William Ward, April 18, 2019
The world is drowning in articles about catastrophic sea level rise (SLR), reminding us that if the ice sheets melt, 260 feet of water will flood our coastal cities. We know that sea level today is 20-30 feet lower than it was at the end of the last interglacial period 120,000 years ago. We also know that sea level has risen 430 feet since the end of the last glacial maximum 22,000 years ago. Research shows this rise was not monotonic but oscillatory, and during periods over the past 10,000 years, sea level has been several meters higher than today. So, evidence supports the possibility of higher sea levels, but does the evidence support the possibility of catastrophic sea level rise from rapidly melting ice?
In this paper, basic science is used to show that catastrophic SLR from melting ice cannot happen naturally over a short period. Additionally, humankind does not possess the capability to melt a large amount of ice quickly even through our most advanced technology. This news should relieve the public, which is routinely deceived by reporting that misrepresents the facts. The public is susceptible to unnecessary alarmism when melt rates and ice-melt masses are presented without perspective and juxtaposed against claims that scientists are worried. This paper uses the same facts but places them in perspective to show that catastrophic risks do not exist.
Ice Sheets Melting: Deceptive Reporting
The growing alarm over melting ice sheets is directly attributable to deceptive reporting. The sheer number of reports inundates the public with an incessant message of angst. A single scientific study can be the source for headlines in hundreds of news articles. With social media repeating the news and the subsequent chorus of lectures from celebrities and politicians, we find ourselves in the deafening echo chamber of Climate Alarmism. However, it is a mistake to assume the real risks are proportional to the frequency or intensity of the message.
The primary problem is that the news writers do not have the scientific background to report on the subject responsibly, and therefore they routinely corrupt and distort the facts. Take for example an article in Smithsonian dated September 1, 2016, entitled “Melting Glaciers Are Wreaking Havoc on Earth’s Crust.” The first two sentences of the article read:
“You’ve no doubt by now been inundated with the threat of global sea level rise. At the current estimated rate of one-tenth of an inch each year, sea level rise could cause large swaths of cities like New York, Galveston and Norfolk to disappear underwater in the next 20 years.”
A sea level rise rate of one-tenth of an inch per year yields 2 inches of SLR in 20 years. Topographical maps show the lowest elevations of these cities are more than ten feet above sea level. No portion of these cities will disappear underwater from 2 inches of SLR.
The news writers seem obligated to pepper the facts with their own opinions such as “… climate change is real, undeniable and caused by humans.” It is often difficult for the reader to discern the facts from the opinions. However, even the facts become troubling because they consist of numbers without the perspective to understand their significance and are wrapped in existential angst. Consider the following excerpt from a June 13, 2018 article in the Washington Post, entitled “Antarctic ice loss has tripled in a decade. If that continues, we are in serious trouble.”
“Antarctica’s ice sheet is melting at a rapidly increasing rate, now pouring more than 200 billion tons of ice into the ocean annually and raising sea levels a half-millimeter every year, a team of 80 scientists reported… The melt rate in Antarctica has tripled in the past decade, the study concluded. If the acceleration continues, some of scientists’ worst fears about rising oceans could be realized, leaving low-lying cities and communities with less time to prepare than they had hoped.”
As reported, the reader assumes a melt rate that has tripled must be dire, and billions of tons of melting ice must be extreme. However, this perception changes if the facts are analyzed to provide perspective. An analysis shows that the original annual melt rate of 1.3 parts-per-million (ppm) has increased to nearly 4 ppm over 26 years. The news writer failed to inform us of these facts which provide perspective. The new melt rate is analogous to losing 4 dollars out of 1 million dollars. Losing slightly less than 4 parts in 1 million each year means that it will take over 250,000 years to melt entirely. No natural process is static, so we should expect variation over time. Most change is cyclical. Sometimes the ice is increasing and sometimes it is decreasing. The average person’s body mass fluctuates by 20,000 to 40,000 ppm each day. By comparison, Antarctica varying by 1-4 ppm over a year should be considered rock-solid stability in the natural world.
Ice Sheets Melting: What Happened Over the Past Century
Antarctica holds 91% of the world’s land ice, Greenland 8%, and the remaining 1% is spread over the rest of the world. Therefore, by understanding what is happening to the ice sheets in Antarctica and Greenland, we understand what is happening to 99% of the world’s land ice.
NASA is a good source for research about what is happening in Antarctica. However, two NASA agencies have recently published studies with conflicting conclusions. The Goddard Space Flight Center recently published research concluding Antarctica is not contributing to SLR. According to the study, snow accumulation exceeded ice melting, resulting in a 0.5-inch sea level reduction since 1900. Contrarily, the Jet Propulsion Laboratory (JPL) reports that the rate of Ice loss from Antarctica has tripled since 2012 and contributed 0.3 inches to SLR between 1992 and 2017. To cover the worst-case scenario, we can analyze the JPL study and provide the perspective to understand their results.
Over 26 years, Antarctica’s average annual mass loss was less than 0.00040% of its total. If Antarctica were a 220 lb man, his mass loss each year would be 0.4 grams or about eight tears. (Eight human tears weigh about 0.4 g.) At this alarming rate that makes our most elite climate scientists worried, it would take 250,185 years to melt all of the ice. It would take over 1,000 years of melting to yield 12 inches of SLR from Antarctica if we ignore natural variability and the cyclical nature of ice volume and assume the melt rate continues uninterrupted.
The best information we have about Greenland comes from a study in the journal Nature, estimating Greenland’s ice losses between 1900 – 2010. Using current ice volume estimates from USGS, we calculate the ice mass in 2010 was between 99.5% – 99.8% of what it was in 1900. Ice melt from Greenland in the 111 years contributed 0.6 – 1.3 inches to SLR. It would take over 1,300 years of melting to yield 12 inches of SLR from Greenland if we ignore natural variability and the cyclical nature of ice volume and assume the melt rate continues uninterrupted.
The average annual inland temperature in Antarctica is -57 °C and most coastal stations average -5 °C to -15 °C. The much talked about Western Antarctica averages several degrees below 0 °C. Southern Greenland does experience summer temperatures above 0 °C and seasonal melting. Northern Greenland stays below 0 °C even in the summer months, and the average annual inland temperatures are -20 °C to -30 °C. The temperatures in Greenland and Antarctica are not warm enough to support significant rapid ice melt. In the past century, we have 1 °C of retained atmospheric heat, and enough heat exchanged with ice in Greenland and Antarctica to raise sea level by 0.9 – 1.6 inches. Despite all of the reports in the media to the contrary, we have no real observations of any ice melt crisis. The past 111 years have been remarkable because of ice stability – not because of ice melting. We are 19 years into the 21st century with no evidence supporting an outcome much different from the 20th century.
