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Elisee Reclus,

If that is addressed to the discussion I am trying to have with Rob-- it may well be true. But as I have been saying all along to no effect, apparently, you have to be specific. Are we talking about the winter maximum and summer minimum, or June 1 and September 1?

Rob could supply some answers if he wanted to, or anyone willing to download and organize some data.


Hi Paul,

"Isn't the 0.2 cloud albedo that Wayne is referring to actually a cloud cover? And actual cloud albedo varies massively, see e.g. "

0.2 is an energy reduction standard (averaged over the years) factor part of the formula for SIMP, it represents 80% cloud cover throughout the entire melt season.
It means 80% albedo. From day to day albedo varies, but if you look at melt season albedo, it is usually quite low during the dark season, then about mid April to mid October becomes very strong. It is what sea ice does, cooling the lower surface troposphere during summer in effect a cloud catalyst. 2007 had a significant drop in albedo in july for a brief period of time and the thickest ice vanished essentially where the greatest cloud break was.

Elisee Reclus


I don't know how much more specific I can be.

A glance at the NSIDC Charctic graphic reveals the last record SIE minimum (September 2012) was in no way foreshadowed by the ice extent the preceding winter.

I bring this up specifically because comparison of summer extent minima is the single most unambiguous and persuasive metric we have in the propaganda war with the denialists. All other empirical measures either rely on models or are vulnerable to charges of cherry-picking or statistical hand-waving.

The linear regression of summer minima has dropped dramatically and continuously (albeit somewhat noisily) since the satellites have been gathering data. The 2012 minimum, both viewed as a monthly average or as the lowest point on the curve, was particularly startling, but will almost certainly be broken this year, if not sometime within the next few years. The minimum extent record has been broken (on the average) about every 4 or 5 years.

I bring this up to emphasize the point I have always been trying to make here. The tortured and complex chains of physical reasoning and calculation we have seen here on these comments are purely speculative, no matter how much we obscure that under appeals to thermodynamics and numerical analysis; and even if one of them turns out to be completely vindicated, we will not know for sure until after the fact. It certainly can't be brushed aside that we have not even been able to achieve any agreement amongst ourselves as to exactly what will happen next year, or why. And our ability to forecast the near future has not been much better. The Arctic is a chaotic physical system, only statistically based arguments about its long-term future carry any weight, and that is limited.

All we know for sure is that the long term trend is unmistakable and undeniable: the Arctic is melting away before our eyes, on the time scale of a human lifetime. And the best evidence we have of that is the ice extent figures (and their long term trends) we have for every month, but particularly for September.


Elisee Reclus,

Yes and no.

There's a difference between what is speculative and what is wrong. That's what I am working on establishing, which I tried to convey in our previous conversation.

Here you are citing "summer minima" as having some significance, when that number means as much as "the millenium" or some other numerologically striking value.

Do you really want to engage in that kind of propaganda exchange with the masters of BS we are up against? You will surely lose; shouting is what they do best.

As difficult as it may be, we are in the position of Caesar's Wife. If someone is going to debate a Denialist, he or she better not be making mistakes from seventh-grade algebra.

And there are things we can explore here as a way of training our thinking, like my suggestion to Rob on looking for factors that might influence the melt rate. What's the harm, as long as it is done correctly.

Elisee Reclus

@ zebra

Of course, there is nothing magic or significant about a very low summer minimum. Even totally random data will exhibit anomalous outliers

However, a pattern of steadily dropping minima scattered across five decades is hard to explain away as a meaningless blip or coincidence. The graphic is dramatic, and most important, it is easily and intuitively grasped as an unambiguous reflection of an underlying reality.

I'm not trying to be obtuse, I'm just questioning the utility of using a few algebraic formulae and powers of ten calculations based on first principles to predict the behavior of a complex and chaotic system. After all, if those of us in the choir who post here argue about exactly how to do these cocktail napkin numbers, what chance do you think they will persuade ideologues and propagandists? We may feel reassured, but no one else will be informed.

On the contrary, it will simply give denialists more opportunities to question our interpretations instead of our data. They will use this to distract the layman from the obvious and demonstrable facts, like summer Arctic ice has dropped by almost half in less than 40 years.

Robert S

Fascinating discussion, but it is running squarely up against the complex system problem. There are simply too many factors at play here to come up with anything with predictive power based on calculations like these.

In order to come up with some accurate estimate of net heat uptake and impact on ice volume loss, we'd need to:
1) calculate daily albedo x gross solar energy input (from imagery and solar angle plus solar energy for the specific time period) across the entire melt season for a series of years.
2) Estimate atmospheric heat transport into and out of the area of interest (arctic ocean) for each day of the melt season in each year.
3) Estimate oceanic heat transport into and out of the arctic ocean for each day of the melt season.
3) divide the sum of 1, 2 and 3 for each year by the total ice loss in km3 for the year.

This would give us a melt effectiveness factor, inherently taking into account energy losses due to radiative and physical transport not already accounted for, etc. It would be interesting to see how much it varied from year to year...

Then in order to have some predictive power, we'd need to add in the feedback loops, like impacts of open water on cloud formation, changes in arctic specific GHGs (yes, those darn clathrates, permafrost CH4, etc.)

If we had successfully completed these steps, the really interesting outcome would be the variance of actual from predicted, which would be a clue to the "unknown unknowns"!

Without all of this, the range of error in any calculations will simply be impossibly great - as shown by the "fudge factors" being proposed in the discussion above, and predictive power will essentially go to zero. A smart denialist will catch this...

Elisee Reclus

Thanks, Robert S. (I presume we're on the same page, here.)

So what do we know for sure?

1)Its getting warmer.
2)The ice is melting.

and we can reasonably conclude

3)Its probably going to have an effect, possibly severe, on the climate.

Everything else, as Eddington once remarked, is just stamp collecting.


ER and RobertS,

If you check back you will see that I have been arguing against predictions but for projections.

You are ignoring the difference.

RobertS, yes, the FF are really flying around here, and people are using terms that they don't understand and aren't even interested in reaching an internal consensus on what the words mean.

But, and I don't know why you would object, there are many topics where people can become better at scientific/quantitative reasoning and reach valid conclusions.

We can figure out, for example, whether or not the Land Snow Cover has an effect on the rate of ice melting between June 1 and September 1.

So, why do you object, and what's your plan?

Robert S

A fair summary, Elisee, although I think that in fact we not only can but need to get much much better at quantifying and predicting the impacts of our tenure on earth. For better or for worse, we're now in charge here, and the only way we're likely to survive our relatively ham fisted management is by really getting to grips with what's going on, and what the impacts are likely to be. In order to do this, we need many orders of magnitude more quantitative information coming in. At the same time, we need to be training everyone, and especially scientists, in observation and qualitative data collection. Our current science education system addresses this part extremely poorly, and the results can be seen all around us, in false statistical attributions and failures to understand complexity.

The thing we tend to forget is that we evolved to be intimately dependent on highly complex systems. Our brains and minds have modalities specifically designed to understand these systems. In particular, intuition is a powerful tool... but only when it is continuously honed with observation, with intimate involvement with the system. So many key scientific breakthroughs came from exactly that place.

And it occurs to me, moving back toward arctic ice, that our current best bet might be to play with PIOMAS. Since it models arctic ice volume based on environmental inputs, playing with those inputs might give us some taste of potential future scenarios, if combined with an appropriate weather model.

Hans Gunnstaddar


"In a swath of the country from San Antonio to New York City, spring arrived two to three weeks earlier than usual. In Washington, DC, spring arrived 22 days early:"

The link has a map showing where Spring has started in the lower 48 states. Spring starting early is not a new phenomenon, but 22 days early in DC is noteworthy.



Poor rodent from Pennsylvania, the ground hog predicted 6 more weeks colder weather!


