Dissipation, continuum mechanics, mixtures and glaciers

by Dan Hughes

A brief continuation of previous discussions about calculation of viscous heat dissipation in the flow of liquids having linear stress/rate-of-strain constitutive description.

The current notes focus on a few papers in the glaciology literature relating to the subject. Papers that applied fundamental continuum mechanics concepts to development of model equation systems for glacier applications is introduced.

These notes are of a nature of short introductions to a few papers and ideas. Very likely of interest to those interested in the subject


These notes are a continuation of the discussions initiated in this previous post at CE. The focus is on the mathematical description of viscous heat dissipation of kinetic energy into thermal energy. In the previous notes I identified the textbook by Bird, Stewart, and Lightfoot [1960] as a valid source for such information. The exact same description appears in a multitude of other textbooks. Because the physical phenomenon is of a foundational nature, its description is generally not open to questions and debate about the year of publication.

The material in the textbooks is a summary of the development given by Bird [1957], in which he used the fundamental local-instantaneous equation for balance of kinetic energy to develop a macroscopic formulation of that equation and the generalized mechanical energy balance equation. The latter is a method of including losses due to viscosity into the Bernoulli equation. Bird’s approach seems to be very appropriate because viscous dissipation of kinetic energy  involves both kinetic energy and viscosity.

I have looked into development of the formulations for viscous heat dissipation as used in the glaciology literature a little ways back into past time. My review is very limited; the literature is vast and goes back into the 19th century.

Viscous heat dissipation could be considered important because the increased fluid temperature associated with the phenomenon has a potential to cause melting of ice in glaciers beyond what would occur if the process did not exist. Additional melting could potentially affect the amount of meltwater that enters the Oceans, and also could provide lubrication for motion of glaciers by way of liquid films between the bottom of the glacier and the solid materials over which they slide. Both issues have been research subjects.

However, there is uncertainty associated with all applications given the complexity of the application domains. In several aspects, the exact topology of glaciers, both interior too and the bounding surfaces of, cannot be known. Some research uses a sensitivity approach directed toward heat transfer, by changing the initial fluid temperature, for example, or direct variation of the heat transfer coefficient, or assuming that the ice and meltwater are at the melting temperature of the ice at the local pressure. In the latter approach, any additional energy in the fluid, by dissipation for example, goes 100% into melting.

Focused Validation on each potential uncertain aspect is very likely beyond what can be accomplished in the complex physical domain of the applications. Presently, Validation relies on use of integrated functional responses and these cannot ensure causality between any one uncertain parameter and the response function of interest.

Mayaud and Macdonald

In a comment at a previous post, I mentioned that Mayaud [2012] in Equation 7 reports the exact formulation for conversion of turbulent kinetic energy into thermal energy that is given in all engineering textbooks on hydraulics, hydrodynamics, fluid mechanics, and engineering fluid flow. Mayaud did not cite a source for the term.

After that, I ran across Macdonald [2013] in which Equation 3.9 reports also the same formulation as Mayaud, and cites Spring and Hutter [1981, 1982]. Both these MPhil Dissertations by Mayaud and Macdonald are from the Scott Polar Research Institute at Cambridge University and acknowledge N. Arnold, who works in the subject area.

Having discovered publications that support my textbook references, I decided to track down additional information about the Spring and Hutter publications. The 1982 publication in the International Journal of Engineering Science is basically application of fundamental mathematical and continuum mechanics concepts to derivation of a model for the hydrodynamics and thermodynamics of glaciers, with a focus on interactions between liquid and solid.

Both publications have an equation for thermal energy, in temperature, that includes the viscous dissipation formulation given in numerous textbooks.

Google Scholar search for Numerical Studies of Jökulhlaups, the 1981 paper, gives 161 hits: https://scholar.google.com/scholar?cites=4486452605670902537&as_sdt=5,33&sciodt=0,33&hl=en

and the journal page says 99 citations: https://www.sciencedirect.com/science/article/abs/pii/0165232X81900069

Google Scholar search for the phrase viscous+heat+dissipation within Spring and Hutter gives about 60 hits:


Google Scholar indicates that the 1982 paper has been cited 92 times:


Continuum Mechanics and Mathematical Models of Mixtures

Spring and Hutter [1982] is among the most thorough that I encountered in the glaciology literature. The work includes development of a local-instantaneous formulation of the fundamental conservation and balance equations, and that development is based upon concepts of continuum mechanics. The resulting equations are then averaged over the cross-sectional flow area of the fluid to arrive at a useful equation system for real-world applications. That system is exactly analogous to the Standard Operating Procedure (SOP) system almost universally used in engineering applications. Engineers have developed 1-dimensional mathematical models of mixtures for flows internal to engineered equipments in a wide range of industries and associated mixtures.

