chosen bin: "Between 3.50 and 4.00 million km^2"

Arctic sea ice / Re: "Stupid" Questions :o
« on: August 10, 2019, 12:23:40 AM »
Uniquorn, the formulae for orthographic projection are here:

They are taken from a book for which the .pdf file is available online:

They are actually simple though, and simplify still further when centred on the North Pole.
phi_0 = 90 degrees
lambda_0 = -45 degrees (example with 'Greenland down')

x = R cos(phi)sin(lambda+45)
y = -R cos(phi)cos(lambda+45)

R ~ size scale of your map. You will presumably have to calibrate it using known coordinates, e.g. Svalbard.

Arctic sea ice / Re: The 2019 melting season
« on: August 08, 2019, 05:46:29 AM »
7 August is another date where Neven has a year-to-year comparison of the U. Bremen AMSR2 sea ice concentration maps.

See figure below. The latest 2019 map is bottom right. It can be compared by eye to some of the previous worst years for sea ice minimum extent. Other recent years are available for comparison on the web page.

2019 looks worse to me on this date than any of the previous years other than 2012 and 2007. (2016 caught up later in the month - see the web page.) Even so, it's still to be determined how much of this year's lowered-concentration regions -- particularly in the Laptev sector, and north of the CAA -- will melt out by the minimum.

Arctic sea ice / Re: The 2019 melting season
« on: August 04, 2019, 09:11:51 AM »
The heat can mostly move through conduction
You mean convection I assume?
Nope. Conduction.  No convection through the halocline unless wave action stirs things up.

Very little heat moves up through conduction - the thermal conductivity of seawater is just too poor.

I just did a quantitative calculation of that here on the Stupid Questions thread. The amount of heat reaching the ice will seldom be enough to melt more than of order 1 millimeter of ice in a year.

Arctic sea ice / Re: "Stupid" Questions :o
« on: August 04, 2019, 05:56:11 AM »
Q. Can it? My response to this statement on the 2019 Melting Thread.

There is more than enough heat in the deep water to melt the ice and keep the arctic ice free year round. 

However, the heat can not move upwards through the halocline. 

The halocline is 50 meters thick (at least) and is very difficult to breach.  If it ever happens, look out!   The arctic will be a completely different place.

I've often wondered if/why the thermal conductivity of seawater is insufficient for significant melting of the ice just by thermal conduction, when the halocline is stable.

So let's see...

Consider the year-round loss of ice thickness due to thermal conduction from a 1-degree-C-warmer layer at a 50 meter depth.



Upwards heat flux = (temperature gradient) x (thermal conductivity) = 2e-2 K/m x 0.6W/mK = 1.2e-2 W/m^2

Thermal energy added to ice in 1 year = (Upwards heat flux) x (time in 1 year) = 1.2e-2 W/m^2  x 3.1e7 s = 3.7e5 J/m^2; multiply by 1e-4 m^2/cm^2 = 37 J/cm^2

Depth of ice melted = thermal energy added / (heat of melting x density)
= 37 J/cm^2 / (334 J/g x 0.9 g/cm^3) = 0.12 cm depth


So the thickness of ice melted over a year in the above scenario is only of order a millimeter.

Indeed, the thermal conductivity of seawater is insufficient to provide significant melting from deep layers of warmer, saltier water below the ice.

For now I'm sticking with last month's estimate: "Between 3.25 and 3.75 million km^2".

I'll keep watching and may exercise my discretion to change it before the poll closes.

July has been at least average and arguably a bit worse than that for the ice. No major storms or events but usually some wind and sometimes a fair bit of sun.

The reference area I always use to compare to is the 80N circle, which encloses an area of about 3.9 million km^2. So I'm guessing the ice extent will end up a little lower than that.

If 'no surprises' then it would probably end up at around 3.8 million but any surprises are likely to push it lower.

Considering the areas where there is currently ice south of 80N:

->  the Pacific side has already almost melted out - more so for this date than happened in any other year besides 2007;

-> The usual 'Beaufort tail' in front of the west CAA will presumably melt away to a large degree as the ice there is already broken up and there appears to be plenty of heat in the water in that region;

-> Yes, the CAA will retain some ice, but it will only be a couple of hundred thousand km^2. To balance that, the Greenland Sea is looking to end barer than in some years, including the record year 2012.

