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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.