The Science
Carbon Maths


Concentration of Carbon Dioxide in the atmosphere:
Between 1751 and the end of 2011, human activity added some 555 billion metric tons of CO2 to the atmosphere, of which 375 GtC are due to fossil fuel combustion and cement production and 180 GtC from deforestation and other land use change.
(This document (Working Group 1 for the IPCC Fifth Assessment Report September 2013) is the most recent and authorative overview of climate science.)

CO2 emissions in 2013 reached a record 36 billion tons.

The excellent Global Carbon Atlas ( was launched in November 2013. It offers engaging, scientifically accurate interactive graphics that tell the history of anthropogenic carbon emissions and anticipate future scenarios.

The 2012 report of the International Energy Agency indicates our overwhelming dependence on fossil fuels. It shows that in 2010, oil provided 32.4% of global energy use; coal and peat 27.4%; natural gas 21.4%; nuclear 5.7%; Biofuels and waste 10% and hydro 2.3%. Renewable energy (solar, wind, geothermal) provided 0.9% of our energy.

Since there is more CO2 in the atmosphere compared to other heat-trapping gases, it has a greater influence on warming. In April 2014, the concentration of CO2 in the atmosphere was 398 parts per million

This is 42% above pre-industrial levels (280ppm) and higher than at any point in the past 800,000 years (p7 "Climate Change, Evidence, Impacts and Choices, National Research Council, USA, 2012) . This rate of increase is at least ten and possibly one hundred times faster than at any time in the last 420,000 years. Concentrations of other greenhouse gases are increasing at comparable rates.

Note: The amount of CO2 in the atmosphere is measured in parts per million (ppm) in a given volume of air. Other gases (e.g. methane, nitrous oxide) also trap heat, so scientists use a 'CO2 equivalent' (CO2(e)) to indicate the heat-trapping influence of all heat-trapping gases combined. The CO2(e) is 20% higher than the figure for CO2 alone.
For a good summary of carbon concentrations and associated temperature rise, see

Regular and continuous measurements of CO2 concentration began at the Mauna Loa observatory in Hawaii in 1958.  These show that the concentration of greenhouse gases in the atmosphere has been increasing for the past 55 years.

The average concentration during 1959 was found to be 316 ppm, which means 65% of the increase in concentrations of CO2 has taken place over the last five decades.  Extensive global measurements confirm this trend in all regions.

Ice core data from air bubbles trapped in Antarctic ice shows the concentration of CO2 in the atmosphere was steady around 280ppm for at least 2000 years before the industrial revolution, but began to rise sharply in the late 19th Century. This data shows that concentrations of CO2 and average temperature are in lock-step (J-R Petit et al ‘Climate & Atmospheric History of the past 420,000 Years from the Vostok Ice Core, Antarctica.  Nature vol 399 pp 429-36, 1999)


To view an animation of the increase in atmospheric CO2 over the last 800,000 years, see:


So far, land, plants and the oceans have absorbed about 55% of the extra carbon that humans have put in the atmosphere.  The remaining 45% will stay in the atmosphere for thousands of years.


Temperature increase:
Average surface temperatures have risen 0.75˙C over the last century, with much of this increase occurring since 1975.. Over 90% of climate scientists agree this has been caused by the accumulation of CO2 and other greenhouse gases in the atmosphere from burning fossil fuels.

To view a map of global temperature anomalies in July 2012, see:

“These changes indicate that the Earth system has moved well outside the range in which the carbon cycle operated over the past half million years.  Change has been unidirectional and of unprecedented rate; that is, humans have pushed the Earth system into uncharted territory.”  (Global Carbon Budget, Tyndall Centre, 2010)


Not the Sun:
Satellite measurements of the sun’s energy on Earth show no net increase in solar forcing over the last 30 years.  Weather balloon data shows a cooling trend in the stratosphere and a warming trend in the troposphere, exactly what would be expected from increased greenhouse gases which trap energy closer to the Earth’s surface.

Continuing Rise in Carbon Emissions from Human Activity:
Due the warming effect of greenhouse gases in the atmosphere, the consensus among climate scientists is that global fossil fuel emissions must peak by 2020 if surface temperature are to rise no more than 2˙C above the pre-industrial average.  However, human-induced carbon emissions continue to rise.  In 2012, they rose by 2.1%, largely due to rising emissions from China, India, Russia, Brazil and other emerging nations (China'sCO2 emissions rose by 5.9% in 2010-11 and now account for 27% of global emissions).
If this trend continues, uncontrollable climate change is inevitable. (Guardian 5/12/11 quoting Prof Corinne Le Quéré, director of Tyndall Centre for Climate Change Research, UEA)

Continuing Rise in Average Surface Temperature:
There are three principal and independent records of temperature at the Earth’s surface: the UK Met Office/UEA Climatic Research Unit (CRU);  NASA’s Goddard Institute for Space Studies, and the US National Oceanic and Atmospheric Administration (NOAA). Their data sets are  in close agreement and indicate that global average temperature has increased by approximately 0.75˙C since 1900.

