Video: How simple math can help predict the melting of sea ice

The new model predicts the growth of small ponds on arctic ice sheets. Scientific Visualization Studio / NASA

Anurag Papolu, The Conversation

To better predict climate change, scientists need accurate models which predict the behavior of many natural processes. One of these is the melting of arctic sea ice, which requires expensive and difficult data collection in the Arctic.

Physicist Ivan Sudakov at the University of Dayton and his colleagues have developed a new method to understand the growth of small ponds on sea ice. They developed a model which borrows ideas from the 100-year-old Ising model that simulates the behavior of ferromagnetic materials.

This video shows how these small ponds form on the ice, and how the model can be used to understand the process more efficiently.

Anurag Papolu, Multimedia Editor, The Conversation

This article is republished from The Conversation under a Creative Commons license. Read the original article.

33 thoughts on “Video: How simple math can help predict the melting of sea ice

  1. “which requires expensive and difficult data collection in the Arctic” of course it does, they have mortgages to pay, kids to put through University.

    • That is exactly the sentence that jumped out at me.

      from the video:

      “this can help improve climate models by reducing the need for difficult and expensive data collection in the Arctic”

      Well of course our “Multimedia Editor” does not actually link to the paper he wishes us all to know about and clearly does not understand the relationship between models and “expensive data collection “. Firstly you need MORE “expensive data collection” to test and validate your model. Only AFTER you have done that and gained such a high degree of confidence in the continued accuracy of your simple model to match the behaviour of complex chaotic, non-linear system will it potentially reduce the need for more data collection, ie. NEVER.

      It’s true that climate models need any help that they can get on modelling Arctic sea ice. First they totally failed to predict the dramatic drop in sea ice area from 1997-2007, they they tried to tweak the models to better match that and totally failed to match the fact it has basically been flat-lining ever since. ( Something which is show for about half a second on the graph in the video ).

      It seems a pre-print is available here:

      Now lets see what it says without the liberal voice-fry voice over.

      • pause the video 0:10 mark and you will see something like this:

        accelerating melting was a reasonable description up to 2012. However, the massive recovery from 2012 to 2013 and the continued higher lever of ice coverage since it NOT consistent with the simplistic idea that ice albedo is the primary driver.

        It is simply dishonest to keep pumping this narrative and ignore the contrary data of the last decade.

        • … since it NOT consistent with the simplistic idea that ice albedo is the primary driver.

          Albedo is a two edged sword. A surface which is a good reflector is also a bad radiator. A surface which is a bad reflector is also a good radiator.

          In the arctic, when it is not dark, the sun strikes the surface at a shallow angle. That reduces the amount of heat the ice gains when the sun shines. It also increases the amount of heat gained by the atmosphere because the sun has to shine through more of it to get to the surface.

          The thickness of the ice depends on the air temperature. The sea water is trying to melt the ice at all times. The colder the air, the thicker the sea ice can be in face of the fact that the water below is trying to melt it.

          In the completely dark winter, decreased albedo due to soot means that the ice will radiate better and become thicker. (How long complete darkness lasts depends on how close you are to the pole.) The radiating soot removes heat from the ice.

          Scientists operating on the arctic ice, and needing aircraft to deliver supplies, log the ice thickness. Their records demonstrate that ice melting starts well before the air temperature exceeds 0 C because the ice is melting from the bottom up. Pond formation on the surface comes later in the process.

          Sometimes ocean dynamics are such that the ice never forms in certain areas of otherwise contiguous pack ice. These are called “mid-sea polynyas.

          • CB, you said “…Albedo is a two edged sword. A surface which is a good reflector is also a bad radiator. …” and this requires some qualifiers. It is true if the reflection and radiation cover the same band of frequency. If, for instance the reflection is visible light and the radiation (emitted power) is thermal then snow is pretty good at both.

          • Kevin kilty June 17, 2020 at 6:23 am

            Snow is an interesting problem. Because of trapped air, it’s a much better insulator than ice. Snow on top of sea ice has the effect of making the ice thinner.

