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Robertscribbler.wordpress.com

Positive AO, an end season jump in area and extent and... The sea ice is starting to crack again (see modis shots). Similar pattern to last year, just about 15-20 days later at initiation. No way to know if it will be as intense. But we have GFS showing highs in the region of Beaufort through March 25. Interesting days ahead perhaps.

https://earthdata.nasa.gov/labs/worldview/?map=-345136.461886,-827635.47106,-45104.461886,-666099.47106&products=baselayers,MODIS_Terra_CorrectedReflectance_TrueColor~overlays,arctic_coastlines_3413&time=2013-06-10&switch=arctic

Jim Hunt

Robert - Your link is to June 2013. Is that what you intended? Here's the Worldview from two days, showing the current "cracks" north of Svalbard:

More over on the Arctic sea Ice Forum

folke_kelm

As a frequent reader of this blog i would like to drop some thoughts about melting here.
A crucial question about Greenland ice sheet melting is how to transfer heat to the inner ice sheet. Melting of surface and melting of the bottom of the outlet glaciers is one point to discuss. the mechanical properties of the inner ice sheet are another. Mechanical stress resistance of ice is strongly dependent of temperature. the warmer the ice is, the less resistant it is. To determine the future resistance of the ice sheet against mechanical disintegration it is important to have measures of the inner temperature of the central ice sheet. Ice is a very bad heat conductor, so it will take a time to warm up the core of the ice. I do not know of a paper which deals with this question, may be one of you knows about something.

The whole picture of Greenland and arctic summer melt is, that still most energy transported to the arctic is used to melt sea ice. If you compare it, roughly 18000 Km3 sea ice is melting against only 450 Km3 of Greenland ice sheet. You see, that only a minor portion of heat is able to provide surface melt or bottom melt at the outlet glaciers. However, this will change fundamentally when we get no sea ice left. This will result in a strong warming of surface water and strong increase in surface and bottom melting. Still the question remains how much of the energy is going into the inner ice sheet, altering the mechanical stability of the whole ice sheet

So, does one know about papers about ice sheet inner temperature and temperature change over time, papers about temperature dependence of ice rheology and implication of this into models of ice sheet behavior?

greetings from a very warm Sweden
Folke

Magma

Folke: "Ice is a very bad heat conductor, so it will take a time to warm up the core of the ice."

The problem is that it is becoming increasing apparent that relatively warm surface water can sluice down through fractures and moulins to the base of the ice sheet, which can already be near its melting point due to pressure and geothermal heat.

This is starting to look like yet another example of bistable behavior with tipping points - a cold, hard, dry, high-altitude, high albedo ice sheet vs. a warm, soft, wet, shrinking and increasingly dark ice sheet potentially subject to surprisingly rapid disintegration.

We'll see soon enough, I suppose.

Al Rodger

folke_kelm,
The famous paper on the internal temperatures of the Greenland ice sheet is Dahl-Jensen et al (1998), memorable because it presents a temperature record preserved within the temperature gradients.

Chris Reynolds

Folke,

Very well put, from the paper Al Rodger links to (thanks Al), it is clear that there is an awful lot of warming to go before all the ice sheet melts away. Yes moulins are a way to get warmth into the glacier, but that will still be localised to where the moulins are.

Take the top 2000m of GRIP, at -30degC.

The spcific heat capcity of ice is 2.108kj/kg/degC. In other words it takes 2,108 joules to warm 1kg of ice by 1 degC.

The enthalpy of fusion of ice is 334kj/kg - in other words it takes 334,000 joules to turn 1kg of ice into water.

Imagine a colum of ice at about -30degC 1m by 1m across and 2000m deep. That takes 794,480,000,000 joules to turn into water. No amount or argument about basal lubrication or any other mechanism changes that physical fact.

Daily average insolation is about 250W/m^2 (wikipedia) - a bit of a meanigless figure, but I'm indulging in reductio ad adsurdum for a purpose.

Let's say the sun shone directly above that column of ice delivering 250W/m^2, that's 250 joules per second. How long would it take to melt that column of ice?

It would take almost exactly a century, that's with 250W/m^2 insolation levels, 24 hours a day, 365 days a year.

Therefore Greenland will be raising sea levels for several centuries.

Magma

@ Chris - I was thinking along the lines of getting the ice out to sea faster, not melting it in place. I think it's fair to say that we don't yet have an accurate handle on the details of how a large ice sheet breaks up.

Jai Mitchell

Greenland mass loss is dominated by ice flow to the sea, surface melting produces this increased rate of flow.

Chasing Ice has a wonderful graphic of this>

https://www.youtube.com/watch?v=ZCifBUtw1sE&t=40m32s

Chris Reynolds

Jai, Magma,

At which point you hit the issue raised in the Pfeffer 'Kinematic Constraints' paper.
http://www.sciencemag.org/content/321/5894/1340

I agree that it definitely will not all melt in one place and that glacier flow will be a large part of mass loss. All I'm saying is that the process will take many centuries. So we face many centuries of SLR.

Fufufunknknk

I thought the major source of melting in Greenland was the warmer air flows coming from a warmer ocean and neighboring continent. I assumed that the ice free line would gradually creep north and have a higher altitude but that at higher altitudes and latitudes, Greenland would actually gain ice from increased snowfalls? Anyone?

(I did try to research this but I don't seem to know what key words to use that return results.)

Clive Mitchell

Chris, you appear to be assuming that the only source of heat available to melt the GIS in situ is direct solar radiation.

An ice-free ocean should produce more water vapor to transfer heat to the ice sheet by condensation. Also, the lack of sea ice to melt and cool incoming surface waters may permit heat from the Atlantic and Pacific to be available to assist evaporation.

Rick Aster

250 W/m^2 is a rule-of-thumb value for average insolation, which takes into account the fact that the sun is not visible at all times and is at different angles at different times and places. If the sun shines directly overhead at a particular moment, that’s peak insolation, and the rule-of-thumb value for that is 1000 W/m^2. So based on that, the Greenland ice sheet could melt away from sun alone, in not much longer than a century. The reason it doesn’t melt so fast is that it is losing heat to its surroundings.

sofouuk

"If the sun shines directly overhead at a particular moment, that’s peak insolation, and the rule-of-thumb value for that is 1000 W/m^2. So based on that, the Greenland ice sheet could melt away from sun alone, in not much longer than a century."

...

you mean, if the sun shone directly overhead, 24-7, 12 months a year? n the reason it doesn't melt so fast is that the sun doesn't?