As for the ice detachment from the CAA, the degree to which that has happened is unprecedented in the years of the satellite record. I still expect the pack to drift back to the land before the extent minimum, but it might not. Also, that ice sanctuary has probably seen more heat than any previous year in the record, so some extent will be nibbled away there.

In addition to the possibility of a strong storm anywhere over the ice pack, I look to the Atlantic side for potential 'surprises' even if there is no such storm. The ice there has held on so far, but what about the claimed 'Atlantification' of the water there within the past couple of years? (More salinity and heat.) The Navy thickness map estimate shown below (for 2019-08-09) has relatively thin ice north of Svalbard and the Fram Strait. As we have seen on the Atlantic ice front in some previous years, some of that ice above the shelf of shallower water might disappear fast due to any heat in the water.

The Laptev sector may also get eaten away to well inside 80N.

So here is my guessed boundary, to be compared by eye with the 3.9 million km^2 enclosed by the 80N line. Again, it looks like "Between 3.25 and 3.75 million km^2".

So guessing a second place finish for low extent, behind only 2012. Guessing a record low volume, beating even 2012.

Arctic sea ice / Re: The 2019 melting season
« on: August 02, 2019, 02:00:13 PM »
Here's Neven's year-to-year comparison maps for Arctic sea ice on 1 August.

2019 definitely appears to be one of the worst years on this date. How bad will this melt season end up compared to previous worst years? Too early to tell?

Arctic sea ice / Re: The 2019 melting season
« on: July 31, 2019, 03:41:39 AM »
Given the accuracy of past Slater projections to minimum, a record should not happen this year, but I don't think a Slater projection for 2012 is available.

Slater's prediction for 2012 can be seen at

His model did successfully predict a record low extent minimum 2012, but not as low as reality. The predicted 2012 minimum was just a bit under 4 million km2 - which is also what the Slater model predicts for this year.

Given its similar predictions for the extent minima in the record year 2012 and in 2019, the Slater model can't be said to rule out a new record low extent this year.

Arctic sea ice / Re: Slater's thread
« on: July 28, 2019, 08:21:59 AM »
OK, I'm somewhere in the middle here.

I do agree with petm that the model does make a prediction for each day.

On the other hand, consider the prediction for 1 September (showing as about the current lowest) vs. the 15 September (which is where we are up to now). The 1 Sept prediction was made with the data for 2 weeks ago.

If the Slater model instead used today's data for the 1 September prediction then it would have more skill than the point shown on the plot because it would be a 36-day prediction rather than a 50-day prediction.

Would a 36-day prediction for 1 September likely be higher, or lower, than the value shown? We might suspect higher, given that later predictions have tended to be higher (and also that the mimimum in prior years has usually (always?) been later than that). That is oren's point.

They don't do predictions for days 1-49 into the future (see .pdf referenced by petm), only for 50 days. So the model hasn't really been optimized for finding the extent minimum - that's not its purpose.

Arctic sea ice / Re: The 2019 melting season
« on: July 28, 2019, 03:36:33 AM »
Slater's model seems to have settled on an early minimum near the end of August of approx. 4 million sq. km.
No. No. No. Those values for the end of August are historical, predicted exactly 50 days earlier in every case.

If you go to that website every day you will see that the curve remains the same. Every day it just gets a new 50-day prediction value added on at the end.

The Slater model's latest estimate of the actual minimum extent is not shown on that plot. Nor is its date. Presumably it's some time in September and is not much less than the 4.25 million square km value shown for 15 September - i.e. 50 days from now.

Arctic sea ice / Re: The 2019 melting season
« on: July 25, 2019, 07:29:23 AM »
it seems that the heat at / near the surface will determine the melt, not the heat 1,000 feet up.

It's a fair question. The short answer is that the air near the surface holds hardly any heat energy because it's a gas and so it contains hardly any mass per unit volume.

In more detail, these 3 points are relevant:

1) If we are just looking at the air temperature then we are ignoring water vapor, which can be important. (The dew point shows how much water vapor is in the air.) But now considering just dry air...

2) The temperature at 2 meters is not representative of the amount of heat in the air column as it is somewhat tied to the ~0 degrees temperature just below it.

3) The (dry) air in the meters just above the ice is carrying very little energy and so can melt only a negligible depth of ice. To get significant melt, a significant fraction of the heat in the air column has to be transported somehow into melting the ice (water vapor, infrared radiation, convection...)

