Wednesday, September 18, 2013

Rates of change

One common misunderstanding about how the current global warming differs from past episodes of warming is the rate of warming.  In this post, I'll show how the rate over the past 30 years stacks up with two of the better-known rates from geologic history.

Past 30 years (1983-2013) rate ± standard error:
UAH: +0.015379 ± 0.003783ºC per year
GISS: +0.015505 ± 0.002491ºC per year
NCDC: +0.014454 ± 0.002489ºC per year
HadCRUT4: +0.014896 ± 0.002824ºC per year

Depending on the data set, the rate of the last 30 years ranges from 0.014454ºC per year up to 0.015505ºC per year.  When I average the four data sets together then calculate the rate, the result is +0.014692 ± 0.003070ºC per year for the last 30 years.

For the geologic rates, let's start with the most recent and work backwards in time.

Over the 5,000 years since the end of the Holocene Climatic Optimum, the Earth slowly cooled by 0.7ºC (Marcott et al. 2013).  That's an average rate of  -0.00014ºC per year.  The current rate is 104x faster than the rate over the previous 5,000 years.

At the end of the last ice age, a process lasting between 22,000 to 11,000 BP, global temperatures rose an average of 3.5ºC over 8,000 years (Shakun et al. 2012).  That translates to an average of 0.0004375ºC per year, which means the average rate of change over the last 30 years is 33.5x faster than at the end of the last ice age.

During the Paleocene-Eocene Thermal Maximum (55 million years BP), global temperatures rose an average of 6.5ºC over 19,000 years (Cui et al. 2011).  This warming was triggered by a release of an average of 6.2 billion metric tons of CO2 per year.  In contrast, humans released the equivalent of 34.8 billion metric tons of CO2 (9.5 billion metric tons Carbon) in 2011 alone (Quéré et al. 2012).  Not only is the rate of CO2 release greater, the rate of change in temperature over the last 30 years is 43x greater than it was then.

Less well known but a subject of active research is the End-Triassic Mass Extinction 210 million years ago.  This extinction was a time when 50% of species went extinct due to a massive disruption of the carbon cycle and climate.  While I cannot find an estimate of the temperature change, the amount of CO2 has been estimated at 12 trillion metric tons of carbon over a period of 10,000 to 20,000 years (Ruhl et al. 2011), which averages out to between 0.6 billion metric tons and 1.2 billion metric tons per year, far lower than the 9.5 billion metric tons of carbon human activities released in 2011 alone.  The cause of that carbon release is disputed, with Ruhl et al. favoring methane clathrates whereas Blackburn et al. (2013) ascribed it to massive volcanic eruptions triggered as Pangea broke apart.

The lesson from examining geologic history is quite clear.  The current rate of temperature is simply far faster than what has been experienced in the past.  This graph of Holocene temperatures sums up that point nicely:

The only thing standing between us today and the major ecosystem changes, species extinctions, etc noted in the geologic record is time, as the current rate of change is more than fast enough to trigger such events if it continues.  Add in the fact that the Milankovitch cycles, which have been the primary drivers of the Ice Ages, are 6,000 years into a 29,000-year cooling phase (Imbrie and Imbrie 1980) and it's not too hard to see that the current warming is counter to the natural cycle and occurring too fast to be natural.

Sunday, September 15, 2013

Arctic temperature vs sea ice extent

One seemingly persistent myth about the Arctic is that there is no correlation between Arctic air temperature and sea ice extent.  At first glance, that myth appears to be true, as Arctic temperatures have noticeably risen whereas sea ice extent shows little overall change.

The correlation appears even worse when plotting sea ice extent versus temperature directly.


Taking a closer look, however, reveals the reason for the apparently poor correlation: The large seasonal cycle in sea ice extent data.  The cycle obscures the overall trend in sea ice data—and the correlation of that trend with the trend in Arctic tropospheric temperature.  Once that cycle is removed via a 12-month moving average, the trend in sea ice extent and the negative correlation between extent and temperature is clearly revealed.


The direct comparison shows that the decline in Arctic sea ice extent has accelerated as Arctic tropospheric temperature increased.
Extent = 11.6846713 + -0.9177708x + -0.2355697x2, where x = temperature

The R2 value for that correlation is quite high, R2 = 0.7865 and p-value = <0.00000000000000022.  Now does that correlation prove that higher Arctic tropospheric temperatures caused the sea ice decline?  No.  Correlation by itself does not imply causation.  It could be warmer ocean currents and/or changes in wind patterns.  However, that argument doesn't address what caused the ocean currents to warm and the wind patterns to change—and the answer is increasing air temperatures cause the oceans to warm and change wind patterns.  No matter what, the physical cause of the ice melt ultimately goes back to warmer air temperatures.  When you have a correlation backed by a physical mechanism, that DOES imply causation.

Tuesday, September 10, 2013

Is it a recovery or not?

One of the current rumors circulating in climate change denier circles is that the Arctic sea ice is recovering, with a record ice gain, and that Arctic ice in August 2013 60% higher than in August 2012 and is the highest in "years."  Let's examine those claims.

First, here's a graph showing the 12-month moving average of Arctic sea ice from January 1979 to August 2013:


Not much to say there.  So far, the 12-month moving average shows no sign of any recovery.  Arctic sea ice extent remains far below the 1979 start point or even where it was before 2005.  However, the claim is that the ice gain since September 2012 set a record.  Normally, Arctic ice extent reaches the yearly minimum in September at the end of summer, with a maximum the following March at the end of winter.  The ice gain is the difference between those months.


March extent has been declining linearly by an average of -36,581 km2 per year whereas the decline in September has been by an average of -87,112 km2 and accelerating by -7,786 km2 per year.  As a result of the accelerating losses in September, the yearly difference between March and September has been growing at an accelerating rate.