Chris Reynolds

Clive, Sofouk,

My point is that it takes a trememdous amount of energy to heat that ice up to freezing and then to cause the phase transition to water.

This applies whether the ice melts in-situ or after calving into the ocean.

Rick,

Greenland's sunlight is receieved at an oblique angle. The average insolation will be held up by the overhead sun in the tropics and generally closer the equator. I picked 250W/m^2 as a convenient figure.

***

Greenland is going to be around for many centuries, but it will be melting and causing massive SLR, and it will be doing that probably long after fossil fuels have virtually run out. At 6m SLR from Greenland if it takes the next 600 years to melt (a more reasonable timescale than seems to be fashionable round here) that's 1m per century!

That's before we get to Antarctica's contribution.

Chris Reynolds

Fufuf,

See Hanna et al 2012, The influence of North Atlantic atmospheric and oceanic forcing effects on 1900–2010 Greenland summer climate and ice melt/runoff.

I quote:

"Multidecadal variations in Greenland coastal surface air temperatures (especially in west Greenland) during summer are significantly related to the AMO on an interannual timescale during two periods of the twentieth century, coinciding with the 1920s–1930s warming, and the more recent warming – especially in west/southwest Greenland. There are signs that this relationship may have been strengthening over the last 30–40 years, suggesting a more dominant influence of recent SST variability on Greenland climate and GrIS surface mass balance."

and, with regards the Greenland Blocking Index (GBI)..

"However, GPH [geopotential height] for the GBI area generally correlates more highly than the NAOI with both Greenland summer temperatures and GrIS runoff, making GBI GPH a potentially useful predictor for changes in GrIS surface mass balance. The GBI (GPH) index appears to be a less useful proxy of mean melt extent over Greenland, which we attribute to runoff being a more quantitative index of climate forcing than melt extent, as the latter is not directly related to the amount of melt/runoff generated."

A major reason for the recent spurt of acceleration in mass balance loss is the GBI.
http://www.arctic.noaa.gov/reportcard/images-terrcryo/gis-fig56-big.jpg
Notice how in 2012 (a year of very strong GBI - high pressure) there is the most massive yearly melt in the series, whereas in 2013 (low pressure over Greenland) losses are neglible. This is happening on top of a pre-existing downward accelerating trend due to AGW.

This is a plot of Greenland GPH (red) for the 500mb level with the general northern hemisphere increase in atmospheric height removed from the Greenland GPH.
http://farm4.staticflickr.com/3705/10230342105_4765d6ffda_o.png

The reason the GBI enhances mass balance loss is that it creates clear skies.

Pete Williamson

Magma says "This is starting to look like yet another example of bistable behavior with tipping points"

The curious thing is why with all these tipping points it seems the earth was perched on the edge waiting for humanity to push it over. Why shouldn't the tipping point be now or in 20oC time?

Chris Reynolds

Rick,

I knew I'd read of a BSRN station on Greenland. There's a graph on this page:
http://www.polartrec.com/expeditions/solar-radiation-on-the-greenland-icesheet-2011/journals/2011-06-05
Search for the string - Graph of Incoming and Shortwave Reflected Radiation at Summit Station, Greenland .

Due to the ice being white the absorbed solar radiation is actually far less than 250W/m^2.

Rick Aster

sofouuk,

To say the point in a more practical sense, the reason Greenland ice is able to stay solid is because of the dynamics of heat transfers, and not because the magnitude of energy in the environment is too small to produce melting. Things like albedo, air temperature, and cloud cover have to be taken into account to determine the speed of melting.

Jai Mitchell

Chris,

the temperature profile of the Greenland ice sheet is closer to -24C due to geothermal heating at the base (basal temp closer to -12C)

The convective warming of a column of ice is much greater than the warming due to incident radiation (since incident is so low)

ablation is the primary method of Greenland ice mass loss.

Greenland's melt rate will increase significantly over the next several decades but its contribution will be dwarfed by the shelf collapse processes currently unfolding in Antarctica.

I believe that a 3 meter rise by 2100 is an optimistic scenario due to non-linear responses to non-linear warming events.

Jai Mitchell

ablation is the primary method of Greenland ice mass loss.

haha! sorry, I meant melting from the ablation zone is. . .

http://www.ice2sea.eu/news/p2013_08/

Al Rodger

I think a few numbers may benefit the discussion.
To give 1m SLR from melting ice, you will require 125 ZJ for the melt plus probably 10% coz the ice is actually well below freezing = 140 ZJ.
Solar insolation is mainly used to keep the planet at 288ºK. Start pinching it to melt ice & the global temperature plummets. What is relevant is the TOA energy imbalance. If this is 1 Wm^-2, the extra energy sloshing round the climate after a century will be 1,600 ZJ. But if the ice remains awaiting melting at the poles, most of that 1,600 ZJ will end up heating the tropics, and then keeping it warm. And if the poles also heat up, there will be more energy needed to maintain that polar temperature increase.
So let's say a very very generous 20% is the maximum that will be available to melt ice. Using 20% of the 1Wm^-2 imbalance for melting, that gives 2.3 m SLR in a century/Wm^-2 imbalance. Say the imbalance is a third the forcing & forcing rises from 2Wm^-2 today to 6Wm^-2 in 2100. The average over the century would thus be 4Wm^-2 forcing = 1.3Wm^-2 imbalance = 3m SLR. And that's from both poles.
These numbers are in my view exceedingly pessimistic. But that is what is required to get multi-metre SLR by 2100 without the ice leaving the poles in search of the heat.

Steve Bloom

Not sure if this has been discussed here, but recent work explaining the rapid collapse of late Pleistocene ice sheets is relevant. Melting vast land-based ice sheets in a few thousand years, as has occurred in each deglacial, requires a mechanical collapse process via an ice-elevation feedback. The basic idea is that once the leading edge of an ice sheet starts collapsing it ceases to be able to hold itself up and a very large domino effect ensues. The resultant ice rubble is at a much lower and thus much warmer elevation (=> relatively rapid melt) and so cannot act as much of a brake on the process.

It seems to me that applying this effect to ice sheets subject to marine influences allows things to happen even faster.

But what does this mean for the present, noting that both the GIS and WAIS weren't wiped out by (orbitally-driven) mid-Holocene warming? They are lower to begin with, meaning the ice-elevation feedback isn't as strong. Even so, I would suggest that the warming currents affecting the marine ice sheets at present may not have been nearly so warm during the mid-Holocene or during the deglacials, bearing in mind that strong orbital forcing at the poles doesn't act to warm the tropical oceans. GHGs very much do, and those currents seem to be warming fast. In addition, GHGs act to keep things warmer during polar night, which makes the ice sheets more vulnerable to summer loss.

