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Showing posts with label global heat budget. Show all posts
Showing posts with label global heat budget. Show all posts

Thursday, August 11, 2022

Global Warming: How It Works

 I have a small collection on the bottom shelf of my bookcase of important books.  The books are: How Things Work (4 volumes), Roger Segalat, translated from German; The Way It Works, Robin Kerrod, 1980; The Way Things Work, translated from Italian, 1989; The Way Things Work, David McCauley, 1988; and two massive volumes on the history of science.  That’s what people do – we figure out how things work, and use that knowledge to understand and manipulate the world around us.  

A friend recently asked me, “What is the best argument that a lot of current climate change is caused by humans, through fossil fuel CO2, methane, and other green house gases?  What are the best data and arguments?”   The most important point about climate science is that we know how it works.  It isn’t speculation or correlation.  We simply know how it works.  Since the 1860s or before, people have known that glass bottles filled with CO2 heat up faster than bottles filled with air.  In 1896, the brilliant Swedish chemist Arrhenius calculated how much the earth would warm if CO2 concentration was doubled.  This happened in the same decade that we invented the manual transmission and radio transmission of Morse code, and about a decade after Edison’s electric lightbulb.  Scientific research has continued since Arrhenius, and we know how the CO2 greenhouse effect works just as well as we know how an AM radio, manual transmission, or incandescent lightbulb works.  

We’ve observed and measured the processes that trap heat in the atmosphere and we’ve made predictions of future warming and related events.  To confirm or deny the theory of global warming, scientists set up a system of instrumentation across the planet and in orbit, beginning about 30 years ago.  The data are clear – oceans are warming from the surface downwards, ice is melting in every setting on the planet, and atmospheric temperatures are rising.  We’ve seen the primary predictions of global warming and second-order climate changes robustly confirmed.  Objections and challenges to the data and interpretation have been evaluated and refuted.

How It Works
The entire spectrum of electromagnetic radiation includes gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves and radio waves.  The high-energy end of the spectrum consists of very short wavelengths, including gamma rays and x-rays through visible light, while the low-energy end of the spectrum has longer wavelengths, from infrared through radio waves.  

Everything radiates electro-magnetic radiation at some wavelength.  It’s called by several names –Planck radiation, black-body radiation, or thermal infrared radiation.  The kind of radiation emitted by objects depends on temperature.  Hot objects emit high energy radiation with short wavelengths, and cool objects emit low energy radiation with long wavelengths.  The sun primarily emits energy in the visible spectrum, because it is very hot.  Atmospheric gases are transparent to the visible spectrum, so most of the sun’s energy passes through our atmosphere to reach the ground.  Visible light strikes the earth’s surface and is converted to heat.  The warmed earth also emits radiation, but at a longer wavelength (infrared) because it is cool. The earth’s infrared radiation mostly escapes back into space.  Carbon dioxide, water vapor and methane, however, are partly opaque to infrared radiation, depending on the specific wavelength.  These gases trap heat in the atmosphere, warming the air, the oceans and the ground.  The phenomenon is called the greenhouse effect, because glass will do exactly the same thing, keeping a greenhouse warm – visible light goes in, but infrared radiation is trapped inside.  

Image credit: Science News.  The yellow lines are actual IR readings from space, compared to the theoretical Planck radiation from the ocean surface shown in dark blue.  Depressions and divots in the yellow lines represent absorption of upgoing IR radiation by various greenhouse gases, notably CO2.  Differences between the yellow lines represent clear and cloudy skies, with cloud tops having cooler temperatures and a different baseline Planck profile.

The natural amount of CO2 and water vapor in the air keeps the earth at a temperature to which we’ve  become adapted.  If the earth’s atmosphere had absolutely no CO2 or H2O, the earth’s average temperature would be about 33 C colder, causing freezing conditions over the entire planet.

Of the sun’s incoming radiation (341 W/m2), about 29% (100 W/m2) is directly reflected back into space, mostly by clouds.  The remaining 241 W/m2 is absorbed by the ground and atmosphere, warming the Earth.  The Earth radiates energy back into space at a wavelength in the infrared spectrum, balancing the energy input from the sun to create a stable climate for the past 6000 years.  But the addition of greenhouse gases to the atmosphere is currently trapping 0.94% (3.2 W/m2) of the sun’s energy reaching the surface.  That heat is ultimately redistributed to the oceans, ice, and air, warming the earth.


This figure simplifies many heat transfers within the atmosphere before energy is either retained on earth or returned to space.  The heat retained by greenhouse gases is given the awkward technical term "radiative forcing".