It has been calculated that the extra energy caused by all human and natural forcing agents between 1750 and 2005 is about 1.6 Watts per square metre, or more than 800 trillion Watts (Terawatts) over the whole of the Earth’s surface.  On a year by year basis, this is about 50 times the energy produced by all the power plants in the world. (page 10)

Analysis of paleoclimate data indicates that doubling the concentration of CO2 in the atmosphere leads to a rapid 3˙C increase in temperature from fast-feedback warming (crudely, the cumulative domino effect of separate warming factors) and a further 3˙C increase from slow-feedback warming over decades or centuries from the weakening albedo effect (the reflection coefficient of the sun’s energy that is reflected off the Earth’s surface by white ice and snow) as summer Arctic sea-ice and glaciers melt and methane is released through melting permafrost. (Abstract of  ‘Target Atmospheric CO2:  Where Should Humanity Aim?, James Hansen et al :

The independent measures greenhouse gases in the atmosphere and uses models to predict temperatures.  If current emissions continue, this predicts that average temperatures will rise by 3.1˙C above pre-industrial levels by 2100, although uncertainties relating to carbon-cycle and climate modelling mean the increase could be as high as 4.1˙C or as low as 2.6˙C.

The Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPPC) 2013 projects, from six emissions scenarios, that global average surface temperatures are likely to increase between 1.1 and 4.8˙C by 2100.

A rise of 4.8˙C would take average temperatures from a pre-industrial 14.8 ˙C to 19.6˙C in just three centuries.  However, even if we could stop fossil fuel emissions overnight, the IPCC states that ‘anthropogenic warming and sea level rise would continue for centuries due to the time-lag associated with climate processes and feedbacks’



Arctic Sea Ice:
In September 2012, the area of summer sea-ice in the Arctic fell below 4m sq km for the first time. (National Snow and Ice Data Center

Climate models suggest temperature increase in  the Arctic will be around twice the global average as highly reflective ice is replaced by dark blue, heat-absorbing ocean.  In 2010-11 surface temperature in the Arctic was 1.5˙C warmer than the long-term average and air temperature 3˙C warmer.
Glacier melt and sea-level rise will accelerate this trend. Nine of the ten highest annual average temperatures recorded in the Arctic have occurred since 2000. 

Melting permafrost in Alaska, Canada, Greenland, Scandinavia and Russia is causing methane, a greenhouse gas 25 times more potent as a warming agent than carbon dioxide (p9), to be released into the atmosphere. Scientists at the University of Alaska Fairbanks have discovered 150,000 methane leaks through ice in lakes in Alaska and Greenland.  They estimate that ten times the weight of methane currently in the atmosphere will be released into the atmosphere as the permafrost melts. The concentration of methane in the atmosphere has risen  from 1600 ppm in 1982 to 1800 ppm in 2012

Ocean Acidification:
So far, the oceans have absorbed around 30% of carbon emissions, which means some 20m tons of CO2 is being added to the oceans each day. Seawater is alkali, but adding carbon dioxide makes it more acidic.  The pH scale, like the Richter Scale of earthquake intensity, is a logarithm, so the measured fall in pH levels from 8.2 to 8.l indicates a 30% increase in acidity.

Present emissions scenarios are expected to see a further pH drop of 0.3 to 0.4 units – i.e. 150 – 200% increase in ocean acidity. This will have severe consequences on ocean ecosystems, especially for species of calcifying organism that produces a calcium carbonate shell.  Since 20% of our food protein comes from the oceans,  it will also affect food security

“If emissions continue at their current rate, model projections suggest that by 2050  the surface oceans will be more acidic than they have been for tens of millions of years, and that the rate of change will be more rapid than during any event over the last 65 million years, with potentially severe impacts on marine ecosystems, including coral reefs.”

“Studies indicate that as the Earth warms, the net uptake of CO2 by the oceans may decrease, which would mean that, for each tonne of anthropogenic (human-induced) CO2 released, the concentration of CO2 in the atmosphere would increase more rapidly than at present. There are indications that the efficiency of CO2 ‘sinks’ in the Southern Ocean and the North Atlantic have begun to decrease, but longer, more comprehensive records of CO2 uptake are needed to confirm this.”

Sea Level Rise:
The IPCC Fourth Assessment Report predicted that sea levels may rise between 18cm and 59cm by the end of this century, but noted that this figure did not take account of feedback mechanisms which will be triggered by rising temperatures, but whose future effects are hard to quantify


A 2011 report by NASA's Jet Propulsion Laboratory suggests notes an acceleration in the contribution of the Greenland and Antarctic ice to sea level rise beyond the rises predicted by the IPCC in the Fourth Assessment Report.
“The authors conclude that, if current ice sheet melting rates continue for the next four decades, their cumulative loss could raise sea level by 15 centimeters (5.9 inches) by 2050. When this is added to the predicted sea level contribution of 8 centimeters (3.1 inches) from glacial ice caps and 9 centimeters (3.5 inches) from ocean thermal expansion, total sea level rise could reach 32 centimeters (12.6 inches) by 2050. While this provides one indication of the potential contribution ice sheets could make to sea level in the coming century, the authors caution that considerable uncertainties remain in estimating future ice loss acceleration.”


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