Why was the "gain" between September 2012 and March 2013 a record?  Simple.  September 2012 was the lowest Arctic sea ice extent on record.  That left plenty of open water to refreeze during the winter, leading to a record "gain" by March 2013.  That denier claim that the Arctic has experienced a record "gain" of ice is just a cynical attempt to distract from the real story of continued decline in Arctic sea ice.  In reality, both March and September sea ice extents continue to decline—and the "record gain" is actually a symptom of that decline, not a sign of recovery.

The second claim that Arctic sea ice is 60% higher in August 2013 than it was in August 2012 is partially true—the ice was higher in August 2013.  But it wasn't by 60%.  Average ice extent in August 2013 was 6.05 million km2.  Ice extent in August 2012 was 4.72 million km2.  That is a difference of 1.33 million km2, which means that the ice in August 2013 was 28.2% higher than it was in August 2012 (1.33/4.72 * 100).  As for the claim that August extent is the highest in years, here's a graph of August sea ice extent since 1979.

The last time August sea ice extent was higher than August 2013's extent of 6.05 million square kilometers?  August 2009, with 6.13 million square kilometers.  And even though August 2013 is supposedly the "highest in years", it's the 6th lowest August ice extent since 1979.  Not much to go on if you're trying to claim that Arctic sea ice is recovering.

Finally, sea ice extent is not the full story in the Arctic.  A larger but less noticeable change is that the sea ice has become much thinner.


The ice has lost nearly 12,000 km3 of volume since 1979.  Even if ice extent does grow, all it means is that the surface is covered with thinner, less stable ice than it used to be.  And thinner ice is more susceptible to melting when conditions are right.

Lastly, there's a little concept in statistics called "regression toward the mean".  In simple terms, data tends to fall around the average, with extreme outliers followed by data points that are closer to the average.  How is that relevant to Arctic sea ice extent?  September 2012 was quite a bit below the trend line.  It's an outlier.  Therefore, we'd expect the monthly average for September 2013 to be closer to the average.  Extrapolating from the trend line gives an expected September 2013 extent of 4.15 million km2.  That represents a 16% increase over the average in September 2012 (3.58 million km2) even if the overall trend remains the exact same.  Figuring in the 95% confidence interval for the trend (4.66 million km2) shows that the average September 2013 sea ice could show an increase of 30% even if the trend remains the exact same.  This doesn't even consider the standard deviation of the data around the trend (± 1.32 million square kilometers), which means that 2013 September ice extent could be as high as 53% higher (up to 5.47 million square kilometers) than in 2012, even if the current trend, standard error, and standard deviation are unchanged.



The main message from the Arctic is simple: The ice continues to melt, regardless of what tabloid articles and deniers say.

Monday, September 9, 2013

Solar influence on climate change

The degree to which the sun impacts climate change is hotly debated, mostly in climate change denier circles, with claims that the current warming is due to the sun.  That claim, however, ignores the actual science.  There have been multiple research studies published since 1998 that show that the sun has very little to do with the current global warming episode.  Solanki et al. (2004), Usoskin et al. (2005), and Scafetta and West (2006) used reconstructions of solar activity to show that the sun contributed little to warming since the 1970s.  Lockwood and Fröhlich (2007) showed that trends in solar output and activity since 1988 are opposite what would be required for the sun to cause global warming.  Meehl et al. (2004), Ammann et al. (2007), and Huber and Knutti (2011) used climate models to show that solar output and other natural climate forces could not replicate the observed temperature trend without adding anthropogenic carbon dioxide.  Lean and Rind (2008) and Foster and Rahmstorf (2011) used regression to show that the sun has been a cooling influence since 1979.

Most of the above studies were done using total solar irradiance (commonly denoted as "S"). However, as the Stefan-Boltzmann law shows, it's the amount of solar energy that actually reaches the Earth's surface that counts.  Approximately 30% of incoming solar radiation is reflected directly into space by clouds, aerosols, snow and ice, and other components of Earth's albedo.  That amount fluctuates due to unpredictable events like volcanic eruptions and increases in the amount of coal burned around the planet.  Around 70% actually makes it to the ground where it is absorbed and changed to infrared radiation.  Now a new study examines how the amount of solar energy reaching the ground has changed since AD 1900.  Wang and Dickinson (2013) used daily temperature range (DTR) as a measure of sunlight reaching the ground.  They found good correlations between DTR and direct solar energy measurements, with many areas having correlation coefficients of >0.7.

Figure 1 from Wang and Dickinson (2013).

They used DTR to calculate changes in the amount of sunlight reaching the ground for each station since AD 1900, then computed regional and global averages.  Their Figure 6A shows the impact changes in sunlight have had on global temperatures.

Figure 6A from Wang and Dickinson (2013)

Of particular note is that solar energy reaching the ground peaked between 1930 and 1960 and has declined until the early 1980s, with a slight recovery since.  That pattern corresponds with estimates of sulfur aerosol emissions due to coal burning power plants (Smith et al. 2011), which peaked in the early 1980s and have declined since due to various Clean Air Acts around the world.

Figure 2 from Smith et al. (2011)

However, the pattern in sunlight reaching the ground does not correspond with global temperature, especially after 1970.  If global warming was due to the sun, then we'd expect a close correlation between solar energy at ground level and global average temperature.  Whereas ground-level solar energy has remained low since 1980 with little or no increase, global temperatures have increased quite noticeably.  This mismatch shows once again that changes in the sun have very little to do with the global warming trend we've experienced since the 1970s, corroborating all the other research on the subject that finds little to no solar influence on the current warming trend.