[Technical note: The sun's radiation, measured in space, has an intensity of 1364 W/m2.  There is a range of reported figures from 1361 W/m2 to 1368 W/m2, depending on the choice of instrument calibration.  The earth receives sunlight according to its cross-sectional area, equal to one-quarter of its surface area.  The earth emits radiation from its entire surface area.  So for a simplified energy budget as shown below, we have to choose a convention of adapting numbers for the cross-sectional area or the surface area of the earth.  Most displays adopt the convention of the whole earth surface area as I've done above.  This requires dividing the sun's input radiation by four, yielding 341 W/m2 to represent the average energy input across the entire earth.]

Under natural conditions, a balance develops between the incoming and outgoing radiation, which keeps the earth’s temperature stable, unless disturbed by other factors such as orbital variation.  The earth’s orbit varies over cycles of 40,000 years and 100,000 years, which triggers feedback mechanisms (including CO2 concentration and reflective ice) producing ice ages. 

Climate-change deniers are fond of saying "The climate has always been changing."  But since the last ice age, for the past 6,000 years, the climate has been stable, as proven by geological studies of sea-level, temperature-sensitive isotopes, and ice-sheet deposits.  This is the entire period of the written record of humanity.  The pre-industrial level of CO2 created a “Goldilocks” climate in which humans and nature thrived.


For the past 150 years, we have burned increasing quantities of fossil fuels – coal, oil and natural gas, and cleared or burned forests to create new farmland.

The CO2 emitted from these human activities has markedly changed the concentration of CO2 in the atmosphere, from the pre-industrial level of about 280 parts per million (ppm) of CO2, to the current level of 420 ppm CO2.  Because CO2 is such a potent greenhouse gas, this small change in atmospheric composition has a marked change in retained infrared radiation. 

You might not think that 400 parts per million is enough to change the retention of radiation in the atmosphere.  I’d like to propose a small thought experiment.  Four hundred parts per million is equivalent to four parts in ten thousand, or one part in 2,500.   One ounce of water contains about 600 drops.  Four and 1/6 ounces of water, about a half-cup, contains 2,500 drops.  Imagine, for a moment (or really try) putting one drop of opaque India ink or dark food coloring into a half-cup of water.  The ink noticeably reduces the visible light transmitted through the otherwise transparent water.  It’s the same with CO2 in the atmosphere.  

Climate Feedbacks
There are further processes known as feedback mechanisms affecting the earth’s heat budget.  Feedbacks are processes that are triggered by changes in Earth’s temperature, which either amplify (positive) or diminish (negative) the primary changes.  The strongest feedback effect is the Planck effect, a negative feedback.  As the Earth’s temperature rises, it radiates energy more strongly, counteracting the influence of greenhouse gases.  The balance between the sun’s incoming energy and the Planck effect is what caused the Earth to settle at a stable temperature.  The second strongest feedback is water vapor.  As the ocean surface becomes warmer, the equilibrium humidity in the air rises.  Also, warmer air can hold more humidity, keeping additional water vapor in the air.  Higher humidity is a positive feedback mechanism, because water vapor is itself a powerful greenhouse gas.  So as the planet warms, more heat is retained by water vapor.  As Arctic snow and ice melt, the surface reflectivity diminishes, causing positive feedback.  Climate change increases cloudiness, causing feedback effects.  Clouds are complex as a feedback mechanism, with both positive and negative impacts.  Depending on the type of cloud, the primary impact may be to reflect sunlight, or may be to retain infrared emissions from earth.  Overall, clouds are considered to be a positive feedback.  There are more complex feedbacks involving biochemistry and methane, and fast versus slow feedbacks, but these are generally an order of magnitude less significant than the physical feedbacks.  This is an area of active climate research.

The Planck effect dominates all other feedback mechanisms, and the total impact of all feedback effects is negative.  This is very good, because a simple modeling exercise shows that the global climate would soon irreversibly blow up if the total feedback were positive.  Nevertheless, there are number of authoritative sources on climate feedbacks (notably Wikipedia and Andrew Dessler’s Modern Climate Change) that neglect to mention the Planck effect among climate feedbacks and assert that the net climate feedback is positive.  This is incorrect.

Global temperature change since pre-industrial times is about 1.1 C, so the current total feedback is -1.3 W/m2.  Combining the greenhouse gas effect with total feedback leaves a positive (warming) climate influence of 1.9 W/m2.  