Ice Sheets Melting: The Process
The lifecycle of an ice sheet begins as snow. Snow falls in the higher elevations and over time it compacts and becomes ice. The ice thickness in Antarctica is over 12,000 feet in the center of the continent and over 9,000 feet over most of East Antarctica. The force of gravity initiates a thousand-year journey where the ice flows from its heights back to the sea. At the end of this journey, when its weight can no longer be supported by the sea, it “calves” and becomes an iceberg. Some icebergs can float around Antarctica for over 30 years before fully melting. So, young ice is born inland from snow, and old ice dies near the coast from seasonal melting or after drifting for years as an iceberg. This process is the natural cycle of ice and not one which should create panic. During some periods we have more snow accumulating than ice melting, such as the period between 1300 CE and 1850 CE, known as the “Little Ice Age.” During other periods we have more ice melting than snow accumulating, such as the Medieval Warm Period and our present time.
In our present time, sunlight alone is insufficient to cause significant changes to ice sheet mass. Sunlight must act in concert with other effects such as cloud cover, water vapor and other “greenhouse” gasses such as CO2. Regardless of the mechanisms, the Earth system must do two things to melt more ice: 1) retain more heat energy and 2) via the atmosphere, transport this heat to the poles and transfer it to the ice. Additional heat energy in the system cannot melt ice unless this transport and transfer happen.
Ice Sheets Melting: Conservation of Energy
A 2007 study by Shepherd and Wingham published in Science shows the current melt rate from Greenland and Antarctica contribute 0.014 inches to SLR each year. For perspective, the thickness of 3 human hairs is greater than 0.014 inches. The results align reasonably well with the other studies mentioned. Despite the minuscule amount of actual SLR from melting ice, NOAA and the IPCC provide 21st century SLR projections that range from a few inches to several meters. The wide range of uncertainty leads to angst about catastrophe; however, the use of basic science allows us to provide reasonable bounds to the possibilities.
Before the start of the American Revolution, Scottish scientist Joseph Black (and others) solved the mysteries of specific heat and latent heat, which gives us the relationship between heat energy, changing states of matter (solid/liquid) and change of temperature. Equations 1 and 2 give us the mathematical relationships for specific heat and latent heat respectively:
(1) E = mc∆T
(2) E = mL
Where E is thermal energy (Joules), m is the mass (kg), c is the “specific heat” constant (J/kg/°C), ∆T is the change in temperature (°C), and L is the latent heat constant (J/kg). Specific heat is the amount of heat energy that we must add (or remove) from a specified mass to increase (or decrease) the temperature of that mass by 1 °C. Latent heat is the thermal energy released or absorbed during a constant temperature phase change. If we know the mass of the ice, water or atmosphere, it is easy to calculate the amount of energy it takes to change its temperature, melt it or freeze it.
Understanding that energy is conserved when melting ice, the equations above can be used to calculate the temperature effects that must be observed in the oceans or atmosphere to support an ice melt scenario. We can provide reasonable bounds and reduce the uncertainty.
See the reference section at the end of the paper for all sources and calculations.
Key #1: Importance of the Latent Heat of Fusion
It is essential to understand the latent heat of fusion because of the enormous amount of heat energy that is required to change the state of H2O from solid to liquid. Figure 1 shows the specific heat and phase change diagram for water. The blue line shows the temperature of water in °C (y-axis) plotted against the change in thermal energy in kJ/kg (x-axis). It shows how temperature and energy are related as we go from cold solid ice to boiling liquid water. The average annual inland temperature of Greenland is -25 °C and this is the reason for Point 1 on the line. If we start at Point 1 and progress to Point 2, this shows how much heat energy must be added to change the temperature of 1kg of ice from -25 °C to 0 °C. It is important to note that at Point 2, the ice is still 100% solid at 0 °C.
Figure 1: Water Phase/Specific Heat Diagram
The diagram reveals something interesting about the behavior of water. As we progress from Point 2 to Point 3, the water undergoes a phase change from solid to liquid. There is no temperature change as the ice becomes liquid water; however, a large amount of heat energy must be added. The energy that must be added to change the phase of water from solid to liquid is the latent heat of fusion. For melting ice, temperature alone does not inform us about what is happening to the system. To assess ice melting, we must understand the net change of energy. Whether we melt 1kg of ice or the entire ice sheet in Greenland, using Equations 1 and 2, we can easily calculate the energy required to do so. Going from Point 1 to Point 3 requires 3.86×105 Joules of energy for each kg of ice mass warmed and melted. For simplicity, we call this quantity of energy “E.”
Figure 1 also shows what happens as we move from Point 3 (0 °C liquid seawater) to Point 4 (seawater starting to boil at 100 °C). It takes a measure of energy “E” to move between Points 3 and 4, just as it does to move between Points 1 and 3. Therefore, as shown in Table 1, the energy required to melt the ice is equivalent to the energy required to heat the meltwater to a boil at 100 °C. (Note: the fresh water from the ice is assumed to flow to the oceans.)
| Energy to melt 1kg of polar ice from -25 °C to 0 °C water | <– Is Equal To –> | Energy to raise the temperature of 1kg of seawater from 0 °C to 100 °C |
Table 1: Relating Energy Between Polar Ice Melt and Boiling Water
Key #2: Total Energy Required to Melt the Ice Sheets
Using Equations 1 and 2, we calculate that the total heat energy required to melt the ice sheets entirely is 1.32×1025 J. This value can be given perspective by calculating the increase in ocean water temperature that would result from adding 1.32×1025 J of heat. We know that deep ocean water below the thermocline is very stable in temperature between 0-3 °C. 90% of the ocean water mass is below the thermocline. The thermocline and surface layer above contains the ocean water that responds to changes in atmospheric heat, whether that be from seasonal changes or climate changes. Therefore, if we constrain the 1.32×1025 J of heat energy to the upper 10% of the ocean mass, we calculate the temperature increase would be 25.6 °C, assuming equal heat distribution for simplicity of analysis. This increase would make the surface temperature of equatorial ocean water close to 55 °C, similar to a cup of hot coffee. Polar seas would be perfect for swimming at nearly 25 °C. According to NOAA, over the past 50 years, the average ocean surface temperature has increased approximately 0.25 °C.
Another way to give perspective is to calculate the increase in atmospheric temperature that would result from adding 1.32×1025 J of heat to the atmosphere. First, we must understand some related facts about the atmosphere. Heat energy must be transported by the atmosphere to the polar regions, or no ice can melt. However, the atmosphere’s capacity to store heat energy is extremely low compared to the energy required to melt all of the ice. The ice sheets contain more than 900 times the thermal energy below 0 °C as the atmosphere contains above 0 °C, and therefore the atmospheric heat energy must be replenished continuously to sustain ice melting. Melting polar ice with heat from the atmosphere is analogous to filling a bathtub with a thimble. The low specific heat of air is one reason the atmosphere lacks heat carrying capacity. The other reason is its low mass.