Robert S ,

fascinating indeed, but ISIMP includes the SIMPlest :) factors possible. Used as a guide, it basically helps project what is coming.
Nansen's days of sea ice had 3 meter packs all the way to Russia,
We know by current sea ice science that this was the thinnest sea ice of the entire pack. But let us admit 3 meters average for the entire pack. That means there was 42,000 km3 of sea ice, once upon a time. Latest SIMP calculation basically suggests not a chance for that sea ice to have vanished in one season. But now, there is one. Why? Because, 3 meter thick sea ice produces a massive fog and cloud complex, far superior than what we have now. Cloud albedo has always been a major player in my projections, now I understand it more in a numerical sense. Therefore must refine the calculations.

Rob Dekker


If you want to be a "citizen scientist", then you have to be willing to undergo "peer review", and you should be willing to "defend your thesis".

It sounds like you are indeed very confused about the math and physics, and unwilling to take the opportunity to get a better understanding.

I gave you the correct way to do this.

Well then, let's take a look at you "correct way to do this" :

I noticed that you need to take 5 points before you determined how much ice melted between June and September.
Yet that number is so easy to calculate by simply subtracting the Sept ice cover from June ice cover.

The fact that you needed 5 points to get there, and that you had to run a regression over some unspecified "regression function" suggests that either you are doing something different from what I did, or you have no clue what you are doing yourself.

The fact that you don't follow up with what is next (after you suggest that you are going to "look for a correlation" in your last point) suggests the latter.

Rob Dekker

While wayne is refining his calculations, I'm looking forward the remainder of zebra's "correct way to do this".

Where is the popcorn ?



I've given you the entire procedure.

The remainder is up to you. Use the data you've downloaded and follow the steps. If you get a correlation, then you can "publish".

I will be very interested in seeing the results.

(And please, read the steps over a few times, carefully, and note what is emphasized in bold type. I read your explanations multiple times to be sure I understood them.)


Well Rob

Your 9.5 meter thickness number basically says there is a lot of sun heat to melt the current ice many times over, is of no other help.
So I wait for you to define that 0.5 with anticipation, the suspense is killing me :). Got plenty of raw broccoli, some caribou meat, wont starve before I get an answer. Mean time I work on refinement, something useful, a guide a little more practical than there is plenty of sunshine!


Top of Atmosphere average input for entire Arctic Ocean from spring Equinox to autumn equinox was corrected to 247 watts/m2, since Arctic Ocean is mostly 70 degrees latitude Northwards, this gives a SIMP of 13,870 km3. For those skeptical, it is a very practical estimate, fitting not by coincidence but by geophysical metrics, all with references and well observed facts. I am a strong believer in the strong high albedo of 80%. Any deviation prompts a massive melt, june july 2007, spring 2008 big blue triggered massive melt ponds, 2012 small el-Nino trended La-Nina mid summer, 2018 spring big Arctic blue, as big as 2008 or longer , started a massive melt. All these were linked with less Arctic clouds.


2016 spring, any trending towards lesser clouds also includes warming of Arctic summer atmosphere. As the temperature dew Point spread increases, under relatively lower total precipitable water, there is less clouds with more heat input.

Robert S

Zebra: You said "We can figure out, for example, whether or not the Land Snow Cover has an effect on the rate of ice melting between June 1 and September 1." Excellent example. We can certainly establish a plausible descriptive causal connection between land snow cover and ice melt, so that's a good start. And we can run statistical analyses over a sample set of 30 (years) or so and find that land snow cover appears to have some correlation. That approach will tell us that under past conditions there is a plausible statistical relationship between the two variables. But the very nature of global warming is that we won't be under past conditions.

To be blunt, this reductionist scientific approach is no longer sufficient to the problems we face. We've actually substantially known this since the 70's, and the more we understand non-eq. thermodynamics and related subjects, the more we have paradigms for approaching complexity as complexity, rather than trying to break it down into parts and understand it in pieces. These are massively interconnected and massively dimensional spaces with intricate positive and negative feedback loops and multiple attractors across different dimensional sets.

As for my approach, I think I'd already given a first example of a very initial approach. I am strongly in favor of developing our scientific understanding of the arctic and arctic ice. I'm not in favor of fooling ourselves.

Robert S

Wayne: The impact of atmospheric moisture/clouds on both albedo and atmospheric insulation is indeed one of those key variables that's going to keep this interesting!

You've got a key advantage over me - you're there, observing. There's no ice in sight here!

Elisee Reclus

Please humor a newbie for a moment.

Just what parameters do we have fairly, complete, high resolution, accurate, continuous and homogeneous data for, covering several decades?

For example, we certainly have ice area and extent numbers from the satellites. We can derive precise insolation at the top of the atmosphere from purely geometric and astronomical considerations. We have fairly good figures for global concentrations of greenhouse gases. Global temperatures are well documented. No doubt there are at least several other primary datasets that are known with some confidence.

Other parameters, such as cloud cover, precipitation and ice thickness, may be known, but at much less precise or resolution levels, or over smaller areas and shorter times. Others may be the result of models and may need to incorporate many assumptions.

There is other information available which may be limited temporally, geographically, seasonally and so on, but let us concentrate on the information we have that is well agreed on and has been accumulating for the entire Arctic region for a substantial amount of time.

Every one of these n datasets varies in a cumulative fashion historically, and may also vary seasonally (such as sea ice area).
We could normalize them by using means or medians.

By itself, each of these parameters can be represented as a line on a graph, where one axis is time. But each line can also be thought of as an axis in some n-dimensional data space. If you multiply each axis by some constant of proportionality so all the parameters fall into roughly the same hypervolume of n-dimensional space, then the ways they interact can be displayed and expressed visually. The human eye is extremely good at picking up spatial relationships that may be elusive in other forms of analysis.

This is an old technique from remote sensing (both terrestrial and from astrophotography) that occasionally reveals some unexpected insights. For example, if you have a Landsat-type satellite which can image simultaneously in seven bands, displaying them on a color monitor and arbitrarily assigning one of them to a different one of the 3 primary color guns can sometimes yield totally unexpected relationships. ("Whoa! What does that big purple feature in the NE part of the image mean?")

It is also possible to combine more than three bands to produce one color image that reveals something new. For example, band ratios, products, sums and differences can be assigned to Red, Green, or Blue, so 6 bands can be combined into one color image. The combinations are endless, and though they don't always lead to an AHA! moment, sometimes unusual relationships across bands
just jump out of the data.

My lab found economically recoverable gold in Nevada once using this technique, applied to data from a multi-channel IR spectrometer. It does work.

Just thinking out loud.

Robert S

Elisee: Yes yes yes! I've used exactly the same process to identify forest edge moisture effects on grassland ecosystems, slash and burn scale deforestation in complex terrain... The human eye and brain is the best pattern-finder we have.

Agreed in general on the quality of the data sets, too. Right off the bat the big gaps that come to mind for me are:
- daily variation in cloud cover
- ocean temperature/thermocline/halocline/mixing
- ice thickness
- black carbon distribution and impacts

I'm sure there are more...


Bonjour Elise

"Just what parameters do we have fairly, complete, high resolution, accurate, continuous and homogeneous data for, covering several decades?"

The basic parameters are well known. It is a matter of applying them, I do think you are right in saying that a consensus conference of sorts need be organized so there can be publication of the numbers into a geophysical standard index table.

It comes down to a calculation, which should be reasonable.

In High Arctic situ I know that it takes very little sunlight to level the sea ice horizon to Astronomical Elevation, but the weather has to be clear, this moment will happen sooner this year at 75 degrees North latitude. When clouds move in, the horizon rises almost instantly, cloud albedo reflects sun power to space, the horizon doesn't rise back to night time altitudes, residual heat from the warmed sea ice emits long wave radiation to bottom of clouds which reflect back the rays. My calculations give very little insolation transmittance to sea ice, in the order on average of 20 Watts/m2. Turns out sea ice 1.5 meters thick emits about 15 to 20 watts upwards, thermal IR. What I see at the horizon is a continuous play of large insolation variances , At Astronomical Horizon from direct sun, latent heat of sea ice builds, other higher altitude levels is a mix
of back radiation combined with occasional cloud breaks.