In sum, the past, even the immediate past, is actually not a very good guide to the near future of the ice sheets.

Chris Reynolds

Jai,

I chose a 2000m column and -30degC due to the plot from GRIP shown in the paper (Dorthe Dahl Jensen) Al Rodger linked to.

"I believe that a 3 meter rise by 2100 is an optimistic scenario due to non-linear responses to non-linear warming events."

As for shelf collapse in the WAIS, I've not read enough to engage in a constructive discussion. But I've not read any scientists saying as much, so at present I am highly sceptical.

Al Rodgers,

Surface area of the earth, 510,072,000km^2, or ~5.1X10^14 sqr metres. (1000 X 1000 metres in a km^2)

1W/m^2 = 1 joule/sec over any square metre, in a century that's:
60 X 60 X 365 X 100 = 1.31X10^8 seconds or 1.31X10^8 joules (a Watt is 1J/sec) per sqr meter for a century.

Multiplying those joules by the surface area of the earth gets me:
6.681X10^22
or 67ZJ.

That's much bigger than your figure.

But Greenland is only 0.4% of the earth's surface. Antarctica is only 2.7%, being in the Southern Ocean, whose thermal mass reduces southern hemisphere warming (along with other oceans) the sensible warming, hence heat fluxes won't be so large. In the NH you have Arctic amplification, I think that's a factor of between two and three, call it three. But even multiplying 0.4% by 3 (1.2%) is still a very long way off 20% of the total energy imbalance.

Steve,

But the main land ice sheets didn't have the geographical constraints of Greenland. That is why Pfeffer et al concentrated on the 'gates' in the mountains, with Greenland being a bowl (depressed by the weight of ice) surrounded by containing higher ground, their Map 1. Pfeffer et al found Greenland's contibution to SLR could be 0.8 to 2.0m by 2100, with the higher end only being feasible if outlet glacier flow was set to the highest conceivable levels.

I feel I should point out that in 'In Defence of Milankovitch' Roe finds that the rate of change of ice sheet extent during the glacials/interglacials varied in lockstep with insolation. Although that doesn't tell us anything about rates this century.

Steve Bloom

Chris, Pfeffer et al. threw in some pretty big caveats, plus I'm not sure how well it holds up to recent data, including the Zachariae speed-up and the newly-discovered deep trench. It's also not clear to me they took into account the ice-elevation feedback, although maybe they didn't need to since they were only doing the 21st century.

Longer-term, when open water encroaches into the interior, kinematic constraints may cease to mean much.

Re the land ice sheets, there wasn't any water to carry off the calved ice, unlike with marine-based ones then and now.

Also, does anyone yet have a good handle on the upper limit to meltwater runoff?

Jai Mitchell

Bamber, J.L., Riva, R.E.M., Vermeersen, B.L.A., and Le Brocq, A.M., 2009. Reassessment of the potential sea-level rise from a collapse of the West Antarctic Ice Sheet. Science, 2009. 324(5929): p. 901-903.

http://stuff.mit.edu/~heimbach/papers_glaciology/science_bamber_etal_2009_wais_sealevel.pdf

Theory has suggested that the West Antarctic Ice Sheet may be inherently unstable. Recent observations lend weight to this hypothesis. We reassess the potential contribution to eustatic and regional sea level from a rapid collapse of the ice sheet and find that previous assessments have substantially overestimated its likely primary contribution. We obtain a value for the global, eustatic sea-level rise contribution of about 3.3 meters, with important regional variations.

Richard F. Katz and M. Grae Worster, Stability of ice-sheet grounding lines, Proc. R. Soc. A 2010 466, doi: 10.1098/rspa.2009.0434

http://rspa.royalsocietypublishing.org/content/early/2010/01/13/rspa.2009.0434.full.pdf+html

Finally, our results suggest that, in contrast to earlier assessments (e.g. Van der Veen 1985; Vaughan & Spouge 2002), the scenario of unstable grounding-line recession on retrograde beds in West Antarctica is likely. Indeed,in the case of the Pine Island glacier, it may be presently occurring.

Colorado Bob

Hell of a discussion here nice work everyone.
Here's some spanners in the works :

Deep ocean current may slow due to climate change

A new study by the University of Pennsylvania's Irina Marinov and Raffaele Bernardello and colleagues from McGill University has found that recent climate change may be acting to slow down one of these conveyer belts, with potentially serious consequences for the future of the planet's climate.

"Our observations are showing us that there is less formation of these deep waters near Antarctica," Marinov said. "This is worrisome because, if this is the case, we're likely going to see less uptake of human produced, or anthropogenic, heat and carbon dioxide by the ocean, making this a positive feedback loop for climate change."


Read more at: http://phys.org/news/2014-03-deep-ocean-current-due-climate.html#jCp

Permafrost thaw exacerbates climate change

The climate is warming in the arctic at twice the rate of the rest of the globe creating a longer growing season and increased plant growth, which captures atmospheric carbon, and thawing permafrost, which releases carbon into the atmosphere. Woods Hole Research Center (WHRC) Assistant Scientist Sue Natali and colleagues engineered first-of-a-kind warming experiments in the field to determine net gains or losses in carbon emissions. The study entitled "Permafrost degradation stimulates carbon loss from experimentally warmed tundra," published in the journal Ecology found that growing season gains do not offset carbon emissions from permafrost thaw.

According to Dr. Natali, "Our results show that while permafrost degradation increased carbon uptake during the growing season, in line with decadal trends of 'greening' tundra, warming and permafrost thaw also enhanced winter respiration, which doubled annual carbon losses."
http://phys.org/news/2014-03-permafrost-exacerbates-climate.html#jCp

Colorado Bob

A Siberian Heat Wave is Breaking Kara Sea Ice In March, So is it Time to Start Thinking about Hot Arctic Rivers?

Ask any resident of this, typically frigid, coastal town and they’ll tell you that today it’s abnormally warm, even hot for this far-north locale. For the average high for this day in Dickson is about 1 degrees Fahrenheit. Typical daily highs of 29 degrees (F) don’t normally appear in Dickson until mid-to-late June.

