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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. 

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.

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 (  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.


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

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.
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 - 700 m

0 - 2000 m

Change in Heat Content
Percent of Heat Change
Change in Heat Content per 100 m
0 - 100 m
100 m - 700 m
700 m - 2000 m

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.

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.  
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.

Wednesday, April 11, 2018

Global Heat Budget #1: Anthropogenic Heat

I have been away from my blogs for far too long.  I will try to post a series on the global heat budget.

Previously, I posted a lot of work on atmospheric CO2, considering the geographic distribution, isotope data, rates of change, comparison to man-made emissions from various sources, and interaction of the atmosphere with global carbon reservoirs.  The latest summary post is here:
I deliberately avoided the question of climate change to focus on the science of atmospheric CO2.

For the past year, I’ve been studying on the problem of global warming (the first-order consequence of greenhouse gases) and climate change (the higher-order consequences of greenhouse gases).  And I’ve been posting less while I worked to understand the data.

I’m going to present what I’ve learned as a series of short posts, rather than writing a book.
The very short version is this:

The Global Heat Budget; The Very Short Version
People have raised the concentration of atmospheric CO2 by burning fossil fuels.  The volume of CO2 released by fossil fuels has increased sharply since about 1950, and continues to increase today.

CO2 and other greenhouse gases retain heat in the atmosphere.  The quantity of heat is easily calculated as a function of the concentration of CO2 in the air.  We can calculate the amount of heat that has been trapped to date, and we can forecast the heat that will be trapped in the future.

Heat is increasing in heat sinks on earth.  Observations show that the amount of heat appearing in earth’s heat sinks is approximately equal to the heat retained by greenhouse gases.  The heat is showing up as rising ocean temperatures, melting ice, and a warmer atmosphere.  The quantity of heat appearing in these systems has been measured by high-accuracy monitoring programs since about 2003.  The warming ocean accounts for about 95 percent of our estimates of anthropogenic heat.  Retained heat due to greenhouse gases is the only credible source for the heat appearing in heat sinks.

Sea-level is rising.  Sea level rise has been documented by tidal gauges for 130 years, and by high-accuracy satellite measurements since 1992.  The amount of sea level rise matches the observed volumes of melted ice, thermal expansion of the ocean, and ground-water extraction.  The fact of rising sea level confirms observations of melting ice and warming oceans.

Higher atmospheric CO2 concentrations are inevitable for the foreseeable future.  Quantitative forecasts of future heating indicate serious and expensive problems will develop for the nation & the world.
Atmospheric CO2 has risen as a consequence of fossil fuel emissions.  The following chart is my version of the Keeling Curve ( showing global CO2 concentration, including high-amplitude seasonal cycles in the Northern Hemisphere, and low-amplitude seasonal cycles in the Southern Hemisphere.
History of Study of CO2 as a Greenhouse Gas
The physics of CO2 as a greenhouse gas is settled science, based on published studies dating back over 150 years.  High accuracy programs to measure melting ice, ocean temperatures, and rising sea level have been in place in recent decades, long enough to yield conclusive results.

Carbon dioxide was first proved to be a greenhouse gas by John Tyndall in 1859, proving speculation that began in 1820.  The planet-wide effect of changing CO2 concentrations was calculated by the Swedish chemist Arrhenius and published in 1896.  Arrhenius was originally attempting to find the cause of the ice ages, but later recognized the possibility that fossil fuel emissions could change the climate, and published that result in 1906.  Quantitative measurements of CO2 and rising temperatures were published in 1938 by Guy Callendar.  Systematic global measurements of CO2 concentrations began in 1955 by Charles Keeling.  Satellite measurements of sea level rise began in 1992.  Satellite measurements of Antarctic and Greenland ice mass began in 2003.  Detailed, comprehensive and continuous measurements of ocean temperatures began in 2004.