Validation
Climate science predicts that the earth should be warming, due to heating resulting from the buildup of greenhouse gases.  These greenhouse gases, particularly CO2, are unquestionably from human activities (see my blog post, https://dougrobbins.blogspot.com/2019/12/understanding-source-of-rising.html).  We have detailed temperature records for much of the world for the past 150 year or so, and we have plentiful temperature measurements of the oceans beginning in about 1950.  However, early climate data have a few issues with data quality and coverage.

Starting around 1990, scientists put in place a comprehensive set of instrumentation specifically designed to detect and measure global warming.  These systems have corrected some of the issues of data collection from early research, and provide unprecedented coverage of our planet.  The results are unequivocal.  The oceans are warming from the surface downwards; the air is warming over the oceans; the air is warming more rapidly over land; the Arctic is warming faster than the rest of the planet; and continental glaciers, Arctic sea ice, and the Greenland and Antarctic ice caps are melting.  Other, second order effects of the heat are well-proven also, including an acceleration of rising sea level and seasonal changes in physical and biological systems.

There is simply no point to denying that global warming and resulting climate changes are happening due to human emissions of greenhouse gases.  These changes are observed to be accelerating, as expected, due to higher concentrations of greenhouse gases.  Previous predictions about climate change have been highly accurate.  There is no reason to doubt further predictions of serious to catastrophic harm from future climate change unless we greatly curtail emissions of greenhouse gases.

Appendices
Appendix 1
Climate change indicators and sources
Air Temperature Over Land and Oceans
https://data.giss.nasa.gov/gistemp/graphs_v4/


Temperature Anomaly Map, 2016-2022 vs. 1951-1980
Note Arctic warming is more intense than the rest of the planet, as predicted by the Macdonald report in 1979.  Also note that air over land is warming faster than air over oceans.
https://data.giss.nasa.gov/gistemp/maps/
Continental Glaciers, World Glacier Monitoring Service
https://wgms.ch/global-glacier-state/

Arctic Sea Ice Extent (July)
http://nsidc.org/arcticseaicenews/
Antarctic and Greenland Ice Sheets
https://climate.nasa.gov/vital-signs/ice-sheets/


Appendix 2, Comparison of Descriptions of Greenhouse Gas Heating
Arrhenius, 1896
“The selective absorption of the atmosphere is…of a wholly different kind [than diffusion of ultraviolet radiation]. It is not exerted by the chief mass of the air, but in a high degree by aqueous vapour and carbonic acid [CO2], which are present in the air in small quantities.  Further, this absorption is not continuous over the whole spectrum, but nearly insensible in the light part of it, and chiefly limited to the long-waved part, where it manifests itself in very well-defined absorption-bands, which fall off rapidly on both sides.  The influence of this absorption is comparatively small on the heat from the sun, but must be of great importance in the transmission of rays [thermal infrared, or long-wave radiation] from the earth.” 
Arrhenius then describes the debate over whether water vapor or CO2 has the greater influence as a greenhouse gas. 

Asimov, 1959
"The light rays of the Sun hit the air, pass through a hundred miles of it, hit the surface of the Earth, and are absorbed. The Earth heats up.  The heated Earth radiates energy at night back into space, in the form of the far less energetic infra-red.  This also passes through the atmosphere.  The warmer Earth grows, the more heat is radiated away at night.  At some particular equilibrium temperature, the net loss of radiation by Earth at night equals that gained by day so that, once the temperature (whatever it is) is reached, the Earth as a whole neither warms nor cools with time.
Carbon dioxide, however, introduces a complication.  It lets light rays through as easily as do oxygen and nitrogen, but it absorbs infra-red rather strongly.  This means that Earth’s nighttime radiation finds the atmosphere partially opaque, and some doesn’t get through.  The result is that the equilibrium temperature must rise a few degrees to reach the point where enough infra-red is forced out into space to balance the Solar input.  The Earth is warmer (on the whole) than it would be if there were no carbon dioxide at all in the atmosphere.  The warming effect of carbon dioxide is called the “greenhouse effect”.
…A recent set of calculations indicate that if the present carbon dioxide level should double, the overall temperature of the Earth would rise by 3.6 C."
Asimov was reporting on the work of G.N. Plass, published in 1958. 

Ramaswamy, 2019
“Interactions of the incoming solar radiation and outgoing longwave radiation with Earth’s surface and atmosphere affect the planetary heat balance and therefore impact the climate system.”

Also see:
Ramaswamy, Radiative Forcing of Climate Change, 2001

Ramaswamy, Radiative Forcing of Climate: The Historical Evolution of the Radiative Forcing Concept, the Forcing Agents and their Quantification, and Applications, 2019

R. J. Bantges & H. E. Brindley, On the Detection of Robust Multidecadal Changes in Earth’s Outgoing Longwave Radiation Spectrum, 2016

A. Dessler, Modern Climate Change, Third Edition, 2022

IPCC Reports, Technical Summaries, various dates.