So I actually see that my latest calculations are reasonable, including the larger picture, vary the cloud cover tremendously
in summer and get the sea ice extent variances we observe. a standard 14,000 Km3 a melt season Arctic SIMP looks cool.

Joindre nos pensees etabliront une meilleur comprehension.

Elisee Reclus

Yo Robert

It looks like we're both showing our age.

Using the eye/brain data processing capability we inherited from our pre-savanna days climbing trees and checking fruit for ripeness high in the canopy...

And with image processing, we had a whole battery of image enhancing capability at our fingertips--contrast stretches, convolutions, resampling, mensuration, pseudo and false-color tagging, density slicing, intensity, hue, saturation processing, Fourier power spectra etc to squeeze patterns out of data so our eyes could pick them up easier.

Today, everybody is hooked on spreadsheets. We didn't even have them back when.

BTW, ever hear of Heat Capacity Mapping Mission? It was a bird designed to map the thermal inertia (a concept similar, but not identical to, specific heat) of rocks from space. It sounds like just what you guys need to play your albedo and thermal IR irradiance games.

Thanks for the stroll down memory lane.

Elisee Reclus

For Wayne--

You lost me at"Astronomical Elevation", and I have no idea what "Astronomical Horizon" is. I am not familiar with the ters either from astronomy or navigation, What do they mean, it sounds very significant. Do you mean apparent sextant altitude distorted by refraction? Or horizon dip caused by height above MSL?

BTW, No hablo frances, aunque mi nom de guerre lo domina.


Correct Elise

Muy Bien, Perdona mi error

Astronomical Horizon, horizon of which would exist if there was no atmosphere

Horizon Elevation : Elevation in degrees of horizon above the Astronomical Horizon

About sea ice: If thermal flux upwards to air is = to downward, Astronomical Horizon is achieved.

It is one of many discoveries I have made, this one turns out to reconcile with my latest calculations. During the Dark Arctic season long night A.H. of sea ice horizon never happens, one must wait till the sun is high enough in the sky to compensate for upward thermal flux. Last year this happened in March 75 N 94.5 W, shortly after local apparent noon, with the view of the entire NW passage, when the sun radiation transmittance through sea ice (albedo 90%) was 18 w/m2, , in clear skies (no cloud albedo), with atmospheric absorption at 23%, .

Puedo ver los flujos térmicos

Elisee Reclus

I'm having trouble with the nomenclature here...

Is "Horizon" being used in the same way we normally use the term, i.e., the line where the earth appears to meet the sky? As in, "The sun is just above the horizon?" Or
"That ship is hull down at the horizon, only her stacks and superstructure are visible."

I mentioned in a post a while back that atmospheric refraction of light allows heavenly bodies that are actually below the horizon to appear above it. This bending of the light is a function of elevation in degrees (and is also affected by atmospheric pressure and temperature). It becomes quite extreme near the horizon, and is zero at the zenith.

The Nautical Almanac publishes corrections for this effect so that navigators can subtract the bending from their sextant observations. This correction is also available online in the Naval Observatory navigational calculator link I published in that post. This correction can be substantial, even at ordinary temperatures and barometric pressure, for a celestial body 10 degrees above the horizon the correction is on the order of -5.3 minutes of arc. Cold weather and high atmospheric pressure also exaggerate this effect. There's a table of corrections in the Almanac for that, too. So theoretically, a navigator could make a sextant observation of a star that would be BELOW the horizon and not visible at all if there were no atmosphere.

The elevation of the sextant above the water surface also makes the horizon seem further away, which must be corrected for as the "dip". This is also published in the Almanac, so for an elevation of 10m above sea level (height of deck above waterline + height of sextant above deck) the correction is -5.6'.

A few minutes of arc can make a big difference in a sextant observation (1' = 1 nautical mile) but its hard to see how this would have a big effect on radiative flux from the sun. Now if we integrate this minute difference over a long polar day as the sun moves round and round the horizon, perhaps it can add up to a substantial amount of insolation, but I haven't taken the time to calculate it.

As for "flux" from and to the sea and sky, I assume you're talking about sunlight in the visible spectrum striking the ice/water vs thermal IR radiated by the ice or water surface. But does it also contain full spectrum light reflected back by the ice?

Sorry about the confusion, but I want to make sure we're talking about the same thing and not just getting lost in some technical terminology I'm not familiar with.



There are many types of refraction, astronomical deals with celestial objects, these are the ones with the greatest shifts above the horizon because they are distant, come from space and at horizon penetrate huge atmospheric thicknesses, so refraction boosts in the order of 5 degrees, not arc minutes, are possible. I use to deal with 2 to 3 degrees about 10 years ago, In the South 40 Arc minutes are more common.

Terrestrial refraction deals with Earth matter, ocean, sea ice, Islands, mountains etc Objects no further than line of sight domain, up to 20 to 40 km with near horizon topography. Here we deal with dip, when thermal fluxes cancel, or become 0, we can observe the astronomical horizon. Therefore I can observe thermal fluxes, positive or negative, how intense they are, by the shifting of the horizon. In particular sea ice horizon.

It seems that some have forgotten that sea ice albedo is huge with snow, very little energy is transferred to sea ice 1.5 meters thick with at least 10 cm of snow. The calculation to consider is the net thermal result. One has suggested taking top of atmosphere Long wave radiation data, that is good but very complex to deconstruct. What I study is surface thermal fluxes from observing the bending of light caused by variations of the lapse rate at the surface to air interface.

Finally sextants are very neat, I have one somewhere, but very 19th century, I suggest modern theodolites, and or telescopes.

Elisee Reclus

I'm not familiar with the extreme refraction you study, or how you apply it in your work. It sounds fascinating.

In celestial navigation, you simply don't shoot anything too close to the horizon if you can avoid it because it is very difficult to correct for refraction--it just isn't very predictable. Since I normally am not interested in studying refraction, I'm trying to get a fix, I try to avoid low altitude observations. I know (anecdotally, I never actually measured it) that refraction can really make a difference between the predicted and observed time of rising and setting of celestial bodies, but that is about the only navigational application I can think of requiring near-horizon observations.

I disagree with your assessments of sextants, though. Except for electronic methods, such as Loran or GPS, astronomical observations are the only way to derive a precise position at sea. You can get highly accurate sextant elevations from the deck of a rolling ship, or even a small yacht (+/- a minute of arc), even in a heavy sea. A theodolite or a specialized telescope such as a zenith tube or a transit telescope can't do that.

A good sextant operator working in good conditions can easily locate his ship to within a nautical mile or so on the surface of the earth, nowhere near as precise as GPS, of course, but the system is self-contained and not dependent on a massive government bureaucracy or a complex technological infrastructure.

And if you're the only guy aboard who knows how to use one, the crew is not likely to mutiny.


Muy bien Elisee

Fascinating is why do this work, I completely agree that sextants are fantastic, but I deal with errors within 10 arc seconds. Si, for centuries every navigator avoided measuring anything below 5 degrees elevation. So my work is quite novel, there are a handful of experts on the subject, the greatest in history was Alfred Wegener and Bessel, with countless observations and work by many others about this curiosity. If you live by the sea, you may appreciate dip with a fix mounted sextant. By the way, I wrote to Alfred Wegener institute about confirming one of his greatest theory about refraction,
a Wegener Blank Strip, I filmed a few of them, the institute did not know about this bit of of massive geophysical background.

Rob Dekker

Since the other commenters here don't offer any assistance in refining your calculations, here is one more piece of evidence that about 50% of TOA insolation makes it to the surface :

This is from the SHEBA project, where scientists measured radiation values in the Arctic.
Of special interest for your estimations is Figure 6a, which shows actual "downwelling SW" (insolation that radiates down on the surface). It peaks at about 300 W/m^2 in mid-June, which (with TOA peak 500 W/m^2) means 60% makes it to the surface.
Eyeballing the 'average' between spring and fall equinox, I estimate some 170 W/m^2. Which is 170/2=85 W/m^2, which is consistent with the number from HadCM3 that I showed you earlier.
Are you now also going to dispute SHEBA measurements, or are you finally convinced that some 50 % of TOA insolation makes it to the surface in the Arctic ?