Calculation of Heat Retained by Greenhouse Gases
Greenhouse gases are mostly transparent to wavelengths of visible light, which carry most of the energy from our sun.  Visible light strikes the earth and is converted to heat.  Normally, some portion of that energy is re-radiated into space as thermal infrared radiation.  But greenhouse gases are opaque to infrared wavelengths, and trap heat in the atmosphere as a function of the concentration of those gases.  As greenhouse gases have accumulated in the atmosphere, lower levels of the atmosphere have warmed.  Higher levels of the atmosphere have cooled, as more heat has been trapped near the surface.

NOAA publishes historical tables of the atmospheric heating coefficients (known by the awkward and uninformative phrase *radiative forcing*) for anthropogenic greenhouse gases, dating back to 1979.  The coefficients are prepared according to international standards, taking into account cloudiness and angle of solar incidence to yield a global average.  You can do the math yourself to calculate annual heat retained by each greenhouse gas, which I have done.  Carbon dioxide represents about two-thirds of the heat retained in the atmosphere by greenhouse gases.  Methane, nitrogen oxide, chlorofluorocarbons (CFCs) and minor greenhouse gases account for the rest of the heat retained by greenhouse gases. 
In 1979, greenhouse gases retained about 7 x 1021 joules.  By 2016, greenhouse gases retained about 1.2 x 1022 joules, an increase of 78% in annual heating.  It’s difficult to conceptualize how much heat is represented by 1022 joules.  A joule is about ¼ of a standard calorie – the heat required to raise a gram of water by one degree C.  It’s a small amount of heat.  But 12,000,000,000,000,000,000,000 joules is a lot of heat.  Later in this series, we’ll consider how the earth can absorb that quantity of heat, and where the heat is going.
Aerosols and Anthropogenic Cooling
Aerosols are the least-well quantified anthropogenic influence on earth’s climate.  Sulfate aerosols cool the atmosphere by making clouds more abundant and reflective.  Sulfates can originate from volcanic eruptions, but are also a common industrial pollutant.  Carbon black aerosols warm the atmosphere by absorbing sunlight. 

Sulfate emissions have dropped dramatically in the United States and Europe over the past 25 years, thanks to regulations intended to limit acid rain, but world-wide sulfate emissions have continued to grow.  The average global impact of sulfates and black carbon aerosols is shown in the following graphs, but the more significant impacts are regional.  South Asia suffers from the greatest carbon black emissions and impact, while China is now the source of most sulfate emissions.

IPCC Net Anthropogenic Heating and Cooling
The IPCC (International Panel on Climate Change) 5th Climate Assessment contains a table of anthropogenic heating and cooling coefficients.  The IPCC numbers for conventional greenhouse gases are identical to NOAA, but IPCC also recognizes other anthropogenic factors, which can both heat and cool the atmosphere.  These factors act by direct absorption of sunlight, or by a greenhouse effect that is restricted to certain levels in the atmosphere.  The IPCC recognizes the warming factors of tropospheric ozone (O3), stratospheric water vapor (H2O), black carbon on snow, and contrails.   IPCC recognizes cooling factors, including land-use changes (which affect the reflectivity of the earth), stratospheric ozone, and aerosols. 

Here is a chart based on IPCC data, showing anthropogenic heating and cooling coefficients (*radiative forcing*).

Primary Anthropogenic and Other Heat
Strangely, to me, the IPCC report makes no mention of another source of anthropogenic heat – the primary heat resulting from burning fossil fuels and nuclear plants, and secondarily, the primary heat resulting from deforestation.  The global heat from non-renewable sources is reported in the BP Statistical Review of World Energy.  The energy released by deforestation can be easily calculated from the volumes of carbon dioxide released, which is estimated in several sources.  These sources of heat represent about 5% and 1%, respectively, of the net anthropogenic heat reported by IPCC, and exceed several other minor sources of heat in the report.

