Thermodynamics and ice melt flows

by Dan Hughes

I recently ran across the paper by Isenko et al. [2005] listed below. The second paragraph of the introduction states:

“According to the conservation of energy, the loss of potential energy for a volume of water is sufficient to warm it by 0.2 C for each 100 m of lowering.”

The described process corresponds to isentropic compression of liquid water by increasing the pressure by about 1 MPa, through a change in elevation of 100.0 m. Note that the temperature change is given independent of any other information relating to flow velocity, kinetic energy, viscosity, dissipation, or any details of the flow channel that might affect conversion to thermal energy by viscous dissipation of kinetic energy. Especially note that for the case of flows in horizontal channels, for which the potential energy change is zero, apparently there would not be any temperature changes. The same can be said relative to flows upward against gravity.

The calculation by the authors is related the same concept that is the subject of this previous post. That is, the total potential energy at the top of a column of water is converted to thermal energy content by the action of viscous dissipation. As in the subject papers of the previous post, the temperature increase is too high.

When the process is considered to be compression of subcooled liquid water isolated from interactions with its surroundings, the temperature increase is estimated to be about 0.01 K per 100 m.

In general, textbooks recommend that temperature increase due to viscous dissipation can be neglected for all but a few special situations. The recommendation is particularly valid whenever thermal interactions between the fluid and channel walls, i.e. heat transfer, is the focus of the application.

The temperature increase for compression of subcooled liquid water is estimated in the attached PDF FILE. [WorkPost03]

Reference

Evgeni Isenko, Renji Naruse, and Bulat Mavlyudov, “Water temperature in englacial and supraglacial channels: Change along the flow and contribution to ice melting on the channel wall,” Cold Regions Science and Technology, Vol. 42, pp. 53– 62, 2005.

Herbert B. Callen, Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatistics and Irreversible Thermodynamics, John Wiley & Sons, Incorporated, New York, (1960).

W. Bridgman, “A Complete Collection of Thermodynamic Formulas,” Physical Review, Vol. 3, No. 4, pp. 273–281, (1914). doi:10.1103/PhysRev.3.273.

W. Bridgman, The Thermodynamics of Electrical Phenomena in Metals and a Condensed Collection of Thermodynamic Formulas, Dover Publications, Inc. New York. (1961).

120 responses to “Thermodynamics and ice melt flows

  1. “isentropic compression of liquid water by increasing the pressure by about 1 MPa, through a change in elevation of 100.0 m.”
    I have no idea what you mean, and why you are pulling in the pressure – what pressure?

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  3. Dan … Using the information you presented, in this post and the last, what conclusions would you (can you?) infer about glacial melt and AGW?

    • As I commented at the previous post.

      Regarding future ice melt estimates. I’ll assume that GCMs are the source of estimates of future ice melt.

      I do not address any issues associated with those estimates, GCMs, or Climate Change/AGW.

      I do not and cannot because I do not have any ideas whatsoever about how those estimates are calculated in any GCM.

      Someone will have to dig into the GCM documentation and/or coding to find out what’s done.

      • Bill Fabrizio

        Dan … I wasn’t trying to back you into a corner, although some on here do get a kick out of that sort of thing. I’m not a scientist or engineer. Just an interested party trying to understand, as best I can, why climate science seems to have such different advocates. Obviously, you have presented some information you think is relevant, in some way, to what this blog undertakes, which is to stimulate open scientific and policy discussion on climate change. My question was does your information have a bearing on what has been presented in the scientific journals, blogs, etc as to the melting of glaciers? Meaning … is your information a confirmation of certain information that has been presented/used, or does it cast doubt? If doubt, to what extent?

        If your purpose was to just have a discussion (just throwing it out there) of a particular facet of the physics involved with melt water, and there is nothing further, no worries.

      • To Bill Fabrizio.

        Your question is a good one. Having followed and commented on Dan Hughes’ previous post, I’m pretty sure that this is a response to concerns about the math he presented in that post.

        The work he presented in the previous post was a critique of a specific paper (https://doi.org/10.1073/pnas.2116036119). The quantitative statement he made was “The power estimate is too large by about at least an order of magnitude.”

        I have been very critical of his methods, so maybe I’m one of the people on here that gets a kick out of trying to back people into a corner. I hope that’s not the case. I genuinely think there’s good reason to be critical.

        To make a quantitative statement using a simplified mathematical model, one has to quantitatively relate the simplifications of the model to the physical situation being modeled. For example: in the paper Dan Hughes is criticising, the theoretical basal melt rate, including the contribution from viscous dissipation, is compared directly to the observed basal melt rate — it attempts to answer the question “how does theory relate to reality?”

        Dan Hughes has not made an adequate effort to relate the column of water described by the math he presents to what actually happens when water descends from the top of a glacier to the sub-glacial flow and eventually makes its way out from underneath.

        This matters because a person who is not a scientist or engineer can read his post and come away with an unsubstantiated impression that the peer reviewed paper that he is critiquing is flawed or weak.

        Simply put, if his previous post (and by extension this post) came from somebody nobody had heard of (such as me), it would just be pseudoscience. However, on Judith Curry’s blog (i.e. with the tacit approval of a credentialed and respected climate scientist) it is climate science misinformation.

      • Bill Fabrizio

        mdander … my comment to Dan wasn’t about the math/physics. As I said, it’s about rendering a conclusion of what was presented other than: “The power estimate is too large by about at least an order of magnitude.” I can’t critique Dan, or you, on the math.

        There’s probably a very good reason Judith posted his remarks. Which is why I try to get as much as I can from everything posted on here. I keep my mind as open as I can.

        Do me a favor. If you want to make comments to Dan, talk straight to Dan. Don’t get cute talking through me.

        As for Judith posting misinformation … if you were on here for a few years you’d see that’s a bunch of bull puckey.

  4. Turbulent, or even laminar , flow will definitely heat water.

    • Ask any power plant feed pump designer about no-flow cavitation.

    • The reactor coolant system at a nuclear reactor is heated from cold conditions to hot conditions…about 400F, by heat produced by running the reactor coolant pumps. The heat added is approximately the power consumed by the pumps minus the power lost because the RCP motors are not 100% efficient. This is large pumps operating on a closed system, and the power involved is measured in MWs.

      In the case of a waterfall, Niagara or a glacier, the work done by gravity must manifest as work done on the surroundings. Including heating of the water but also the noise made by the waterfall, etc.

      That said, you put those RCPs on an open loop at the same flow rate and the temperature rise in the fluid would be barely noticeable. That is why textbooks ignore the effect in most cases. In an operating reactor the temperature rise due to pump heat is a very small fraction of the temperature rise due to reactor heat.

  5. Cavitation isn’t the issue. Early on in thermodynamics studies, a common apparatus consisted of a weight driven paddle wheel in water. The energy imparted into the water could be calculated from how far the weight dropped. This transferred energy to the water as heat. Falling water is being driven by gravity instead of a paddle wheel, but the result is the same.

    https://www.aps.org/publications/apsnews/201506/physicshistory.cfm

    • When a feed pump flow is reduced below a certain point the water in the pump boils and changes to steam (with large mass/volume changes). Increasing the flow slowly brings about a host of problems, including the possibility of shearing the shaft. Unbalance of shaft thrust can instantly destroy bearings (used to cost about 100k per set).
      A minimum amount of water needs to be allowed to flow – recirculate – to avoid trouble.