Thanks Rob

Very kind of you to help as well as usual,

It is a nice paper about clouds. I do remember the project from publicity it made.

At any given day you can have a great deal of radiation coming as paper suggests, when it is clear figure 2,

"T"otal cloud forcing (the sum of all
components) is about 30 Wm-2 for the fall, winter, and spring, dipping to a minimum of -4 Wm-2 in early
July. "

I like this, that is very right reflection from sea (under ice) as a source of energy, but especially the july w/m2.

I can't figure out the dating system used, but look at the net SW flux figure 6, as suggested and it is less than 50 % than the model (probably from TSI) . I deal with direct incoming radiation, with the understanding that downward LW fluxes meet with upward probably making a small net.

A single location near land 75 N 143 W(There was more ice then), does not make the entire Arctic Ocean. You may have extraordinary low albedo in one region and not so for the rest of the Arctic. As often Beaufort sea opened up for shipping even in the 19th Century.

Thanks , will reread, I do remember Judith being on board on one of the Shebas. That is when she was female anakin skywalker before she turned to the dark side.

Rob Dekker

You are welcome, wayne.
Quick note :

I can't figure out the dating system used, but look at the net SW flux figure 6, as suggested and it is less than 50 % than the model (probably from TSI)

The model represents "clear sky" conditions, while the solid line in figure 6 represents "all sky conditions" (which is what you were looking for).
This is explained explicitly in the text :
The annual cycle of downward, upward and net surface SW fluxes are
shown in Figures 6a, 6b, and 6c, respectively, where the dashed lines
represent clear sky modeled fluxes and the solid lines are the measured fluxes under all conditions.

Since you were so interested in the "all sky" conditions, are you now convinced that measured fluxes under all conditions are about 50% of TOA insolation ?



But of course look at the cloud conditions graph, there wasn't much over Beaufort during the summer, as normally happens from summer to summer, I can't figure out the date system, note 6 c the net.....

Elisee Reclus

I'm sorry, Wayne---

Until your last post, I did not have a clue what you were talking about. I was thoroughly confused. It wasn't until you mentioned "Wegener Blank Strip" and I looked it up on the Net (and watched the youtube video) that I realized you studied extreme refraction phenomena. My comments on sextant navigation must have really come across as a complete non sequitur

I was brought up on the west coast of Florida where conditions are ideal for the Green Flash (I've seen quite a few (and even photographed one) so I am familiar with low-sun phenomena, but I never realized they were studied so rigorously as you mention.

I understand this sort of atmospheric mirage displays are very common at high latitudes. When I was in the Navy, one of my shipmates remarked that years earlier when he was steaming in Arctic waters he had once seen a mirror reflection of his own ship sailing upside down on the horizon.

Do you think this sort of unusual atmospheric manifestations actually play a significant role in the Arctic's radiation and energy budget?


Si Elisee

They are made by the thermal fluxes, in Florida look at beach horizon for a nice warm day when Ocean is cooler , wait till the same sea warms up substantially with respect to same surface temp and laser same location, note the dropping horizon. Let us know when you've seen an apparent drop in sea level :).

Rob Dekker

wayne, the dating scheme is days since Jan 1, 1997.
Are you going to answer my question at all ?

Are you now also going to dispute SHEBA measurements, or are you finally convinced that some 50 % of TOA insolation makes it to the surface in the Arctic ?


It does Rob!

When not so cloudy, look at figure 5, you can have more than 50% when not cloudy. I would dare say 77% of TOA. The date scheme clumps days together apparently:

"A year long data
set of measurements, obtained on a multi-year ice floe at the SHEBA camp, was processed in 20 day
blocks to produce the annual evolution "

I would have never done it that way.

Rob Dekker

zebra said

I've given you the entire procedure.

No you did not. The last remark in your "procedure" is
We can list the the rate for each year next to the June LSC for each year, and look for a correlation. Does the rate go up/down when the LSC goes down/up? You have that function on your spreadsheet as well.

Apart from the fact that I don't use a spreadsheet, you have not given ANY indication of how you are going to proceed. For example, what would you do to determine the correlation between Land Snow Cover and sea ice extent ?

So once again, it looks like you have no clue what I did, and you have no clue what you are doing yourself either.

Rob Dekker

wayne, it seems that you question the SHEBA results from figure 6 as well. Just like you questioned the HadCM3 results.

OK. I could have expected that.

You seem to question ANY scientific find that contradicts your own beliefs. What I don't get is why, wayne ? Why do you question such obvious scientific findings ? What is there to loose ?

Let me give it one last try :
Here is a TOA albedo graph from Hudson 2011 :

Note that less than 50% makes it back into space.



I dont know where you get this idea that I don't believe in these results, they are fine, I try again, there was very little clouds during the summer during Sheba. I just said 77% can reach the surface. The net is sea ice results from sea ice albedo which drops as summer progresses. . Don't be fixated over a 50% figure which may vary.

Well thanks for the graph , now I finally know what you are talking about, cloud albedo cant be more than 50%???? That is not what I have read, and also especially may I remind figure 5 of the first paper. .8??? Tamino seems a bit off, dont tell it to him :). But its good to know what he has calculated.

Bye the way, very much appreciate your trying to help, but don't infer I reject Sheba, only your 50% fixation.

Rob Dekker

wayne, It's not a fixation. SHEBA figure 6 shows clearly that 50% of TOA insolation makes it to the surface.

You say you accept these findings, but meanwhile you note that "here was very little clouds during the summer during Sheba" without providing any evidence for that.

Finally, before you start to dispute Hudson 2011 as well, note that that is TOA albedo.

Either way, it is at this point (after HadCM3, SHEBA and Hudson 2011) quite incomprehensible why you don't want to accept the evidence that about 50% of TOA insolation makes it to the surface.

Rob Dekker

I forgot to mention :

That is not what I have read, and also especially may I remind figure 5 of the first paper. .8???

Figure 5 show albedo development over time.
Apart from the fact that it shows albedo being around 0.5 during the melting season, it has NOTHING to do with the amount of sunlight that makes it to the surface.

You realize that, don't you ?


He gash Rob

"without providing any evidence for that."

Figure 5 !!!! Day 550 is early July

I think we are talking about 2 different things.

Rob Dekker

Yes. With albedo at 0.5. What's your point ?


Wouldn't these variations be caused by clouds by any chance? Don't you see the .8 albedo as well? before day 500, after day 600....

Please Define TOA albedo? Does it involve everything including sea ice albedo?

Very interesting

Rob Dekker

You sound like a Trump tweet.
Once again, albedo has NOTHING to do with downwelling SW (the amount of solar radiation that makes it to the surface).


"albedo has NOTHING to do with downwelling SW"

Thank goodness for that! Where did I ever say it has anything to do with that?

Please define TOA albedo, and don't insult poor Don Don.


Thanks Rob

Not one single chance that there is 50% constant SW to surface, cloudy not cloudy, sorry that concept is extraterrestrial. Not observed by me in any way. I believe I calculate cloud cover DSW completely differently then may be most academics may do? I wonder. But my calculations are coherent and reflect what is observed. Here is to the new way, may it be better than the older way.

Much appreciated that you brought this to light.


Notwithstanding figure 5, this SHEBA paper should have included cloud altitude graph. Would have been very illuminating. Not possible to process proper albedo analysis otherwise.


Rob Dekker,

Now you are being silly. Here's a quote from your original post:

When I use this formula as the 'predictor' I get improved correlation numbers (especially for the shorter terms if you use only 'Area' or 'Extent' as a predictor), which suggests we are on the right track!