            On the other hand, since the arctic is basically a desert, there’s darn little snow on top of the ice. Because of the wind, it’s pretty much swept clean. The snow will form long drifts behind anything that sticks up like a tent for instance.

    • It has been found that if a melt pond parameterization is
      included in climate model simulations, then predicted September ice volume from 1990 to 2007 is nearly
      40% lower than in simulations which do not incorporate ponds, and is in much closer alignment with

      There are NO observations of sea ice volume before cryosat2 in 2011. All there is are guestimates made from ice area/extent observations.

      It is telling that when publishing in 2020, he chooses end his claim of “much closer alignment with
      observations” in 2007. After 2007 climate models predict continued and accelerating sea ice decline. Presumably his super new model which produced 40% MORE melting is even worse at modelling the post 2007 evolution of Arctic sea ice which is why he chooses to keep quiet about it.

      I guess that’s the kind of blinkered attitude which won him the “Green Talent” award from the german govt. in 2013.

      While this pre-print may be useful in modelling melt pool evolution and distribution, clearly it contributes NOTHING to our understanding of the fundamental drivers of Arctic sea ice. We have no idea why the “run away ” melting from 1997-2007 stopped, this it is clear that the predominant and naive dogma open water leads to more melting is fundamentally wrong.

    • Thanks, that published text varies somewhat from the pre-print on Sudajov’s site.

      They have obscured the fact that claimed improvement in match with observations stops in 2007 and no longer applies to post 2012 sea ice.

      and the yearly Arctic sea ice minimum can be accurately forecast from melt pond area in spring

      This claim in attributed to another paper from 2014 which claims:

      Our results help explain the acceleration of Arctic sea-ice decrease during the past decade. The inclusion of our new melt-pond model promises to improve the skill of future forecast and climate models in Arctic regions and beyond.

      It would be prudent to test whether this predictive ability is still there while the general trend for arctic sea ice minimum has been an increase since 2012. How well did it work in 2013 when sea ice volume was 65% HIGHER than in 2012 ?

      This all would be powerful tests of these models. Not surprisingly they do not even mention anything later than the 2012 OMG minimum and the notable end of the “run away melting” they have been screaming about since AR4.

      Don’t mentions the end of run away melting !

      It’s getting a bit like John Cleese’s ” don’t mention the war”.

      How can they seriously publish on this in 2019 and ignore most of the last decade of ice data.

    • “Ising model”, “Glauber”, “metastable”,”anisotropic random Fourier surfaces”, and more, with a thrown in Zeta function exponent analysis….this paper seems to be the work of mathemagical monkees typing random buzzword phrases on their keyboards….

  2. ” … scientists need accurate models …”
    First, define accurate.
    Second, if your model predicts accurately, show how accurately.
    To do this, you need more than the wave of an arm. There are established methods and numerical procedures to assess and report accuracy in a meaningful way. Why not use them in your advertising blurb?
    Geoff S

    • Geoff — Why do we need to define accurate & show how accurately when we have the all knowing Mosher doing drive by posting and explaining it all for us nitwits??

  3. The Climate Dowsers don’t want accurate models. They want models that confirm what they want them to show. CMIP6 ensemble getting hotter over CMIP5, which everyone knows runs hot, proves that the climate dowsers don’t want accuracy. They want alarm.

    These UDayton guys are just trying weasel in on a piece of the climate rent action with their code project.

    • It may give some useful insight into development of melt pools but nothing more. The constant pushing of failed and simplistic “albedo feedback” hypothesis just a political narrative not science.

      As always they focus on anything which promotes “the cause” and ignore the rest.

      How does glazing incidence affect reflection on these relative flat pools of water. How does IR emitted by open water ( nearly “black” at thermal IR wavelengths ) affect the total energy budget? How does increased evaporation work out?

      Open water works acts 24/7 and since there is much more of it than in 1990s, that is counteracting the solar albedo .