The mathematical research by Spring and Hutter is detailed to an extent usually associated with derivation of PDE systems for the hydrodynamics and thermodynamics of mixtures of fluids such as the liquid and vapor phases of a single pure substance, like water, or a mixture of a liquid and solid, for examples. The results are applicable to a wide range of mixtures. The theoretical approach is less ad hoc than the approaches that preceded its development.

Spring and Hutter [1981] provides a brief summary of the theoretical developments. The 1981 paper is freely available and is much more accessible than the 1982 Engineering Science paper. Both reports are based on Spring’s Dissertation, which is in German: https://www.research-collection.ethz.ch/handle/20.500.11850/136573, and https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/136573/eth-34999-02.pdf?sequence=2&isAllowed=y An application is given also by Clarke [2003].

Following up on the literature associated with a continuum mechanics approach, Google Scholar revealed that Kolumban Hutter at ETH Zürich Switzerland continues to be active in that area: https://scholar.google.com/scholar?start=210&q=author:%22Kolumban+Hutter%22&hl=en&as_sdt=0,33&as_vis=1

Hutter has co-authored papers with J.M.N.T. Gray who focuses continuum mechanics of granular mixtures, such as mixtures of snow and air flow during avalanches: https://scholar.google.com/citations?hl=en&user=paP4fxYAAAAJ&view_op=list_works&sortby=pubdate William Gray

An example is: J. M. N. T. Gray (1996), Water movement in wet snow, Philosophical Transactions of the Royal Society of London. Series A, Vol. 354, pp. 465–500, https://doi.org/10.1098/rsta.1996.0017.

Continuum mechanics formulations of fundamental equations for mixtures of all kinds has been a growth industry for over 60 years, and counting. Bedford and Drumheller [1983] cited 296 sources; about 40 years ago. The mixture of ice plus liquid water plus air, for example, is of interest in the hydrodynamics and thermodynamics of glaciers; Meyer and Hewitt [2017]. R. M. Bowen [2014] has published extensively on continuum mechanics of mixtures. He has synthesized the mathematics that evolved over periods of times of uncertainty associated with fundamental issues.

The paper by Meyer and Hewitt includes an equation for balance of thermal energy in terms of the temperature. That equation does not include viscous heat dissipation. This situation is common in almost all engineering analyses that include accounting for energy exchange between the fluid and channel walls. The dissipation contribution is omitted in comparison with the other contributions in thermal energy equations.

As noted in my original post, conversion of kinetic energy into thermal energy by way of viscous dissipation is about 0.4%, i.e. 0.004 per unit mass, of the pressure change due to wall-to-fluid friction, for water flowing full in a channel: Ehat = 4 (DP_fric) / Rho, Eps = W*Ehat.

Several papers noted in my original post calculated VHD by assignment of the complete potential energy change along the potential gradient to viscous heat dissipation. i.e. viscous dissipation of potential energy / “(frictional dissipation of gravitational potential energy)”.


Byron Bird, Warren E. Stewart, and Edwin N. Lightfoot (1960), Transport Phenomena, 1st Edition, John Wiley & Sons, Inc., New York.

Byron Bird (1957), The equations of change and the macroscopic mass, momentum, and energy balances, Chemical Engineering Science, Vol. 6, pp. 123-131.

Spring and K. Hutter (1981), Numerical studies of Jökulhlaups, Cold Region Science and Technology, Vol. 4, pp. 227–244.

Spring and K. Hutter (1982), Conduit flow of a fluid through its solid phase and its application to intraglacial channel flow, International Journal of Engineering Science, Vol. 20, No. 2, pp. 327-363.

Jerome Mayaud (2012), Modelling meltwater drainage in the Paakitsoq region, western Greenland, and its response to 21st century climate change, (MPhil Polar Studies, Scott Polar Research Institute, University of Cambridge thesis).  https://doi.org/10.17863/CAM.9650

Macdonald (2013). Modelling the subglacial drainage system of Petermann Glacier, north-west Greenland, (MPhil Polar Studies, Scott Polar Research Institute, University of Cambridge thesis). https://doi.org/10.17863/CAM.21249

R. Mayaud, A. F. Banwell, N. S. Arnold, and I. C. Willis (2014), Modeling the response of subglacial drainage at Paakitsoq, west Greenland, to 21st century climate change, Journal of Geophysical Research: Earth Surface, Vol. 119, doi:10.1002/2014JF003271.

Colin R. Meyer and Ian J. Hewitt (2017), A continuum model for meltwater flow through compacting snow, The Cryosphere, Vol. 11, pp. 2799-2813.

Garry K. C. Clarke (2003), Hydraulics of subglacial outburst floods: new insights from the Spring-Hutter formulation, Journal of Glaciology, Vol. 49, No.165, pp. 299-313.

A Bedford and D. S. Drumheller (1983), Theories of immiscible and structed mixtures, International Journal of Engineering Science, Vol. 21, No. 8, pp. 863-960.