But what I was really interested in, is if by tweaking these weight factors (which after all were just educated guesses), if we can improve the correlation numbers even more. If it turns out that the 'optimum' correlation is way off from the weight factors I suggested above, then we know that the physical effects of 'albedo' amplification are simply not significantly visible in the later ice cover numbers.

So I used the 1995-2012 series (long enough for statistical quantity and short enough to not be affected by completely different melting regions) and tweaked the numbers until I found optimal correlation.

Either you used some software to get your "correlation number" (and your "regressions") or you were just pretending-- what we would call "citizen scientific fraud".

So, to get the correlation, click on the same icon, or type in the same command, or whatever the mechanics are in your software.

It really sounds like you just don't want to find out if what you thought-- that there would be a correlation-- is wrong. That's not uncommon; that's why we have the term "confirmation bias".

Hans Gunnstaddar


Anybody know why Piomass Ice Volume is only updated through mid-January?

Hans Gunnstaddar


Ok folks the jury is in, and we can now conclude that Trump is a full fledged denier. Here's an excerpt.

"WASHINGTON (Reuters) - The White House is proposing to slash a quarter of the U.S. Environmental Protection Agency’s budget, targeting climate-change programs and those designed to prevent air and water pollution like lead contamination, a source with direct knowledge of the proposal said on Thursday."

That money siphon is going to the military, when it actually should be going to renewables on a war footing.


Hans, what if you thought about it like this: the IPCC still exists.

Rob Dekker

zebra said

It really sounds like you just don't want to find out if what you thought-- that there would be a correlation-- is wrong. That's not uncommon; that's why we have the term "confirmation bias".

Boy, oh, boy (shaking head).
If you just want to ask something to do for you, let me suggest that you ask it nicely.

Something like : "Rob, you did nice work correlating three different variables (land snow cover, water-close-to-ice, and plain old ice 'area'). Since you have all that data available, could you do me a favor and run a correlation between just land snow cover in June against ice melt between June and September ?"

I would respond with something like this :
"Thank you zebra, and I can sure do that. But even better, I can give you the correlation between each individual variable and ice melt, and not just for June, but also for May and for April. Here it is :".

Just ask. Nicely.

Rob Dekker

wayne said :

Not one single chance that there is 50% constant SW to surface, cloudy not cloudy, sorry that concept is extraterrestrial. Not observed by me in any way.

Did you measure downwelling SW yourself ?


Hi Rob,

Yes, i measure this stuff every day, indirectly, so forgive me if I find that concept good for 2 dimensions. I am being polite.


his page will continue to take a long time to do, because finding pictures for anybody without training to understand requires particularly clear shots with sharp contrasts.

There is a belief of a Polar total sky Albedo “constant” , likely , yet not defined officially, as a view from space and a measurement with radiometers from ground.
Radiometers may not distinguish cloud back radiation from direct radiation always likely giving the same net radiation ratio measured on top of sea ice. But at any rate, this constant is said to be 50%. which can be from sea ice or clouds, therefore the 2 reflect the same thing They are indistinguishable.

There is a couple of problems with that concept. First of all, if total sky albedo
is the same whether there are clouds or not, the surface will always have 50% of Downwelling solar radiation from space. For that to be true, there should be, optically wise, a constant thermal flux action measured on the surface. In other words , there should be no difference, whether cloudy or not, in daily thermal flux action. Which I observe readily indirectly by studying
sea ice horizon refraction. I am not sure whether this 50% albedo concept is the common academia understanding of sea ice thermal flux processes. But it lacks verification. Which is why I present the following, in a series of coming pictures. Basically cloud presence matters, on of top of, not merged with sea ice albedo, these are two different incoming flux reflections, some clouds allow SW some reject rather reflect these rays readily, Arctic sea ice has also different albedo properties throughout the seasons, or sun elevations. The proper rebuttal is simple, if total sky albedo over sea ice is irrelevant to clouds, then there should be no thermal flux difference between a cloudy or sunny day.

Or Partially cloudy or clouds moving in or out, total sky albedo is always 50%, apparently?

This link will provide the clearest examples possible of sea ice horizons shifting vertically with all known albedo conditions. There is no such thing as an Arctic albedo constant driven by Downward Flux, there is a great deal of variations, all very pertinent to various sky conditions. This is always mirrored on the horizon.


Rob Dekker said:

Something like : "Rob, you did nice work correlating three different variables (land snow cover, water-close-to-ice, and plain old ice 'area').

But you didn't do "nice work".

What you did may even qualify for that famous quote: Not Even Wrong.

It's hard to tell if there's anything "right" in your "analysis", but in an effort to be positive, I provided you the correct methodology-- not because I want you to do it for me, but because it would be a way for you to gain some understanding.

If that's too painful, OK.

I also provided it so that lurkers could see the difference. It might discourage some, but if people do want to be "citizen scientists" they should be willing to put in the effort to read and understand, and learn the terminology and methods, so that you can communicate your work in a clear and complete form.

You can't just wing it and make stuff up.

Frank Pennycook

I can't take it any more. I mainly lurk here, because arctic ice is not my field, and I benefit from others' expertise. I have an understanding of the science, but I am not a scientist. I am a mathematician.

Zebra, please. Your so-called "correct method" is deeply misguided in so many ways it is hard to know where to begin.

The issue is the relationship between June conditions and September conditions.

You narrowed this down to the question of whether June land snow cover is correlated to September sea ice. This is not very relevant to Rob's multi-factor analysis. There could be very well be zero or low correlation, or even anti-correlation, for one factor, yet a reliable and quantifiable relationship based on the multiple factors.

Then to address this you propose to fit a straight line to a non-linear variable, sea ice extent, which is seasonally cyclical.

However, as you remark, over the range concerned (Jun-Sep) the curve does look fairly straight. OK. But to the extent that it is straight, you don't need to fit it, because its slope can be determined from the end datapoints. And to the extent that it is not straight, your method will give the wrong answer because a "best fit" line has no meaning for this dataset.

Rob pointed this out further up the thread. It seems clear to me that if you want to investigate the relationship between September data and June conditions you use the values at one end (as dependent variables) and the values at the other (as independent variables).

You stress that you concentrate on the "rate" of sea ice loss. But over the fixed period concerned the daily rate is only the amount of ice lost divided by a number of days, which is always the same number of days. So this is division by a constant, and will make no difference to any correlations observed.

So you propose an outrageously convoluted method to inaccurately calculate a correlation that will not in any way shed light on the work which Rob did. And you tell him he is confused about maths and physics.

Incidentally, you repeatedly carp at others for supposedly using spreadsheets. What's the problem here? Statistics can be correctly computed using all sorts of tools. It doesn't matter if I use R, a python library, pencil and paper or Napier's bones. If the correct procedure is followed the answer should be the same.


Frank Pennycook,

I understand what you are saying. I appreciate that someone who has a grasp of the math and can communicate his position wants to help clarify things.

For starters, could you just explain, as a mathematician, "the work that Rob did"? I don't care about using spreadsheets-- I just assume that's what people use because they are available-- but I still haven't seen from him any description of a process that I could replicate.

I can imagine some approaches that I might use, for a multi-variate analysis, but I certainly would not use them before I established a correlation that is consistent with physics.

In any event-- go ahead and describe Rob's actual method from what he has written, and we can deal with the physics later.

Frank Pennycook

In my opinion Rob's description of the procedure he followed is mostly self-explanatory.

In a nutshell, he picks three measurements which can be known in June and seeks a linear combination of these variables as a predictor of September sea ice (extent or area). The choice of the variables is based on physical intuition and he has an initial guess at the coefficients as a test. Even this guess seems to have a relationship with the historical data, so he goes on to improve the fit.

The aim at this point appears to be to vary the coefficients in order to maximise the correlation coefficient (between observed and predicted sea ice in September). Exactly what tool or iterative approach he used for the optimization I'm not sure -- I'm guessing if you asked Rob (nicely) he'd tell you. But the theory is clear.

The outcome then is a linear formula that predicts September sea ice from values known in June, which is based on physical reasoning, and which has excellent fit with the historical record.