  6. ‘For almost every other flow of interest in the atmosphere and ocean, Re is very much greater than one. For instance, in the atmospheric boundary layer (ABL), L ≈ 1000 m, U ≈ 1 m/s (or more), and ν ≈ 1.5 × 10−5 m2/s, leads us to estimate Re ≈ 108 (or more). This means that, if one were to measure the contribution of various terms in (1) to the momentum balance of ui one would expect to find that the viscous term is entirely negligible — fully eight orders of magnitude smaller than the other terms. And while this is true for components of the flow of scale L this is not to say that viscosity plays no essential role. Paradoxically, even when Re is large, the dissipation terms in (1) are usually not small. The paradox disappears when one realizes
    that simple scale estimation or dimensional analysis is not reliable in this matter, since turbulence comprises an exceedingly broad range of scales: for larger scales of motion, which may contain most of the energy or scalar variance, Re is large and the evolution is essentially conservative over a characteristic advective (or eddy turnover) timescale of L/V ; whereas for small enough scales of motion, which may contain most of the variance of vorticity and scalar gradients, the relevant
    Re value is small and the dissipation rate is dynamically significant.’ http://people.atmos.ucla.edu/jcm/turbulence_course_notes/turbulent_flows.pdf

    There is a qualitative difference between a water parcel under hydrostatic pressure and a free surface flow such as water falling in the atmosphere. When water in free fall hits bottom there is a quasi instantaneous conversion of kinetic energy to heat. I presume as shock waves induce eddies at the intermolecular scale.

  7. This dissertation is directly related to melt-water flows on Greenland: Jerome Mayaud, “Modelling meltwater drainage in the Paakitsoq region, western Greenland, and its response to 21st century climate change,” MPhil Polar Studies, University of Cambridge, June 2012.

    https://aspace.repository.cam.ac.uk/bitstream/handle/1810/264244/Mayaud-2012-MPhil-thesis.pdf?sequence=1&isAllowed=y

    Equation 7 gives the melting rate due to viscous heat dissipation. The dissipation is in agreement with the frictional dissipation concepts cited in my original post. The dissipation is based on wall-to-fluid friction, a phenomena that is based on viscosity and related viscous effects. The dissipation is not based on gravity head.

    In a comment to the original post, regarding the concept of viscous heat dissipation and its mathematical description, I wrote:

    “Additionally, the description, again by definition, should be applicable to all flows; horizontal flows, flows downward with gravity, and flows upward against gravity.”

    In the recent post I wrote:

    “Especially note that for the case of flows in horizontal channels, for which the potential energy change is zero, apparently viscous heat dissipation fails to occur. The same can be said relative to flows upward against gravity.”

    Viscous dissipation always occurs in flows for which there are no changes in potential energy, and flows for which the potential energy increases in the direction of flow.

    Horizontal flows for which we get to set the potential energy reference level anywhere we want to has no changes in potential energy. If the elevation reference is set at the center-line of the channel, which is almost universal, the potential energy is zero everywhere.

    For flows upward against gravity, potential energy increases in the flow direction.

    How does the concept of potential energy = = dissipation work for these cases? How does the concept of “shedding potential energy” and thus heating the fluid fit in with these situations ? How do downward steady state flows in constant-area channels accommodate both a decreasing velocity in the direction of flow and conservation of mass?

    A mathematical description of viscous dissipation and conversion of kinetic energy into thermal energy should, by definition, involve processes associated with velocity, kinetic energy, viscosity, channel-geometry, and turbulence. Additionally, the direction of flow relative to gravity and the location of portions of the channel relative to an arbitrary reference elevation are of no importance.

    The equations that I presented, taken out of textbooks, have not been shown to be in error: no term in any equation has been shown to be wrong, and no complete equation, either. By the same token, equations for the alternative approaches have not been shown: shedding of potential energy, its conversion to kinetic energy, and dissipation of that to thermal energy remain only vague and incomplete verbal descriptions.

  8. Take a 10 foot long tube. Put a nozzle on one end, fill it with water and hold up the open end with your thumb over the tip. There’s 6 feet of vertical tube, a bend and 4 feet of horizontal tube along the ground terminated at a nozzle.

    Take your thumb off the open end that you’re holding up, and open the nozzle so that water sprays out.

    If we use this as a qualitative analogy to meltwater descending from the top of a glacier, your math is an appropriate model of the vertical portion of the tube.

    As the water sprays out of the nozzle, how much viscous dissipation occurs in the vertical portion of the tube? Extremely little (your model confirms this — and that’s all it does).

    The gravitational potential energy of the water in the vertical portion of the tube is shed as it descends. But we must have conservation of energy, so where does it go? It is converted to kinetic energy and a little bit of heat at the nozzle.

    I’ll be 100% clear. I am not suggesting that you can model the sub-glacial flow by looking at a model of a horizontal tube and a nozzle. I’m pointing out that you have failed to identify how your model relates to sub-glacial flow with any quantitative analysis and so it is inappropriate for you to make quantitative assessments of the how much viscous dissipation is occurring.

    My point? Same as it always was: your math may be perfectly fine, but it does not model how gravitational potential energy is converted to kinetic energy and heat as water descends from the top of a glacier to the sub-glacial flow. Not even close.

    • George Turner

      The gravitational potential energy in a small unit of water as it descends in a column of water is converted to head pressure, which is another form of potential energy. If you have a hula hoop full of water and slowly rotate it in any direction, there’s no actual energy flow going anywhere, other than the small bit of kinetic energy you imparted by rotating it, which you get back out when you stop it, as if the hula hoop was a solid body.

      So there need be no change in heat as the melt descends into the glacier unless the water freefalls (increase in velocity but not pressure). So that moves the potential energy to the bottom of the glacier, still with no heating to speak of, and the flow will do some work eroding the bottom of the glacier before it finds an exit. The amount of work done can be extremely significant, as it would require an immense amount of diesel fuel for bulldozers to dig out the Great Lakes or create various Western flood landscapes.

      But another way to look at the problem is that a bucket of ocean water evaporates, travels up into the sky, condenses (releasing the heat of vaporization, some of which is radiated away), and then falls back down to the ocean again, unless the cycle is interrupted by Greenland. If that happens, the bucket’s energy cycle is on pause until the melt occurs, and then the water ends up back on top of the ocean where it should’ve ended up anyway in a normal cycle. So the glacier might not be the right point in the heat engine cycle to start the calculation.

      The albedo effects of being paused as a reflective glacier for a couple thousand years surely swamp the error in the energy budget numbers for the bucket of water.

    • The local-instantaneous PDE for conservation of total energy, represented by the sum of internal plus kinetic plus potential energy, has the usual LHS of the time-rate of change of this sum plus convection of this sum.

      The RHS side includes the rate of energy change by conduction within the fluid, plus rate of work done by body forces, usually limited to gravitational forces, plus rate of work done by pressure forces within the fluid, plus rate of work done by viscous forces. The rate of work done is of course power.

      Potential energy due to gravity, a conservative force, gets to be included in the time derivative because as a vector gradient of a scalar potential it is time constant. Other body forces that meet this requirement can be also included.

      Nowhere in the conservation of total energy equation does viscous dissipation of kinetic, or potential, energy appear. The latter with good reason.

      The various local-instantaneous PDE formulations for conservation of thermal energy, in terms of internal, or enthalpy, or temperature, contain accounting of effects of the irreversible rate of thermal energy increase due to viscous dissipation. And it is always an increase, viscous dissipation being always positive.

      The local-instantaneous PDE formulation for kinetic energy RHS also includes the viscous dissipation term that we’re looking for, and it is negative definite; always a loss.

      The reason the term does not appear in the equation for conservation of total energy is because the process is an interconversion within the fluid and cancels when the sum of the equations is formed.

      I’m certain that The Google, plain or scholar, can lead you to exhaustive developments and discussions of all these equations in reports, papers, videos, and lecture slides, filled with all the partials, del, div, grad, and tensor calculus your heart could ever want.

      Additionally, again because of association with viscosity and kinetic energy, the RANS literature, both 2-parameter and Reynolds-closure, is filled with exhaustive development of viscous dissipation, that being one of the 2 parameters.

      Bird [1957] developed a macro-scale version of the kinetic energy equation. That equation is used because if the subject is viscous dissipation and conversion of kinetic energy into thermal energy, the kinetic energy equation sound like a good starting point. Bird, Stewart, and Lightfoot [1960], and thousands of others, have summarized Bird’s results.

      R. Byron Bird, “The Equations of Change and the Macroscopic Mass, Momentum, and Energy Balances,” Chemical Engineering Science, Vol. 6, pp. 123-131, (1957).