Figure 2 shows the vertical profile of the Earth’s atmosphere. The red line in Figure 2 shows the temperature of the atmosphere in °C (x-axis) plotted against the altitude in km (y-axis). 75% of the mass of the atmosphere is contained in the Troposphere, where all life (outside of the oceans) exists on Earth. Figure 2 reveals that most of the atmosphere is far too cold to melt ice. We can ignore the Upper Thermosphere as the mass of atmosphere contained in that layer is negligibly small. Only the Lower Troposphere below 2.5 km altitude contains air at a warm enough temperature to melt ice. (See the region of the graph enclosed in the yellow oval.) 35% of the atmospheric mass exists below 2.5 km, and the average temperature is ~ 8 °C.
Figure 2: Vertical Profile of Earth’s Atmosphere
Using Equation 1 with E = 1.32×1025 J, the mass of the atmosphere below 2.5 km and solving for ∆T, we can calculate what the temperature of the air below 2.5 km would be if it contained the energy required to melt all of the ice. The atmospheric temperature would have to be 7,300 °C, which is 1,522 °C hotter than the surface of the sun. Life on Earth would be in jeopardy from the increased atmospheric heat long before all of the ice melted. While there are no plausible thermodynamic pathways to heat the Earth’s atmosphere to such temperatures, the calculations of energy required are accurate. According to NASA, the global average temperature over the past 50 years has increased approximately 0.6 °C.
Key #3: SLR From Incremental Atmospheric Heat Exchange with Ice Sheets
It is said, “you can’t have your cake and eat it too.” Similarly, you can’t have atmospheric heat and melt with it too. If the ice consumes heat, then the atmosphere cools. If the atmosphere retains its heat, then no ice melts. So, let’s examine some scenarios where we trade energy from the atmosphere with ice to see how much corresponding SLR we can get.
Using Equation 1, we can determine the change in energy for a 1 °C temperature decrease in the atmosphere below 2.5km. We can then apply this energy to the ice, assume maximum melting volume and translate that to SLR. For every 1 °C of atmospheric energy transferred to the ice, we get 0.4 inches of SLR. Some IPCC scenarios project a 4 °C rise in “global average temperature” in the 21st century, due to increased atmospheric CO2. An increase in temperature does not melt any additional ice unless the heat is transferred to the ice. If 4 °C of energy from the atmosphere is transferred to the ice, we get a corresponding 1.7 inches of SLR and an atmosphere that is 4 °C cooler. If we transfer all of the energy in the atmosphere above 0 °C to the ice, then we get 3.4 inches of SLR and a world where the entire atmosphere is at or below 0 °C. The global average temperature would be 6 °C less than the coldest experienced during the depth of a glacial period.
To raise sea level by 12 inches would require the atmosphere to heat up by 28 °C before exchanging that energy with the ice. As we would experience it, the atmosphere would have to heat up by some incremental value, then exchange that incremental value of energy with the ice, thus cooling the atmosphere, and then repeat this process until the 28 °C of atmospheric heat is consumed.
Key #4: Maximum Ice Melt Potential from Technology
Keys #1-3 don’t offer much to support the possibility of large quantities of ice being melted rapidly by natural causes. The next obvious question is, can humankind generate enough heat with our most advanced technology to melt a significant amount of ice rapidly?
The power of the atom is one of the most awesome powers humankind has harnessed. There are 8,400 operational nuclear warheads in the world’s nuclear arsenal, with a total yield of 2,425 Megatons of TNT. It is interesting to note that the energy contained in this nuclear arsenal is over 800 times the equivalent explosive power used in World War II. It is said that there are enough nuclear weapons to destroy the world a hundred times over. So, perhaps this is enough energy to melt the ice sheets entirely. For this exercise, we assume the nuclear weapons release their energy slowly – only fast enough to melt ice and no faster. For maximum melting, we evenly distribute all of the weapons in the ice. However, when we convert 2,425 MT to Joules, we get a number that is far below the energy required to melt all of the ice. The SLR we could get by using all of the world’s nuclear weapons for melting ice would be 0.002 inches. For reference, the diameter of a human hair is 2.5 times thicker than this. If we want all of the ice to melt, we need to duplicate each weapon more than 1,300,000 times. So, it looks like our current arsenal of nuclear weapons is no match for the ice.
What other sources of power does humankind have that could be used to melt a significant amount of ice? The annual global energy production of electric power is 25 petawatt-hours (25×1015 Whr) or 9×1019 Joules. If we could, through some advanced technology, transfer all electric energy generated over one year to heaters buried in the ice, and do this with no transmission or distribution losses, then how much ice could we melt? The answer is 0.02 inches of SLR (equivalent to 4 human hair diameters). This scenario would require that humans not use any electric power for that entire year, for anything other than melting ice. Humanity would have to forego the benefits of electric power for over 146,000 years to melt all of the ice, assuming static conditions in the ice.
Ice Sheets Melting: Analysis
Since 1900 we have 1 °C of retained atmospheric heat, and enough heat consumed by the ice sheets to produce 0.9 – 1.6 inches of SLR. From Key #3 we learned 1.7 inches of SLR results from trading 4 °C of atmospheric heat for ice melting. Therefore, as a worst-case approximation, if there had been no net ice melt since 1900, the atmosphere would have heated by approximately 5 °C. We can conclude that ice melting consumed 4 °C of heat, leaving the atmosphere with 1 °C of retained heat. We observed a 4:1 ratio of consumed heat to retained heat in the 20th century, worst case. For the best-case approximation, we use the lower estimate of 0.9 inches of SLR, which yields a 2:1 ratio of consumed heat to retained heat over the same period. In one of the more extreme scenarios, the IPCC climate model projects 4 °C of atmospheric temperature rise in the 21st century. For a 4 °C rise scenario, using the worst-case ratio of consumed to retained heat, we can estimate a 6.4 inch SLR over that period. In a more moderate scenario, the IPCC projects a 1.5 °C temperature rise. For a 1.5 °C rise, using the best-case ratio of consumed to retained heat, we can estimate an SLR of 1.4 inches. Unfortunately, none of the climate models have been able to predict the climate accurately, and none of them backtest successfully. We are one-fifth of the way through the 21st century and do not appear to be on course for the IPCC’s worst-case temperature projections. Therefore, it is reasonable to assume the results for the 21st century will likely be very similar to the 20th century, with 1-2 inches of SLR.
