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.
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