So, in essence, summertime has arrived in Dickson in March and there we see temperatures that are a shocking 28 degrees Fahrenheit above average. Human caused climate change at its most brazen. But we haven’t seen a thing yet…

As we can see in the map below, Dickson is but one location sitting beneath a vast and spreading Siberian and Arctic heatwave:

http://robertscribbler.wordpress.com/2014/03/20/a-siberian-heat-wave-is-breaking-kara-sea-ice-in-march-so-is-it-time-to-start-thinking-about-warm-arctic-rivers/#comment-10424

Al Rodger

Chris Reynolds,
I think the discrepancy between our two figures is you have managed to use 1 hour days. 67 ZJ x 24 = 1608 ZJ ≈ 1,600 ZJ (Note a comma is used not a decimal point. Sorry for the confusion caused.)
Perhaps to add reason for why I see a 3m 2100 SLR is "exceedingly pessimistic", it is worth pointing to Vallis & Farneti (2009) who show a figure for the meridional heat transfer into the two polar regions of 2 x 1.5 PW or ~100 ZJ pa. This represents about 3% of the planet's 3,850 ZJ solar heating being sucked towards the poles because they are comparatively so cold. My exceedingly pessimistic" SLR would require 20% of the additional warming to be sucked towards the far smaller Greenland & Antarctic ice sheets due to a far smaller temperature differential.

Chris Reynolds

That's the problem of posting when tired, thanks Al.

Jim Hunt

For anyone who has yet to become embroiled in the "Recursive Fury" controversy, here's a personal view from Soggy South West England:

http://GreatWhiteCon.info/2014/03/recursive-fury-from-david-rose/

"Contrarians bully journal into retracting a climate psychology paper. After threats of frivolous libel and defamation lawsuits, a journal will retract an academically sound paper"

Fufufunknknk

Hi Chris, thanks for the response. I'll go read the article you suggested.

Living in a mountainous area, my experience with snow and ice melt is intuitive: sunlight melts ice but the main factors are weather conditions. A rain, even a cold rain, causes much more melt than sun. Likewise a warm wind can remove cm's per hour while sunlight on a cold day has almost no effect. Sunlight's greatest effect is where there is a dark colored wick to absorb and re-radiate/transport the solar heat.

Because of this, I assumed that on a cold summer day in the high altitudes, the ice would remain relatively constant. I wonder how constant the temperatures are over the surface of the ice: if micro-climates don't play a large role in melting the ice at high altitudes.

Hubert Bułgajewski

So, it started
http://arcticicesea.blogspot.com/2014/03/arctic-news-po-wschodzie-sonca.html

Jim Hunt

Hubert - Jim Pettit also has a pot of crow stew simmering on the back burner over on the forum!

http://forum.arctic-sea-ice.net/index.php/topic,778.msg22649.html#msg22649

Jai Mitchell

Jim,

one should never use the term "contrarian" when discussing those who oppose basic science, often for personal profit, at the expense of hundreds of millions of human beings.

I would prefer to use the term "sociopathic amoralists" to the term "contrarian", or at the very least, "self-serving greedy pondscum who should be relegated to an isolated island in the Maldives until their falsified statements are proven wrong in a very personal way".

VaughnA

Thank you Jai, although those are somewhat kinder words than I have for them!

Chris Reynolds

Fufuf,

All good points, but search for "BSRN station on Greenland" on this page and you'll see a link to a page with incoming and reflected sunlight at Greenland summit graphed.

The difference between them (absorbed) is very small, but multiplied over the whole of Greenland the clear skies of the GBI do cause a substantial amount of sunlight to be absorbed, resulting in large changes in run off.

Hansen has been concerned (rightly) that as the climate around Greenland warms the risk of rain (not snow) could cause a massive increase in run off. watch for that when the Arctic transitions to seasonally sea ice free. watch for increases in melt on the northern flank as well!

I do agree that the WAIS and Greenland combined could well cause more then 2m of SLR in the rest of the century. My disagreement is with those claiming just Greenland could cause that.

Jai Mitchell

My disagreement is with those claiming just Greenland could cause that

while unlikely, you are certainly not taking into consideration the possibility of a 50Gt methane hydrate release from the arctic between 2065 and 2075.

David Archer's model is telling:

http://climatemodels.uchicago.edu/slugulator/

In it he shows that a 10 year emission of 50GT of methane (38.25 Gt of carbon in the form of methane) Would raise globally averaged temperatures by 2.8C within 10 years.
This would raise Greenland temperatures by between 6 and 8C, on top of whatever warming we will already incur from anthropogenic emissions. Combine that with the increased warming due to albedo loss and midlatitude precipitable water migration during the summer and we are looking at the potential for Greenland surface temperatures in 2080 to be between 14C and 20C warmer than today.

(6-8C due to CH4 emission)
(6-9C due to anthropogenic warming)
2-3C summer warming due to albedo change and hydrology shifts)

compare with current melt rates

Jim Hunt

Jai/Vaughn - That bit was a quote from Dana Nuccitelli in the Guardian, possibly wary of all the libel suits allegedly flying around?!

Here's another quote, this time from Stephan Lewandowsky's video.

"The bottom’s falling out of the Arctic, so we have a serious problem. We have a problem with the planet, but we also have a problem with the fact that in my opinion the public’s right to be informed accurately is being violated through the injection of disinformation at a time when the clock is ticking and the planet is accumulating energy"

As Bob Ward of the Grantham Institute put it last summer:

"The UK public is being hoaxed by the Mail, Telegraph and Express newspapers over climate change. It is a national scandal."

Beyond that I couldn't possibly comment!

Boa05att

High predictability of the winter Euro–Atlantic climate from cryospheric variability

Seasonal prediction skill for surface winter climate in the Euro–Atlantic sector has been limited so far1, 2, 3. In particular, the predictability of the winter North Atlantic Oscillation, the mode that largely dominates regional atmospheric and climate variability, remains a hurdle for present dynamical prediction systems4, 5. Statistical forecasts have also been largely elusive6, 7, 8, but October Eurasian snow cover has been shown to be a robust source of regional predictability9, 10. Here we use maximum covariance analysis to show that Arctic sea-ice variability represents another good predictor of the winter Euro–Atlantic climate at lead times of as much as three months. Cross-validated hindcasts of the winter North Atlantic Oscillation index using September sea-ice anomalies yield a correlation skill of 0.59 for the period 1979/1980–2012/2013, suggesting that 35% of its variance could be predicted three months in advance. This skill can be further enhanced, at the expense of a shorter lead time, by using October Eurasian snow cover as an additional predictor. Skilful predictions of winter European surface air temperature and precipitation are also obtained with September sea ice as the only predictor. We conclude that it is important to incorporate Arctic sea-ice variability in seasonal prediction systems.


