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How Much Global Warming Are Humans Causing

How much global warming are humans causing?

A common difficulty people have is understanding quantitatively how much global warming humans are causing, and how we know.  Many people believe that this is a subject of significant debate among climate scientists, but in reality it's very well established science.  Here's a description of how it's calculated.


Humans have increased the levels of greenhouse gases in the atmosphere


Specifically, humans have increased the amount of carbon dioxide (CO2) in the atmosphere by about 40% over the past 150 years.  There are several ways we know this.


  • Common sense.  The concentration of atmospheric CO2 had been relatively stable for hundreds of thousands of years prior to 150 years ago.  Based on ice core data, we know atmospheric CO2 levels varied between about 180 and 280 parts per million by volume (ppmv) over the past 400,000+ years.  There were times during that period that the planet was roughly as hot as today, yet the atmospheric CO2 level did not rise above 280 ppmv.  So why is it suddenly spiking 40% higher, coincidentally when humans have started burning large amounts of fossil fuels?




  • Simple accounting.  We have a good idea as to how much CO2 has been released due to humans burning fossil fuels.  We also know how much the amount of CO2 in the atmosphere has increased.  As it turns out, only about half the CO2 emitted by humans has ended up in the atmosphere.  The other half has been absorbed by natural carbon sinks, mainly the oceans.  We know this because the pH of the oceans has decreased - when CO2 dissolves in seawater, it increases the hydrogen ion concentration though the chemical reaction CO2 + CO32- + H2O2HCO3-, thus decreasing the pH of the oceans in a process known as ocean acidification.  This is another major environmental concern in its own right, and another reason why we need to reduce human greenhouse gas emissions.  For example, modern corals build their skeletons from aragonite, which is more soluble than the calcite used by corals during the Mesozoic era, so modern corals are more vulnerable to these chemical reactions.


  • Isotopic analysis.  Carbon is composed of three different isotopes, 14C, 13C, and 12C, with the latter being by far the most common in nature.  CO2 produced from burning fossil fuels or burning forests has quite a different isotopic composition from CO2 in the atmosphere, because plants have a preference for the lighter isotopes (12C vs. 13C); thus they have lower 13C/12C ratios.  Fossil fuels have virtually no 14C, and less 13C than air.  As CO2 from these materials is released into, and mixes with, the atmosphere, the average 13C/12C ratio of the atmosphere decreases, as does the fraction of 14C.  The half life of 14C is 5,700 years, which means that if the 14C fraction is decreasing, the carbon being added to the atmosphere is from a very old carbon source (such as fossil fuels).  Analysis of these ratios from tree rings and ice cores shows that at no time in the last 10,000 years were the 13C/12C ratios in the atmosphere as low as they are today. Furthermore, the 13C/12C and 14C/12Cratios begin to decline dramatically just as the CO2 starts to increase — around 1850 AD, during the Industrial Revolution.


A common misconception is that volcanoes emit more CO2 than humans, but the opposite is true.  Humans emit over 100 times more CO2 than volcanoes on an annual basis, as discussed in Myth #3 of the Global Warming Myths Wiki.


The multiple lines of evidence that humans are responsible for the 40% increase in atmospheric CO2 are incontrovertible, and accepted by virtually every climate scientist.  So what does that tell us?


Downward longwave radiation at the Earth's surface has increased


The aforementioned increase in atmospheric CO2 and other greenhouse gases has increased the amount of infrared radiation absorbed and re-emitted by these molecules in the atmosphere.  The Earth receives energy from the Sun in the form of visible light and ultraviolet radiation, which is then re-radiated away from the surface as thermal radiation in infrared wavelengths.  Some of this thermal radiation is then absorbed by greenhouse gases in the atmosphere and re-emitted in all directions, some back downwards, increasing the amount of energy bombarding the Earth's surface.  This increase in downward infrared radiation has been observed through spectroscopy, which measures changes in the electromagnetic spectrum.




This increased energy reaching the Earth's surface causes it to warm.  So how do we quantify the amount of warming that it causes?


Radiative Transfer Models


Radiative transfer models use fundamental physical equations and observations to translate this increased downward radiation into a radiative forcing, which effectively tells us how much increased energy is reaching the Earth's surface.  Studies have shown that these radiative transfer models match up with the observed increase in energy reaching the Earth's surface with very good accuracy.  Scientists can then derive a formula for calculating the radiative forcing based on the change in the amount of each greenhouse gas in the atmosphere.  Each greenhouse gas has a different radiative forcing formula, but the most important is that of CO2:


ΔF = 5.35 ln(C/Co)


Where 'ΔF' is the radiative forcing in Watts per square meter, 'ln' is the natural logarithm function, 'C' is the concentration of atmospheric CO2, and 'Co' is the reference CO2 concentration.  Normally the value of Co is chosen at the pre-industrial concentration of 280 ppmv.


Now that we know how to calculate the radiative forcing associated with an increase in CO2, how do we determine the associated temperature change?