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

      • George Turner

        I’m suggesting a simpler approach.

        The amount of energy in the bucket of water is determined by the energy put into the water, back when it was floating on the ocean and evaporated. It got swept up to high altitude, condensed, and released most of that energy as heat, then started falling back down as droplets or snow flakes, dissipating much of the remaining energy. As it passed below a few thousand meters of altitude, there wouldn’t have been much energy left, but what energy it did retain is easily calculated as PE=mgh, where m is the mass of the bucket. If it had landed behind a dam we could’ve tapped some of that energy to make electricity.

        But instead it landed on top of a glacier. It regained a bit of energy from sunlight, enough to melt, and then continued the very last leg of its inevitable path back to the ocean. In terms of climate and temperature, this energy is likely irrelevant because the bucket of water didn’t have any more energy than other buckets of water that evaporate and rain back down, all over the planet, every day.

        I’m not sure a finer accounting is really needed. If Greenland wasn’t there, the change in albedo would completely swamp the fact that rain is landing back on the ocean instead, just as it does elsewhere across the North Atlantic.

        So you could say, instead of trying to find the precise answer to the question, I’m suggesting the answer probably doesn’t even matter, except that someone perhaps gave the wrong answer and there is an engineer’s compulsion to correct them. ^_^

  9. Plumbers know that there is a pressure drop as water flows through plumbing pipe. For a given pump pressure, the rate of water flow will depend on the length of pipe. Flow rate is an extrinsic property dependent on the length of pipe, all else being equal, not an intrinsic one. So for a short length of pipe, the flow rate will be faster, but the same throughout the length of pipe. For a longer pipe driven by the same pump pressure, the flow rate will be slower, but again the same for any given point on the pipe.

  10. The physics of water are amazing… there’s your ‘control knob.’

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  15. Dan’s equation 2 is incorrect. In the Bernoulli equation – linked at hyperphysics below – both sides are equal and neither is equal to zero. The bigger issue is how the problem is framed. Thinking viscous dissipation happens only in the quasi horizontal channels to the ocean.

    http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

    The problem as I understand it involves water free falling vertically some distance.

    e.g. https://scitechdaily.com/images/Hydropower-Schematic-1536×1182.jpg

    In such a case we can neglect most of the terms of the Bernoulli equation – and the potential energy at the top is approximately equal to the kinetic energy at the bottom. Most of that is lost on impact. I’d suggest it is converted from mass movement to internal molecular kinetic energy – heat – by impact shock waves.

    • REI, we are in agreement. Equations (1) and (2), the equations used in the papers cited in the previous post, are wrong. Those equations are the focus of the discussions.

      Those are not my equations. Those equations reflect the approach to VHD that is used in the papers listed below. For estimating viscous heat dissipation, the equations are not the equations that should be used.

      I think the correct approach is used in this dissertation that is directly related to melt-water flows on Greenland: Jerome Mayaud, “Modelling meltwater drainage in the Paakitsoq region, western Greenland, and its response to 21st century climate change,” MPhil Polar Studies, University of Cambridge, June 2012. https://aspace.repository.cam.ac.uk/bitstream/handle/1810/264244/Mayaud-2012-MPhil-thesis.pdf?sequence=1&isAllowed=y [ Note, I think that is some kind of Instant Download link ]

      Equation 7 gives the melting rate due to viscous heat dissipation. The dissipation is in agreement with the frictional dissipation concepts cited in my original post. The dissipation is based on wall-to-fluid friction, a phenomena that is based on viscosity and related viscous effects. The dissipation is not based on gravity head.

      There are a multitude of videos and lecture slides and discussions by university faculty of the Bernoulli equation: The Google will lead you there. Here are a couple of examples:

      Energy equation and head loss: https://www.youtube.com/watch?v=pU_I5sc_-B8

      Hydraulic Grade Line and Energy Grade Line: https://www.youtube.com/watch?v=q89YrFmyHY4

      The Bernoulli Equation, of course, doesn’t know anything about viscosity. So that equation cannot tell us anything about viscous dissipation.

      The Energy Grade Line and Hydraulic Grade Line can be calculated by solutions of the continuity and momentum equations with wall-to-fluid friction dropped from the latter.

      The Papers Listed below
      News release, “Accelerating Melt Rate Makes Greenland Ice Sheet World’s Largest “Dam” – Generating Huge Amounts of Heat From Hydropower,” https://scitechdaily.com/accelerating-melt-rate-makes-greenland-ice-sheet-worlds-largest-dam-generating-huge-amounts-of-heat-from-hydropower/

      K. D. Mankoff and S. M. Tulaczyk, “The Past, Present, and Future Viscous Heat Dissipation Available for Greenland Subglacial Conduit Formation,” Cryosphere, 11, 303–317, (2017). https://tc.copernicus.org/articles/11/303/2017/. SI doi:10.18113/S1WC71

      Nanna B. Karlsson, Anne M. Solgaard, Kenneth D. Mankoff, Fabien Gillet-Chaulet, Joseph A. MacGregor, Jason E. Box, Michele Citterio, William T. Colgan, Signe H. Larsen, Kristian K. Kjeldsen, Niels J. Korsgaard, Douglas I. Benn, Ian J. Hewitt, and Robert S. Fausto, “A First Constraint on Basal Melt-Water Production of the Greenland Ice Sheet,” Nature Communications, 12, 3461 (2021). https://doi.org/10.1038/s41467-021-23739-z

      Tun Jan Young, Poul Christoffersen, Marion Bougamont, Slawek M. Tulaczyk, Bryn Hubbard, Kenneth D. Mankoff, Keith W. Nicholls, and Craig L. Stewart, “Rapid Basal Melting of the Greenland Ice Sheet from Surface Meltwater Drainage,” PNAS 2022 Vol. 119 No. 10 e2116036119. https://doi.org/10.1073/pnas.2116036119

      Evgeni Isenko, Renji Naruse, and Bulat Mavlyudov, “Water temperature in englacial and supraglacial channels: Change along the flow and contribution to ice melting on the channel wall,” Cold Regions Science and Technology, Vol. 42, pp. 53– 62, (2005).

      • Dan – neither side of the Bernoulli equation is equal to zero. I never make too much of typos – but I did stop reading there. Perhaps your source was incorrect. But look at what’s involved in the pressure, kinetic and potential energy terms.

        In the real world an empirical friction factor is added to account for energy losses to the downstream point. But this is not the problem at hand.

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  19. To Dan Hughes

    The failure of the peer-review process is a common theme on this blog, but do you remember Resplandy et. al.? Nic Lewis found a flaw in a peer-reviewed paper which resulted in (aside from some well deserved showboating by Nic Lewis and Dr. Curry) a correction and resubmission and re-acceptance of the paper.

    With your pdf, there’s no third party to adjudicate the validity of a critique. This is not fair to people who read your work and think that it is valid because it appears on Dr. Judith Curry’s blog. It is also not fair to you — you shouldn’t have to defend your work from every crank that wants to have a go at backing you into a corner.

    So with respect to your mathematical rigour, let’s revisit my complaint: I am not challenging your math! You made a quantitative statement: “The power estimate is too large by about at least an order of magnitude.” and you substantiated it with a model of water descending from the top of a glacier to the bottom.

    But you did not quantitatively relate your model to the actual path of water! This is necessary. At the very least you have to substantiate that your model is conservative (i.e. that it overestimates viscous dissipation — but it’s pretty obvious that there will be more viscous dissipation of heat if the same rate of water flows through 100 small channels vs. one large channel so it is NOT conservative).

    The point is that the entire path of the water (possibly several 100 kilometers long), from the top of the glacier to where it exits the sub-glacial flow, is relevant to how the gravitational potential energy is converted to kinetic energy and/or heat. You haven’t attempted to model that entire path (I don’t blame you, it’s not even remotely possible), so you can’t make a conservative estimate of the viscous dissipation along that entire path.

    So you don’t get to say “The power estimate is too large by about at least an order of magnitude.”