http://www.nature.com/ngeo/journal/vaop/ncurrent/abs/ngeo2118.html

MattOClimateW

Here's a way to get heat into the Greenland ice sheet: cryo-hydrologic warming

http://onlinelibrary.wiley.com/doi/10.1002/jgrf.20079/abstract

folke_kelm

Regarding to my questions sme days ago i will thank you for your answers. AlRodger, Dahl-Jensen is really good, i have not reaaly been aware of it before.
Nevertheless, the link from MattOClimateW is exactly what i was looking for. You must not warm the ice sheet to melt it, the point is, that you can tranfer heat to the inner ice sheet due to refreezing liquid water in the depth of the ice sheet, and this is much energy. the warmer the ice is, the less restistent it is to mechanical stress, and this is the point of concern for GIS and WAIS.
It is not surface melting, ablation which is responsible for the majority of mass loss, it is glacier discharge and that will grow with warmer core temperatures and resulting much less viscosity of the ice.

Steve Bloom

Thanks, Matt. See also this new citing paper. Just based on the abstracts, the idea that meltwater will drain through and out before it can do a lot of damage seems to be in some doubt.

Chris, re the possibility of major GIS melt this century, probably you're correct to be conservative, but I would point to a) the revolution in our understanding of ice sheet behavior relative to the "big ice cube" conceptualization that was still prevalent as recently as 10 years ago, b) related to that, the steady stream of nasty surprises like the Zachariae glacier acceleration, c) the fact that the (accelerating) forcing we're placing on the ice sheets has no accessible historical analog, and d) the further fact, based on Pliocene research, that present CO2 levels will raise sea levels ~ 25 meters once equilibrium is reached. The combination makes me nervous.

Chris Reynolds

Jai,

I'm very sceptical of the claims made in Shakhova's EGU presentation that:

"...we consider release of up to 50 Gt of predicted amount of hydrate storage as highly possible for abrupt release at any time. That may cause ~12-times increase of modern atmospheric methane burden with consequent catastrophic greenhouse warming."

My reasons boil down to:

I am not convinced that the reasoning that leads to the 50Gt is sound.

Pockmarks caused by eruptions indicate sporadic largescale releases, but not as big as 50Gt. The pockmarks are limited in extent - suggesting the process does not continue across a given region. Similarly with slides of sediment.

There were no large methane emissions during periods such as the holocene climatic optimum, or during the Eemian or Holsteinian warm periods (when the Greenland was substantially reduced).

For what it's worth I agree with David Archer that methane emissions from the continental shelves are likely to be chronic, not catastrophic.

Steve Bloom

"There were no large methane emissions during periods such as the holocene climatic optimum, or during the Eemian or Holsteinian warm periods (when the Greenland was substantially reduced)."

Yes, but there's a difference between orbital forcing and GHG forcing in terms of warming Arctic subsurface currents. Enough to matter?

Jai Mitchell

Chris,

We know that the potential for methane release began with the inundation of the ESAS floodplain during the older dryas. That began the thaw of subsea permafrost.

We can assume that this also occurred during MIS-11 ~400kyr ago.

lake El'Gygygtgyn boreholes show that temperatures regionally were about 8 degrees above pre-industrial. or about 6 degrees above today.

https://www.youtube.com/watch?v=YxbOSB7zDgY&t=10m45s

we know that this was driven by summer insolation and not by greenhouse gasses so the winter temperatures were much cooler than today.

this then provides a significant modulation to the warming trend in the MIS-11 interglacial. We will likely surpass MIS-11 arctic warming rates within the next 60 years.

therefore we are much more likely to experience a sudden release than we would have experienced had the region warmed slowly over several thousand of years.

I do not find the comparison to today absolutely credible.

Jai Mitchell

. . .sorry inundation at 10Kyr bp, end of younger dryas. . .

NeilBlanchard

So, it appears that we have just seen the peak area of Arctic ice.

http://nsidc.org/data/seaice_index/images/daily_images/N_stddev_timeseries.png

And rather late, too.

Tony

I just looked at today's (actually, 23rd March) graphs for SIE and SIA. SIE is heading down but SIA took a big jump down, the lowest for at least the last 7 years. From the same site as the sea ice area graph, SIE also took a sharp drop. Not sure why the two sites are different for SIE, unless it's just a time thing and the former will catch up tomorrow.

Is there any news on the situation up there?

Jim Hunt

Tony - There is much discussion along these lines over on the ASIB's companion forum:

The 2014 Melting Season

We haven't mentioned NORSEX yet, but we will now!

D_C_S

This is mostly recreational, but the graph by Chris Reynolds at the link below gave me the idea of looking for a relationship of September arctic sea ice volume and extent combined on one axis vs time on the other axis.

http://dosbat.blogspot.co.uk/2014/03/what-caused-volume-loss-in-piomas.html

First I did a hyperbolic fit to each of volume vs time and extent vs time, forcing a horizontal asymptote to the left in each case. The positions of these horizontal asymptotes were about 16.742 and 7.664 respectively (using the same units that Chris used). The intersections of these fits with 0 volume or extent were at years 2018.21 and 2036.25 respectively (a whole number year represents September of that year).

I looked for a relationship of the form Extent = c Volume^p as Chris did. Instead of using x = volume, I used x = volume^p to get a linear fit between x and y. Since extending the asymptotes of each of the volume vs time and extent vs time fits back to eternity under constant conditions should result in infinitely many points near each of the respective asymptotes, I included infinitely many copies of the point at about (16.742^p, 7.664), in addition to the other points for years 1979 through 2013. This way a linear fit would be forced to go through this point, and I also forced it to go through the point (0,0) since volume and extent would be zero together. The slope of the line that goes through these two points is about 7.664 / 16.72^p. Then I divided the y-coordinates of every point by this slope (this is equivalent to changing the linear unit from km to some nonstandard length unit, whose length isn't important) to get a new set of points, for a reason that I will explain shortly. This gives a line with a slope of 1, and the equation y = x, because the line now goes through (0,0) and about (16.742^p,16.742^p). Next I found the value of p that minimized the sum of the squares of the perpendicular distances of each of the new points to the line y = x. This resulted in a p-value of about 0.3960 (close to Chris's p-value of 0.4275). After projecting each of the new points (corresponding to each of the years 1979 - 2013) onto the line y = x, I calculated the distance of each of these projections from (0,0). These distances then became the y-coordinates of another set of points with x-coordinates being the corresponding years (1979 - 2013). I also calculated the distance of the point about (16.742^p,16.742^p) from (0,0) which would become a horizontal asymptote to the left of a hyperbolic fit to this last set of points. When calculating each of these distances, if one coordinate of a point is much larger than the other coordinate of that point, then the larger coordinate dominates in this distance, which is why I divided the y-coordinates of each of the original (volume^p, extent) points by the slope, making the y-coordinate of any given point about the same magnitude as its x-coordinate. I found the best hyperbolic fit to this last set of points, with a horizontal asymptote as already noted. I expected the 0-distance intercept year to be about halfway between the 0-volume intercept year of the original volume vs time fit (2018.21) and the 0-extent intercept year of the original extent vs time fit (2036.25), but it turned out that this intercept was at about year 2033.79, so much closer to the 0-extent intercept year (it would have been even closer to the 0-extent intercept year if I hadn't divided each of the original y-coordinates by the original slope).