Ray M. Bowen (2014), Porous Elasticity: Lectures on the Elasticity of Porous Materials as an Application of the Theory of Mixtures:


Related Material

Weertman (1969). Water lubrication mechanism of glacier surges. Canadian Journal of Earth Sciences, Vol. 6, No.4, pp. 929–942. doi:10.1139/e69-097

F. Nye (1976), Water flow in glaciers: Jökulhlaups, tunnels, and veins, Journal of Glaciology, Vol. 17, No. 76, pp. 181-207.

Röthlisberger (1972), Water pressure in intra- and subglacial channels, Journal of Glaciology, Vol. 11, No. 62, pp. 177-203.

Weertman (1972), General theory of water flow at the base of a glacier or ice sheet, Reviews of Geophysics and Space Physics, Vol. 10. No. 1, pp. 287-333.

L. Shreve (1972), Movement of water in glaciers, Journal of Glaciology, Vol. 11, No. 62, pp. 205-214.

Kenneth M. Golden, Luke G. Bennetts, Elena Cherkaev, Ian Eisenman, Daniel Feltham, Christopher Horvat, Elizabeth Hunke, Christopher Jones, Donald K. Perovich, Pedro Ponte-Castañeda, Courtenay Strong, Deborah Sulsky, and Andrew J. Wells, (2020), Modeling Sea Ice, Notices of the American Mathematical Society, Vol. 67, No. 10, pp. 1535-1555. DOI: https://doi.org/10.1090/noti2171

Joseph S. Walder (2010), Röthlisberger channel theory: its origins and consequen

82 responses to “Dissipation, continuum mechanics, mixtures and glaciers

  1. Pingback: Dissipation, continuum mechanics, mixtures and glaciers - News7g

  2. People study glaciers to no end, but none I have read mention the most significant facts about glaciers, especially sequestered ice in polar regions.

    The ice is there, in the first place, because when tropical currents remove sea ice, there is evaporation and snowfall and resulting IR out of tropical stored energy from the sun that is radiated out of the polar regions without immediate cooling of the climate system. Cooling of the climate systems occurs after the ice accumulates enough to push ice into the turbulant salt water currents, to chill them to below freezing as salt and ice and water in an ice cream maker. this forms sea ice to stop the accumulation of ice but the already accumulated ice cools the climate system until the ice is depleted.

    Ewing and Donn explained this seventy years ago. Peer Reviewed Climate Consensus prevents this powerful self-correcting climate forcing to even be discussed.

  3. Iain Climie

    I apologise for being blunt but can I suggest there is a lot of effort being applied here which is academic (in an unflattering sense) when there are actions which make sense regardless of what climate change throws at us. I’ve gone into detail here:


    regards, Iain

    • Yeah. What’s with all this ‘academic’ stuff? There’s no need to study anything. We should accept every doomsday scenario, reject out of hand any questioning of this and all react emotionally and hysterically and there’s absolutely no chance of knee jerk reactions or vested interest among those convinced we’re all going to die in a roasting inferno.

      After all there’s absolutely no benefit to burning fossil fuels so let’s stop now ‘just in case’. What could possibly go wrong?

  4. The quantum mechanics of the CO2 molecule define its affect on the Green House Gas Effect. CO2 thermalizes 2.7, 4.3, and 15 micron LWIR. No one denies that. 2.7 and 4.3 micron LWIR aren’t really emitted from the earth except over Volcanoes or very very hot spots, so we are only really dealing with 15 micron emissions and thermalization. No one denies that. The oceans are warming. No one denies that. 15 micron LWIR won’t penetrate or significantly warm water. No one denies that. Wavelengths are associated with temperatures, especially IR wavelengths. No one denies that. 15 micron LWIR is associated with a black body of temperature -80C, no one denies that. Ice emits shorter higher energy LWIR than CO2 does. No one denies that. Radiation from CO2 doesn’t even have the energy to melt ice, let alone warm water. No one denies that. The quantum mechanics of a CO2 molecule simply doesn’t support CO2 causing catastrophic climate change. CO2 represents 1 out of every 2,500 molecules in the atmosphere or 400 parts per million (approx), it would take very high energy vibrations for 1 out of 2,500 molecules to materially impact the thermal vibrational state of the other 2,499 molecules of the atmosphere. CO2 doesn’t absorb the high energy wavelengths that would be required to do that. It would be very easy to prove me wrong. Simply take a long pass filter isolating 12 to 18 microns of LWIR, shine a light through it onto a bucket of water, and measure the temperature change. I find it curious that I haven’t been able to find that foundational experiment actually being run. Controlled experiments after all are the foundation of real science. Here is the closest I’v come to finding someone that understands these basic and critical principals.

