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Bill Fothergill

"Perhaps, the development of intelligent life is not a desired evolutionary trait."

One is reminded of Monty Python's "Galaxy Song" - especially the final line.




Lord Soth

I would remind that Trump has been a rabid anti-AGW denier, perhaps got infected by the habit which spread elsewhere.

Need I say more??? 2011 when HAL went murderous mad in 2001
when given the right to lie.

Was your latent heat of fusion for sea ice taken from a standard Including salt content? I am not sure if there is a commonly used Latent Heat number used out there.. I suggest 5%, which would give
286 kJ/kg


Wipneus already has the new numbers. It looks like those who said that the exponential volume trend line from 2012 was highly irregular and should therefore be disregarded were wrong... PIOMAS volume is now below that old trend line again.

Bill Fothergill

@ Wayne

Sorry, I think I was being lazy earlier, and probably just quoted a Latent Heat of Fusion value of ~334 or ~335 kJ/kg. That, as I'm sure you know, is the value for pure water, but the value for sea water is a bit lower than that. I don't know of a "standard" value for this property of sea water, but that certainly doesn't mean there isn't one.

The United Nations link below quotes a value of between 77 and 80 kcal/kg for the LHF of sea water. (With 80 kcal/kg being the LHF for pure water.) The conversion factor is 4.184, so that gives a range of between 322 to 335 kJ/kg.


I'm not sure how you arrived at the 286 kJ/kg figure which you offered, but that's considerably lower than even the bottom end of that range.

There's a load of pretty heavy-going literature surrounding this topic, and, by way of example, you might want to have a quick decko at either of these two...



Alternatively, there's many far more knowledgeable people than me on this blog, and one (or more) of them might provide you with a better answer.


Hi Bill


I'll take it may be 2%, is a question of knowing about it for first year 1.5 to 2 meter ice.


Bt the way Bill

That U.N. Table is spot on thanks..

I'll take 78.5 Kcal/kg


not UN fisheries and agriculture department....

Rob Dekker

you guys have me seriously confused :

Bill said to wayne :

I'm not sure how you arrived at the 286 kJ/kg figure

wayne said (in this post) :

Sea ice latent heat of fusion = 3.37e17 j/km3 US fisheries and agriculture department

Which is 337 kJ/kg.

Did wayne just change that number, Bill ?


Lord Soth,

The word 'intelligent' is just a word. Secondly, I am hoping Trump is going to backflip on Climate Change using the levers of Government in an intervened marketplace and batting away any complaint by simply acknowledging that the first priority was to win the vote.

He only just won and he won more than anyone has ever won- so he can justify it all!

Let us also not forget that HE IDENTIFIED THE MEDIA AS FUBAR and so via this clearly identified global message- yes, globally identified message- has won his credibility to do stuff.?

I'm looking forward to backflips in conjugated language- personally speaking!

[How he can't win two terms is beyond me so of course I pray for such postives!]

Bill Fothergill

@ Rob "Did wayne just change that number, Bill ?"

No. Wayne asked me a question about this value a little earlier in the thread. [Two comments above my previous. Wayne's question date stamped March 06 18:08]

By the way Rob, since there's just been a page increment on this thread, did you notice the comment I directed to you yesterday. (It was immediately after your most recent - prior to today.)

Bill Fothergill

@ everyone

I don't know if it's my machine, but, from about halfway through AiG's comment, everything seems to be appearing in bold.

Bill Fothergill

@ Wayne

The FAO link I referenced yesterday is, as I said, a UN source. FAO is the Food and Agricultural Organisation of the United Nations.


(Everything is still displaying as bold. I tried starting this comment with the < / b > HTML tag, but to no avail.)

Bill Fothergill


When I Previewed the previous, it displayed in bold, but appeared normal when posted.

My brain hurts.


Thanks Bill,

The numbers involved are so big, one small change to any density or salinity changes the result by 1000's km3

My latest : UN middle of the road sea ice density 890 kg/m3 gives 2.92e17 j/km3, which doctor ONO Chart gives a salinity of 1% at -2 C

ASIMP with cloud albedo 80& = 15,081 km3, not bad!

Rob Dekker

Bill, yes, FDD would be a nice variable to include in the prediction method. To follow physical behavior it should be included as SQRT ( FDD ) in the formula, since FYI thinkness roughly (theoretically) relates to the square root of FDD.

The main issue is : Where do I find FDD for (many) Arctic winters past ?

Bill Fothergill


Glenn Tamblyn asked a similar question of Jim Hunt over on the Great White Con, and Jim rapidly knocked up a zip file. Perhaps that contains what you need, otherwise ask Jim directly over on the GWC. Please see...


PS You might enjoy the fun Jim and I are having over on that particular thread.