Appendix 3, Discussion of Climate Feedback Discrepencies
Wikipedia asserts that there is a net positive feedback to warming.  However, a check of the referenced IPCC Technical Summary for AR5 (2014) is less clear and does not explicitly mention Planck radiation, the strongest negative feedback.  Andrew Dessler’s Modern Climate Change also concludes that total feedbacks are positive.  Dessler also does not mention Plack radiation as a feedback parameter.  [Dessler quantifies the total feedback relative to radiative forcing, rather than temperature change, which makes direct comparison of the feedback numbers a little more difficult.]  On the other hand, Global Climate Models, by D.L. Hartman, clearly identifies each feedback component, including Planck radiation.  Hartman states “the best estimate of the total feedback is about −1.2 ± 0.6 W m−2 K−1, but it is uncertain by about ±50%.”   The IPCC AR6 preliminary Technical Summary also concludes that total physical feedbacks are negative, with a best value of about -1.2 ± 0.7 W m−2 K−1.  I think that the value of -1.2 W m−2 K−1 is likely to be the best estimate.

References:
Svante Arrhenius, On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, 1896.
https://www.rsc.org/images/Arrhenius1896_tcm18-173546.pdf

Isaac Asimov, "No More Ice Ages?", 1959
In Fact and Fancy, 1972

Ocean heat content, NOAA
https://www.ncei.noaa.gov/access/global-ocean-heat-content/ 

ARGO Ocean Temperature Program Homepage
https://argo.ucsd.edu/ 

NOAA Annual Greenhouse Gas Index
https://gml.noaa.gov/aggi/aggi.html 

Lambeck et al, Sea level and global ice volumes from the Last Glacial Maximum to the Holocene, 2014
https://www.pnas.org/doi/10.1073/pnas.1411762111

Doug Robbins, atmospheric CO2 and related charts, 2022.
http://dougrobbins.blogspot.com/2022/04/charts-of-atmospheric-co2-carbon.html 

NASA GISS Annual Mean Temperature over Land and over Oceans
https://data.giss.nasa.gov/gistemp/graphs_v3/

G. Macdonald, JASONs presidential science advisory report, excerpt, 1979.
https://climatestate.com/2019/07/10/the-jason-report-the-long-term-impact-of-carbon-dioxide-on-climate-1979/
Whole report:
https://irp.fas.org/agency/dod/jason/co2.pdf 

Dennis Hartmann, Global Climate Models, 2016 (feedback chart)
https://www.sciencedirect.com/topics/earth-and-planetary-sciences/climate-feedback
IPCC AR6 Technical Summary (feedback chart, pg. 96)
https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_TS.pdf

Andrew Dessler, Introduction to Modern Climate Change, Third Edition, 2022

Wednesday, June 27, 2018

Global Heat Budget #3 – Ice


This is the third in a series of posts about the global heat budget. 

Ice is melting around the world. 

Greenland’s ice cap is melting.  Antarctica’s ice cap is melting.  Arctic sea ice is melting. Continental glaciers are melting.  Arctic permafrost is melting.  The melting is happening at a rate that is readily visible to people who live near natural ice.  From decade to decade and year-to-year, glaciers are visibly retreating, and can be directly verified by the most casual observer.   

Melting ice is the second most important heat sink on the planet, after the ocean (albeit a distant second).  Melting ice accounts for about 3% of anthropogenic heat retained in the atmosphere.  Melting ice is the second most significant proof that human-caused climate change is happening.  Melting ice may be the most significant consequence of climate change in terms of costs and damage to humanity. 

The data is unambiguous and irrefutable.  The volumes of melted ice have been measured by a variety of methods, including high accuracy satellite measurements.  The heat required to warm and melt this volume of ice can be calculated and compared to the heat trapped in the atmosphere by greenhouse gases, and the rising heat content of the oceans.  The volume of meltwater entering the ocean can also be compared to measurements of rising sea level.   The rate of sea level rise is already 3 times the rate of the past 7500 years, and accelerating.  The observed volumes of melting ice and the measurement of rising sea level provide unambiguous proof that climate change is real. 

Greenland
Ice on Greenland is melting.
Greenland covers an area one-fifth the size of Australia.  Almost all of Greenland is covered by ice, ranging between 1 and 2 miles of ice thick.  The Greenland Ice sheet contains more than 2.8 million cubic kilometers of ice.  That is enough to make sea level rise by 20 feet if it all melted.