I would make a suggestion, though. If I were doing it I would skip the step of making the line (alpha+beta*F). I'll show you why. Call the measurements in June M1 M2 M3 and the coefficients p1, p2 and p3.

Then the so-called melt factor F = p1.M1 + p2.M2 + p3.M3

And the prediction for September, S = alpha + beta * F.

But then S = alpha + beta.p1.M1 + beta.p2.M2 + beta.p3.M3

I would view beta.p1 as a single coefficient, the weighting for Snow Cover or whichever measurement M1 represents. Call it a1. Call alpha a0 (because I can't do a Greek font here!).

Now S = a0 + a1.M1 + a2.M2 + a3.M3

From my point of view I find it clearer to see it this way. To find the best fit coefficients I would use "least squares", that is, minimize the sum of the squares of the residuals. This is multivariate linear regression.

I believe, but am not certain, that Rob's method would produce the same answer as mine. It might be that in order for this to be guaranteed we would have to make some assumptions about the random variables being well-behaved (normal or so on). I would have to crunch some equations to check this.

Oh, and Rob, useful work, very interesting. I've been following this blog for a couple of years but hadn't come across this item of yours before.


Zebra, either the snark disappears, or you disappear. Show some respect and possibly some work. Rob has done his bit many times over.

Frank Pennycook

In my opinion Rob's description of the procedure he followed is mostly self-explanatory.

In a nutshell, he picks three measurements in June and seeks a linear combination of these as a predictor of September sea ice (extent or area). The choice of the variables is based on physical intuition and he has an initial guess at the coefficients as a test. This guess already shows a relationship with the historical data, so he goes on to improve the fit. He varies the coefficients in order to maximise the resulting correlation coefficient (between observed and predicted sea ice in September). Exactly what tool or iterative approach he used for the optimization I'm not sure -- I'm guessing if you asked Rob (nicely) he'd tell you. But the theory is clear.

The outcome then is a linear formula that predicts September sea ice from values known in June, which is based on physical reasoning, and which has excellent fit with known observations.

I would make a suggestion, though. If I were doing it I would skip the step of making the line (alpha+beta*F). I'll show you why. Call the measurements in June M1 M2 M3 and the coefficients p1, p2 and p3.

Then the so-called melt factor F = p1.M1 + p2.M2 + p3.M3

And the prediction for September, S = alpha + beta * F.

But then S = alpha + beta.p1.M1 + beta.p2.M2 + beta.p3.M3

I would view beta.p1 as a single coefficient, the weighting for Snow Cover or whichever measurement M1 represents. Call it a1. Call alpha a0 (because I can't do a Greek font here!).

Now S = a0 + a1.M1 + a2.M2 + a3.M3

From my point of view I find it clearer to see it this way. We would find the best fit coefficients using "least squares", that is, minimizing the sum of the squares of the residuals. This is multivariate linear regression, and would be a more standard approach. I believe, but am not certain, that Rob's method should come to the same answer anyway. It's possible we would require some assumptions about some distributions being well-behaved (normal or so on). I would have to crunch some equations to check that.

Oh, and Rob, useful work, very interesting. I've been following this blog for a couple of years but hadn't come across this item of yours before.



I think I did show my work, which I stand by, and which I'm happy to discuss with Frank.

This is difficult to do if we can't agree about what we are disagreeing about.

If that's OK, I will continue if Frank indicates that he is interested. I will try to avoid snark, and if I find myself getting too frustrated I will simply move on, which I was ready to do before he commented.

Frank Pennycook

Zebra, I'm happy to hear what you've got to say, so long as Neven is content.

However, I commented as part of a group discussion. I'm not committing myself to a one on one. If I don't reply for some time it's likely I'm away or perhaps haven't got anything to contribute at that moment.

But I'm here now. Go for it.



That sounds like what I thought Rob was doing. But I don't see the physical justification for such an approach.

First, you asked me why I would do a best fit on the (yearly) data instead of subtracting the last data point from the first. Well, why would we ever do a best fit? The answer is, because we are trying to distinguish the underlying signal, which is the result of a physical process, from the noise, which may be the result of other physical processes.

The single most important thing I've learned lurking here myself is that there is an enormous level of variability.

So, the first step I would take to avoid error is to determine just how correct my assumption of linearity would be, and also to get a slope that has not been influenced by some storm, on August20, for example.

Now, having decided that the melt rate is constant, I would try to imagine what physical factors determine that melt rate.

If the first guess is that Land Snow Pack on June1 has an effect on the melt rate, why would you call it "convoluted" to simply test for a correlation? It is, to me, the obvious next step.

Frank Pennycook

Trying to best fit a seasonal cycle with a straight line is not the way to separate signal from noise. If you wish to eliminate daily variability take a range such as averaging +/- 5 days of each endpoint.

But there is no need for that. Because the function of sea ice extent or area with time is a continuous one. Not a scatter plot.

Best fit lines should be used when it is reasonable to hypothesize that the underlying relationship might be linear. Not otherwise. Am I wrong?

If you wish to test whether the Land Snow Cover on (or around) 1 June has an effect on September extent, yes, it is reasonable to check for a correlation. Have you done so?

But, importantly, that is not "the first guess". The first to fifth or sixth guesses have already been made and we have in front of us the useful analyses of Bill Fothergill and Rob Dekker to build on. Yet you have done little except pour scorn on them and their work.

I have not seen a single calculation from you beyond links to interactive plotters such as woodfortrees.

r w Langford

A new study on Arctic ocean Aragonite levels shows increasing CO2 levels are reducing Aragonite levels. The arctic Ocean is the canary of ocean health around the world. Temperatures increase poleward but CO2 (i.e. acid levels) increase from the poles southward. A large percentage of atmospheric oxygen is produced by marine organisms depending on calcium based shells. Shellfish species also. It does not take very much of a shift to cause irreparable harm as the metabolic precursors are in very small concentrations at normal pH levels.





What ever happened to being calm and polite?

I was snarky (which I have said I will avoid) about Rob (not Bill, with whom I didn't interact) because I thought he was being defensive and not forthcoming with his process.

Now you are taking a similar oppositional attitude when all I did was explain my own reasoning, as requested.

Anyway, I'm not following what you are saying about "a continuous function". It's data points, some are daily and some are monthly averages. When we fit a straight line, which in science we always try first if the eyeball reads it that way, then we are establishing a continuous function.

But what I am most not getting is what you are saying about "first to fifth guesses". I haven't read every single post and every single comment, but I thought this idea of Land Snow Cover influencing the melt rate was exactly the new idea that Rob came up with.

In fact, what I said when I was "asking nicely" for more information was that I thought it was an interesting hypothesis well worth exploring.

The question at hand, from my perspective, is the correct methodology, which is what we are disagreeing about. What would be the value of me testing for the correlation?

Frank Pennycook

(1) Continuous functions of time: the sea ice extent is a value which exists at any time. You could measure it at 12:00 and 12:01. It cannot be very different at 12:01 from what it was at 12:00. This differs from a plot of points to which one might try to fit a line.

(2) Fifth guesses. I indulged in rhetoric here. You described your idea of a correlation between Land Snow Cover and melt rate as "the first guess". But it is not. It is a step backwards from the information gained by considering the influence of several factors simultaneously.

(3) "What would be the value of me testing for the correlation?" I don't know, it's your suggestion.


Frank said:

"the information gained by considering the influence of several factors simultaneously."

Frank, generations of scientists have spent their lives trying to eliminate "the influence of several simultaneous factors".

A "gold standard" experiment is one in which we gain information about how a single variable influences another single variable.

All of our knowledge of the physical world is built up this way. Step by forward step.

Which is why my method is correct and Rob's is incorrect.

This is very basic "scientific method" and "philosophy of science" and "best practice" and so on. This is why we have Ockham's Razor. This is why we have formal statements of experimental hypotheses.

So, unless you can tell me why any serious investigator would refrain from taking the simple step of testing for a correlation as I described, you are not engaging in a serious debate.