Kevin O'Neill

Rob: "Where do I find FDD for (many) Arctic winters past ?"

Rob, they can be easily calculated from any temperature dataset. I've used the DMI N80 data to produce the FDD charts that I've posted. Reanalysis can be used to generate temperature data as well and could provide coverage for more than the N80 domain.

Rob Dekker

Thanks guys, DMI North of 80 FDD numbers are worth checking out (for correlation with Sept extent).

But I realized something :
What we are really after is thickness of FYI. After all, the majority of ice that melts out each year is FYI.
So rather than assuming a super-simple model (taking the SQRT of a measure (FDD) of freezing) from an area that contains mostly MYI, why not find a much better model that produces FYI thickness : PIOMAS !

What I'm after for that experiment is the sea ice thickness from PIOMAS for the areas that are known to be FYI : The areas outside of the prior year September sea ice minimum.

So I need to go to a gridded source of PIOMAS.

Rob Dekker

For Frank : Two over-due comments :

(1) I just realized that the correlation table I presented in this post :
is the correlation of absolute sea ice 'area' in September against any of the (June) variables mentioned.
The correlation between Ice MELT between June and September and the variables mentioned (which refers to the "feedback" of the variables) is smaller. When used as a 'predictor', the standard deviation of the residuals of course remains the same : About 340 k kM^2 for the June->September prediction.

(2) Regarding Petty et al, thanks for the link ! It seems an extension to the work done by Schroder, who is also a contributor to the SIPN Arcus network. The issue I have with their method is that the standard deviation over their predictions is not much better than a simple linear extrapolation of sea ice melt. They produce 500 k km^2 standard deviation over the June->September prediction, while my (simple) statistical method sits at 340 k km^2.
Yet their predictive methods for months before June (like March and April) exceed my method.



I also read the Petty et al. paper with interest, and would like to point out the following findings, which are somewhat related to your fine work and your ideas to improve on it.

1) Petty et al. find that early spring melt onset (preferably already starting in March) in front of the mouths of great rivers such at McKenzie, Ob and Yenisei will lead to significantly lower SIE in September. This signal bears some resemblance to the early snow melt parameter in your model.

2) Petty et al. also find that low sea ice concentration in certain areas in May and June leads to less SIE in September. Taking the SIC within a limited area is somehow equivalent to your SIA parameter.

3) Finally, Petty et al. find that a high melt pond fraction in June and July in the Central Arctic also leads to less sea ice in September. The formation of melt ponds in this region may be somehow correlated with the “Freezing Power” you are looking for. It is not only the ice thickness, it is also the density, homogeneity and lack of salt in the ice as well as the lack of snow cover, which may lead to more melt ponds later in the season.

I hope that you will be able to find a simple correlation between the FDDs from October through March, melt pond fraction during the summer and the subsequent SIE in September.

Rob Dekker

Thanks P-maker,
For the moment, I'm still confused about that DMI temperature data (as a source to calculate FDDs from past years).
I'm taking with Jim about this starting here :

One thing that is revealing already is that that DMI 80N temp graph that we use here at Neven's so often :


appears to be not "area weighted". Specifically the following declaration from DMI is important :

However, since the model is gridded in a regular 0.5 degree grid, the mean temperature values are strongly biased towards the temperature in the most northern part of the Arctic! Therefore, do NOT use this measure as an actual physical mean temperature of the arctic.

Humbling thoughts...



Thank you for refreshing my memory through that link to Jim’s site.

It is exactly my point. Using the N80FDD as an indicator, which has a spatial bias towards the North Pole, should reflect the spatial pattern of significance in the Petty et al. paper (hatched areas in right hand columns labelled MP in fig 4, 5 & 6 here: http://onlinelibrary.wiley.com/doi/10.1002/2016EF000495/pdf ).

I should think that the 2002 glib discussed elsewhere, will only be a minor bump on the road. After all, we have seen a significant drop in the Winter (Oct-Mar) “Freezing Power” since the 1980’es, a time dependent parameter you will also include by using an FDD time series in your analysis.


Andrew Slater also had an FDD graph for the whole Arctic Ocean (see here and click 'about this data'). Wouldn't that be more useful?



Slater's diagrams are based on 925 hPa temperatures, which are easier to model because this level is mostly above the ground throughout the Arctic. When it comes to "Freezing Power", we need to be as near to the surface as possible due to the (normally) strong inversions during the Arctic winter.

Now - for our purpose presumably - DMI has decided to plot both the overlapping timeseries in 2002 ( http://ocean.dmi.dk/arctic/plots/meanTarchive/meanT_2002.png ) which give us a rough estimate of potential errors in the dataset.

Rob Dekker

P-maker, indeed.
Even if we work out these irregularities in the DMI data, it still does not serve as a good indicator of the ice thickness in the melting zone (70-80 deg), because the data is not area-weighted.