  20. Dan could “create” an example glacier drain channel. Then apply the technique used to obtain the result that’s alleged to be too high, then apply the calculation believed to be correct by Dan. Show the math and point out the bits that are believed to be wrong. That way, the magnitude of the error could be illustrated.

    • George Turner

      I think the error bars in a real world experiment would swamp the results of the calculation. What’s the temperature gradient inside the glacier? What’s the 3D geometry of the channel, and its length, and how much of the heat in the melt water would be conducted to the ice along the route? So you get into surface area and turbulent flow calculations to figure up the heat transfer.

      Is it a small flow volume, which is just going to end up averaging the the ice temperature of the massive glacier, or is it a big volume? Does it end up rapidly existing the glacier before getting anywhere near thermal equilibrium? The top of the glacier is typically going to be much colder than the bottom of the glacier, so if significant heat transfer occurs at the start of the meltwater’s journey, it could be much colder than it started out as by the time it gets deeper down into the glacier. Or not, depending on all those variables.

      • For the purpose of this exercise, Dan could design it as he likes – just use the same one in both calculations.

      • George Turner

        Well, I have another question.

        Assume a large spherical glacier in thermal equilibrium with the surrounding atmosphere. A bucket of water moves 100 meters down the face of the glacier. One calculation claimed it would warm by 0.2 K, and one calculation says it will only warm by 0.01 K. But the moist adiabatic lapse rate says that in moving down 100 meters, the local environment around the water warmed up by about 0.6 K. So the the water temperature dropped by either by 0.4 or 0.6 degrees C relative to the local elevation’s equilibrium temperature.

      • These are Dan’s questions to answer. He made the claim. I’m just trying to find a path to proof. He can design the glacier and drainage as he will. He is the expert.

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  22. Robert David Clark

    When I put this in many moons ago I had a mistake. The salt water at the bottom of the oceans is 28 degrees saturated.

    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.

    THAT IS WHERE WE ARE NOW.

    IN ABOUT ANOTHER 100,000 YEARS THE ICE BLOCKS WILL BE COMPLETELY GONE, THE OCEAN WILL DROP FOR ABOUT ANOTHER 8,000 YEARS. AS THE ICE IS PUT BACK ON THE CONTINENTS.

    • Robert David Clark

      I knew it was 28-degree saturated salt water which is heavier than fresh water. Read it many times over the past 2 years. and read what I wanted to see. At least now I know why nobody understood the system designed by nature.

  23. For the sake of clarity and focus, it’s worth occasionally circling back to the reason why the author has posted something in the first place. It’s a particularly good idea in this case where we’re now commenting on a post that Dan Hughes made as a response to his own earlier post (https://judithcurry.com/2022/03/08/viscous-dissipation-heating-by-flows-of-melted-ice-on-greenland/).

    That previous post is a critique of the findings of a peer-reviewed paper, Young et. al. (https://www.pnas.org/doi/full/10.1073/pnas.2116036119).

    If you have commented here or are considering doing so, you really should make an effort to understand what the thesis of that paper is.

    I’ll summarize: Young et. al. makes the assumption that, in Greenland, all the gravitational potential energy of surface meltwater becomes heat (via viscous dissipation) and contributes to the basal met rate (BMR).

    Before that contribution is included, the calculated BMR from theory is WAY less than the observed BMR. Once they included BMR from viscous dissipation the theory matches the observed MUCH better.

    All that is very clearly shown in Figure 3. Graph 3c shows the observed BMR complete with error bars. Graphs 3a and 3b show the theoretical BMR, including each of the contributing heat sources (conductive heat loss, geothermal, frictional, additional enthalpy and viscous dissipation).

    Young et. al. spends a fair bit of effort attempting to support the theory of viscous dissipation, but have they done an exhaustive job of it? No. They clearly acknowledge: “the evolution of basal drainage system efficiency, and channels’ ability to form under thick ice, remain highly uncertain”.

    Dan Hughes is challenging the theory that the viscous dissipation can be responsible for the amount of heat that Young et. al. suggests. As I have repeatedly explained, Dan Hughes doesn’t have a better model of the basal drainage system, and he has not provided adequate evidence to make the quantitative claim that “The power estimate is too large by about at least an order of magnitude”.

    The thesis of Young et. al. is supported by the correlation between theoretical BMR and observed BMR. Given that it is nigh impossible to adequately model the basal drainage system, challenging their findings on purely theoretical grounds is pointless.

    What’s more, anyone with Dan Hughes’ analytical abilities should know this. Dr. Judith Curry, if she’s even paying attention, absolutely knows this. So I challenge Dr. Curry to show up and justify why she has provided a venue for this post.

  24. Ireneusz Palmowski

    Be warned of a very cold April in eastern Canada and the northeastern US.
    https://i.ibb.co/G2qj7TM/gfs-T2m-us-62.png

  25. Thermodynamics and ice melt flows by Dan Hughes

    Seek and ye shall find.

    “Modelling meltwater drainage Jerome Mayaud
    Although the description of hydrological ice sheet drainage should include a formulation for englacial water routing, it can be assumed that all meltwater reaches the bedrock and drains along the base of the ice sheet (Björnsson, 1982”

    Applying a bit of commonsense one can break Glaciers into 3 types
    Open and small.
    Open and large
    Closed.

    A small open glacier is the last vestige of a bigger glacier or the start of a new one.
    In these glaciers only in summer , when melt and melt water occur the base of the small glacier is open to being accessed by melt water once temperatures drop below freezing.
    It will not move anywhere as it is too small to have any forward momentum of note and will just shrink and reform in winter.
    .
    A closed Glacier, as in central Greenland and the Central Antarctic basin does not go anywhere, just higher or lower.
    Height loss is by sublimation, Any water that melts forms shallow low pressure ponds that can move lower through ice fractures but due to the very low temperatures at depth rapidly freeze over.
    The concept of actual liquid water at the base of any deep glacier is highly theoretical and practically does not exist.

    Consequently the statement expressed above is extremely vague and only appropriate to small open glaciers.

    When we consider large open Glaciers we have to consider that at one end, reaching the sea or a higher temperature inland drainage spot a tiny bit of open and small might occur.
    In general though the meltwater on large open Glaciers follows normal gradients on the surface to drain in rivers streams or underground seepage to lower areas and hence to the sea.
    It can go down through fracture lines but the increase in coldness due to the increased distance from any heating source of note [sun] means that it will refreeze as it goes lower and never lubricate the bottom surface of any large glacier to any observable [other than theoretical physical] extent.

    Glacial flow is faster the bigger and larger the Glacier [hence the colder the Glacier].
    Glacial flow can have a theoretical water lubrication effect which is invisibly small.

    Glacial flow, like Glass flow, is a result of the elasticity of the solid ice and will occur with pressure weight and volume build up at temperatures that really preclude the effect of any water existing let alone lubricating the ice
    .-
    Thank you Dan for adding to my knowledge of possible temperature pressure gradient effects.

    Thank you mdander for your repeated disparaging comments on Dan and Judith.
    These only show you as a self serving commentator not interested in the subject at hand but merely pushing your hatred of skeptic ideas.

    • Hi Angech.

      Dan Hughes’ reference to Jerome Mayaud’s academic thesis is certainly relevant to the development of a model of sub-glacial flow.

      Based on that and his other references along with his model, Dan Hughes could make a QUALITATIVE statement like: “I disagree with the theoretical development of viscous dissipation presented in Young et. al.” — I would not have had any problem with that.

      However, Dan Hughes chose to make a QUANTITATIVE statement: “The power estimate is too large by about at least an order of magnitude”. That quantitative statement was not properly substantiated — I have explained this w.r.t. failures in his model to describe sub-glacial flow; I have explained this w.r.t. failures to quantitatively relate his model to either observations of BMR (as is done in Young et. al) or to a reasonably exhaustive enumeration of sub-glacial flow scenarios; I have explained this w.r.t. his failure to demonstrate that his model provides a conservative estimate.

      No amount of references are going to do that legwork for him.

      You said “Seek and ye shall find.” I sought and I did not find.