Kevin O'Neill

zebra - I went back and reread this thread just to make sure I wasn't jumping to conclusions based on a couple of ill-written comments. I think you ought to drop the condescension and maybe do some actual work with the physics and daily/monthly/yearly values.

Rob Dekker has been one of the few here that has *always* been ready to change his opinion when data warrants it.. Along with Chris Reynolds he is one of the best citizen scientists we have in this community. He has always been forthright in presenting both his data and his formulas.

Your self-righteous and condescending attitude stands in stark contrast to what I admire about Rob and Chris. Sorry, but I'm just tired of reading your crap.

Frank Pennycook

Your outline of a philosophy of science strikes me as impoverished. There are times when an experiment to isolate a single cause is critical, and fundamental laws can be unified thereby. Equally there are times when science examines more complex networks of causation.

But we are not talking here about a search for Newton's Laws. We are examining a single system, that inevitably is influenced by multiple factors, all within the framework of basic physics and chemistry of course.

I do not accept your criterion for deciding if I am engaging in a serious debate. Perhaps you are a "serious investigator". Why then have you refrained from testing the correlation you describe?

I have already explained why I do not think such a single factor correlation, or the lack of it, would be instructive. Your "method" is not correct, and I have explained my reasons for saying so.

Hans Gunnstaddar

"Sorry, but I'm just tired of reading your crap."

I'm right there with you on that one, Kevin, and suggest zebra you get lost if you can't play nice. This site has in the past been a comfortable, non-aggressive place to air out different ideas. I hope that can continue.


OK guys.

I have admired this blog for its ability to convey lots of excellent observational science.

I have learned about the complexity of the Arctic geography and physical systems-- ice transport, melt ponds, leads and compaction, all the "seas" and how each has its own characteristic interactions, and so on.

That richness of information is great, but in the final analysis, as I said earlier in a response to ER, the "other side" gives no quarter in this conflict. To my mind, right or wrong, the reality/science-based community has to be really committed to a high standard.

The actual climate scientists, who are subject to all kinds of abuse and time wasted refuting spurious arguments, would probably appreciate some support on this front.

If it's OK for people "on our side" to make speculative arguments with no physical basis, and dismiss the "rules" that got us to where we are in science and technology, then it becomes impossible to criticize the Denialists. But, if that's the approach that makes you comfortable, "be happy in your work."

Rob Dekker

Thanks for the nice words, guys ! Very much appreciated.

Frank said :

Now S = a0 + a1.M1 + a2.M2 + a3.M3

From my point of view I find it clearer to see it this way. We would find the best fit coefficients using "least squares", that is, minimizing the sum of the squares of the residuals. This is multivariate linear regression, and would be a more standard approach.

Yes, I realize that multivariate linear regression would have been a more standard approach. For one, I would not have to manually tweek the parameters to obtain the best correlation, which was rather time consuming as you can imagine :o)

I choose simple linear regression on a single variable (melt function F) simply because I had a program written already that runs flawlessly on the data at hand. I contemplating using Principal Component (PC) analysis, but since statistics is not my main area of expertise, I did not feel comfortable writing a new program that may or may not contain bugs. Do you know of any publicly available implementation that can do multivariate linear regression (or PC analysis) that can be used to solve this problem ?

Either way, thank you much for your feedback, and I hope you will 'unlurk' more often. Your insight (as a mathematician) contributes to the quality on this fine blog.

Rob Dekker

zebra said

If it's OK for people "on our side" to make speculative arguments with no physical basis, and dismiss the "rules" that got us to where we are in science and technology,

Please, zebra. Nobody made any speculative arguments with no physical basis. My analysis specifically confirms the albedo feedback effect : the darker the Arctic, the more energy is absorbed by the surface. I made an educated guess on the fractions of absorption and the regression results on actual ice melt confirm these.

And neither did anyone dismiss any "rules" of science and technology.

Frank Pennycook

Hi Rob, maybe I should unlurk more! Thanks.

It's probably worth the initial effort getting set up for multiple regression, as it would then be so much easier to add more variables or repeat the analysis to include data from recent years.

Your program for linear regression - what's it written in? In most languages there's going to be a stats library.

I'm mostly using python at the moment. Here's some info about statistical methods in it (incl MLR):

If you have the data handy, or could point me to it, I'll have a look at it if that would help.

Incidentally, how does the correlation come out for the individual factors?

Robert S

Rob Dekker. Your approach definitely makes sense. I'm curious: once you have achieved a best fit weighting for your variables, have you calculated annual September ice projections year over year, and charted the annual variance of the projection against the actual? Is there any trend? I find that the most interesting part of any statistical analysis is the demons that are lurking in the error bars, and that unpacking that component more often leads to breakthroughs than the core statistical analysis.

Robert S

It's interesting that the "pole of cold", which usually moves around Siberia, has been moving around the Ellesmere/Greenland area for the past couple of weeks, has been sitting over the ice north of Ellesmere for the past five or six days, and is projected to continue to sit in that area for a while. This may be adding some meaningful ice thickness right in the area which is likely to be the "last redoubt" of the multi-year ice.


Robert S

Indeed, the latest Cold Temperature North Pole is likely moving South from its origin of central Ellesmere. I would like to say it is the single 'vortice" within the entire Polar Vortex, usually with 2 vortices with one more over Siberia.

I have added more examples contrasting "clear sky albedo" thermal effects vs "cloud albedo" as seen horizontally, several more to do:




The whole fields of systems engineering, systems analysis, control systems engineering, complex dynamic modeling and many more are all about understanding the complex web of interactions involved in real world dynamic situations. Far from simplifying down to a single variable affecting a single output, the real world involves extraordinarily complex dynamics with feedbacks of all sorts. These range from immediate simple linear feedbacks to highly complex, dynamic and chaotic feedbacks with all sorts of spatial and temporal factors including varying ranges of temporal delay.

Figuring out how those work and being able to predict them and utilize them is what these fields are all about.

Said differently, in the relatively simple world of psychological analysis of how people think and handle problems there is a simple (and not entirely correct) model of people belonging to two classes; 1) linear thinkers, and 2) gestalt thinkers.

Linear thinkers do precisely as you describe. The entire world is simple linear immediate effects with direct deterministic cause and effect every time.

Gestalt (whole world) thinkers on the other hand process the dynamics of feedbacks and the complex web of interactions fairly well.

Neither is right or wrong. Neither is better or worse. Both have their place.

Linear thinkers dominate in fields like accounting. Gestalt thinkers dominate in fields like engineering. Each is better at doing some things than the other. For example: a person who thinks in gestalt is generally good a complex dynamic interaction systems design. Linear think would fail in that endeavor. A linear thinker 0n the other hand can go for weeks processing the counting of objects, tallying numbers, correlating their direct relationships etc... A gestalt thinker would likely go nuts and make errors trying to do the same.

Trying to impose linear models on a complex dynamic and often chaotic (in the mathematical sense) world is pure fallacy. the world is no such thing.


Susan Anderson

Dear Zebra,

Please calm down. This community has a long traditional of interesting and in-depth conversations about a variety of approaches to understanding and absorbing information as it develops in the cryosphere.

It is my understanding that Neven has been trying to give himself some space (hardly a sabbatical, but at least some time for him to have a home life and deal with regular affairs). His peacekeeping intelligence should not have to be invoked to restore goodwill between good people with different views. Things are difficult enough without us attacking each other.

A dogged insistence on being "right" is not always the best way to tackle the issues we all face. More tolerance, less heat and more light, is what I recommend. Some of us have time on our hands, in which case perhaps a creative effort elsewhere might be more useful.

There are, in general, no people lacking goodwill and intelligence in this community. Let's keep it that way.

Rob Dekker

Frank, I wrote my little program in 'awk' (remember that one? :o).

For anything more complex than linear regression, I know I have to switch to something better. I really like R with all its statistics support but did spend enough time with it to feel comfortable coding in R. I'll take a look at that Python package, but I'm not fluent in Python either.
I may resort to C/C++, since that is my life.