NASA’s GRACE (Gravity Recovery and Climate Experiment) satellites have monitored the mass of the Greenland ice cap since 2002.  Gravity observations were supplemented by altimetry and radar data from overflights and satellites.  Other satellite observations include NASA’s early ICESat, and the ESA’s currently operating CryoSat2.

There is a strong seasonal signal in the history of ice loss from Greenland, with a slight build in ice mass during the Northern Hemisphere winter, and a stronger decline in the summer.  From 2002 to 2016, Greenland lost about 3900 gigatonnes of ice due to melting.  Each gigatonne is a little more than one cubic kilometer of ice by volume, and produces one cubic kilometer of fresh water when it melts.  Altimetry data show that most of the melting was concentrated near the coast, particularly on the western side.  Six feet to fourteen feet of ice has melted around the edges of the entire island. 

The GRACE satellite, designed for only a five-year life, actually worked for nearly fifteen years.  The last data was recorded in June 2017.  The replacement mission, GRACE Follow-On, is scheduled to be launched in five days, on May 19th, 2018.  

NASA’s IceBridge is an airborne project using laser altimetry and ice-penetrating radar data to measure the elevation, snow cover, and total thickness of Greenland and Antarctic ice.  IceBridge will provide data to connect and calibrate data from the new GRACE satellites.   IceBridge was originally designed to replace data from the ICESat satellite, which failed after seven years of service.  ICESat-2 is planned to be launched in September, 2018, to replace ICESat.

Antarctica
Ice on Antarctica is melting.
Antarctica is about seventeen times larger than Greenland, and nearly twice as large as Australia.  Ice covers 98% of the continent, to an average thickness of over a mile.  Antarctica holds about ten times the volume of ice as Greenland.  If all of the ice on Antarctica melted (which would require centuries to occur), it would raise sea level by about 200’, placing most of the world’s major cities and human habitation under water. 

The GRACE data for Antarctica is noisier than the data for Greenland and shows a weaker seasonal cycle.  It seems likely that the melting season over Antarctica is not (yet) as profound as over Greenland. 

As with Greenland, the Antarctic ice sheet has been monitored by NASA’s Grace and ICESat satellites, and the IceBridge aerial observation program.  Earlier observations were integrated by the European Space Agency’s IMBIE (ice sheet mass balance comparison exercise) to provide the ice balance record from 1992 to 2010.  The chart showing both IMBIE data and GRACE data is shown below.  From 1994 through 2017, at least 2450 gigatonnes of ice on Antarctica melted.

I should note that gravity methods will not detect ice loss on the portions of the ice sheet that are floating (and more susceptible to ice loss).  Ice floating on water will have the same net density as ice-free water.  So, altimetry methods must be combined with gravity methods for a full determination of ice loss on Antarctica.  The East Antarctic (Filchner-Ronne) and West Antarctic (Ross) ice shelves are approximately 900,000 square kilometers in area.  Dozens of smaller ice shelves also exist.  The actual loss of ice from Antarctica may be greater than 2450 gigatonnes, because losses from these floating ice shelves are not detected by gravity. 

While melting of floating ice shelves is difficult to observe, it is also true that the melting of floating ice will not cause sea level to rise, at least as a first-order consequence.  The same buoyancy of ice shelves that makes sea-ice loss invisible to gravity detection means that sea level does not change when a volume of ice is converted to water.  Melting ice shelves matter to the earth’s heat budget, but not (directly) to sea level. 

The rate of future ice loss in Antarctica depends on feedback mechanisms.  The principle feedback mechanism is the restraining force that ice shelves exert on flowing glaciers.  Ice shelves impede the flow of ice from the continent and into the ocean; when those shelves melt, the rate of ice loss will accelerate.  The timing and amount of acceleration are unpredictable, so the best estimates of future sea level rise are uncertain on the high end.  We are fairly certain about the minimum expected sea level rise, but the maximum possible sea level rise is very uncertain.

Antarctic Sea Ice
For many years, Antarctic sea ice was not subject to the declines seen in Arctic sea ice (seen in the next section).  This was often referenced in commentaries on climate-change deniers’ web sites.  In recent years, Antarctic sea ice has declined, but it is likely to continue to show an irregular response to climate change.  The reason is simple.  Antarctic sea ice is regularly replenished by calving from Antarctic glaciers and ice shelves.  Anyone with tour-boat experience in Alaska knows that sea ice actually increases following calving events.  So, with a huge reservoir of ice in the Antarctic ice cap, Antarctic sea ice is likely to fluctuate, but not disappear, as the mother-lode of ice continues to flow and break apart, feeding the sea ice around the continent.