      Dan Hughes’ quantitative legwork is still missing, so his quantitative statement is invalid.

      • Hi mdander

        Dan Hughes did make a QUALITATIVE statement like: “I disagree with the theoretical development of viscous dissipation presented in Young et. al.”
        Dan Hughes also chose to make a QUANTITATIVE statement:

        You state without proof that
        “The power estimate is too large by about at least an order of magnitude”.

        That quantitative statement was substantiated — by Dan

        You have not shown that his maths is incorrect with the values he has stipulated.

        You may disagree with his estimations til the cows come home but that does not disprove the calculations he has made based on his assumptions.

        Now if you were to prove the actual maths wrong? , but that , by inference, is beyond your pay grade or you would have done so.

      • Hi again Angech.

        You’ve hit the nail on the head. Dan Hughes did substantiate his quantitative statement. As I have clearly pointed out, his math can be correct without being properly applied.

        But for anyone who isn’t particularly science literate or really wants to believe that all alarming climate science is actually “alarmist”, why would they take my word for it?

        Well here’s the thing. If Dan Hughes is correct and “the power estimate is too large by about at least an order of magnitude” in the peer-reviewed paper that he is critiquing (Young et. al. https://www.pnas.org/doi/full/10.1073/pnas.2116036119) then his mathematical support for that assertion should be submitted to the authors. If it is correct, it would result in a correction. Like it or not, the peer-review process has built in accountability.

        That’s the difference between a qualitative critique and a quantitative one. If Dan Hughes is correct then Young et. al. is wrong — it’s not a matter of opinion.

        But Dan Hughes is never going to submit his findings. Dr. Judith Curry (if she’s paying attention) knows it. He may have made no mathematical errors, but for the reasons I’ve already stated several times, he failed to make the case.

        That is the proof in the pudding — watch this space. I guarantee that his pdf is going nowhere.

        So why would Dan Hughes put in so much effort and why would Dr Curry invite him to be a guest contributor?

        Simple. This stuff is oxygen for the community of “climate science skeptics” that believe that their own citizen science common sense and thought experiments have value in our collective effort to understand how human activity is affecting the climate and how that is going to work out for all of us.

        Look around at the legions of commenters that contribute to every post on this site. They include people that think that because CO2 is a trace gas, it can’t possibly cause warming. They include people that think that more CO2 is better. They include people who think that mainstream climate scientists are all getting huge paychecks to support a massive conspiracy. Pick whatever silly climate science theory you want and it’s probably represented in these comments.

        Intentional or not, Climate Etc. does not encourage people to become more science literate — it provides a venue for the perpetuation of mistrust / disdain for peer-reviewed science. I find that sad.

  26. Sebastian Magee

    I haven’t read the paper Dan Hughes is reviewing, but it seems clear to me that the potential energy is not going to be dissipated by viscous forces, it is mostly used to produce work on the fluid (changing the pressure against the volume ). This is basically Bernouilli’s equation:
    gz+P/rho+v²/2 = constant

    g—>gravity
    z—>height
    P—>Pressure
    rho->density
    v—->velocity

    since the kinetic energy is very small compared to the potential energy (gz~1000, and probably v²/2<1, in any case v²/2<<gz )
    this equation basically reduces to gz + P/rho = constant

    of course Bernuilli's equation is not exact for viscous fluids and there are energy losses due to viscosity:
    gz + P/rho + v²/2 + viscous_terms = constant

    but the relation of the kinetic term to the viscous term is the Reynolds number:
    Re=rho*v*z/mu
    if v=1m/s, z=100m, nu=mu/rho=1e-6 m²/s
    Re=10000
    This implies the viscous terms are 10000 times smaller than the kinetic terms, which are themselves already small.

    if speeds where as low as v=1e-4 m/s Re=1. In this case viscous and kinetic terms would be equal but completely irrelevant.

    • George Turner

      I’m reluctant to get into the math of the particulars because I have my doubts that the answer is particularly meaningful.

      If you have a ton of water (1000 kg) on top of a 100 meter high glacier, the gravitational potential energy is PE=mgh = 980,625 Joules. Let’s just call it a megajoule. The debate is what happens to that energy on the way down, and how much gets converted to sensible heat, or temperature rise in the water, etc.

      Now up on top of the glacier where the ton of water started, you have ice, or perhaps an ice and water mix, with an albedo of 0.5 to 0.9, because charts of snow albedo run from 0 to 1 like a big scatter plot, depending on wavelength, zenith angle, and of course the nature of the snow.

      So let’s assume our water is up in the arctic with a very low average solar insolation of 2.2 kWh per square meter per day, which is about 8 MJ per day/m^2. The higher range of albedos (0.5 to 0.9) would be a variation in absorbed energy ranging from about 1 MJ to 4 MJ per day.

      Now our ton of water used to be ice, and to melt a ton of surface ice that was at 0 C takes 334 MJ. We’re only getting 8 MJ per day of sunlight, and at least half that gets reflected, so it’s going to take between 3 months and a year to melt our little patch. During that time the error bars on our energy absorption due to albedo is about 1000 MJ. But we lose heat at night, so we could have refreezing, so lets try to get the experiment done in one day by increasing the glacier area producing the tonne of water to 334 square meters, so that even with an albedo of 0.1, we still get our meltwater sample.

      But now our energy range due to albedo runs rom 334 MJ to 1.336 GJ, which is again 1000 MJ.

      The effect we’re looking for from the drop in potential energy is 1 MJ, so we’re looking for something that’s 0.1% as big as the error bars in the solar energy calculation. This leads me to conclude that from a climate perspective, the answer doesn’t really matter. But I’ve been wrong before!

      • Hi George Turner.

        I’m only replying to you because it’s such a great example of how people try to use math to mislead people. Did anyone read what you wrote and actually think that “from a climate perspective, the answer doesn’t really matter”?

        I wonder.

        You’re off by one order of magnitude in your power calculation because your glacier is only 100m high instead of 1km high.

        But more importantly, I think if you consider the melt that’s occurring on the full 2 million square km of Greenland, instead of analysing the solar insolation of one square meter, you will find that the amount of power that we’re talking about is actually quite significant.

        That’s kind of the point of the paper (Young et. al.) that Dan Hughes is criticising. You should probably read it.

      • George Turner

        I’m off by a factor of 10?

        PE = mgh = 1000 kg * 9.806 m/sec^2 * 100 m, which is 9.8 * 100,000 or 980,000 Joules.

        Scaling up to 2 million square kilometers doesn’t solve the problem. The 3 MJ/m^2 range of energy inputs over 1 day would be an energy range of 6.0e18 Joules per day, which would be equivalent to 6.0e12 tonnes of water dropping a hundred meters. That would be 6,100 cubic kilometers a day, whereas Greenland loses water at a rate of about 0.5 cubic kilometers a day.

        Compared to what it takes to melt the ice, or the energy that the glacier reflects into space, there’s just not much significant energy in dropping 100 meters. A ton of water dropping that much, even if the energy was completely converted to heat, is only enough to melt 3 kg of ice. But we had to melt 1000 kg just to get the 3 kg extra.

        And note that the water on the glacier likely fell as snow from about 6000 meters, so there’s only 1.6% of its original potential energy even left to give up in that last 100 meters. Across most of the planet the ice pack question doesn’t even come up, and the water just comes shooting down the mountain. Yet I’ve never heard anyone claim that streams are a significant source of heating.

      • mdander | April 7, 2022

        ” I’m only responding to your comment to George Turner because it’s another great example of how people try to use math to mislead people
        When people read what you wrote do you think they do not notice your bias?
        I wonder.”

        You said
        “You’re off by one order of magnitude in your power calculation because your glacier is only 100m high instead of 1km high.”

        You re deliberately wrong.
        It does not matter about whether the Glacier is 100 meters, a 1000 meters or 10000 meters high.
        The energy calculations purely refer to the energy produced by a mass moving a distance, not from how high its starting point was.

        Try a simple thought bubble.
        Drop an ice cube.
        Work out how much heat is produced when it hits the ground.
        Extrapolate.
        How many ice cubes would you have to drop to make a cup of hot tea?