It would be great if you could give it a shot. For the 'extent' and 'area' for all months I use NSIDC (on Neven's 'graph' page) :
For land snow cover I use Rutgers Snow Lab monthly data :

It would be great if you could confirm my findings for June data as a predictor for September ice "extent" (R=0.94 with my formula).
And correlation is even better for ice "area".

Here are the correlation factors against ice melt (Sept 'extent' - earlier "area") if we use only individual variables in prior months as melt formula F : (using 1992 - 2015 data).

                 April     May        June
 F = area        R=0.19    R=0.54     R=0.90
 F = extent      R=0.10    R=0.20     R=0.76 
 F = snowcover   R=0.73    R=0.81     R=0.90 
 F = extent-area R=0.25    R=0.5      R=0.69 
 F = year        R=0.87    R=0.87     R=0.87 
Note that land snowcover in June is a good projector for how much ice will melt out until September, and so is "area" in June. But for earlier months, the best predictor is "year" which is simply reflecting the linear trend of reducing sea ice.

Explicitly note that ice "area" and "extent" in earlier months (April) are very poor predictors for ice melt until September. I think someone upthread asked about.

Rob Dekker

RobertS, are you talking about the "residuals" ? The noise that is left over after linear regression ? If so, you are right that "demons that are lurking in the error bars", but in our case it really seems to be noise (most likely due to variability of summer weather.
The standard deviation of the residuals (1992-2015 data regression with my formula) is 340 k km^2.
And no, it does not have a 'trend', since that would have been taken out already by linear regression.

Rob Dekker

For those of us not familiar with statistics, the standard deviation of the residuals of a linear regression between June data and September data is simply a measure of the uncertainty in the prediction.



It's interesting that you say that. Everyone I've ever worked with/for has told me that my value was particularly in what you call gestalt thinking: Seeing the path to an elusive solution.

But the first time someone (kindly) said that it was a mathematical physicist that I asked for help because... I didn't know how to "do the (particular) math". In other words, seeing the path, even when others don't, doesn't matter, if you can't walk.

A very valuable lesson; I've learned it at every level of development, from people with more experience than I had. You can't wing it, and you can't make stuff up, however clever you are (or think you are).

So, what we are talking about here has nothing to do with complex systems. It has to do errors from Physics 101. I try, from time to time, to pay the lesson forward.

Jim Hunt

Neven's still out on the road, so here are the February 2017 PIOMAS Arctic sea ice volume numbers, together with lots of other numbers too:

"Facts About the Arctic in March 2017"

Here too are the SMOS thickness numbers, courtesy of Lars Kaleschke from the University of Hamburg:

Need I say more?



The updated PIOMAS imagery and data are very appreciated.

Robert S

Rob Dekker: Interesting. Regarding the issue of a "trend", I think that there still can be one. For instance, the size of the residuals could be gradually increasing (more "chaos" in the system), decreasing, etc.



Well presented, comes to no surprise though, what matters is not reported, it is our planet, the billions are mostly left uninformed. The only journalists covering this seem to be the crazy ones claiming that the whole thing is a made up panic for more funds.

Is there a standard total Arctic sea ice ice salinity and density, I wonder?

Elisee Reclus

IN the "February 2017 PIOMAS Arctic sea ice volume numbers" graph posted by Jim Hunt, shouldn't the units on the y-axis read "thousands", not "millions", of cubic kilometers?

Hans Gunnstaddar

"Need I say more?"

No Jim, except I'm just glad this increasingly troublesome situation can be swept under the rug via top US political level GW denial (and budget cuts). Hopefully acceptance of, interest in, funding and real action are conversely proportional to reducing greenhouse gasses. Otherwise we might have been in real trouble. Sarcasm aside thanks for the update.

Frank Pennycook

Hi Rob, yes awk -- an old friend! I don't have much call for it now, mostly, but I'm an everyday user of vim and grep.

Any of those langs - R, C, python (plus others) would do, the thing is to get used to one and stick with it. If you use C (and/or ++) that's going to be fine. I love working in C, but I do find python easier to get up and running for a one-off "quick and dirty" investigation.

Thanks for the data. I will have a go. Just give me a few days to get around to it. I may report in this thread if it's still going, or on the forum.

From eyeballing the numbers it is striking how considerably higher the correlations are in June from May and April, as if the season's outcome is more or less set by then. And also, since "year" is such a strong factor, should it not be included in the analysis? To reflect, as you say, the long-term trend.

Jim Hunt

Elisee - It should indeed! Thanks.

A fix will be implemented forthwith.

Hans - Re those proposed budget cuts, please see another pet project of mine:




I continue explaining albedo interpretations with text, especially explaining a different way to calculate sea ice melts, new photos later.

Rob Dekker

Frank said :

since "year" is such a strong factor, should it not be included in the analysis? To reflect, as you say, the long-term trend.

If we include the "year" variable, then indeed the correlation goes up a little bit more. However, time by itself does not increase heat in the Arctic.

What I wanted to do is to see how we can explain the decline in Arctic sea ice using PHYSICAL variables only. Specifically the ones that we KNOW have an effect on heat absorption : sea ice "area", water close to ice (extent-area) and land snow cover. And with these, with the proper weighting factors, we already obtain R=0.94, explaining (R^2) 88 % of the variability between June and September. Which is pretty darn good.

I've contemplating using other physical variables (like temperature during winter; which relates to the thickness of FYI and thus how fast it will melt out in summer) but I don't want to include too many variables, since as the saying goes : "With four parameters I can fit an elephant, and with five I can make him wiggle his tail".

Bill Fothergill


From the perspective of a female elephant, I would imagine that it's quite important how realistically you "can make him wiggle his tail". ;-)

When you talk about introducing additional physical variables, such as temperature, would I be correct in thinking that you might try to incorporate this in the form of FDDs?

If this semi-assumption of mine is correct (and they're usually not) and you were to attempt assimilation of one of the various FDD<>thickness empirical formulae, current conditions are not doing you any favours.

As I'm sure you know, any empirical formula tends to get "tuned" in order to optimise its skill over the most meaningful range. In recent years (and I'm obviously thinking especially of the 2016/17 winter) the cumulative FDD value tends to be considerably below historic levels. Obviously, this would result in thinner FYI. However, as the relevant formula would have been developed in days of yore, its skill with such a low cumulative FDD is possibly questionable.

Hope that made some sense.

Hans Gunnstaddar


Jim, saw your attempt there - good luck. At the link above is a YouTube video using gumballs to explain something. I won't go into detail what is being explained, but it occurred to me that gumballs could be used to try to explain to people about carbon emissions. Maybe we all missed something really simple, that people respond to colored tiny balls because they can equate them better than if given large numbers. "Each one of these gumballs represents a ton of carbon emissions and X number of these gumballs equals the tons of carbon emissions since 1880. This jar is how much is added each year..." You get the idea. Not sure if it could help.

Maybe also a video using gumballs to explain how much ice is being lost in the Arctic. Maybe denialists would say, "Oh my goodness, why didn't you tell us before using gumballs!? Now we get it."

Frank Pennycook

Rob, sure, "time by itself does not increase heat in the Arctic", I can't disagree with that! What I meant was that since we know there is a secular trend it might pay to work it in for predictive purposes. However, I see the value of not *assuming* it. In fact it is implicitly included in that June extent and the other variables are themselves subject to the trend and the results of warming.

Indeed, the correlations are very good, with the physical variables alone. By the way, I think NASA might have worked out their own similar method, this was published last week:

Petty et al, Skillful spring forecasts of September Arctic sea ice extent using passive microwave sea ice observations, Earth's Future, 27 February 2017

Lord Soth

Trump is rolling back EDA (Environmental Destruction Agency) pollution controls on vehicles and dismantling the Clean Power Plan.

Just what we need, more coal-fired generating stations, and a U-Turn on electric vehicles.

Perhaps we should change anthropogenic to Trumpogenic Climate Change.

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

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