Detailed analysis of the claimed Earth energy imbalance is beyond the scope of this paper. The analysis presented here exposes the effects that must occur from an imbalance that leads to catastrophic melting. The ice must absorb large quantities of heat energy for sustained periods. Therefore, inland temperatures over Antarctica and Greenland would need to be maintained well above 0 °C for significant portions of the year. Atmospheric heat lost to the ice would need to be continually replenished to perpetuate the process. The oceans store heat energy, but the large mass of the oceans with the high specific heat of seawater blunts the possible effects from that energy. The energy that would raise the first 2.5 km of atmospheric air by 1 °C would raise the first 1,000 feet of seawater by only 0.0035 °C. The 2nd law of thermodynamics requires a temperature difference to transfer heat energy. Small increases in ocean temperature cannot lead to large movements of heat energy to an already warmer atmosphere. Finally, the system must transport more heat energy to the polar regions. In reality, the Earth maintains a very large temperature gradient between the equator and the poles. Our observations do not show gradient changes that would support significant additional heat transport. Without the increased energy storage and transport, and sustained polar temperatures well above freezing, catastrophic ice melt scenarios are not possible.
Ice Sheets Melting: Summary
Despite the overwhelming number of popular news reports to the contrary, studies of ice sheets melting over the past century show remarkable ice stability. Using the proper scientific perspective, analysis of ice-melt rates and ice-mass losses show the ice sheets will take hundreds of thousands of years to melt, assuming the next glacial period doesn’t start first. An application of basic physics shows that for every 1 °C of atmospheric heat exchanged with the ice sheets we get a maximum 0.4 inches of SLR and a correspondingly cooler atmosphere. Over the 20th century, we observed a worst-case 4:1 ratio of consumed heat to retained atmospheric heat. It is proposed that this ratio can be used to assess potential ice-melt related SLR for a hypothetical atmospheric temperature increase scenario over the current century. Using a reasonable range for all of the variables we can estimate an SLR of between 1.4 – 6.4 inches, but our current observations support the rise being toward the lower end of that range.
The atmosphere and oceans do not show the increase in energy necessary to cause catastrophic SLR from rapidly melting ice. Humankind does not possess the technology to melt a significant amount of ice because the energy required is enormous and only nature can meter out this energy over very long periods. With the proper scientific perspective about the amount of energy required to melt ice, it should be much more difficult for Climate Alarmists to scare the public with scenarios not supported by basic science.
References
NASA Study: Mass Gains of Antarctic Ice Sheet Greater than Losses: https://www.nasa.gov/feature/goddard/nasa-study-mass-gains-of-antarctic-ice-sheet-greater-than-losses
Ramp-up in Antarctic ice loss speeds sea level rise: https://climate.nasa.gov/news/2749/ramp-up-in-antarctic-ice-loss-speeds-sea-level-rise/?fbclid=IwAR2Vnkbxxa-NTU_v0lRUUGGDffMs4Q6BGvHX-KHzcHM7-q2B7IO59wCEiQc
Sea Level and Climate (Fact Sheet 002-00): https://pubs.usgs.gov/fs/fs2-00/
Spatial and temporal distribution of mass loss from the Greenland Ice Sheet since AD 1900: https://www.nature.com/articles/nature16183
Recent Sea-Level Contributions of the Antarctic and Greenland Ice Sheets: http://science.sciencemag.org/content/315/5818/1529
All of the constants and calculations are provided in the associated Excel file located here: https://wattsupwiththat.com/wp-content/uploads/2019/04/Ice-Atmosphere-Ocean-Energy-20190407-1-1.xlsx
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Thank you, William Ward, for an excellent common sense approach to ice melt and atmospheric temperatures.
What the comments and the article neglect to mention is the increasing reduction in sea ice in the Arctic. I that’s perhaps forgivable since both (comments and article) focus on sea level rise and Arctic ice does not _directly_ cause sea level rise.
It does, however, cause an increase in mean sea temperature which, due to thermal expansion, cause sea level rise. But what concerns me with dismissals of reduced Arctic sea ice is the National Security issues.
The US Coast Guard has two (very old) ice breakers. Russia now has in excess of 40 ice breakers, and Russia and China are both building more. These will allow Russia to control the Arctic (they now claim all waters from Siberia to the North Pole), and all the natural resources below. The Chinese shipping company COSCO now has cargo ships with reinforced hulls capable of transporting containers from China ports to Europe.
Chris,
You said, “It [reduction in sea ice in the Arctic] does, however, cause an increase in mean sea temperature which, due to thermal expansion, cause sea level rise.”
The claim, about “dark water” is frequently made. I have yet to see a defense of it. I have made the point that it is over-rated:
https://wattsupwiththat.com/2016/09/12/why-albedo-is-the-wrong-measure-of-reflectivity-for-modeling-climate/
It is easy to demonstrate thermal expansion by bringing a pan of cold water up to boiling. It isn’t so easy when it is claimed for an entire ocean. You then are dealing with the same problem of where is the energy necessary to make it happen coming from as you are with melting all the ice.
chemamn
I’m not questioning thermosteric expansion. I’m questioning the commonly made claim that melting Arctic ice exposes “dark water” that then absorbs sunlight and becomes warmed. I believe the effect is negligible.
Chris,
Regarding Arctic sea ice, the topic was too much to add to the paper. I don’t think I could do it justice without making the paper too long. I have plans to do a separate paper on the subject, with similar exposures about the ridiculousness of the Alarmists’ claims.
Arctic Sea Ice Extent (ASIE) is one of the metrics pushed onto the public to create panic. ASIE may have some scientific value, but the way it gets trotted out to the public is entirely misleading. The ASIE metric by definition is a mess scientifically speaking. If the concentration of ice in any of the observed gridded areas exceeds 15%, then it is counted as ice. At 14% and below it is considered to be ice-free. 100% concentration is valued the same as 15%. Equating 15% and 100% concentration is an absurdity, and if you look at the latent heat of fusion graph, you can see how much difference in energy there is between 15% and 100% conversion. There is a small difference between 15% and 14%, but they are treated as if the difference is massive. Ice thickness doesn’t even enter into the equation. If it did, then ASIE becomes even more absurd.
We do have the Arctic Sea Ice Volume (ASIV) metric. ASIV is not trotted out to the public because it doesn’t give a reason for alarm. It shows the ice has been stable since 2007. See the graph which I updated on Tuesday of this week. Data from DMI.
https://imgur.com/mpOJRc2
Not sure about the heat to melt the ice being transported by the atmosphere.
I would guess that much more heat is transported by ocean currents.
While I buy this “static” analysis conclusions for what is examined, natural systems are not usually so static. Let me propose an added complexity (likely or not).
The Antarctic Ice sheet lying over the Ocean (sea ice) can obviously be melted at a greatly increased rate due to the heat transport potential of water. Melting current sea ice does nothing to raise sea levels, but bear with me.
Ice that is piled high and deep deforms in a plastic manner, generally running downhill but even capable of filling in a sink and overflowing it, overcoming some amount of vertical height (assuming there is enough ice flowing from an even greater height). Antarctic ice fits this description, if its piled up high enough it flows as glaciers and even larger ice sheets. It already does.