      • dougbadgero

        Certainly all is not turned into thermal energy on the way down. Imagine a quantity of water falling from height but not moving in relation to its own geometry from when it began to fall. Almost no viscous dissipation is occurring as it falls. Falling down an ice slope will turn more PE into thermal energy but certainly not all of the PE at the top will become thermal energy as it falls. IMO the question is what happens to the KE at the “bottom”. There are many possibilities, some will result in increased glacial melt rate and some will not.

        Every situation will be complicated and unique. Whatever is happening it is the same thing that has always been happening as glaciers melt.

      • George Turner

        @Angech

        Since ice has a heat of formation of 334,000 Joules/kg, melt it with an impact that converts its kinetic energy to thermal is easily calculated. If you formed it into a 150 grain 30 caliber bullet and shot it from a 30-06 with a muzzle velocity of 2,681 feet per second, the bullet would completely melt when it hit.

        Or you could drop it from around 111,700 feet (34.067 km) over Greenland, in a vacuum, so that it hit with a velocity of 817.3 meters per second. That calculation gets complicated once you get into an oblate rotating spheroid following Newton’s square law for gravity, and of course it depends on whether the block of ice, near the edge of space, was rotating with the Earth or was just held in a fixed position relative to the planet’s orbit, but which makes on oblique impact with the rotating Earth.

        100 meters get you 0.3% of the way there! I suppose that’s why people don’t drown in avalanches as they turn into flash floods.

        Of course if the ice isn’t right at the freezing point, you’d need to add about 2 kJ/kg of kinetic energy for every degree below zero.

      • Thanks George for that bit of maths.
        Ice skating may be an example of viscosity with the pressure of the blades but they dot develop pools of water and the ice base never detaches or moves

  27. “When the process is considered to be compression of subcooled liquid water isolated from interactions with its surroundings, the temperature increase is estimated to be about 0.01 K per 100 m.”

    Water is amazing stuff.
    Triple points, whatever they are.
    Being denser when warmed up from 0- 4 degrees.
    Before starting to expand again.
    Would ice float in boiling water or sink? Who knows ?
    I would guess that being close to 10% lighter, and as water is fairly incompressible, does not seem to change level in the electric jug, it probably still floats being approx 10% lighter.

    Where does this lead?
    No ice on the bottom of of deep seas at normal earth insulation.
    If ice forms on the ground the ice on the surface interface does not melt,
    No matter what the pressure.
    Because it forms there first, got it?

    Any effect of increasing pressure is more than compensated by the extra cold at that depth.
    People who wish to query this should first check up on the concept of a frost line in and under the earth surface.

    So the problem is not moot.
    Proper Glaciers do not move because of water lubrication which cannot exist.
    No water lubrication , no need to consider viscosity or heat generated by viscosity.

    Glacial movement refers to the slow flow of solid ice (just like glass) caused by pressure from height throughout the whole glacier.
    Glacial edge increase and retreat is a combination of sublimation, presume it works both ways, surface melt , snow and rain and wind effects and insulation.

    Why complicate the issue with fairy stories about 4 foot high glaciers in the driveway in winter cleared by salt, snowploughs and a shovel.

    • Robert David Clark

      If I understand you correctly you said the ice block that began forming on the frozen earth when the oceans were at their lowest point, about 400 feet lower than today, are still on the solid ground.
      They probably have lost ice that broke off because of the overhang breaking off.
      They still have an overhang with the 28-degree saturated salt-water making it longer.
      Thew still a very large portion of the bottom resting on the earth.

  28. Interesting comments from mdander | April 11, 2022
    Hi again Angech
    “You’ve hit the nail on the head. Dan Hughes did substantiate his quantitative statement. “
    Accepting reality for one second.
    Then retreating into his morass of anti JC, any Dan Hughes comments by retracting this statement and continuing his misrepresentations under his what if guise.

    “As I have clearly pointed out, his math can be correct “

    “But”

    “If “

    Since you admit “Dan Hughes is correct and “the power estimate is too large by about at least an order of magnitude” in the peer-reviewed paper that he is critiquing (Young et al” -“it would result in a correction.”

    Since “the peer-review process has built in accountability”

    There is no difference between a correct qualitative critique and a quantitative one.
    Since you yourself stated above “Dan Hughes is correct.”
    Your other comments hit the nail on the head
    “Young et. al. is wrong “

    “it’s not a matter of opinion.”
    -removing your obfuscations ( buts and ifs that you already excluded) again

    “Dan Hughes submits his findings. Dr. Judith Curry publishes them. He has made no mathematical errors.He makes the case.”

    “That is the proof in the pudding “

    Dan Hughes put in so much effort , shows according to you that a paper must be wrong so Dr Curry invites him to be a guest contributor?

    “Simple.”

    “This stuff is oxygen for the community of “climate science skeptics” that believe that their own citizen science common sense and thought experiments have value in our collective effort to understand how human activity is affecting the climate and how that is going to work out for all of us.”
    -Thank you for that endorsement of science.

    “Look around at the legions of commenters that contribute to every post on this site.”

    Thank you for the endorsement of JC.
    Legions you say.

    Climate Etc. does encourage people to become more science literate , intentionally

    It provides a venue for peer-reviewed science. I

    You say you find that sad.
    That sums up your problem exactly.

    Please make an effort to understand where your logic has to go off the rails,
    Next try to understand why.
    Logic driven by a pre imposed motivation cannot work if the motivation excludes the logic from considering that the motivation itself has flaws in it.

    • I wonder why it is so difficult for Angech to understand mdanders point. Dan Hughes makes an explicit, quantitative criticism of the Young et al paper, based on his (mathematically correct) calculations of an inappropriate model. Get it: inappropriate model. If Angech read the Young et al paper, this would be plain as day.

      mdander makes the further points that (1) Dan Hughes could have made a constructive contribution by corresponding with the authors of Young et al or submitting his critique to the journal editors, rather than (or in addition to) posting his stuff here; and (2) J. Curry, by allowing (inviting?) this post is either implicitly endorsing a misguided critique (with consequences for readers) or just isn’t paying attention (one suspects the latter).

  29. Double teamed by two critics of this site whom I do not recall having posted in the past often or at all under these names.

    Double teamed also in the identical nature of the comments.
    Where are Willard and Mosher when you need some help?

    Fizzy,
    Get over it.
    Unless you are married to him/her.

    Mdander criticised Dan firstly for having his maths wrong.
    Therefore he said the criticism of the paper was not well founded.
    He then admitted that the maths was correct.

    Since the maths was correct Dan’s comments on the paper were well founded.

    He then tried to change his argument to say that even though the maths was right this had no relevance to the paper, a complete volte face from his original comment.
    And not correct if you read his first comment in the comments section.

    I do not have to wonder why it is so difficult for Fizzy to understand angech’s point.

    He does not want to concede a lost argument.

    Better still he attacks Dan and JC in the same mealy mouthed way that mdander did. Polite on the surface but full of vitriol.
    Dan put up a post on the mathematics.
    “ The calculation by the authors is related the same concept that is the subject of this previous post. That is, the total potential energy at the top of a column of water is converted to thermal energy content by the action of viscous dissipation. As in the subject papers of the previous post, the temperature increase is too high.”
    Judith allowed him the courtesy of doing so.
    His point was that this should lead to a discussion and review of the assumptions made in a paper because they may be wrong.

    He does not have a responsibility to put out a paper on this.
    The authors of Young et al would have been made aware of this by now.
    As would any decent editor of their possibly mistaken paper.

    Which rather begs the question of course.
    Are you or mdander in any way related to the authors or editors and have your noses out of joint?

    Logical deduction from the tone of your comments, I would say.

    Where is Mosher?
    He could explain it to you better.

  30. Robert David Clark

    Ice Shelf

    If you look at a map of the North or South Pole you will see areas they call an Ice Shelf. You have to accept the fact these areas are what I call ICE BLOCKS which were constructed from the beginning of this ICE AGE to present.