Climate sensitivity


As the name suggests, climate sensitivity is an estimate of how sensitive the climate is to an increase in a radiative forcing.  The climate sensitivity value tells us how much the planet will warm  or cool in response to a given radiative forcing change.  As you might guess, the temperature change is proportional to the change in the amount of energy reaching the Earth's surface (the radiative forcing), and the climate sensitivity is the coefficient of proportionality:


ΔT = λ*ΔF


Where 'ΔT' is the change in the Earth's average surface temperature, 'λ' is the climate sensitivity, usually with units in Kelvin or degrees Celsius per Watts per square meter (°C/[W/m2]), and 'ΔF' is the radiative forcing.


So now to calculate the change in temperature, we just need to know the climate sensitivity.  This subject is covered in more detail in the Climate Sensitivity Wiki, which describes that studies have given a possible range of values of 2-4.5°C warming for a doubling of CO2.  Using these values it's a simple task to put the climate sensitivity into the units we need, using the formulas above:


λ = ΔT/ΔF = ΔT/(5.35 * ln[2])= [2-4.5°C]/3.7 = 0.54 to 1.2°C/(W/m2)


Using this range of possible climate sensitivity values, we can plug λ into the formulas above and calculate the expected temperature change.  The atmospheric CO2 concentration as of 2010 is about 390 ppmv.  This gives us the value for 'C', and for 'Co' we'll use the pre-industrial value of 280 ppmv.


ΔT = λ*ΔF = λ * 5.35 * ln(390/280) = 1.8 * λ.


Plugging in our possible climate sensitivity values, this gives us an expected surface temperature change of about 1–2.2°C of global warming, with a most likely value of 1.4°C.  However, this tells us the equilibrium temperature.  In reality it takes a long time to heat up the oceans.  This is known as 'thermal inertia', and for this reason there is currently a planetary energy imbalance, and the surface has only warmed about 0.8°C.  In other words, even if we were to immediately stop adding CO2 to the atmosphere, the planet would warm another ~0.6°C until it reached this new equilibrium state.  This is referred to as the 'warming in the pipeline'.


Of course this is just the temperature change we expect to observe from the CO2 radiative forcing.  Humans cause numerous other radiative forcings, both positive (e.g. other greenhouse gases) and negative (e.g. sulfate aerosols which block sunlight).  Fortunately, the negative and positive forcings are roughly equal and cancel each other out, and the natural forcings over the past half century have also been approximately zero, so the radiative forcing from CO2 alone gives us a good estimate as to how much we expect to see the Earth's surface temperature change.




We can also calculate the most conservative possible temperature change in response to the CO2 increase.  Some climate scientists who are touted as 'skeptics' have suggested the actual climate sensitivity could be closer to 1°C for a doubling of CO2, or 0.27°C/(W/m2).  Although numerous studies have ruled out climate sensitivity values this low, as discussed in the Climate Sensitivity Wiki, we can calculate how much of a temperature change this low value would generate.  Using the same formulas as above,


ΔT = 1.8 * λ = 1.8 * 0.27 = 0.5°C.


Therefore, even under this ultra-conservative unrealistic low climate sensitivity scenario, the increase in atmospheric CO2 over the past 150 years would account for over half of the observed 0.8°C increase in surface temperature.


The science is settled

Putting it all together, human greenhouse gas emissions can effectively account for nearly all the global warming we've observed recently.  Additionally, the fact that all known natural radiative forcings have been approximately zero tell us that not only can human effects account for the warming, but natural effects cannot.


In the early 20th century, there was an increase in solar activity and a decrease in volcanic activity, both of which are positive natural forcings.  Combined with the increase in human greenhouse gas emissions during this period, these forcings caused a global warming trend in the early 1900s.  Studies have concluded that overall over the past 100 years, humans have caused approximately 80% of the warming.  Over the past 40 years, humans have caused approximately 100% of the global warming.  There is of course some uncertainty in that estimate, since we don't know the exact climate sensitivity value or understand all natural forcings perfectly.  Taking these uncertainties into account, climate scientists have estimated that humans have caused 80-120% of the warming over the past 40 years, since natural factors may have caused a small amount of warming or cooling over that period.


So the next time somebody tells you that humans aren't responsible for a significant amount of the recent global warming, point them to this page and explain to them that they're making a physically incorrect statement.  Using empirical observations and fundamental physical formulas, even with an  unrealistically conservative climate sensitivity value, humans are still responsible for the majority of the current global warming, and in all likelihood we're responsible for almost all of it.  There's just no way around this reality without rejecting fundamental physics. 


In addition to this physical and mathematical calculation quantitatively demonstrating that humans are the primary source of the current warming, there are also numerous key Fingerprints of Human-Caused Climate Change which confirm it further.


When scientists say "the science is settled," this is what they're talking about.  There are of course many climate science questions which remain unsettled, such as the precise climate sensitivity value, when various feedbacks will kick in, how much we need to reduce human greenhouse gas emissions, and so on.  But when it comes to the cause of the current warming, the science is indeed settled - it's human greenhouse gas emissions.


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