If you “warm” ice, you increase its ability to flow even though it’s still ice. Think of ice as a rock, and heating the rock up but not quite melting it – it will deform easier. So if you “warm” enough of the ice, it could, in theory, begin to flow faster. Note: I am NOT talking about liquid water forming a lubricant under the ice as I am assuming the ice is not warm enough to have liquid water under it. If there is liquid water, it likely comes from some geothermal source, not from the atmosphere.
So, using the scenario described in this posting, it is possible that a certain amount of warming could cause an increase in ice flow, and that ice flow pushes additional ice off of land and over onto the ocean, thus you have additional sea ice. This already happens at a slow steady rate, so I am saying what if the rate increases? Then you have ocean water that can melt the additional ice at a much increased rate.
Ignoring this less static possibility of the ice means the SLR projections are at best, optimistic when trying to calculate the potential of Antarctic Ice to raise sea levels. Of course, it is also possible that a warmer atmosphere will cause more snow to be dumped onto Antarctica, canceling or even reversing this additional SLR. That’s the main problem with trying to predict what a natural system will do – they are always complicated.
Do I buy my own scenario? Let’s just say it’s possible, but I’ll believe it when I see data supporting it. Ice sheets and glaciers likely have a normal variability in flow rates that will make an general increase in flow rate hard to spot. We are much more likely to observe this in Greenland; not the Antarctic (any time soon).
Robert of Texas,
This is something to think about: how the movement of the ice to the sea could impact the analysis. Here are a few thoughts.
Ice melting in the sea takes the same amount of energy out of the system as ice melting in the air. So, melting doesn’t come for free. The Earth System has to give up heat energy to do it. The water involved is likely surface water, which is more tightly coupled with air, so the melting has to be accounted for just the same.
Regarding warming ice becoming more plastic and accelerating its journey to the sea, it is helpful to detail the situation. We have a 10,000 ft mound of ice in Greenland. A ring of mountains surrounds the mound of ice, whose inland temperature averages -25°C to -30°C. Have you ever looked at a 3D map of Greenland? See image at this link:
https://imgur.com/Z4C3mbZ
The mountains act as a bowl, holding back the ice. If the inland temperature increases by a few degrees C, how deep does the temperature change go into the ice and how much does a few degrees at that depth affect the plasticity?
My opinion is that all of the current estimates are likely created with all assumptions geared to emphasize/exaggerate the melting. We are probably safe to take the lower end of the estimate ranges, but even if we take the higher end estimate and double it, it now takes 125,000 years to melt entirely instead of 250,000 years. We get 12 inches of SLR in 500 years instead of 1000, assuming that we are on a non-stop course of warming/melting. The history shows the warming and cooling are cyclical within the interglacial. No one has proclaimed the Quaternary Ice Age over, so the next thing awaiting us is more ice, not less.
The statement in the text, namely
“The news writers seem obligated to pepper the facts with their own opinions such as “… climate change is real, undeniable and caused by humans.” It is often difficult for the reader to discern the facts from the opinions.”
The idea that these are opinions ought to reference the founding mission statements of the UN IPCC. The question is, if the United Nations tells you such & such is true, is it then your opinion?
Hello John,
You asked: “The question is, if the United Nations tells you such & such is true, is it then your opinion?”
The IPCC is a political organization that gives us incantations of science to validate their policy recommendations. So, I’d say whatever they tell us is an opinion. Perhaps a “scientific opinion” – but not proven science that is repeatable in the lab with consistent results. We are told that their computer models, which can’t backtest, project an inevitable future, and we should accept their statements as having equivalent validity to F=ma, V=IR, E=mc∆T or Maxwell’s equations. If a news writer repeats that opinion, then it is still an opinion.
William Ward,
Excellent presentation! Keep up the good work!
Thank you, J Mac. I have more things like this on my list to write about.
Put into a proper perspective the amount of energy needed to melt the ice sheets is relatively
small. Taking Mr. Ward’s estimate of 10^25J and dividing by the incident solar flux (about 10^17 W)
you find that every 2.5 years the earth receives enough energy from the sun to melt all of the ice
sheets. Even if you take into account the fact that 50% of the incident solar radiation is reflected
back that still means that it would only take 5 years to melt all of the ice using solar power. So
there is certainly more than enough energy available to melt all of the ice on a century timescale.
The issue is of course (as Mr. Ward points out) the energy transport from the equatorial regions where most of the solar energy is to the poles where most of the ice is. How fast this will happen is
still uncertain but if the earth continues to absorb more energy than it radiates thanks to increasing CO2 levels then it will happen.
IW,
Is your comment meant to be serious?
It is as serious as the suggestion that the atmosphere would need to be heated to
7300 degrees in order to melt all the ice. No one other than this author is suggesting
that the ice sheets will melt instantaneously and simultaneously — which of course
requires a ridiculous and impossible amount of energy. Melting a substantial fraction
of the ice sheets over the course of a century (enough to cause several metres of sea level rise) is easily feasible and the energy requirements are relatively modest.
You leave me without words.
In all fairness to Mr. Ward his point was to compare the specific heat of air to the latent heat of ice and demonstrate the great difference of the two. It was not meant to be a serious proposal of how hot the air must become to melt ice. In a similar vein, your calculation of the time required to melt all ice using sunlight is of the same class. It is not a serious proposal about how fast ice could melt since nearly all of that 10^17 W of sunlight are needed to maintain the current earth steady temperature distribution and are not available to melt ice. The difficulties involving transport are on top of the tiny amount available.
Thank you, Kevin. Your words accurately represent my intentions with the calculation.
I did state that there are no thermodynamic pathways to heat the atmosphere to 7300°C. However, the amount of energy to melt the ice entirely would/could raise that mass of atmosphere to that temperature if the temperature source were available. The point is to provide perspective. News writers mention the “warming” air and then go on to tell us about the impending disaster. The “warming” air is the description given to air that goes from -15°C to -9°C, which can’t melt ice, or perhaps -1°C to 3°C for a few hours of the day for a short period in an isolated location. With perspective, that news gets an eye-roll and a yawn.
The 7300°C figure provides perspective to the energy that must be cumulatively transferred to melt the ice entirely. While we know energy is not measured with temperature, for a fixed mass of atmosphere with a fixed specific heat, temperature can be a proxy for energy, via E=mc∆T. We can calculate that transferring 1°C of energy from the atmosphere (below 2.5km) to the ice yields 0.4 inches of SLR from melting. We would have to experience 7,300 episodes of transferring 1°C atmospheric energy to the ice to melt it entirely. We appear to have transferred 2-4°C to the ice in the last century. To argue for greater SLR in this century should require an explanation of what changed. What is different about the solar radiation now vs. the past? The claimed changes need to be brought back to energy and transport. We must see this in the atmosphere – precisely the atmosphere where the ice is located.
Thank you Messrs. Kilty and Ward for those comments.
Although I appreciated the head post’s order-of-magnitude comparisons–and heartily agree with Mr. Ward’s comments about the press’s deplorable failure to include context–those comments addressed what seemed to me seemed an omission in the head post: it didn’t compare total latent heat with the energy in incoming radiation with total latent heat.