    • Cam Thomas

      Agree, I’ve been saying this for 20 years. Additionally, controlled experimentation on whether a 1 in 10,000 increased in the concentration of atmospheric CO2 increases the temperature of that atmosphere by +1 degree C has probably never been done. If it had, QED for AGW related to atmospheric CO2.

  5. I believe it was the NSIDC that used to have a prominent graph of Northern hemisphere land ice volume mass estimates. It was a pretty fantastic thing seeing it plummet prior to 1950. The latent heat change must’ve been fantastic.

  6. Pingback: Dissipation, continuum mechanics, mixtures and glaciers – Climate- Science.press

  7. “The focus is on the mathematical description of viscous heat dissipation of kinetic energy into thermal energy.”

    Dr. Curry, no discussion about the GHG effect is complete without a discussion of the Quantum Mechanics of the CO2 molecule. CO2 thermalizes 13 to 18, peak 15 Micron LWIR. No one denies that. CO2 is 400 PPM (Rounded to make the math simple) or 1 out of every 2,500 molecules in the atmosphere. 15 Micron LWIR has the energy of a black body of temperature of -80C, in other words, ice emits higher energy LWIR than CO2 does. Does it make sense that vibrating 1 out off ever 2,500 molecules to a degree consistent with a black body of -80C can cause the other 2,499 molecules to vibrate in any material way? Can you warm something by adding -80C energy? Can you warm coffee by adding ice? Also, 15 micron LWIR won’t warm water and the oceans are warming. Incoming visble radiation warms the oceans, not outgoing LWIR.

    • Robert David Clark

      Look above. July 2021 the monthly death was at its lowest, as we are now. What would it take for the 535 elected members of Congress to pass a bill allotting $2 billion to complete the wall?
      Gun control is more important than 350 individuals Dieng in the USA daily?

  8. Clyde Spencer

    “… or assuming that the ice and meltwater are at the melting temperature of the ice at the local pressure. In the latter approach, any additional energy in the fluid, by dissipation for example, goes 100% into melting.”

    However, it takes 80X as much energy to transition from ice to water (with no temperature change) as it takes to increase the temperature of the melted water 1 K. The ice can soak up a lot of energy.

    • Dan Hughes

      The assumption is based on pressure-melting of the ice at the base of a glacier that can be many, many meters thick. I have not looked into the details of that phenomenon.

      • Robert David Clark

        Positive 56,471
        Tests 2,173,968
        % of total tests 2.60
        Total deaths 266
        Average % of total tests last 7 days 3.38

    • Robert David Clark

      It appears the CDC employees had a 3-day weekend
      The readings for this weekend were useless. The COVID-19 will continue here if allowed.

      • Robert David Clark

        MARCH, 2020 26,061
        APRIL, 2020 75,571
        MAY, 2020 23,283
        JUNE, 2020 23,362
        JULY, 2020 29,717
        AUGUST, 2020 28,607
        SEPTEMBER, 2020 27,798
        OCTOBER, 2020 24,271
        NOVEMBER, 2020 38,500
        DECEMBER, 2020 77,967
        JANUARY, 2021 99,352
        FEBRUARY, 2021 74,211
        MARCH, 2021 39,672
        APRIL, 2021 24,923
        MAY, 2021 20,271
        JUNE, 2021 10,436
        JULY, 2021 9,090
        AUGUST, 2021 27,410
        SEPTEMBER, 2021 60,182
        OCTOBER, 2021 52,027
        NOVEMBER, 2021 35,449
        DECEMBER, 2021 45,574
        January, 2022 61,445
        FEBRUARY, 2022 65,929
        MARCH,2022 33,362
        APRIL 14,245
        May, 2022 10,626

      • Robert David Clark

        June, 2022, 11,005

      • Robert David Clark

        Look at July of 2023. Now May & June of 2022.
        With the present open border, I believe we will see a rapid growth all the way to the election!!!!!

    • Robert David Clark

      Positive 4,522
      Tests 2,869
      % of total tests 159.28
      Total deaths 11
      Average % of total tests last 7 days 4.01

      Positive 5,600
      Tests 4,922
      % of total tests 113.77
      Total deaths 7
      Average % of total tests last 7 days 4.89

      Positive 32,707
      Tests 719,420
      % of total tests 4.55
      Average % of total tests last 7 days 4.39

      Instead of debating a bill on gun control this week, it would be nice to see a bill passed to complete the wall on the southern border. If completed this month, by the end of the year, it would save 10,000’s of lives in the United States of America

    • Robert David Clark

      Positive 73,033
      Tests 851,021
      % of total tests 8.58
      Total deaths 196
      Average % of total tests last 7 days 2.97

    • Robert David Clark

      Positive 90,268
      Tests 2,182,237
      % of total tests 4.14
      Total deaths 305
      Average % of total tests last 7 days 4.59

      Total deaths from COVID-19 in USA for May, 2022 was 10,626
      That is an average of 353 per day.
      Finish the border wall. The gun control bill can wait a month.