For example, in the DMI temperature graph (on a 0.5 deg grid) attaches 40x the significance to the temperature within 0.5 deg of the NP as compared to the significance of a similar area at the 80 deg North lateral. And since area/distance around the NP is a quadratic function, the DMI graph is for 50% determined by the temperature between 87.5-90N, which is only 25% of the area North of 80deg.

And Slater's data seems to be area-weighted, but as you correctly point out it is 925 hPa, which is too far from the surface to be indicative of ice growth during winter.

I can (and will once I have the time) still run the correlation between these data sets and the September sea ice extent, but I think it is simply is too far from the melting zone to be significant.

I have more hope for the PIOMAS ice thickness south of 80 deg, but for that I need access to gridded PIOMAS data, which requires some work (and more importantly : time, which I chronically lack).

Rob Dekker

Wait a minute. Slater also reports 2m temps :
with the following note :

The +80N T2M images on this site are similar to those shown by the Danish Meteorological Institute (DMI) except that I use the NOAA model (vs. ECMWF) and area weighting is applied.

That is encouraging. Let me dig a bit further into that data.

Also, Nico (Tealight) posts FDDs on Neven's graph page :
https://sites.google.com/site/cryospherecomputing/degree-days-freezing which suggests he uses the DMI data.

And Slater's data seems to be area-weighted, but as you correctly point out it is 925 hPa, which is too far from the surface to be indicative of ice growth during winter.

I understand, but the surface and 925 hPa aren't entirely independent from each other, are they? Isn't there some correlation, or do inversions etc totally screw that up?

The nice thing about the 925 hPa temps Slater used, is that it is Arctic Ocean-wide. Wouldn't that be better than just 80N?


Neven ,

Over the current Arctic Ocean 925 mb should represent at most times the warmest air point or the approximate location of the average inversion peak, that is a very important and smart level to study.

Rob Dekker

There probably is a correlation between 2m temps and 925 hPa temps. Slater has both temps posted.
The tricky part appears to be to retrieve these temps from CFS(v2).
It looks like we need at least a GRIB2 parser and then need to figure out exactly which files (and at which index) contain the temp data, 2m or 925 hPa :

Jim Hunt

Rob - Don't forget the reanalyses from ECMWF:


and NCEP:


Bill Fothergill

Rob said... "For example, in the DMI temperature graph (on a 0.5 deg grid) attaches 40x the significance to the temperature within 0.5 deg of the NP as compared to the significance of a similar area at the 80 deg North lateral."

I happened to already have a little spreadsheet which does areas on a 5 deg X 5 deg grid, so it was a trivial exercise to tweak this such that the step size was 0.5 deg.

Taking a mean planetary radius of 6,371 kms, the 0.5 deg triangle at the NP has an area of only ~ 13 sq kms, whereas the isosceles trapezium between 80N and 80.5N has an area of ~ 523 sq kms. Which, as Rob said, represents a x40 weighting factor.

Near the equator, things are markedly different. A 0.5 deg "square" sitting between 0N and 0.5N has an area of ~ 3,091 sq kms, whereas between 9.5N and 10N, the grid area drops to ~3,046 sq kms - a difference of just 1.5%.

The moral? Whilst getting the grid area weighting spot-on at lower latitudes is of arguably secondary importance, it's a totally different matter in the high Arctic.



Thank you for clarifying. My point was that in Rob’s original formula, he gave a lot of weight to the lower latitudes continents through his snow parameter. In addition, he has already given weight to the marginal ice zone through his ice area parameter (ice area in the central Arctic has so far had very little variability, and thus contributing very little to the signal). What is missing, in my view, is an indicator of the “Freezing Power” in the Central Arctic Ocean, which may be related to the Melt Pond factor identified by Petty et al.

All three parameters carry caveats to some extent. Eventually snow cover will move from the continents to coastal glaciers and sea ice, thus marginal sea ice area and snow parameters will respond in a similar way (go together). Marginal ice zones may eventually also be dominated by glacial rubble and brash ice, once the Arctic becomes ice free in September.

In the old days (such as 2012) melt ponds could still form in the central Arctic after a pretty normal freezing season. Nowadays - and into the future - such type of solid, impenetrable first year sea ice may become a rare incident and thus of reduced statistical significance. However, the “Freezing Power” of the central Arctic Ocean is still of value in order to estimate when we should expect to get rid of the last ice there in our lifetime.

Bill Fothergill


A few quick comments on a couple of your points...

"... Marginal ice zones may eventually also be dominated by glacial rubble and brash ice ..."

I think that one of the ship's log entries on Northabout's polar circumnavigation voyage last year mentioned something to that effect. I believe a Greenland native had told the crew that sailing in the local waters had actually become more dangerous in recent years due to the greatly increased calving.