As someone observed, melting all that ice would take the total incident solar energy for over two years. Perhaps if there’s a subsequent revision of the head post that fact could be included together with how great a reduction in the earth’s effective radiation temperature would be needed to retain a significant fraction of that incident energy for ice melting.
Hi Joe Born,
You said: “As someone observed, melting all that ice would take the total incident solar energy for over two years. Perhaps if there’s a subsequent revision of the head post that fact could be included together with how great a reduction in the earth’s effective radiation temperature would be needed to retain a significant fraction of that incident energy for ice melting.”
In the analysis section, I said: “Detailed analysis of the claimed Earth energy imbalance is beyond the scope of this paper. The analysis presented here exposes the effects that must occur from an imbalance that leads to catastrophic melting. …”
The claimed imbalance is approximately 0.6W/m^2. I’m skeptical of this imbalance. First, it is only a theory that there is a control system type feedback that establishes a “balance” according to a CO2 based “setpoint” or “reference.” I’m not aware of actual proof that this balanced state existed in the past. The Holocene Optimum, Medieval Warm Period and Little Ice Age seem to counter that theory. Also, 0.6W is probably less than the error range of the instruments. Where is this excess energy going? We have the oceans ate my warming excuse/theory, but not the means to correctly measure it. They may be correct, but I’m skeptical. We certainly don’t see it in the atmosphere or ice.
What can we deduce from an analysis? The Earth sits in space with a temperature a few degrees above absolute Zero K (0K). Without the Sun, the Earth would reach equilibrium with space, except for perhaps heat from the Earth’s molten core. So, the heat energy coming from the Sun and the heat energy leaving Earth to space are close to equal now except for the small changes to atmospheric and ocean temperature. Clouds, seasonal Earth tilt, albedo, and other things would contribute to variations we see in sea and air temperatures over time. If we want to consider all of the incoming energy going to melt ice, then that means that the energy must come from somewhere else on planet Earth. The atmosphere only has enough energy to increase sea level by 3.4 inches. After that, it is out of ammunition. The oceans must replenish it.
The average temperature of the ocean is ~3C. You will find numbers +/- this from different sources. However, it is the upper 10% of the ocean mass above the thermocline that is actively engaged with the atmosphere. And within that, only water much closer to the surface if we are dealing with short timespans. The top 5 or 10% of the ocean mass doesn’t have enough energy to melt the ice entirely. Additionally, as more ice melts, the oceans get colder. Then the 2nd law of Thermodynamics limits the rate at which heat transfers, as the ocean and atmosphere get close to equilibrium.
You also have to explain how the gradients on Earth change. What is going to cause the equators to become cold and the poles to become warm? This is the only option because the energy has to come from somewhere, and we know that what is entering and exiting is very close to even.
That’s why I said in the analysis (to keep the paper shorter): “The analysis presented here exposes the effects that must occur from an imbalance that leads to catastrophic melting. The ice must absorb large quantities of heat energy for sustained periods. Therefore, inland temperatures over Antarctica and Greenland would need to be maintained well above 0 °C for significant portions of the year. Atmospheric heat lost to the ice would need to be continually replenished to perpetuate the process. The oceans store heat energy, but the large mass of the oceans with the high specific heat of seawater blunts the possible effects from that energy. The energy that would raise the first 2.5 km of atmospheric air by 1 °C would raise the first 1,000 feet of seawater by only 0.0035 °C. The 2nd law of thermodynamics requires a temperature difference to transfer heat energy. Small increases in ocean temperature cannot lead to large movements of heat energy to an already warmer atmosphere. Finally, the system must transport more heat energy to the polar regions. In reality, the Earth maintains a very large temperature gradient between the equator and the poles. Our observations do not show gradient changes that would support significant additional heat transport. Without the increased energy storage and transport, and sustained polar temperatures well above freezing, catastrophic ice melt scenarios are not possible.”
Mr. Ward:
Thank you for that extensive response, and I apologize for not being clear enough to have spared you the trouble. I had already recognized (although I didn’t as I was originally reading your post) that radiation is not a significant factor in this context.
I merely meant to make a suggestion that might forestall difficulties for future readers like me, who don’t think things through as quickly as some do. Specifically, I thought you might say something like, “Even if the earth’s radiation temperature fell to that of the tropopause—which is as low as it could go—the imbalance would be only __ W/m^2, which, over the Antarctic + Greenland area of __km^2, would take __years to melt the ice.
As you can see from the lacunae in that suggestion, I don’t know whether such a statement would actually work out, but I was trying to help.
Anyway, thanks again for your very thorough response. (And the head post taught me a lot, for which I also thank you.)
Joe Born,
Thanks for your help! I’m glad you asked the question. I wanted to deal with that subject more directly but couldn’t figure out how to do so succinctly. Fortunately, I think we can simplify the analysis by just observing what is going on with atmospheric temperature and ice melting. Even though there are many problems with our temperature records, and the associated errors likely exaggerate the temperature to the favor of Alarmists, using the given temperature works very well to ascertain rough bounds of melt potential.
There was an important aspect of the paper that didn’t get any comments. That is my proposal to use the ratio of observed “consumed” heat to “retained” heat to guide projections for the future. The Earth System is complex, but we can observe the result of that complexity. Using the “best” research available, we analyze the data to calculate the ratio of consumed to retained heat was between 2:1 and 4:1 last century. (Note: I could have used other research to lower the best case ratio to 0.1:1, but I felt I had enough margin in my argument to not push it.) The claimed Earth Energy Imbalance is not a new thing. According to the proponents, it has been happening for 100-150 years. What we observe already includes that “excess” energy if it exists. It shows up in atmospheric temperature, net ice melt mass, and ocean temperature. The ocean temperature data is weak, but the analysis can still be undertaken because the energy exchange between the air and ice is most critical. We know what happened last century. It should be incumbent upon someone claiming the current century will be worse to justify that claim. What will cause that ratio to go beyond the maximum we saw in the 20th century?
“We know that sea level today is 20-30 feet lower than it was at the end of the last interglacial period 120,000 years ago.”
Actually we don’t. It could justa easily be half that. The evidence for that standard figure is actually astonishingly weak, being based on a small number of sites of very dubious reliability.
tty,
Regarding the sea level today being 20-30 feet lower than at the end of the last interglacial, you said: “Actually we don’t. It could just [as] easily be half that. The evidence for that standard figure is actually astonishingly weak, being based on a small number of sites of very dubious reliability.”
A “small number of sites and very dubious reliability” perfectly explains our instrumental temperature record. But that was not your point, I know. I didn’t create that estimate. I’m just repeating the “best” information we have. It is worth mentioning for the sake of perspective. It is also important to state because Climate Alarmists tell us our current conditions are the worst ever experienced and are caused by humankind. Whether the past interglacial was 5 feet, 15 feet or 30 feet higher than today, that fact kinks the Alarmists’ claims.