 Arctic Sea Ice
Arctic Sea Ice is melting.
In contrast to Antarctica, the Arctic has no mother-lode of ice feeding the polar sea ice.  The sea ice freezes and melts in a seasonal cycle.  For the past forty years, each cycle has ended with less ice, on average, than the previous cycle.  The loss of ice has accelerated over that period.   There was about 250,000 square miles less sea ice in the 1990s than during the 1980s.   From the 1990s to the 2000s, the decadal average showed a loss of about 500,000 square miles of sea ice.  The annual data from the current decade suggests an even greater rate of loss. 


Area is not the only measure of sea ice.  Some sea ice persists through multiple seasons, gaining thickness from season to season.  However, against the background rate of general melting, less and less ice persists from season to season, and the overall thickness of Arctic sea ice is also declining.   Between 1984 and 2016, 94% of the sea ice more than four years old had disappeared.
Image by M Tschudi and S. Stewart of the University of Colorado, and W. Meier and J. Stroeve of NSIDC.

Some researchers have attributed 30 percent to 50 percent of the loss of Arctic sea ice to natural variability, and 50 to 70 percent to anthropogenic influences, including direct warming by greenhouse gases, and the second-order influence of atmospheric circulation patterns. 

Overall, Arctic sea ice has declined by 12,000 cubic kilometers since 1980.   As noted in the section about Antarctica, there is no sea level impact due to the melting of floating ice, but there is an impact on the earth’s heat budget. 

The loss of sea ice in some of the peripheral seas of the Arctic Ocean (Chukchi Sea, Bering Sea, Barents Sea, and others) is more evident.  
Image Credit, Rick Thoman, National Weather Service, Fairbanks


Continental Glaciers
Continental glaciers are melting. 
People who live near glaciers are well aware of the historical and current melting of glaciers.  In Alaska and Western Canada, popular glaciers often have signposts or old photographs showing the earlier extent of the glaciers.  Some examples are the Columbia Ice Field in Alberta between Banff and Jasper National Parks, and in Alaska, Root Glacier near Kennecott mine, Exit Glacier near Seward, Portage Glacier and associated glaciers near Anchorage, and the many tidewater glaciers along the Alaskan coast, including Glacier Bay near Juneau, College Fjord near Valdez, the glaciers of Kenai Fjords National Park, and Columbia Glacier near Valdez.  Glaciers are in retreat, on a scale which is noticeable from year to year and dramatic over the course of decades. 

The UN Glacier Monitoring Service and its predecessor organizations have measured the melting of continental glaciers, other than Greenland & Antarctica.  WGMS issued major reports in 2008 and 2015; each report shows overwhelming evidence of melting of glaciers worldwide.  WGMS includes data on about 100,000 glaciers, with digital outlines of about 62,000 glaciers; data on glacier fluctuation includes over 35,000 length observations for nearly 2000 glaciers (as of 2008).  Detailed mass balance observations are conducted on a smaller number of reference glaciers (including the most volumetrically significant glaciers).  Data from reference glaciers are extrapolated to other glaciers on the basis of regional association, altitude and latitude.

At any given time, a small number of glaciers are growing, due to natural fluctuations of snowfall, warmth, and air circulation. But the great majority of glaciers worldwide are melting. 

Annoyingly, the WGMS does not report summary ice loss in terms of cubic kilometers or gigatonnes.  Glacial Mass Balance is reported in terms of meters of water equivalent, a vertical measure of average ice melted.  Volumes of melted ice can be calculated from the reported total area of glaciers under study.  Those volumes can then be used for purposes of understanding the global heat budget and sea level rise. 

Sea Level
The earth entered a period of cyclic ice ages about 3 million years ago.  The last 600,000 years have been characterized by ice age cycles of about 100,000 years, apparently triggered by variations in earth’s orbit.  The influence of the orbital cycles is enhanced by feedback mechanisms, including CO2 and the reflectivity of ice.  The peak of the last glacial cycle occurred only about 20,000 years ago, and remnants of ice may have persisted in Ontario until about 8,000 years ago.

Deglaciation following the last ice age was mostly complete by 8000 years ago.  We know this from studies of sea level and sediment cores.  Sea level rose by about 80 meters between 14,000 years ago and 8000 years ago, an average rate of 1.3 cm/year.  From 7500 years ago to the 20th century, sea level rose only 5 meters, a rate of 0.07 cm/year.   Through the 20th century, sea level rose at about 0.2 cm/year, a significant increase over the background rate.  Satellite data over the past 25 years shows that sea level rise has accelerated to 0.35 cm/year, five times the rate of sea level rise for the past 7500 years.  This is a clear indication that global warming from human greenhouse gases is contributing to melting ice.
Additional heat retained by greenhouse gases will result in a faster rate of melting ice, and higher sea level rise.  Current forecasts of sea level rise range from about 2 feet to 8 feet by the end of the century.  Sea level rise of only 4 to 6 feet would seriously damage some coastal communities around the world, including the inundation of barrier island and low-island communities.

