Global temperature versus current carbon dioxide levels

One of the persistent issues bedeviling public understanding of global warming is the apparent disconnect between CO₂ levels and global temperatures since 1998.  Skeptics claim that warming has slowed since 1998 while CO₂ has risen at an increasing rate.  At first glance, they might have a point—but only at first glance.  Here is the 12-month running average of Mauna Loa CO₂ measurements and GISS surface temperatures:

As you can see, CO₂ has risen steadily since 1998, at an average rate of +1.985 ppmv per year (standard error = 0.03636 ppmv, p-value = < 2.2 x 10^-16).  GISS surface temperatures have also risen by an average of + 0.005967ºC per year (standard error = 0.002057ºC, p-value = 0.004183) but far less steadily and well below the 0.016ºC per year rate of the last 30 years.  Shouldn't temperatures track CO₂ levels?

There are several reasons you wouldn't expect surface temperatures over short time periods (and 15.33 years is short in terms of climate) to track CO2 very closely.  First, the El Niño/La Niña cycle has large effects on surface temperatures on short time periods (see Foster and Rahmstorf 2011).  El Niño, of course, is when ocean heat is dumped into the atmosphere, thereby raising surface temperatures.  La Niña is when the ocean absorbs heat from the atmosphere, thereby lowering surface temperatures.  We had mostly El Niño conditions over the first 7.5 years, with 1998 experiencing the most extreme El Niño in recorded history, and La Niña or neutral conditions dominating since 2010.  That alone would flatten any warming trend by raising surface temperatures in the early part of the time period and lowering them in the later portion.  Using Foster and Rahmstorf's method to accounting for El Niño/La Niña, changes in solar output, and aerosols removes much of the discrepancy:

R code for adjusting temperature data from Foster and Rahmstorf (2011) available online here

The average rate of temperature rise after adjusting for El Niño/La Niña, solar output, and aerosols?  +0.013602ºC per year (standard error = 0.001821ºC, p-value = 3.302 x 10^-12), only a little below the 30 year rate.

Second, CO₂ does not raise surface temperatures directly.  Carbon dioxide and other greenhouse gases work by decreasing the amount of heat that leaves the atmosphere, thereby reducing the thermal gradient between the atmosphere and the surface and trapping more heat at the surface.  That trapped energy then goes into the oceans, glaciers, polar ice caps, and land as well as the atmosphere.  In fact, the atmosphere holds only 2.3% of the total heat trapped by the greenhouse effect.  Over 90% of total heat is found in the oceans (i.e. Murphy et al. 2009, Church et al. 2011, Nuccitelli et al. 2012, Balmaseda et al. 2013), where it helps raise sea levels due to thermal expansion.  Sea levels have been rising at an increasing rate since 1880 with just under half coming from thermal expansion (Church and White 2011, Church et al. 2011).  While atmospheric temperatures have been measured longer, total heat content (atmosphere + oceans + ice + land) is actually the best measurement of global warming as it measures all of the heat from global warming, not just 2.3% of it.  Since 1998, total heat accumulation has averaged +8.145 x 10²¹ J per year (standard error = 2.693 x 10²⁰ J, p-value = 1.957 x 10^-13).

Data from Nuccitelli et al. 2012.  Available here

Third, changes in CO₂ levels will not (and indeed cannot) change surface temperatures instantaneously.  There's always going to be a lag between increases in CO₂ and surface temperatures.  The Earth's energy imbalance is the physical manifestation of that lag.  Global warming won't stop until the atmosphere warms up enough to radiate as much infrared energy out as there is solar energy hitting the ground and the imbalance is zero.  With the imbalance currently running around 0.75 J/s/m², we have another 0.61ºC of surface warming in store at current CO₂ levels.  If we were to put it into an equation, it would be

Total warming due to CO₂ = Current surface temperature + Future warming (via energy imbalance)

According to GISS, we've already warmed by an average of 0.79ºC since the 1880s (calculated by taking the difference between the 1880-1890 average and the 2003-2013 average).  At the current energy imbalance, we're looking at a total of 1.40ºC of surface warming due to current greenhouse gas and aerosol levels, very close to the 1.48ºC of total surface warming we'd predict for CO₂ alone using the equilibrium climate sensitivity equation (ΔT = λΔF) and the Myhre et al. (1998) equation for ΔF due to CO₂ (ΔF = 5.35 W/m² * ln(C/C₀)).

In short, when you actually examine the issue, there really is no disconnect between CO₂ and global surface temperatures.  Global surface temperatures are very close to what you'd expect at the current level of CO₂.  The reasons for the apparent disconnect since 1998 are two-fold.  First, starting a trend at the strongest El Niño on record guarantees a lower estimate of surface warming (as examined here).  Second, more La Niñas over the past 7.5 years means more heat going into the oceans rather than the atmosphere.  The main issue is how to communicate this to the general public, as the explanation won't fit on a bumper sticker.