      As a powerful politician said yesterday

    • Robert David Clark


    • Robert David Clark

      Positive 46,180
      Tests 645,838
      % of total tests 7.15
      Total deaths 322
      Average % of total tests last 7 days 3.47

    • Robert David Clark

      Positive 13,854
      Tests 188,383
      % of total tests 7.35
      Total deaths 17
      Average % of total tests last 7 days 4.70

    • Robert David Clark

      Back in April 2021 I missed the 6-day rule. Since then, over 680,000 individuals have died of COVID-19 and Joe Biden is our President.
      Above is a website I have been sending copies of what I have been doing.
      I am sending this to it. If you are still out there, send the below to Ms Melania Trump
      Mr. Clark needs your help.

    • Robert David Clark

      Positive 33,568
      Tests 429,665
      % of total tests &.81
      Total deaths 88
      Average % of total tests last 7 days 4.81

    • Robert David Clark

      Positive 59,661
      Tests 1,077,623
      % of total tests 5.54
      Total deaths 290
      Average % of total tests last 7 days 4.94

    • Robert David Clark

      Positive 65,659
      Tests 1,591,699
      % of total tests 4.13
      Total deaths 186
      Average % of total tests last 7 days 5.49

    • Robert David Clark

      Positive 55,480
      Tests 914,527
      % of total tests 6.07
      Total deaths 148
      Average % of total tests last 7 days 5.18

    • Robert David Clark

      Looking at the Average % of total tests last 7 days it appears the Federal Government has eliminated TITLE 42.

    • Robert David Clark

      Positive 77,081
      Tests 2,421,217
      % of total tests 3.18
      Total deaths 168
      Average of total tests last 7 days 4.96

    • Robert David Clark

      I just watched 2000mules. It cost me $20.00 and about 1.5 hour online.

      • Robert David Clark

        It would be nice if former Attorney General Bill Barr watched the above.
        If yes would have recommended inditement of any of the mules after seeing the evidence?

      • Robert David Clark

        Evidently Mr. Barr has seen 2000mules. He does not believe the analyses of the cell phones is acceptable as proof of fraud.
        I no longer have faith in him, but I will finish reading his book. I am in chapter 13

    • Robert David Clark

      Positive 27,915
      Tests 308,960
      % of total tests 3.95
      Total deaths 58
      Average % of total tests last 7 days 3.95

    • Robert David Clark

      Positive 10,721
      Tests 240,471
      % of total tests 4.46
      Total deaths 17
      Average % of tests last 7 days 4.73

    • Robert David Clark

      Positive 22,197
      Tests 397,180
      % of total tests 5.59
      Total deaths 67
      Average % of total tests last 7 days 4.58

    • Robert David Clark

      Positive 59,098
      Tests 682,140
      % of total tests 11.60
      Total deaths 239
      Average % of toal tests last 7 days 4.85

    • Robert David Clark

      “I don’t want to hear any more about reckless spending. We are saving people’s lives!” President Biden.
      586,004 have died in the USA from COVID-19 since January 31, 2021.
      Build the wall!!!!!

    • Robert David Clark

      Positive 57,675
      Tests 684,723
      % of total tests 8.42
      Total deaths 247
      Average % of total tests last 7 days 5.49

    • Robert David Clark

      Positive 62,871
      Tests 671406
      % of total testd 9.36
      Total deaths 157
      Average % of total tests last 7 days 5.88

    • Robert David Clark

      Positive 62,721
      Tests 378,857
      % of total tests 16.56
      Total deaths 147
      Average % of t0tal tests last 7 days 11.3c

    • Robert David Clark

      Positive 7,469
      Total tests 118,571
      % of total tests 6.30
      Total deaths 22
      Average % of total tests last 7 days 6.93
      Average % of total tests last 7 days up 46.5% since 6/12/202

    • Robert David Clark

      Positive 17,928
      Tests 233,516
      % of total tests,,7.68
      Total deaths 30
      Average % of total tests last 7 days 9.16
      The border crossers are raising the AVERAGE % OF DAILY POSITIVE CASES very rapidly. It appears TITLE-42 is no longer being used!!!!!

      • Robert David Clark

        Robert David Clark | June 15, 2022 at 11:28 am | Reply
        “I don’t want to hear any more about reckless spending. We are saving people’s lives!” President Biden.
        586,004 have died in the USA from COVID-19 since January 31, 2021.
        Build the wall!!!!!

    • Robert David Clark

      Positive 19,474
      Tests 174,158
      % of total positive 11.18
      Total deaths 29
      Average % of total positive last 7 days 9.76

      • Robert David Clark

        A while back I said Donald J. Trump has one major flaw, “Every time he opens his mouth, he must tell the truth as he believes it. The majority of the time he is correct.”
        Complete the wall!!!
        In November we need American Patriots with full control of both houses of Congress!!!!!