Heat Budget

From 2003 to 2016, greenhouse gases retained 1.6 x 1023 joules of heat in the atmosphere, according to tables of radiative forcing published by NOAA (https://esrl.noaa.gov/gmd/aggi/aggi.html).  This figure for anthropogenic heat does not include the effect of cooling or warming aerosols, primary heat from fossil fuels and deforestation, or other minor sources of heat.  Estimates for some of these other anthropogenic disturbances are found in the IPCC 5 report, but only through the year 2011.

We have good estimates of the cumulative ice lost from Antarctica, Greenland, Arctic sea-ice and Continental Glaciers from 2003 to 2016, due to high-quality satellite observations.  About 10,400 gigatonnes of ice was lost over that period.  The heat required to warm (+10 C) and melt that volume of ice is 3.7 x 1021 joules, or about 2.3% of the total heat retained by greenhouse gases.  The allocation of heat to warm the ice by 10 degrees C was to reflect heating of an equivalent amount of ice, which has not yet melted.  Average temperatures of -10 C from core-holes in Greenland and Antarctica were taken as the ambient temperature of ice before melting. 

Considering that about 2.9% of the earth’s surface is covered by ice, this seems like a reasonable distribution of greenhouse heat which is going to warm and melt ice.  Looking forward, if a higher percentage of heat goes towards melting ice, sea level will necessarily rise faster.  Possible reasons for faster melting of ice could be more rapid ice flow from Antarctica and Greenland.  This might occur as the base of the ice is lubricated by meltwater, or when restraining ice shelves are lost around Antarctica.


References

Antarctica and Greenland
NASA GRACE Ice Mass, Antarctica and Greenland

Grace Data
Wiese, D. N., D.-N. Yuan, C. Boening, F. W. Landerer, and M. M. Watkins (2017) Antarctica Mass Variability Time Series Version 1 from JPL GRACE Mascon CRI Filtered. Ver. 1, PO.DAAC, CA, USA. Dataset accessed [2017-06-07] at http://dx.doi.org/10.5067/TEMSC-ANTS1

IMBIE:  Ice Sheet Mass Balance Inter-Comparison Exercise
Integrated Methods Measuring Ice Mass

Arctic Sea Ice
Arctic Sea Ice Volume
Chart with relative volume loss (km3) to 1980. 

Charts of Arctic Sea Ice Extent by Month

Image of declining multi-year Arctic Sea Ice.  Image by M Tschudi and S. Stewart of the University of Colorado, and W. Meier and J. Stroeve of NSIDC.

Arctic Sea Ice
Multi-year ice grows up to 4 meters thick, while single-year ice is 2 meters thick at most.

the area covered by Arctic sea ice at least four years old has decreased from 1,860,000 square kilometres in September 1984 to 110,000 square kilometres in September 2016.

Continental Glaciers
World Glacier Monitoring Service bi-annual update, 2015

Volume estimate for Glaciers and Ice sheets (other than Antarctica and Greenland.


Saturday, April 21, 2018

Global Heat Budget #2: Oceans


The world’s oceans are warming.  Ocean warming is the strongest confirmation that greenhouse gases are warming the planet. 

The heat capacity of water is among the highest of common substances.  That means that water can absorb a large amount of heat while its temperature changes only slightly.  The measurable warming of the world’s oceans indicates that a very large amount of heat has come from somewhere.  The only credible source for so much heat is the retention of heat by atmospheric greenhouse gases.  Let’s look at the source of the data, and the numbers.

ARGO Oceanographic Program
Rising ocean temperatures have been measured by oceanographic surveys since the 1970s.  However, these ocean surveys were limited in geographic coverage and continuity of data acquisition.  A more comprehensive system, ARGO, was put in place beginning in the early 2000s, with improvements and new deployments continuing today.  Today, ARGO consists of nearly 4000 floats which continuously measure ocean temperature, salinity, density and currents from the surface to 2000 meters. 
ARGO floats measure temperature to an accuracy of two-thousands (0.002) of a degree Celsius.  The floats are “parked” at 1000 meters, and every ten days submerge to 2000 meters and return to the surface, where data is broadcast to satellite receivers.  The system provides comprehensive coverage worldwide except for polar latitudes, and continuous measurements.