Furthermore, that figure is not critical to anything I presented.
I just started reminding people that everything is displacing its own mass in MAGMA anyway so it doesn’t matter.
Regarding sea level rise, I recall reading that many famous ports in the days of the Romans are now well inland , so obviously the sea level has fallen.
Regarding the ice in the likes of Antarctica melting, first there was no
mention of the volcanos under the West Antarctica end. Also I recall reading that way back before ice could be made commercially, ice blocks were cut from frozen lakes, packed in sawdust and shipped in slow moving ships which went to all parts of the world.
There was quite obviously enough ice left unmelted to make this a viable commercial undertaking.
Obviously ice is very slow to melt.
MJE VK5ELL
William Ward ==> Very nicely done.
Thank you, Kip, for the feedback and the generous support!
Mr. Ward,
My complements or compliments (those words allwaze confuze me). Vary thot proevoeking. Eggstreemly well composted. Your epherts are not in vein.
Seriously now: Is it possible conventional climate models accidentally, or explicitly, reflect heat transfer between ice sheets and the atmosphere plus oceans? If so, are their temperature projections the net outcome of the heat transfer?
DM,
For a moment, I thought you might be Dutch. 🙂
Climate models: I believe there are over 100 in use. The exact number of them that backtest is ZERO. Besides, if one works, you don’t need two, and certainly not 100+.
If they are using conservation of energy in the models, then it shows the extent to which they buy into the theory that the Earth is absorbing massive quantities of energy that we can not measure.
TY for replying.
Still thinking about the points you made:-)
Will postpone additional follow-up questions until the immediate flurry abates. That way other readers get a fair share of your epherts, and you do not need to labor vanely into the night.
I found this paper to be quite interesting. But, I have one question. It is stated that anarctic ice begins as snowfall and ends 1000 years later as an iceberg melting in the sea. If I understand it correctly, there would be no ice in Antarctica that is more than 1,000 years old. How is it that ice core samples could be taken of ice that is several hundred thousand years old?
Tim Doyle,
That is a good question. I recommend you check other sources for a definitive answer.
As I understand it, the ice that flows to the sea usually starts at the highest peaks and works its way down the mountain valleys. There are likely plateaus and other areas of stability that are not in line with the “currents” of flow. Additionally, within a mountain range, it is common to find bowls or areas that are surrounded by a ring of ridges or peaks. In places like this, the snow can accumulate and pack down and never experience any flow due to the topography. This is where a core sample would be taken I assume.
Not related to the point of discussion but something interesting that I thought of: the snow to ice compression ratio can be close to 20:1. So, 20 inches of snow becomes 1 inch of ice after many years. The thickest ice in Antarctica is over 13,000 feet thick. If it stayed snow and never compressed, its height would be over 260,000 feet. Of course, it is not possible to remain uncompressed, but it gives you an idea about how much snow went into creating the ice.
Thank you for your reply. It makes sense to me. I’m not a researcher, just a retired hydraulic engineer trying to understand this whole global warming obsession.
Hi Tim,
Nice to meet another fellow engineer! I’m a “retired” electrical engineer. Although I work just as much as ever! I’m not a researcher either – just using applied science (engineering) to study the claims about climate. The dependable, proven science that is repeatable in the lab underpins all fields of science. Research is built upon it as is engineering. I think you would agree that we don’t have to go deep into a different discipline like “climate science” to be able to evaluate its foundations.
The primary failings I see in climate science are metrology (uncalibrated instruments and improper measurement techniques), failed modeling, wrong assumptions, and wild unsupportable extrapolations. You might be interested in reading another paper I did about how the instrumental temperature record fails to comply with the Nyquist Sampling Theorem.
Full Paper: https://wattsupwiththat.com/wp-content/uploads/2019/01/Violating-Nyquist-Instrumental-Record-20190101-1Full.pdf
WUWT Post and Discussion: https://wattsupwiththat.com/2019/01/14/a-condensed-version-of-a-paper-entitled-violating-nyquist-another-source-of-significant-error-in-the-instrumental-temperature-record/
As a hydraulic engineer, I can see why you would be interested in the flow of the ice. Do you have any additional thoughts about this?
Thank you for a discussion at or near the avetage punter’s level. It is stated that sbout 1or 2% of ice is outside Antarctica and Greenland but that is still “a lot”. Much of that would be as permafrost especially in Sibetia where mamoths tusks are now being retrieved during their summer. The heat must be coming from the atmosphere (as well as the sunlight). Besides the possible direct contribution of that meltwater to the Arctic ocean, it is reported that large plumes of methane are being released which would add to the greenhouse gas effect as a feedback loop to global atmospheric temperature rise. Am I being “alarmist”?
Ralph Boardman,
Regarding fears about permafrost melting, you said: “Am I being “alarmist”?”
Let me ask you, why do you believe the reporting is correct?
I assume you read my section about what is actually happening to the polar ice sheets. The annual SLR from Antarctica and Greenland is less than three human hair diameters. Now that you know this, how do you square that with the countless articles reporting about the accelerated melt rates and billions of tons of meltwater flowing into the oceans? Why are you okay with reports of imminent coastal flooding when I just showed you that it would take over 250,000 years to melt the ice entirely and over 1000 years to add 12 inches to SLR? In areas where SLR is a concern, the land subsidence is a far greater threat than the eustatic rise from melting ice. Yet, the reporting is about the ice, and the melting is attributed to humankind without the slightest proof.
The land covered by permafrost is quite expansive. Have you spent time looking at the land around the entire Arctic circle, or only the cherry-picked locations where some anomaly is occurring?
This link may be helpful:
https://data.giss.nasa.gov/gistemp/stdata/
Scroll down to the bottom of the page where you can interact with a “3D” model of the Earth. You can see each monitoring station used by NASA. You can click on the dots representative of each station and see annual “mean” temperature over the life of the station. The absolute best thing is for you to self discover. Don’t believe what others tell you, including what I tell you. Investigate for yourself. Look at station data from around the Arctic Circle and north. What do you see? How can permafrost be melting when the average annual temperature is -10°C? You will need to look for additional information to see what the summertime temperatures reach and what the trends have been. I think you will find there has been an increase in temperature in the Nordic countries, where the annual mean has gone from ~2°C to ~4°C over the past few years. So perhaps there would be more melting in those locations. But the vast majority of the Arctic is well below 0°C. Finding some examples of melting does not define the whole of the Arctic.
Beware of anecdotes. I recently read an article about some Arctic home foundations collapsing as the permafrost melts. A more in-depth investigation showed that a new more effective heating system was added to a poorly insulated home. The heat from the home heater melted the ice under the house, and the foundation collapsed. Bad story for the homeowner. An unfortunate mistake. Alarmists twist the news to manipulate people into believing something else is happening – man-caused climate change.