      • Robert David Clark

        9.76 7-day average is growth of 106% from 06/12/2022. You are seeing the definition of LOGRYTHMIC GROWTH.

      • Robert David Clark

        Look at the monthly chart above, July 2021. that is when the open borders police from January 2021 passed the testers and contact tracers!!!!!

    • Robert David Clark

      Positive 38,935
      Tests 401,865
      % of total tests 9.69
      Total deaths 147
      Average % of total tests 10.03

    • Robert David Clark

      Positive 50,453
      Tests 992,182
      % of total tests 5.09
      Total deaths 283
      Average % of total tests last 7 days 9.76

    • Robert David Clark

      Positive 54,550
      Tasts 887,581
      % of total tests 6.15
      Total deaths 229
      Average % of total tests last 7 days 7.89

    • Robert David Clark

      Positive 60,920
      Tests 623,249
      % of total tests 9.78
      Total deaths 168
      Average % of total tests last 7 days 4.82
      We will see if today is here tomorrow.

    • Robert David Clark

      Positive 76,103
      Tests 862,056
      % of total tests 8.83
      Total deaths 193
      Average % of total tests last 7 days 5.21

    • Robert David Clark

      Ms. Curry
      I just saw your post.
      Everything I did I tried to keep out of the way and together
      I apologize if it bothered you, but it may have saved many lives.

      • I for one have no idea what those posts were even about, that was the problem. What country? Global? etc.

      • “I apologize if it bothered you, but it may have saved many lives.”

        How could anyone use the data you post to their benefit?

  9. Robert David Clark

    There are three methods of heat transfer. They are conduction, convection, and radiant heat. Heat transfer to or from the earth can only be done by radiant. All material contains heat and is radiating it to cooler surfaces or absorbing it from warmer surfaces. The difference is the heat gain or loss of the material.

    The earth gains heat radiated from the sun and losses heat it radiates to outer space, called black sky radiation. Outer space is considered absolute zero.

    The amount of radiant heat hitting the earth from the sun daily is relatively constant. The radiant heat lost daily by the earth thru black sky radiation is relatively constant since absolute zero is constant. A 1 to 2 degree rise in 522 degrees is relatively constant. The amount of heat gained by the earth’s surface depends on the surface area of the earth covered by water relative to that covered by land. Land area absorbs a larger percent of the radiant heat relative to the water area since the surface of the water reflects a percentage of the radiant heat back to outer space. The daily access heat, or loss of heat, is transferred to the oceans thru conduction and convection where it works its way to the poles and it freezes water adding to the polar ice caps or melts the polar ice caps thus keeping the surface temperature of the oceans, thus the earth, relatively constant. As the polar ice caps grow or melt, the surface area of the earth covered by land relative to that covered by water changes. This is the definition of global warming. I call it Global Ice making and Global Ice Melting.

    That radiant heat absorbed by oceans and land masses is transferred to the atmosphere thru conduction and convection. When it is winter in one hemisphere it is summer in the other and the same with spring and fall. I would think the average temperature of the lower 5,000 feet of the atmosphere changes about 10’F to20’F each day. This takes more heat than man has added to the earth in the last 50 years. That heat man adds to the atmosphere each day is radiated to the black sky and the infinitesimal amount left helps melt the ice during global warming, should be called Global Ice Melting.

    Absolute zero is -459.68’F and the average surface temperature of the sun is between 7,300’F and 10,000’F. If we could go back in time 18,000 years, the end of the last ice age, we would probable see that the average daily temperature of the earth was in the mid 60’F as it is today. You must understand the amount of heat gained every 24 hours is almost equal to that lost during the same 24 hours. Angle of the earth’s axis is 23.5’. Radiant heat striking the earth surface every day is larger than that radiated from the surface to the black sky. That retained by the surface is dependent by the surface area of the earth covered by water.

    The average surface temperature of the earth surface is about 63.5’f. The difference between the earth’s average surface temperature and absolute zero is 522’F. The heat loss to black sky radiation every 24 hours is constant. The average radiant heat striking the surface of the earth is constant. Because the sun is an active star the average surface temperature will change over centuries. As the surface area of the earth covered by water increases, the more radiant heat is reflected to the black sky increases. When the daily radiant heat gained by the earth from the sun in 24 hours became less than that lost by black sky radiation, we began the making of ice, thus the new ice age. Looking at the ice core from the Antarctic we can see that the earth began the new Ice Age about 18,000 years ago.

    The Vostok Ice core shows 4 Ice Ages in the last 4 hundred thousand years. I will assume that during that time the CO2 emitted by the actions of nature is constant. The lowest CO2 level is about 190ppm and frozen during the Ice Making somewhere in the middle of the Ice Making cycle, but the actual end of the Ice Making cycle is much later. The beginning of the rise in CO2 is the beginning of the next Ice Making cycle.