I don't know whether or not this is significant, but I thought that this unexpected result was interesting enough to post. In reality, volume should be more significant than extent in projecting a September with no arctic sea ice, at least near the end.

econnexus

Apologies for any duplication. I'm trying to evade the spam filter by arriving via OpenID instead of Facebook.

Tony - The question you pose about NORSEX area is currently being discussed over on the Arctic Sea Ice Forum:

The 2014 Melting Season

The preliminary consensus is a glitch in the underlying SSMI data.

Jim

Jim Hunt

Slightly off topic, but in the absence of an "open" thread and to test my shiny new OpenID, here's the:

US Navy's 2014 to 2030 Arctic Roadmap

"Reduction of Arctic Ocean sea ice is expected to continue, and major waterways will become increasingly open. By 2020, the Bering Strait is expected to see open water conditions up to 160 days per year, with 35-45 days of shoulder season. The Northern Sea Route will experience up to 30 days of open water conditions, with up to 45 days of shoulder season conditions."

Shared Humanity

NeilBlanchard

So, it appears that we have just seen the peak area of Arctic ice.

And rather late, too.

That late peak in SIE sure is disturbing but I am even more concerned by the late peak in SIA.

http://arctic.atmos.uiuc.edu/cryosphere/IMAGES/seaice.recent.arctic.png

Both, combined, would suggest their is some fairly fragile ice that could melt out rapidly. The ice just hasn't had enough time to strengthen.

D_C_S

"The slope of the line that goes through these two points is about 7.664 / 16.72^p."

should read

"The slope of the line that goes through these two points is about 7.664 / 16.742^p."

folke_kelm

S.H.
"Both, combined, would suggest their is some fairly fragile ice that could melt out rapidly. The ice just hasn't had enough time to strengthen."

As we say in Sweden, it is un-ice (ois)
you should not walk on it

wayne

With Maxima behind, the quick gain of ice extent last week should disappear at the same rate formed. I am also quite impressed with further a link between ENSO and Arctic cloud coverage. We remember a short lived LaNina after a brief surge towards El-Nino at end of January. Well its been remarkably cloudy and not cloudy in the same sequence in the NorthAmerican sector of the Arctic, which prompted the return of the Arctic Ocean Gyre driven by strong anticyclones. Our world is smaller meteorological wise than I once believed.
Finally remnants of winter only lingers in Central to Eastern North America, while the rest of the Northern Hemisphere basks in warmer temperatures. This is an example of what might have happened during the medieval warming period, suggesting that a warm North Pacific and Atlantic may have played a role.

Chris Reynolds

Jai,

You said:
"...we know that this was driven by summer insolation and not by greenhouse gasses so the winter temperatures were much cooler than today."

I don't think this is necessarily the case.

Most of the current Arctic Amplification is due to sea ice loss. Rather than refer to the Screen 2010 paper on this subject I'll refer to Serreze et al 2009, "The emergence of surface-based Arctic amplification". The authors find:

"To summarize: 1) Starting in the late 1990s and relative to the 1979–2007 time period, Arctic Ocean SAT anomalies in the NCEP reanalysis turned positive in autumn and have subsequently grown; 2) Consistent with an anomalous surface heating source, development of the autumn warming pattern aligns with the observed reduction in September sea ice extent, and temperature anomalies strengthen from the lower troposphere to the surface; 3) Recent autumn warming is stronger in the Arctic than in lower latitudes; 4) Recent low level warming over the Arctic Ocean is less pronounced in winter when most open water areas have refrozen; 5) There is no enhanced surface warming in summer; 6) Conclusions 1–5 hold for both the NCEP and JRA-25 reanalyses, the major difference being that temperature anomalies in JRA-25 are somewhat smaller."

It is reasonable to expect that for the Holocene climatic optimum and Holsteinian and Eemian that the same process was at work. It is very fundamental - open water during the summer stores an immmense amount of solar heat which is then vented to the atmosphere over autumn as the ice forms, and the resultant thinner ice also vents heat to the atmosphere over winter (NCEP/NCAR shows low level warming over the ice in recent winters). This is the cause of the marjority of warming.

However at mid latitiudes winter insolation would probably have been reduced due to the precessional cycle driving the summer increase in insolation. So there may have been less warm influx from mid latitudes. Siberia may have been colder in winter than in recent years.

As I discussed in this blog post:
http://dosbat.blogspot.co.uk/2012/12/lake-elgygytgyn-and-arctic-warming.html

We seem to be about at the lower limit of the Holocene Climatic Optimimum temperatures (about 1 to 2 degC warmer than 'at present' - the difficulty is when do Melles et al refer to as present, 1951 to 1980 or preindustrial?). However they also find Arctic super-interglacials which were 4 to 5 degC warmer than 'at present' - temperatures are for July. My point is that those temperatures were applied for centuries (possibly a millenia or two) and there was no methane blow out.

DCS,
You're striding so far ahead it's hard for me to keep up! I'll re-read what you say later in the week when I'm a bit fresher in mind.

Steve Bloom

Chris, in terms of potential clathrate melt the temperature of the surface and atmosphere seems to me to be a distraction. Other than, potentially, some of the very shallowest deposits, the risk of a major release is consequent to encroaching warming currents at depth, e.g. what we are seeing with the increasing Agulhas leakage (origin in the Indian Ocean tropics).

So a question we should want the answer to is whether this leakage happened to a similar extent during times when the Arctic was also being warmed. If so, great, probably no problem. But my understanding is probably not since GHGs do a much better job than orbital forcing of warming the tropics and poles at the same time.