  4. The computer model is shown in the video from 0:46. Is it a coincidence that the computer model looks like the “game of life”?
    Press play and have fun!
    These climate scientists may have borrowed their code there…

    • Sadly, the Game of Life author passed away in April.
      John Conway (26 December 1937 – 11 April 2020)
      We regret to announce that John Conway, the John von Neumann Professor Emeritus of Applied and Computational Mathematics and Professor Emeritus of Mathematics, died April 11. He was 82. —Princeton University

  5. Horizontal heat transfer. Through ice. In the Arctic. I’m sure it’s HUGE..

  6. Note that the calculations use what the author calls the “average albedo of melt ponds.” It isn’t described how that was defined or measured. At about 38 seconds into the video, there is an image showing that the sun glint off the water is distinctly brighter than the snow, while the audio claims that the dark water is absorbing more light than the snow!

  7. Strange how it is always about how ice melts in summer and never about how ice & snow accumulates during the winter.

    If we have truly left the LIA then the poles and low elevation glaciers should naturally melt and shrink.
    And if the planet is warming up then this should help dampen the prevailing winds to the north and south of the equator so they become increasingly wetter in these regions. This additional rain over tropical deserts will over time help to make the planet greener and make the biosphere productive.

    If however this last 100 years or so has been just a mere warm blip in the otherwise continuing LIA, (and probably to be compounded with the potential of a grand solar minimum) then the extreme weather of the LIA will return. And with such changes to a climatically cooler planet survival in the biosphere becomes so much tougher.

    Nature is in charge of this planet’s climate changes not humans.

  8. I have the feeling that these melt ponds on top of the ice reflect more of the incident sunlight and SWIR than anyone gives them credit for. Snow (and to a somewhat lesser extent, névé or firn) look white from almost any viewing angle because they diffuse incident light. The ponds look dark, but we are not seeing any reflection from their surfaces because we’re not looking at the appropriate angle to see it.

    If you’ve ever been out fishing on a lake on a sunny day, you will almost certainly have noticed the blinding reflection from the water if you look towards the sun. You can also feel the heat on your face from the reflection, and this tells you that a significant portion of the incident IR is also being reflected.

    Reflectivity of a water surface is highly dependent on the angle of incidence, varying from zero (no reflection) at 90° to 1 (total reflection) when the angle of incidence tends towards zero. In the Arctic summer, the sun is low in the sky for most of the day, so there will be significant reflection from smooth pond surfaces. If it’s windy and the water surface is wavy, there will be strong reflection from those parts of wave surfaces where the angle of incidence is low. The same is also true of open water, obviously.

    This type of reflection is called specular, as opposed to diffuse reflection, what we get off snow, clouds, matte white paint, etc. I wonder if specular reflection is taken into account when they try and calculate the energy budget of Arctic ice in the summer? My guess is that it’s not. They just use albedo, which only accounts for diffuse reflection.

    • Smart Rock
      You remarked, “You can also feel the heat on your face from the reflection, and this tells you that a significant portion of the incident IR is also being reflected.” Indeed, the higher the value of the specular reflectance, the more closely the reflected light matches the spectrum of the source. At, an angle of incidence of 90 deg, the spectrum of the source and reflected light rays are identical.

    • Reflected sunlight
      Yes, learned that one salmon fishing
      Always put sunscreen everywhere, got the worst sunburn under my chin

    • The reflected light when the sun is low in the sky is dominated by the perpendicular component, hence why polaroid sunglasses are important while fly fishing. At 53º incidence all the reflected light is perpendicular all the parallel component is absorbed

      • Phil
        Does the Brewster Angle have some bearing on my point that the spectrum of reflected light is the same as the incident light at glancing angles?

        You have the relationship backwards. It is the perpendicular component that has a minimum reflectance at the Brewster Angle.

  9. Arctic ice extent shrunk considerably from 1996 to 2006 and has plateaued ever since. MASIE, DMI, JAXA and NSIDC all confirm this.

    But never let the facts interfere with a good story.

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