    These are ice blocks sitting on the earth’s solid surface formed at the beginning of this Ice Age when the ocean’s surface was about 400-feet lower than present. These Ice Blocks were formed by nature to replace the radiant heat lost to the black sky daily.

    As nature dropped Ice on the frozen areas the liquid water filled the oceans.

    Eventually the ocean water was reflecting more heat to the black sky than it retained, and the oceans began to drop.

    Salt water is saturated at 28-degrees farenheight. Cool it below that and the salt begins to drop out.

    As the oceans rose touching the ice blocks the 28-degree saturated salt water began melting its way in under the ice block forming a shelf.

    When the radiant heat lost to the black sky equaled that required to melt the ice breaking off the ice blocks the ocean level stopped falling. We will remain here for about 100,000 years, when the ice blocks will be gone, and the ocean starts down putting the frozen ocean on the continents.

    • Robert David Clark

      If you look at a map of the Arctic that shows water depth you will understand how much of the area had ice blocks covering it. The ocean floor is nowhere as flat as the Antarctic. That 400-feet or less would have been an Ice Block when the earth began losing more radiant heat to the black sky than it retained.

  31. Robert David Clark

    “An ice shelf is a large floating platform of ice that forms where a glacier or ice sheet flows down to a coastline and onto the ocean surface. Ice shelves are only found in Antarctica, Greenland, Northern Canada, and the Russian Arctic. The boundary between the floating ice shelf and the anchor ice (resting on bedrock) that feeds it is the grounding line. The thickness of ice shelves can range from about 100 m (330 ft) to 1,000 m (3,300 ft).”

    They are not ice blocks sitting on the earths solid surface.
    They do not exist at the North Pole proper.
    Ice in large amounts that is grounded is probably best referred to as a glacier, not an ice shelf though one may contribute to the other.

    Ice shelves are not static and though an ice shelf might be present for thousands of years it is highly unlikely that any of the ice in it has been there that long. It extrudes and melts annually at the edges and is replaced at the ground line by glacial flow to the shelf.

    Ice ages actually begin when the sea level is quite high.
    The sea level then drops by 400 feet or more as the ice age develops.
    The reason, large glacier sheets were formed, grounded but up to 3 km high over vast areas keeping the water from returning to the seas.

    The earth’s climate and structure go through cyclical phases and non cyclical phases for a multitude of reasons.

    • Robert David Clark

      I believe the Ice Block theory and the 28-degree saturated saltwater theory is the only explanation of how nature keeps a constant average surface temperature of the earth.

      • “I believe the Ice Block theory and the 28-degree saturated saltwater theory is the only explanation of how nature keeps a constant average surface temperature of the earth.”

        Fair enough, we all have our own ideas.
        I would think that when you allow of two different reasons you open the Pandora’s box for other theories that might be valid but you have not considered
        .-
        The idea that there is a constant average temperature is sort of forcing nature to do what you want to see.
        There has been an average surface temperature range within the constraints of keeping life going on earth for a couple of billion years.
        There are scientific reasons why this might be so but no guarantee that this must persist..

        The stability of the sun output is one such factor.
        The stability of the established orbit is another.
        The stability of the earth consistency is a third.
        This would happen with any planet sun arrangement with or without water and ice and salt in the makeup.
        They do not control the planet temperature, they merely respond to the initial conditions.

      • Robert David Clark

        The dominant variable is the average surface temperature of the sun. As it rises the oceans go down and vice a versa. The other is the diameter of the sun. Because the sun is an active star the diameter is decreasing thus the ice ages are getting longer.

      • Robert David Clark

        When an iceberg the with a surface area the size of Manhattan breaks off it was not floating. The thickness of the edge attached to the shelf could be up to 400-feet thick plus that above the ocean level before it broke off.

      • Robert David Clark

        The two items we need to know are the thickness of the broken off iceberg below the water to the bottom of the iceberg next to the break also, the distance from the iceberg bottom to the ocean floor. Hopefully the first one will be 400 feet or a little less, and the second will be 0 feet.
        Now I will know if my wife is correct, or I am not wasting my time.

      • Robert David Clark

        This is a paragraph I found talking about the ice shelf.
        The assumption of hydrostatic equilibrium is only valid if the ice shelf is freely floating. This is typically only the case at a distance of several ice thicknesses from the grounding line. The first point of hydrostatic equilibrium (defined as point H in Reference Fricker and PadmanFricker and Padman, 2006) is at the outer boundary of the first fringe of tidal displacement from double-difference InSAR (Reference RignotRignot, 1996). The distance between the first point of hydrostatic equilibrium and the grounding line depends on a number of factors in addition to thickness, including ice rheology, dynamics and bedrock topography. Estimates of the distance for two locations on Institute Ice Stream flowing into the Filchner–Ronne Ice Shelf vary between ∼4.2 and 6.4 km (Reference Fricker and PadmanFricker and Padman, 2006) and 9 km on Thwaites Glacier (Reference RignotRignot, 2001). On the Ross Ice Shelf, a mean width of 3.2 km, with a standard deviation of 2.6 km, and two cases of grounding zone widths greater than 10 km have been reported (Reference Brunt, Fricker, Padman, Scambos and O’NeelBrunt and others, 2010). Thus, in general, hydrostatic equilibrium may not be valid up to ∼10 km from the grounding line. Equation (1) employs a single ice density that is constant throughout the column below the firn layer. This assumption is unlikely to be robust in areas of crevassing and also when marine ice is present (discussed in more detail below).
        To me this says it was not ice sliding off the higher continent, but put down as the oceans rose at the beginning of the Ice Age.

      • Robert David Clark

        The above explanation of the ice shelf is exactly as I explain the how the ice blocks and 28-degree saturated salt-water keep a relatively constant surface temperature of the earth

      • Robert David Clark

        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.

        THAT IS WHERE WE ARE NOW.

        IN ABOUT ANOTHER 100,000 YEARS THE ICE BLOCKS WILL BE COMPLETELY GONE, THE OCEAN WILL DROP FOR ABOUT ANOTHER 8,000 YEARS. AS THE ICE IS PUT BACK ON THE CONTINENTS.

    • Robert David Clark

      If you look at the photos of the ice breaking off what I call ice blocks in the Antartica the top of the broke off section is the same height as the part that remains.
      It does not appear there was any significant depth of saltwater under it.

      • Robert David Clark

        I have a simple question.
        If the frozen water, at the beginning of this Ice Age landed on frozen ground at the poles and above freezing areas on the rest of the earth, would the depth of the frozen areas rise about 20% faster for the same weight of water?

      • Robert David Clark

        I asked that because it explains how they are much thicker than the 400 feet lower than the lowest ocean level.
        THEY ARE STILL GROWING VERTICALLY!!!!

  32. Robert,
    Ideas and contributions are always good.
    Thanks for giving yours.

  33. Robert David Clark

    I am forced to move again so here I am.
    THIS IS THE DAILY covid-9 results.
    Both are together, easier to find and out of the way.

    Positive 31,064
    Tests 649,781
    % of total tests 4.78
    Daily deaths 308
    Average % of total tests last 7 days 3.75

    • Robert David Clark

      Last night the CDC added 32,299 positive and 42,761,590 total tests to the closing numbers of the 12:00 GMT data!!!!!

      • Robert David Clark

        Positive 15,734
        Tests 209,468
        % of total tests 7.51
        Total deaths 69
        For 7 day average I will wait 6 days and see if I believe it will be useful.

      • Robert David Clark

        Positive 34,170
        Tests 363,707
        % of total tests 9.39
        Average % of total tests last 7 days 5.02

    • Robert David Clark

      Beginning tonight it will average for the last 6 days leaving out yesterday.

    • Robert David Clark

      Positive 42,173
      Tests 42,792,709
      % of total tests 0.10
      Average of total tests last 6 days 6.02

    • Robert David Clark

      Positive 40,607
      Tests -40,181,442
      % of total tests USELESS
      Total deaths 150
      % of total tests last ? days USELESS
      Until the CDC shows actual figures that make sense 7 day average is useless.