Tony

Thanks, Jim. It looks like the decline on NORSEX SSM/I has become more "normal" now. The recent part of the graph shows a dotted "unfiltered" data line and a rogue data point there can change the apparent picture.

Steve Bloom

Jim Hunt, it wasn't clear to me whether you were serious about attending EGU 2014 when I raised the question before, so please clarify. If so I'll make some itinerary suggestions relating to this blog's main points of interest.

Neven
If so I'll make some itinerary suggestions relating to this blog's main points of interest.

Don't rub it in, please. :-)

Steve Bloom

In which I fail to get the joke.

Neven

Sorry, I thought you were implying I should go to EGU.

econnexus

Steve - I'm still masquerading as one of my many alter egos in order to avoid TypePad's over zealous spam filter.

My remark about EGU 2014 was at least semi-serious, and to point out that "reporting for the Arctic Sea Ice Forum" got me into something vaguely similar in the past in case anyone else fancied trying that angle.

However I'm afraid I haven't pursued that line of enquiry further, not least because I have a much delayed appointment at the local eye hospital on April 28th. It currently looks as though if I did go to Vienna I wouldn't be able to see much!

Jim

econnexus

P.S. In somewhat similar vein it has just come to my attention that there will be live webcasts from next week's 2014 Sea Ice Prediction Workshop in Boulder!

Neven
there will be live webcasts from next week's 2014 Sea Ice Prediction Workshop in Boulder!

I've been asked to hold a small talk (via phone) about the ASIB.

Hubert Bułgajewski

Two animations (on my blog) show where the recently melted.: http://arcticicesea.blogspot.com/2014/03/szybkie-topnienie-po-dugim-zamarzaniu.html

econnexus

I've been asked to hold a small talk (via phone) about the ASIB.

Which sounds like a topic worthy of discussion on the ASIF!

Jai Mitchell

Chris,

according to Julia Brigham-Grette's presentation here temperatures were significantly warmer but summer insolation was 520 Watts per meter squared in the summer, compared to todays 480 Watts per meter squared.

while the temperatures were much warmer, for longer, it took many thousands of years to raise the sea floor temperatures, compared to todays double dip where we get to warm to interglacial levels and then boost arctic temperatures another 6- (14??) degrees C above Holocene optimum in the space of 150 years.

I hypothesize that this is a potential clathrate release mechanism that is not analogous to any previous interglacial.

Jai Mitchell

chris, sorry I should have read your link first, wish there was an edit feature!

in your link you said

But we have two substantially different base processes driving now and the changes in the ice ages. During the HTM the driver was increased insolation, as far as I'm aware this was mainly due to the precessional cycle (tilt of the Earth). So while this delivered 40W/m^2 in July at 65degN, it would also have implied substantially reduced insolation in winter, whereas now the forcing from CO2, its resultant global warming and the warming of extra-Arctic atmospheric heat flux, operates year round. This is especially important in winter, when the Arctic is in darkness and infrared emission is the key player in heat loss, especially in view of the importance of infra-red emission for sea ice thickening. These considerations may explain why a 40W/m^2 forcing produced similar effects that a forcing of under 2W/m^2 is producing now, e.g here.

However crucially, the temperatures and sea ice conditions I have referred to in this article were applied to a greater or lesser degree for millennia. It's hard to see how out of all the past warmings there were not conditions similar to now with regards the inundation of the East Siberian Shelf. And yet we did not see a catastrophic methane blow out.

The point is that the likely thawing during a normal interglacial in the circumstances you describe above (warmer summer colder winter) are more likely to allow a slow release of methane from clathrates that will not result in a detectable pulse signal in the paleo record. The clathrates likely did release, just on a timescale that is 1/1000th the rate. This is especially true if one considers the potential for talik formation and hydrological coring of methane deposits in a massive release scenario.

Cross sectional temperature profiles under arctic lakebeds is a good analog to the rate of warming in a normal interglacial. see: http://www.pet.hw.ac.uk/icgh7/papers/icgh2011Final00684.pdf image 15a (center of lake temp profile)

you can see that the difference in 300meter depth warming from 3kyr to present is much greater than previous rates. This indicates that it takes (normally) tens of thousands of years to warm at significant depth profiles a 4C ocean bottom temps. So during a normal interglacial those clathrates would never have time to thaw. But today they likely will, since they have already been held at Holocene temps for 10,000 years and now are looking to receive an additional heating boost.

Chris Reynolds

Jai, Steve,

I did point out the major difference between orbital forcing and AGW forcing in my reply above - orbital (precessional) implies reduced winter insolation that counters the summer increase in insolation.

Keeping the subject to the ESS, I don't disagree that we are about to invoke massive emissions of carbon from land permafrost, but due to thermal interia considerations land warming will proceed faster than sea floor. The arctic ocean forms a cap of insulating ice during the winter, and growth is all the more vigorous the colder the overlying atmosphere is. So sea temperatures are kept relatively high during the winter, and by no means is all heat gain from increased melt and insolation in summer lost. Integrate this process for thousands of years (Melles et al MIS11 superinterglacial was about 20k years long) and I still maintain that whatever inundated permafrost in the ESS that had been substantially below freezing prior to inundation would have ample time to get to zero degrees C. Having in at least one instance 20,000 years to do so. As this warming occurs the methane stability zone between geothermal heat below, and warming from above would progressively reduce. Yet in all this time there was not a methane blow out, with catastrophic GW and a run away into a hypthermal state.

Once again, I am not saying there will not be massive emissions from the ESS, I am saying I am very sceptical of claims of imminent catatrophic release causing massive (further) GW this century. I agree with Archer that it will be a chronic process, large emissions keeping raditive forcing up for centuries, possibly millenia.

As I see it the real problem begins as continental shelves around the world start to release their methane stocks. That is highly improbable this century, and as it happens what will be seen is a gradual increase in atmospheric CH4. Within that gradual climb will be pulses as 'pockmarks' are formed by localised destabilisation and eruptions of methane. It is verging on the inherently improbable that simultaneous destabilisation globally would happen within a century. During the End Permian it took something of the order of 10,000 years.

D_C_S

Chris:

Never mind about the fit to those points reaching zero being closer to where that extent fit reached zero than to where that volume fit reached zero. Something much more significant to do with our power curve fits of extent vs volume has since occurred to me, which I plan to post about when I have more time.

Jai Mitchell

Chris,

Do you have any indication that this gradual increase scenario might have occurred during MIS-11 at ~400ky bp?