To illustrate point 3, consider how much warm air would be required to melt, e.g., a 1 cm thickness of ice.

 (We assume some quasi-static conditions where the air column above the ice causes the melt directly below it - with the caveat that this is not normally a very good assumption.)

To melt, e.g.,  a 1 cm depth of ice requires (334 J/g specific heat of melt) x 0.9 g/cm^3 = 300 J/cm^2.

So 300 J would need to be supplied by the air column above each square cm of ice.

But the specific heat of air is only 1 J/g.(degree C) and the mass of air in the entire column all the way up into space is only about 1000 g/cm^2 (i.e one atmosphere) What average loss of air temperature, dT_air, would be needed to supply the 300 J/cm^2 to melt a 1 cm thickness of ice?


dT_air[Celsius] x 1.0 J/g.[degree C] x 1000 g/cm^2 = 300 J/cm^2

=> dT_air = 0.3 degrees C.

So THE ENTIRE COLUMN OF AIR UP INTO SPACE would need to lose 0.3 degrees C to melt a 1 cm depth of ice. Obviously, the air just directly above the ice can't melt much ice at all.

Arctic sea ice / Re: The 2019 melting season
« on: July 25, 2019, 06:44:45 AM »
What you miss in the basic picture of the process - is basics about how absorption works. You assume that all 180...300 W/m2 goes into melting the ice. In reality it does not: like already mentioned above, some of that energy is lost via evaporation (mostly from liquid water at the surface, but even dry ice actually evaporates slowly).

Further, whenever there is any noticeable open water - most of those 180...300 W/m2 gets absorbed at significant depth of downwards water column, since you know, water is a transparent thing. Noticeable amounts of light are present even at ~200 meters depth if my memory serves, - that's basically how deep significant fraction of absorption happens.

Same effect also happens to a lesser degree through the ice itself whenever there is no snow cover on it, increasingly so when the ice getting thinner: much sunlight simply goes through it and into water column below it, since ice is often significantly transparent, itself.

With water density being the highest at +4 Celcius iirc, a layer of colder melt water often remains near remaining ice, with warmer water sinking down as it's a bit heavier (though this much depends on water column mixing factors present at the location), which is another "sink" for some absorbed heat.


Sadly, this kind of calculations takes more than a single small napkin.

Yes, I assumed the bolded part as an approximation: that the heat absorbed by the ice goes predominantly into melting the ice.

 I've further speculated that -- before even reaching the ice -- a significant fraction of the solar insolation incident at the top of the atmosphere (at an elevation angle of only about 20 degrees above the horizon, remember) may have already been lost through absorption or scattering in the atmosphere before it gets to reach the ice, and that applies even in what appears to be 'clear sky' conditions.

But back to considering only that part of the insolation that has already been absorbed by the ice...

Someone else already suggested an alternative mechanism -- namely, heating of the ice up to zero degrees C -- that may use some fraction of the energy. I already posted the back-of-the-envelope calculation for the size of that, and shown that it should indeed be much smaller than melting.

Now you've suggested several further mechanisms where heat that's already been absorbed by the ice might be lost or absorbed elsewhere, rather than melting the ice. (Likewise, I've assumed all of those to be fractionally much smaller than melting.)

I do invite you to bring out your napkin as calculations on envelopes and napkins are used all the time in science with complicated processes, in trying to assess what is relevant or important and what is not.

So which one of your stated mechanisms do you think is the most important in competing with direct melting to use up the solar energy absorbed by the ice? I suggest you pick one and then do a back-of-the-napkin calculation to estimate the fraction of absorbed solar energy that is lost to your chosen process instead of melting the ice.

I'm skeptical that any of them are important but it will be interesting to see which of the other processes you suggest, if any, are comparable in energy scale to the energy that goes into melting the ice.

Arctic sea ice / Re: The 2019 melting season
« on: July 24, 2019, 11:47:12 PM »
If I'm not mistaken, your calculation assumes the ice is already at a temperature of 0°C.

Yes it does. It's a back-of-the-envelope calculation with implicit approximations and assumptions.

The assumption is a reasonable approximation because:

1) The specific heat of ice is only 2.1 J/g-(degree Celsius), whereas the melting heat is 334 J/g. So even if the ice starts at, say, -10 degrees C, then that is only a 6% effect.