"... melt ponds could still form ... such type of solid, impenetrable first year sea ice may become a rare incident and thus of reduced statistical significance ..."

My take is very slightly different. As the sun is still going to spend ~4 months per annum below the horizon at 80N, I think we'll still see widespread melt pond formation come the summer months. However, I think these melt ponds will be somewhat ephemeral, and that they will drain relatively quickly (days?) due to the "rotten" nature of the underlying ice.

Lower cumulative FDD values and higher sea temperatures are precisely what the doctor did NOT order.

Rob Dekker


What is missing, in my view, is an indicator of the “Freezing Power” in the Central Arctic Ocean,

Actually what is missing is an indicator of the "Freezing Power" in the marginal ice zone : the area of the Arctic that tends to melt out.
The Central Arctic is less relevant, since that's where the MYI hangs out ; the ice that does not affect the minimum "extent" in September that much.

@Bill Thanks for the additional notes on area "weighted" temperatures, versus unweighted DMI numbers.


"The Central Arctic is less relevant, since that's where the MYI hangs out"
Not exactly - https://www.climate.gov/news-features/videos/old-ice-arctic-vanishingly-rare
or -

Sometimes what appears to be a multiyear ice shelf - https://worldview.earthdata.nasa.gov/?p=arctic&l=VIIRS_SNPP_CorrectedReflectance_TrueColor(hidden),MODIS_Aqua_CorrectedReflectance_TrueColor(hidden),MODIS_Terra_CorrectedReflectance_TrueColor,Reference_Labels(hidden),Reference_Features(hidden),Coastlines&t=2017-03-15&z=3&v=355341.8684741816,-1099815.355097055,692493.8684741816,-936999.355097055

is likely a mix of small chunks & thinly frozen leads. smoothed over with snow -

Rob Dekker

Bdwo, from your first link :

The ice that survives at least one summer melt season is typically thicker and more likely to survive future summers.

My point exactly. That's the ice in the Central Arctic, which tends to survive multiple melting seasons...

Rob Dekker

Jim said :

Rob - Don't forget the reanalyses from ECMWF:
and NCEP

Yeah. Thank Jim, you just tripled the amount of work to be done to find FDDs for past winters :o)

Kevin O'Neill

Rob, when I started posting FDD graphs on the forum last fall I made note that the DMI N80 data is not a perfect proxy, but if anything it is probably conservative.


Second century [already!!] this year at
ADS-NIPR: 13,818,067-13,705,959 means minus 112.108 km2.
2017 again at record lowest level, and bottom line as last year, it is as bad as it looks like.


Century followed by a near-century: 13.705.959-13.607.502 means minus 98.457 km2. Remember, according to ADS-NIPR standards.

We aren't already in Summer, are we? Or do I have it wrong?

Jim Hunt

I think you're on the wrong thread Kris? See the March version:


Personally I reckon the "melting season" has officially started, but Summer is still a few months away!

Rascal Dog

Take the PIOMAS daily ice volume data:


Find the day 59 data from each year. (last day for 2017 file)
Find the minimum volume for a day each year.
Calculate the yearly delta, day59-yearly minimum.
Calculate the median and standard deviation for the series of yearly deltas.

I calculate 14.64 and 1.27 for the mean and standard deviation.
Day 27 for 2017 is 18.608 10^3 km3

2017 day 27 - mean
---------------------- = 3.1
standard deviation

In other words, zero ice volume is about 3 standard deviations of this sample away from the current value. About a 0.3% chance.

However, this is a simplistic computation, I can easily list a bunch of issues with it.

An "Ice Free Arctic Ocean" isn't zero ice volume, as commonly defined, as some sea ice near Greenland and Canadian islands is expected to last for decades longer.
The statistics are based on a normal distribution, and that isn't likely.
PIOMAS is a model based on measurements, and might not be accurate.
Ice isn't homogeneous.
Melting isn't linear, both another way of saying the distribution isn't normal, but also pointing out that the melting delta increases over the sample.

Looks to me based on this that there is a rough order of magnitude of a 1% chance of an ice free Arctic Ocean for at least a few days this summer. Not a basically zero chance, like all preceding years. Not a large chance at this time.

To see the graph:




Fitting an exponential trend, which has an increasing acceleration of ice volume loss, to September arctic sea ice volume from 1979 to 2012 projects to 0 volume by 2017.

Even fitting a hyperbolic trend (with a horizontal asymptote to the left and an oblique asymptote to the right), in which the acceleration of ice volume loss approaches 0, to September arctic sea ice volume from 1979 to 2012 projects to 0 volume by 2019.

I think that it is very likely that the trend of loss of arctic sea ice volume has already begun to decelerate, and that that will become more apparent in the next few years.

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