    The last Ice Age, from lowest ocean level to lowest ocean level, was about 120,000 years.

    The first 8,000 years taking ice from the continents and putting the water in the oceans. RAISING THE LEVEL OF THE OCEANS.

    The next about 8,000 years, taking water from the oceans, freezing it, dropping the ice on the frozen parts of the continents. The ocean levels begin to drop. The radiant heat radiated to the black sky is equal to that retained by the earth from the sun.

    When the ocean levels began to rise, as it got to the new ice blocks the 28-degree salt water began melting the underside of the ice blocks. WHEN THE HEAT MELTING THE ICE BREAKING OFF THE ICE BLOCKS EQUALED THE HEAT LOST TO THE BLACK SKY THE OCEANS STOPPED GOING DOWN.



    There are two rules of water that control the world.

    We all know that fresh water expands as it cools from 39 degrees farenheight to 32 degrees farenheight.

    The other is salt water is saturated at 28 degrees farenheight. As nature tries to cool it below that the salt drops out and it is less Dence. As the 28degree touches the bottom edge of the ice block it eats its way under the ice block as the 32degree farenheight hugs the bottom of the ice block on its way out. This causes the overhang.

    • Dan Hughes

      The article by Golden et al. cited in the post is an indepth mathematical exposition of the many multi-discipline aspects of sea ice, including mixture aspects.

      It is open access, but far from an easy read.

      Kenneth M. Golden, Luke G. Bennetts, Elena Cherkaev, Ian Eisenman, Daniel Feltham, Christopher Horvat, Elizabeth Hunke, Christopher Jones, Donald K. Perovich, Pedro Ponte-Castañeda, Courtenay Strong, Deborah Sulsky, and Andrew J. Wells, (2020), Modeling Sea Ice, Notices of the American Mathematical Society, Vol. 67, No. 10, pp. 1535-1555. DOI: https://doi.org/10.1090/noti2171

      • Robert David Clark

        Earth’s sea ice packs in a changing climate. The sea ice
        covers of the polar oceans are a critical component of the
        global climate system. They are vast in areal extent, covering millions of square kilometers, but are only a thin veneer of ice a couple of meters thick. Sea ice serves as both
        an indicator of change and as an amplifier of change. Consider the Arctic sea ice cover. The amplification of global
        warming long predicted by models has come to pass. Observations show that the Arctic is warming at twice the
        rate of the rest of the planet. Satellite observations from
        the past four decades show decreasing ice extent in every
        month of the year, with the greatest losses occurring in
        September, at the end of the melt season. Indeed, there
        has been interest in predictions of when we might first see
        substantially ice-free summers. The sea ice cover has also
        undergone a fundamental shift from older, thicker, more
        resilient perennial ice to primarily younger, thinner, less
        resilient seasonal ice. This is clear evidence of a warming
        If my belief about the HUMONGOUS size of the ice blocks sitting on solid earth IS CORRECT the above is debunked.

    • Robert David Clark

      The one thing that may not be clear is how much heat is added to the atmosphere daily. The frozen water dropped at the poles daily is the access heat lost to the black sky daily. The liquid water, rain, dropped daily is replacing most of the heat lost daily.

    • Robert David Clark

      Am I gone from here also?????

      • Please make your comments relevant to the thread. If you have general comments, post them on week in review. Please don’t post a bunch of incomprehensible numbers without clear explanation as to what they mean and why you are posting them.

    • Robert David Clark

      The cause of weather.
      As the sun radiates heat to the oceans it heats the surface. The warmer surface water flashes to water vapor in the dry air above. The heavier air pushes the lighter surface air to the west following the sun. This causes the air at the equator to flow from east to west following the sun. This causes a high-pressure area ahead of the humid air and a low-pressure area behind, thus a west to east flow to the lower pressure behind in the northern and southern hemispheres.
      This is a simple explanation of how nature maintains a relatively constant surface temperature.

  10. Ireneusz Palmowski

    The sea ice in May in the north looks very good.

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  12. Dr. Curry, Dr. Jim Steele has created the most comprehensive and devastating series of science based videos that totally destroy the CO2 drives warming theory that I’ve seen. Most importantly he address how CO2 won’t warm the oceans, and as I’ve always said, if you can’t explain how CO2 warms the oceans, you can’t blame CO2. His video series is game over for CAGW.

  13. There are all kinds of knock on effects due to the heat transfer effect as a result of GW and that is science whereas, AGW is political science.

  14. “Viscous heat dissipation could be considered important because the increased fluid temperature associated with the phenomenon has a potential to cause melting of ice in glaciers beyond what would occur if the process did not exist.”

    On a layman’s level I thought this an interesting comment.