2) By the start of August, I presume that the ice will anyway be close to zero degrees C.

Arctic sea ice / Re: The 2019 melting season
« on: July 24, 2019, 11:05:59 PM »
i'd say we can safely settle on very approximate range of ~180...300 W/m2 absorbed at the surface under clear skies (high pressure systems) for late July / early August

So about 5-9 cm of ice per day might be melting under the clear skies of the big high pressure system soon to arrive in the CAB.

Reason: it takes about 35 W/m^2 to melt each centimeter of ice per day:

Energy flux to melt 1 cm thickness of ice per day [in units of W/m^2] = 1 cm x (10^4 cm^2/m^2) x (334 J/g latent heat of melt) x (0.9 g/cm^3 density) / ( 3600x24 seconds/day)
= 35 W/m^2

(Uses the definition W = J/s)


Doesn't that seem a bit high?

Let's say, roughly speaking, that the Arctic sea ice is observed to lose on average about 2 cm per day (that's 200 cm over a 100 day melt season). Then, from the above calculation, that's 70 W/m^2 delivered to the ice on average from all sources combined: sun, air and water.

Is that compatible with the insolation plot shown - where 'clear skies' are presumed to add 180-300 W/m^2 - and that is for more than a month past the Summer solstice?

If we believe '180-300 W/m^2' then it seems like only a small fraction of 'clear skies' over the ice would use up the energy budget to produce the amount of melt we observe.

So I'm skeptical that all the insolation shown in the plot actually does get to heat up the ice, even under 'clear skies'.

Asking the experts then: is that insolation plot for the top of the atmosphere and, further, is a considerable fraction of that energy lost even under what we consider to be 'clear skies'?

That's my suspicion.

Arctic sea ice / Re: The 2019 melting season
« on: July 24, 2019, 10:34:43 PM »
Another gain on Slater today, appears to be that their model predicts the first August minimum rather than a September minimum.
No, that's not how the plot works. Each day, an independent estimate of extent is produced and added to the plot. The older estimates are still displayed in the plot but their current estimates for those August dates are not shown. Presumably, their current estimates for those August dates will be higher than the old extent estimates that are displayed and also higher than the current predictions for 11 or 12 September.

Arctic sea ice / Re: The 2019 melting season
« on: July 24, 2019, 08:14:25 AM »
Thanks uniquorn and aslan for your replies on the salinity trends.

The amount of model data sounds huge.

The actual physical data though - the salinity data recorded from tethered buoys, drifting buoys and ships - is presumably quite manageable.

Wouldn't looking at the actual physical data give us some idea of salinity changes prior to the modelling from June 2017? (It's a genuine question - I don't know how sparse or rich the physical data is, and I don't know how easy or difficult it would be to notice salinity trends from looking at the physical data.)

I posted a suggestion for one way to present the salinity physical data, on the "Arctic Ocean salinity, temperature and waves" thread.

Arctic sea ice / Re: Arctic Ocean salinity, temperature and waves
« on: July 24, 2019, 04:37:04 AM »
Inspired by your salinity movies, uniquorn, the illustration below is a suggestion for displaying the actual physical data they are based upon.

It would give a 'traffic light' of salinity at e.g. 0m, 30m, and 100m at the location of each recording device on that date - whether from a tethered buoy, drifting buoy or a ship.

My main immediate motivation in suggesting this is that it would allow a movie that extends back before the June 2017 start of the mercator display movie that uniquorn posted here on the 2019 melting season thread. That would give us a longer term view of how the salinity has changed.

I realize that it would probably be a lot of work to make this, but I think to could be a useful visualization tool. The picture is just an illustrative cartoon - I'm hoping someone will be kind enough and interested enough to produce such a display, or similar, using the actual data. (It's beyond my own personal skills at the moment, unfortunately.)

Arctic sea ice / Re: The 2019 melting season
« on: July 23, 2019, 11:34:34 PM »
Yay! The Slater prediction has updated.  :)

The latest prediction is 4.11 million square kilometers for 11 September 2019 - which should be around the date for the extent minimum.

Bearing in mind that the map is indicative only, and is posted as a courtesy, it is seen that neither the Alaskan side nor the Russian side are predicted by the model to advance much inside 80N.

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