Ocean *Weather*
Like the atmosphere, ocean temperatures are seasonal, cyclic, variable, and turbulent.  The large number of ARGO floats was designed to adequately measure and characterize the variable temperatures of the ocean.  The volume of data acquired allow scientists to make maps of the changing water temperature and calculate the total heat content in the ocean.
Observations
Surface temperatures are warming the fastest.  NOAA presents charts of average ocean temperature and ocean heat content according to water depth, based on ARGO observations and earlier oceanographic studies.

Surface waters (0 – 100 m) have warmed by about 0.6 degrees C on average since the late 1960s. 
Intermediate waters (0 – 700 m) have warmed by a little over 0.2 degrees C on average since the late 1960s. 
Relatively deep waters (0 – 2000 m) have warmed by about 0.1 degree C on average, since the late 1960s.
Over all depth increments observed, the rate of warming seems to be slightly increasing.

Heat Content
The changing heat content of the ocean is a simple function of the change in temperature.  The heat capacity (or specific heat) of water represents the amount of heat required to change the temperature of a given volume of water.  From an observed change in temperature, we can back-calculate the amount of heat that has entered the ocean.  The density and heat capacity of water change slightly with pressure (and water depth).  NOAA has calculated the heat content of the ocean over various depth intervals from the temperature data and heat capacity.  

The heat content of the ocean at intermediate depths (0 – 700 m) has increased by about 2 x 1023 joules since the late 1960s. 
The heat content from the surface to 2000 meters (0 – 2000 m) has increased by about 3 x 1023 joules since the late 1960s.  This means that the heat content over the interval from 700 m to 2000 m has increased by about 1 x 1023 joules, about half of the increase in heat content at intermediate water depths.
Source of Increasing Heat
NOAA unfortunately did not report temperature change or heat content in separate depth intervals, but only in overlapping intervals of 0 – 100 , 0 – 700, and 0 – 2000 meters.  Starting from the average change of temperature for each interval, I calculated the heat content for 0 – 100 m, 100 – 700 m, and 700 – 2000 m.  My figure for total heat content calculated from temperature change exceeds the heat content reported by NOAA by 14%, probably due to errors in my single-point values for temperature or heat capacity over these depth intervals.
Temp Rise (C)
Volume (km3)
Density (g/cc)
Mass (kg)


Heat Capacity (J/kg-C)
Change in Heat Content (J)
0 - 100 m
0.6
5.23E+07
1.025
5.10E+19


3928.00
1.20E+23
0 - 700 m
0.2
3.69E+08
1.034
3.57E+20


3421.50
2.44E+23
0 - 2000 m
0.1
1.36E+09
1.329
1.02E+21


3339.04
3.41E+23
Intervals
Change in Heat Content
Percent of Heat Change
Change in Heat Content per 100 m
0 - 100 m
1.2E+23
35%
1.2E+23
100 m - 700 m
1.2E+23
36%
2.1E+22
700 m - 2000 m
9.6E+22
28%
7.4E+21

There is a large difference between the heat gained in the upper 100 meters of the ocean and the heat gained at deeper levels by equivalent volume.  The ocean is clearly heating from the surface downward.  About 35% of the total heat increase has occurred in the upper 100 meters of the ocean, about 36% in the next 600 meters, and about 28% in the next 1300 meters.  Research on deep ocean currents shows that heat is also being introduced into the deep ocean by currents, rather than by conduction. 

The geographic distribution of ocean heating also shows atmospheric influence.  The ARGO ocean data shows distinct heating anomalies between 30 and 40 degrees of latitude, north and south.  These are the down-welling points of large atmospheric convection cells termed Hadley cells.  You can see atmospheric circulation in observations of ocean warming.


Conclusion
The first post in this series quantified anthropogenic heating and cooling, primarily from greenhouse gases, particularly CO2.  This post looked at the largest heat sink on earth – the oceans.  

Net Anthropogenic heat absorbed by the planet from 1970 to 2016 was about 3.4 x 1023 joules.  Over the same period, the heat content of the oceans has increased by about 3.0 x 1023 joules.  Anthropogenic heat is the only credible source for the heat appearing in the ocean, and the warming oceans confirm that greenhouse gases are, in fact, warming the planet.  
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References
Global Heat Budget #1: Anthropogenic Heat



Ocean heat content figures.

Ocean temperature figures.

Gridded temperature data in map view.

The Oceans Their Physics, Chemistry, and General Biology, UC Press E-Books Collection, 1982-2004, University of California Press 
Physical properties of sea water.