The temperature profiles are much higher than the milankovitch forcing would produce. As far as I can find this is still a mystery but that the previous glacial maximum was so warm that it was barely glacial for 40,000 years.

Perhaps we did get that methane release, only on a slower time scale back then.

With all due respect, and I do! I don't think that you can possibly rule out the potential for a massive release subsequent to a 14C temperature rise in the arctic (especially during the winter months!) within the space of 15 decades, ESPECIALLY when this pulse follows a 10 Kyr interglacial. It is good to be skeptical but to say that it is even remote is a bit foolhardy if you ask me (not that you are ;-)

idunno

I think that there is another factor to consider, besides the temp increase: lack of pressure increase due to the lag in sea level rise.

Past temp increases were slower, so they will have been accompanied by a corresponding sea level rise. If temperature rises say, 2C over 1,000 years, this might cause, say, a sea level rise of 10metres over those 1,000 years.

Under current AGW, temps are skyrocketing, but sea level rise will take much longer.

So under palaeo conditions, you get a 2C increase, but at 40m depth in ESAS, its now 50m deep. Pressure increases from 5 bar to 6 bar. This 20% increase in pressure would have helped with clathrate stability.

In the current rapid change scenario, it won't help. There is no way that sealevel is going to rise sufficiently to mitigate rising temperatures.

Twemoran

idunno
The lag in sea level rise is something I'd not considered & I think it's possibly a game changer.
Is anyone aware of the age of the undersea permafrost that we're worrying about? If it resulted from groundcover laid down during the most recent ice age then past interglacials and their CH4 releases may not be good proxies for what we're facing.
The floor of Hudson Bay has large pingo features that postdate the breakup of the Laurentide ice sheet. With the seasonal loss of ice over the ESAS why would we not expect massive CH4 releases as the bottom water warms without the additional pressure that thawing ice sheets will eventually provide?
The ocean temperatures off the MacKenzie Delta have been extreme in recent years. This is an area that also seems ripe for catastrophic blowouts.
Terry

jdallen_wa

Twemoran, I dunno - it should theoretically be predictable, looking at three factors - pressure, temperature and available sensible heat. The pressure/temperature gradient could be mapped as a three dimensional surface in the water. As clathrate dissociation would be endothermic, there would need to be sufficient energy available to supply that. I'm not sure of the specific limits, but theoretically, we ought to be able to map out what conditions need to exist at a given sea bottom location for methane release to start.

Chris Reynolds

Jai,

I might be foolish on this issue, and I accept I could be wrong.

As far as I am aware there is no data on sediment temperatures during MIS11. The only attainable option would be modelling.

In doing some digging amongst the papers I have I find that temperature of the upper ESS sediment is already at just below zero. See Shakhova 2013, figure 3:
http://www.see.ed.ac.uk/~shs/Methane/Shakhova%202013.pdf
If we take the black trace as indicative of temperatures before the inundation at the start of the holocene, and the red as conditions now. It seems the warming has already happened, in under 10,000 years.

However Romanovskii 2004 shows (fig 3) that the relic permafrost underlying Shakohva et al's bore hole is much deeper.
http://lin.irk.ru/pdf/6679.pdf
That also indicates that their model gives a decline in the depth of the zero isotherm during MIS11. As I understand it, it is the fate of the relic permafrost that determines the possibility of a massive methane release (on short time scales).

I am a bit rusty on methane, I've not read much about it since writing a series of blog posts on the subject. So I may be missing something or mis-remembering the papers I've just cited.

With regards whether there was a methane emission during the MIS11: We can look to Greenland ice core records, I've only managed to find this dataset:
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/greenland/summit/gisp2/gases/gispch4.txt

That only goes back to 110k years ago. MIS11 was 420k to 370k years ago. However Vostok goes back much further, and shows no methane pulse during MIS11 that exceeded present day concentrations.
http://www.giss.nasa.gov/research/features/200409_methane/core1.gif

idunno,

That may be a factor. But the relic permafrost is very deep.

Jai Mitchell

Shakhova says that the current concentration of methane in the arctic is the highest measured in 400kyr

This indicates that the methane release during MIS-11 was comparable to current anthropogenic releases. Not sure if it was much more, but it lends more credence to the possibility of a long-slow release of subsea methane during that period (as opposed to the potential sudden release caused by anthropogenic warming pulse of 14C above current temperatures.

https://www.youtube.com/watch?v=eD8hU-lbqpE&t=2m13s

Shakhova also responded to Gavin Schmidt's critique by saying that their survey revealed a subsea permafrost semiliquid layer at temperature profiles below -2C.

She says that this has been changing very rapidly in the decade that they have spent up there (I bet!!!)

Remember, the 60GT emission scenario was supposed to occur over a decade.

Jai Mitchell

From over on the forum

In some oceanographic sections, a number of plumes over 100 m in diameter were joined into a multirooted enormous plume over 1000 m in diameter (Fig. 2), which exceeds greatly the dimensions of plumes registered formerly in the Sea of Okhotsk and in other areas of the World
Ocean where the typical plume diameter usually varied from a few meters to tens of meters. The integrated hydroacoustic and geophysical surveys permitted us to identify the plume roots going deep into the 15 to 20m layer of the ESS sediments, which are enriched in organic matter

D_C_S

Chris:

Very briefly, treating September arctic sea ice volume (V), extent (E), and average thickness over that extent (T) as continuous variables instead of discrete variables, and using V = E T and beginner calculus, we have

dV/dt = E dT/dt + T dE/dt

I was thinking of using the fact that if E, T, and V were all approaching 0, reaching 0 simultaneously, then dV/dt would have to approach 0 as V approaches 0, and therefore slow, unless dT/dt and / or dE/dt were to approach negative infinity as T and E approach 0.

However, my approach appears to be more problematic and less useful than I had expected, so I probably won't pursue it more, at least not for now.

I also used the power relation that you found between E & V, which was roughly E ~ V^(3/7), and the one that I found, which was roughly E ~ V^(2/5) (using "~" to mean "is proportional to" or "is a positive constant times"), together with V = E T to write each of V & E in terms of T. This came out to be

E ~ T^(3/4) and V ~ T^(7/4)

using E ~ V^(3/7), and

E ~ T^(2/3) and V ~ T^(5/3)

using E ~ V^(2/5).

Again, this was more problematic and less useful than I had expected, as I wasn't able to constrain DT/dt as well as I had hoped.

I'll probably go back to doing some pure math for a while.

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