Methane is a very weak greenhouse gas – at least relative to CO2. Methane will oxidize to CO2 naturally in the atmosphere. Despite all of the cries to the contrary, there is not one shred of evidence that CO2 is currently warming the planet. There is not one shred of evidence that it ever has. It may. We don’t have any evidence. There is no correlation in the ancient reconstructions or the modern record. The ice core data only shows CO2 following temperature with a 500-800 year lag. Saying this does not deny the greenhouse effect of CO2. But it is evidence that the effect it has may saturate well below 180ppm. Here is a link to 85 peer-reviewed scientific papers that claim additional CO2 in the atmosphere will have no effect (or minimal effect) on temperature.
https://notrickszone.com/50-papers-low-sensitivity/#sthash.VcuWbQua.R8NoeIWA.dpbs
There is no proof – and no “consensus” as to the effect of additional CO2 in the atmosphere.
You will have to decide if you want to accept everything you read uncritically or not. For me, the permafrost issue is just one more unsupportable claim made by Alarmists. The claims do not stand up to any scrutiny.
To answer your question, I can’t say whether or not you are being an Alarmist, but if you believe what you read uncritically, then you are being manipulated by Alarmists.
I hope this helps and thanks for bringing up the topic, Ralph.
William: I find it much easier to do calculations in terms of W/m2. You may find it valuable to approach your calculations from this point of view. Rising GHGs reduce the rate of radiative cooling to space, doubled CO2 by about 3.6 W/m2. That power per unit area is available to warm the planet until the radiative imbalance created by a forcing is eliminated by a warmer planet radiating (or reflecting) more heat to space. If the planet radiates an additional 1 W/m2/K upon warming, ECS will be 3.6 K/doubling. 2 W/m2/K becomes 1.8 K/doubling. 3.3 W/m2/K (expected for a gray body with emissivity 0.61 and average temperature of 288 K) become 1.1 K/doubling.
The tricky part of W/m2 is calculating a heat capacity per unit area. This involves specifying the average depth of water warmed or the depth of ice melted. Simple calculations should show you that a radiative imbalance of 1 W/m2 is capable of warming a 50 m mixed layer of ocean (include a few percent of the power for the atmosphere) at a rate of 0.2 K/year. This is the initial warming rate ASSUMING all of the heat remains in the mixed layer and warming has yet to increase radiative cooling to space. The mixed layer and atmosphere come into near equilibrium with a radiative forcing in a decade or less.
It takes 40-fold more energy to melt ice than to raise the temperature of water 1 degK. So 1 W/m2 could warm 10 m of water at an initial rate of 1 K/yr, or melt 1/4 m of ice. The current radiative imbalance estimated from ARGO is about 0.8 W/m2, so the real world situation involves a [radiative] power flux capable of melting 0.2 m/yr of solid ice. Over a year, 1 W/m2 is a large amount of power per unit area! Sometimes that power is used to warm the ocean, sometimes to melt ice if it is already at 0 degC, and a tiny amount is needed to warm the atmosphere.
In the long run, it makes no difference if radiation melts ice directly, OR if the ice flows into the ocean and radiation warms the water that is melting the ice, OR if warm air melts the ice.
Seasonal changes involve releasing a lot of heat into the atmosphere when snow falls and taking up a lot of heat from the atmosphere when snow melts. From a climate change perspective, we can ignore seasonal changes because they net to zero during the average year.
So how much can 0.2 m/yr of melting ice raise SLR? About 3% of the planet’s land surface is covered with permanent (not seasonal) frozen water or 4.3% of the ocean surface. So if a radiative imbalance of 0.8 W/m2 were taken up by frozen water that melted, that would be about 9 mm/yr. This doesn’t mean that SLR should be rising 9 mm/yr. It just says that the average radiative imbalance on the planet could melt that much ice if all the power ends up there. In reality, the surface of ice and only melt when it is 0 degC and the rest of the time it can’t melt. However, surface of ice that flows into the ocean off of ice sheets is melting all of the time.
Frank,
You said: “I find it much easier to do calculations in terms of W/m2.”
Thanks for your thought out reply. The subject of the “Earth’s Energy Imbalance” (EEI) is too large for complete treatment. As I said in my analysis section, I specifically avoided this analytical approach. My approach captures what would be observed should any “imbalance” exist.
I find much scientific fault with the EEI hypothesis. I don’t see any evidence that a control-system type of feedback is operating with the climate. There is no consensus about climate sensitivity. There is an abundance of peer-reviewed papers claiming that additional CO2 will cool the atmosphere. Some papers claim that somewhere below 150ppm the effect of CO2 is saturated and there is little to no warming from additional CO2. There is no evidence of a causal correlation between CO2 and temperature historically. Glacial periods always start when CO2 is at its highest, and interglacials always start when CO2 is at its lowest. I don’t think our instruments are capable of measuring an “imbalance” accurate to 0.6W/m^2. While the ARGO floats are improved instruments, they still lack the accuracy and calibration. They only sample temperature every ten days, so they likely violate Nyquist sampling requirements – introducing error into the measurement.
The first thing of importance I tried to accomplish was to provide perspective. The media quotes melt-rate multiples and ice melt mass figures in thousands of billions of tons. Because people have no frame of reference, these figures can be used to scare people. If the news writers (or scientists who feed them the data) convert the melt mass to percent mass loss per year, then the story goes away, because Antarctica losing 0.00040% of its mass each year is not exciting to the average person. Knowing it will take 250k years to melt at that rate is not something you can alarm people with.
The next thing of importance I try to accomplish is to use proven basic science (specific heat, latent heat and the conservation of energy), combined with our best observations over the past century, to place a reasonable upper limit on what can happen this century. Using temperature projections and the observed ratio between ice melting and atmospheric heating we can accomplish this. If the EEI exists, then it is captured in what happened last century. All of the complexities of climate avail themselves in the net results over time. It is reasonable to use these observations as a guide to the future. It is reasonable to use the atmosphere as the reference because the atmosphere, due to its low mass and low specific heat, will be the most responsive to changes in system energy.
You said: “In reality, the surface of ice and only melt when it is 0 degC and the rest of the time it can’t melt. However, surface of ice that flows into the ocean off of ice sheets is melting all of the time.”
The widespread assumption is that a decrease in ice mass must be from warm air melting the ice – and proof of a “warming world.” Ice melting from “warm” air is only one possibility. Ice evaporates (sublimates from solid to gas). Direct solar radiation melts ice, even at temperatures below 0°C. As you said, ice that calves into the sea eventually melts. So, four things cause the ice sheets to lose mass, and only one that causes the ice mass to increase, and that is snow. It is quite remarkable that snow precipitation and the four ice loss factors are only out of balance by 4.5ppm/yr globally! That is not a strong case for a “warming world” or an “energy imbalance.”