    I would have thought that the concept would have already been built into the existing physics..
    Not to knock or deny the phenomenon.
    Simply to say that if it exists, which seems correct, then it is just part of the explanation of heat production and loss [work] that already exists and is accounted for.
    That is the increased fluid temperature due to the process is already embedded in the physics and data and does not represent an extra or new term of importance.
    In other words it does not produce extra melting of ice in glaciers beyond what would occur if the process did not exist.”

  15. Hmm.
    Not having exactly the meaning I meant

    “In other words it does not produce extra melting of ice in glaciers beyond what would occur if the process did not exist.”

    The process exists, the melting exists but it is already factored in and therefore cannot be double counted.

  16. I just want to re-frame the situation. CO2 is 400ppm, or 1 out of 2,500 molecules in the atmosphere. 15 micron LWIR cause CO2 to go into a vibrational state, a vibrational state consistent with a black body of temperature -80C. Those vibrations are believed to materially impact the kinetic energy of the other 2,499 molecules to the degree that it actually raises the temperature of the entire atmosphere. Does that even sound plausible? Can I warm my coffee by adding ice to it?

    • Of course you can- .

      Fill a large thermos bottle with dry ice and add a cup of coffee.
      Insert a thermometer and wait until the temperature equilibrates.

      Add ice cubes and watch the temperature rise.

      • Russell, I think you have it backwards. CO2, -80C is being added to the Coffee. The Coffee already exists (Atmosphere without anthropogenic CO2) and then you add CO2 which is vibrating at a rate less than ice and absorbing kinetic energy from existing molecules that collide with it. Does that result in warming? This is ignoring that you can only absorb 100% of outgoing LWIR and H2O already does that up to a level of about 3 km.

  17. We have another winning Video that destroys the CAGW Myth.

    It is well worth watching, and it highlights that once again, LWIR of 15 microns won’t warm water, especially the deep oceans. What warms the oceans warms the atmosphere, it is that simple. Explain the oceans and you explain the climate.

    In this graphic it clearly highlights how wavelengths are associated with temperatures. Note how 15 Micron and CO2 line up with the 210K Planck Curve. 210k is -63C. Those curves however are misleading because they are equal size. LWIR has very very very little photon energy.


    I love using Wikipedia to disprove the nonsense they support.


    I will say this for the nth Thousand time. There is a Nobel Prize waiting for someone to simply shine light thorough a Long Pass Filter isolating 15 micron LWIR onto a bucket of water and comparing the temperature change to a control bucket of water. The fact that that experiment hasn’t been done pretty much proves climate scientists aren’t looking for the truth…or they don’t even understand the basics.

    • Curious George

      I am not a CAGW believer, but your arguments need a lot of polishing. They simply don’t make sense to me. For example, a wavelength does not “line up” with temperature. For a radiation of an idealized “black body”, the relationship is the Planck’s Law – at any temperature, the body radiates at all wavelengths. And if you believe that shining a 15 micron laser on a bucket of water won’t increase its temperature .. please formulate your ideas better.

  18. Dr. Curry, there has been a seismic shift in the Climate Change and ESG. A HSBC Analyst MADE PUBLIC STATMENTS implying that Financial Models are manipulated to produce a favorable result. He gives specific examples. The due diligence requirement for a fiduciary just became prohibitive. While the analyst stuck to the financial models and claimed that he believed the climate was changing, he really opened the door for even the most mediocre lawyers to win lawsuits. Best yet, a series of videos by Dr. Jim Steele highlight how CO2 and 15 micron LWIR won’t warm the oceans. Proving CO2 can cause the oceans to warm is crucial to the CAGW Hoax,

    The WAPO to this day continues to make the claim that CO2 warms the oceans.

    But there is increasingly little doubt that human-caused warming is heating ocean-surface temperatures, which fuel big storms. The result appears to be stronger hurricanes.

    Public statements will now force these Charlatans to defend their models in a court of law. They will simply be destroyed in cross examination.

  19. The ocean is warmed by solar irradiation at SW, which penetrates to maybe 800 meters or so. LWIR from GHGs warms the top 3 microns or so of the water which evaporates, removing 540cal/gm from the ocean and depositing it in the upper troposphere from whence it finds its way out to space.

    • Robert David Clark

      The BTU’s finds its way to the black sky while the frozen lands at the frozen area of the poles and liquid water the rest of the of the surface.

      • Robert David Clark

        Thus, keeping a constant ocean height. We will remain at this level of the oceans until the ICE BLOCKS at the poles are gone. At that time the oceans will begin to drop, about 8,000 years, when the next ICE AGE will begin.

  20. Dan Hughes, you’ve apparently done some fine research to produce this post. However, you have forgotten one essential thing. You forgot to circle back to the point.

    What’s your thesis? Sure, I could go back and read your original post and from there, I could find the paper that you were criticizing in that original post and I could dig through what you wrote to find the specific bit of science that your entire effort is purporting to dispute. But you could have (and really should have) devoted a single paragraph here to clearly state the finding that you disagree with and how your analysis challenges that finding.