Here is a chart showing the calculated anthropogenic heating and cooling, based on IPCC estimates for radiative forcing, plus heat from primary energy.
I considered and calculated the incremental accumulation of geothermal heat, due to the retention of heat by greenhouse gases.  Geothermal heat is normally in a steady state, with heat flux from the planet balanced by thermal radiation into space.  The quantity of heat retained is quite small, however, and not worth adding to the heat budget. 

Agriculture has a significant influence on the planet’s seasonal CO2 cycles, due to the preponderance of agriculture in the temperate Northern Hemisphere.  Changes in atmospheric CO2 necessarily imply changes in heat, through the reduction and oxidation of carbon.  Agriculture appears to be a zero-sum influence on the long-term heat budget but may be significant in seasonal climate modeling. 

Net Anthropogenic Heat
The net heating coefficient (*radiative forcing*) for all anthropogenic heating and cooling was about 2.4 watts/min 2011.  The global average for solar insolation at the top of the atmosphere is 1361 watts/m2.  About 1000 watts/mof the sun's radiation reaches the earth's surface.  Anthropogenic heat represents a small but noticeable increment to the natural heating of the earth by the sun, about 0.24% above the natural, steady state of solar heating and radiative cooling.

Using the IPCC heating and cooling numbers, plus primary heat, we see that net global anthropogenic heating was 9.8 x 1021  joules in 2011. That’s enough heat to melt about 29,500 gigatonnes of ice, or to bring 14,000 gigatonnes of water from room temperature to boiling.  Of course, the icecaps are much larger than 29,500 gigatonnes of ice, and the ocean is much larger than 14,000 gigatonnes of water.  So the changes we see in a single year are subtle.
Net anthropogenic heat from 1970 to 2016 is about 3.4 x 1023 joules.  The effect of heat retained by greenhouse gases is cumulative. Over time, the consequences are not so subtle.  In the next few posts, we will look at how anthropogenic heat is being distributed in earth’s heat sinks.  
NOAA Radiative Forcing Tables

IPCC climate change references
31 page Summary

VOX article on BECCS (Bio-energy and Carbon Capture and Sequestration) requirement to keep temperatures less than 2 degrees higher than pre-industrial levels.

2013 Full IPCC report, 1500+ pages

Fourth National Climate Assessment

BP Statistical Review of World Energy
Primary Heat from Fossil Fuels and Nuclear Energy

Primary Heat from Deforestation
Primary heat calculated from CO2 released.
Houghton, R.A. 2008. Carbon Flux to the Atmosphere from Land-Use Changes: 1850-2005. In TRENDS: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A.

IPCC 5th Climate Assessment, pg. 1446.

Aerosols caused by human activity play a profound and complex role in the climate system through radiative effects in the atmosphere and on snow and ice surfaces and through effects on cloud formation and properties. The combined forcing of aerosol–radiation and aerosol–cloud interactions is negative (cooling) over the industrial era, offsetting a substantial part of greenhouse gas forcing, which is currently the predominant human contribution. The magnitude of this offset, globally averaged, has declined in recent decades, despite increasing trends in aerosol emissions or abundances in some regions. (emphasis mine).

By nucleating a larger number of smaller cloud drops, aerosols affect cloud radiative forcing in various ways. (A) Buffering in nonprecipitating clouds. The smaller drops evaporate faster and cause more mixing of ambient air into the cloud top, which further enhances evaporation. (B) Strong cooling. Pristine cloud cover breaks up by losing water to rain that further cleanses the air in a positive feedback loop. Aerosols suppressing precipitation prevent the breakup. (C) Larger and longer-lasting cirrus clouds. By delaying precipitation, aerosols can invigorate deep convective clouds and cause colder cloud tops that emit less thermal radiation. The smaller ice particles induced by the pollution aerosols precipitate more slowly from the anvils. This can cause larger and longer-lasting cirrus clouds, with opposite effects in the thermal and solar radiation. The net effect depends on the relative magnitudes.