    • Robert David Clark

      Positive 11,758
      Tests 192,520
      % of total tests 6.11

    • Robert David Clark

      Positive 23,520
      Tests 216,598
      % of total tests 10.86
      Total deaths 108

    • Robert David Clark

      Tests are down but the positive seems to be rising. I see no reason for this except the border opening are less thus more testing there. and less COVID-19 individuals being sent through-out the country, thus less testing. WE will see when back to showing the 7-day average.

    • Robert David Clark

      Positive 29,526
      Tests 845,727
      % of total tests 3.49
      Total deaths 349

    • Robert David Clark

      Positive 42,889
      Tests 1,797,521
      % of total tests 2.39
      Total deaths 270

    • Robert David Clark

      Positive 52,093
      Tests 693,828
      % of total tests 7.51
      Total deaths 200

      • Robert David Clark

        4/29/2022
        Positive 49,956
        Tests 1,233,436,405
        % of total tests 4.05
        Total deaths 206
        Average % of total tests last 7 days 4.35c

    • Robert David Clark

      Positive 19,942
      Tests 403,899
      % of total tests 4.94
      Total deaths 102
      Average % of total tests last 7 days 4.27

    • Robert David Clark

      Positive 13,106
      Tests 109,019
      % of total tests 12.02
      Total deaths 11
      Average % of total tests last 7 days 4.36

    • Robert David Clark

      Positive 25,412
      Tests 280,932
      % of total tests 9.05
      Total deaths 80
      Average percent of total tests last 7 days 3.24

      • Robert David Clark

        January, 2022 61,445
        FEBRUARY, 2022 65,929
        MARCH,2022 33,362
        APRIL 14,245
        The above is the monthly death from COVID-19 for the last 4 months.
        I believe this indicates that the STATES are gradually takng control of the border.

    • Robert David Clark

      Positive 41,588
      Tests 1,341,717
      % of total tests 3.10
      Total deaths 256
      Average % of total tests last 7 days 4.18

    • Robert David Clark

      Positive 53,031
      Tests 662,801
      % of total tests 8.00
      Total deaths 247
      Average % of total tests last 7 days 8.00

    • Robert David Clark

      Positive 54,567
      Tests 778,021
      % of total tests 7.01
      Total deaths 173
      Average % of total tests last 7 days 5.36

    • Robert David Clark

      Positive 70,409
      Tests 2,353,905
      % of total tests 2.99
      Total deaths 262
      Average % of total tests last 7 days 2.99
      From 2300 GMT to 2400 GMT THEY ADDED 2,353,905 TO TOTAL TESTS.
      NOW WE KNOW WHY THE LAST FEW WEEKS DID NOT MAKE SENSE!!!
      Hopefully in 7 more days the numbers will be accurate.

    • Robert David Clark

      Positive 28,456
      Tests 303,689
      % of total tests 9.37
      Average % of total tests last 7 days 4.92

      • Robert David Clark

        Total deaths 77
        23 more days and the COVID-19 build back better program resumes!

    • Robert David Clark

      Positive 13,931
      Total tests 266,843
      % of total tests 6.42
      Total deaths 21
      Average % of total tests last 7 days 4.84

      • Robert David Clark

        Robert David Clark | May 9, 2022 at 8:24 pm |
        Positive 34,170
        Tests 363,707
        % of total tests 9.39
        Average % of total tests last 7 days 5.02

        I erred again. I put it at the top of this section

    • Robert David Clark

      Positive 51,184
      Tests 697,607
      % of total tests 7.34
      Total deaths 241
      Average % of total tests last 7 days 5.69

    • Robert David Clark

      Positive 71,976
      Tests 2,054,999
      % of total tests 3.50
      Total deaths 194
      Average % of total tests last 7 days 3.50

    • Robert David Clark

      Positive 74,521
      Tests 559,418
      % of total tests 13.32
      Total deaths 173
      Average % of total tests last 7 days 5.51

      • Robert David Clark

        The 6-day rule says on the 5/29/2022 the Testers and Contact Tracers will begin to see results of dropping 42. on the 23rd. It took from February to September to overcome the true heroes of controlling this virus in 2021.

      • Robert David Clark

        What the USA needs right now is a respected businessman, with 4 years’ experience in government to run for Congress in the 21st Congressional district in Florida

    • Robert David Clark

      Positive 65,458
      Tests 533,421
      % of total tests 12.27
      Tota l deaths 187
      Average % of total deaths last 7 days 12.27

    • Robert David Clark

      Positive 23,293
      Tests 1,150,468
      % of total tests 2.02
      Total deaths 48
      Average % of total tests 6.00

      • Robert David Clark

        In my mind the above shows the testers, contact tracers and states are beating the border crossers.
        If Congress can write a bill in a week to show those of the 535 elected members of Congress are for what they call women’s rights, they can do the same for those that are for finishing the wall and saving lives of those individuals in the United States of America dying of covid-19.
        AT LAST THAT WOULD NOT BE WASTED LIKE A LARGE % OF THE OTHER CRAP THEY PASS.
        A PAGE BILL THAT DOES ONE THING!!!!!

    • Robert David Clark

      Positive 19,217
      Tests 180,208
      % of total tests 10.66
      Total deaths 18
      Average % of total tests last 7 day. s 6.13

    • Robert David Clark

      Positive 42,057
      Tests 398,834
      % of total tests 10.54
      Total deaths 87
      Average % of total tests last 7 days 6.24

    • Robert David Clark

      Positive 62,044
      Tests 535,755
      % of total tests 11.51
      Total deaths 208
      Averago % of total tests last 7 days 6.62

    • Robert David Clark

      Positive 74,286
      Tests 1,836,091
      % of total tests 4.05
      Total deaths 221
      Average % of total tests last 7 days 6.95

    • Robert David Clark

      Positive 108,741
      Tests 1,497,173
      % of total tests 7.26
      Average % 0f total tests last 7 days 6.44

    • Robert David Clark

      Positive 74,532
      Tests 462,038
      % of total tests 16.13
      Total deaths 210
      Average % of total tests last 7 days 6.67
      Today they extended Title-442
      Now the only chance we have is the completion of the wall!!!!!
      Lets hope it is a simple bill that just funds the completion of the wall!

  34. CO2 emits 15 micron LWIR, Ice emits 11 to 12 Micron LWIR. CO2 backradiation won’t even melt ice. CO2 emissions are consistent with a black body of -80C.

  35. On a lighter note the last day of April and soon a new global temperature for April.
    Currently the year is running about 6th warmest.
    We have had two of the weakest La Ninas I have ever seen after a strong El Nino with carried on warmth between the two La Ninas which hardly budged the BOM chart.

    Now we have a series of interesting factors in play.
    Cold waters coming up the South American Coast.
    Cool Eastern Pacific waters.
    A SOI of 21.8 when it looked like going negative.
    A mild rise in UAH only in March.
    Antarctic ice still under but rising slightly.
    Arctic Ice in the 10th lowest and has been 12th lowest recently.
    The ducks are all lined up in a row for a drop in April Global Temperatures.
    I hate writing this because Roy Spencer reads it and it causes the UAH to go the other way.

    Nonetheless a big drop in temperatures for April.
    If Only.

  36. Dietrich Hoecht

    Well, the gravity drop heating is valid physics to investigate. However, the Greenland ice melting must be seen as one big picture. Such as including evaporative cooling of the melt water, the penetration of air temperature into the depth of the glacier, the ground drainage flow, the heat transfer from water spray into air, geothermal heat input of varying distribution, and finally, the ice replenishment on top. It is about 1.6 meters per year, some 17 kilometers inland from the southern ocean edge. This is evidenced by the 120 meter move below surface of the Mosquito planes that had landed there in 1944.

  37. Glaciology makes EOS Science News by AGU:

    https://eos.org/opinions/glacial-knowledge-gaps-impede-resilience-to-sea-level-rise

    “Changes to the support, culture, and community organization of U.S. glaciology are needed to advance understanding of glacial change and better predict rising seas and other ice loss impacts.”

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