Only the first few annotated
-1. 30-year climate and the 21-year band.
0. The need to include the Sun in estimating climate sensitivity.
During 1000-1850, the greater part of a millennium, atmospheric CO2
remained within 5 ppm of 280 ppm according to analyses performed in
Adelaide, Australia of ice cores drilled at the
Law Dome site in Antarctica. After 1850 CO2 rose to above 285
ppm and has not returned since. Instead the quantity CO2 −
280 has, to within 5 ppm, been rising at 2% a year. This is still true
today: in December 2016 it had reached 124.42 ppm and over the following
12 months it rose a further 1.9% to 126.82 ppm. This behavior is
illustrated in the following figure.
A common argument against CO2 as a major contributor to global
warming is that climate, understood as the HadCRUT4 record of combined
land and sea temperature since 1850, has not increase steadily the
way CO2 does, but fluctuates seemingly at random. These fluctuations
have no obvious human cause and are therefore likely to be of natural
Prior to about 1980 the expected impact of CO2 has been small
compared to these presumed natural fluctuations. We have found
empirically that these fluctuations can be largely removed from
HadCRUT by filtering with a 63-year moving average or boxcar filter,
yielding the red curve in the following figure.
The light blue curve is 1.7*log2(CO2) normalized to average zero over
the 30 years 1956-
1. The hiatus in 2012 and now.
The following graph shows monthly HadCRUT4 since 1990, in blue up to
2012 and in purple to the end of 2017. Based on the data available
at the time, it forecasts future climate in respectively 2012 (thin)
and now (thick) based on two trend models, respectively linear (red)
and parabolic (green).
In 2012 it was clear that a linear trend model would predict continued
warming while a parabolic (i.e. quadratic) model would predict imminent
Five years later the linear trend model's forecast had barely changed. The
parabolic model on the other hand had so completely changed its forecast
as to end up on the other side of the linear trend model!
One conclusion might be that linear models predict more robustly than
nonlinear. Given this, another conclusion might be that climate deniers
attach little importance to robustness in choosing between models.
2. A correlation between solar cycles and 21-year climate
The following graph plots sunspot numbers (blue) and global climate
(red) for the period 1865-2000. The latter is filtered with a 21-year
bandpass filter so as to reject periods significantly higher or lower
than 21 years. (This rejection is not sufficient however to remove an evident
63-year cycle well correlated with the inverse of Length of Day, LOD,
whose manifestation in climate has a significantly larger amplitude
than this 21-year cycle, more on this later.)
Bandpassing is accomplished by convolution of HadCRUT4 with a
Ricker or "Mexican hat" convolution kernel tuned to pick out the
21-year band. Each 10-11 year sunspot cycle is numbered according
to a convention established by Rudolf Wolf in 1848. Following solar
max of the even-numbered cycles the heliomagnetic field (HMF) of the
solar wind is polarized parallel with Earth's magnetic field, and
anti-parallel after solar max of odd-numbered cycles. Earth cools
during an anti-parallel HMF and warms back up after a parallel HMF.
Another way to see the above-mentioned 21-year oscillation in HadCRUT4
fit trend lines to every decade or so of HadCRUT4, revealing
essentially the same cycle.
As mentioned before this can explain the so-called ``hiatus'' during
the first decade of this century, which was one of these downturns,
along with the subsequent very steep rise during this decade, which is
currently halfway through one of the upturns.
To date there is no agreed-on cause for this apparently strong
correlation. What we do know is that Earth's magnetic field normally
shields Earth from cosmic rays but this shielding is weakened when
it couples to the anti-parallel HMF. One possible explanation
of the 21-year climate oscillation is that water vapor molecules
condense on aerosols ionized by cosmic rays, creating a nucleus for
further condensation, similarly to how silver iodide seeds clouds.
The resulting increasing cloud cover then cools the Earth. To date
however no 21-year cycle in cloud cover has been detected. Hence
either that effect is too small to be observed directly, or the
explanation lies elsewhere, for example as an expression of the
Gnevyshev-Ohl rule that odd-numbered cycles have more sunspots than
The most recent downturn in climate began in 2000 at solar max of cycle
23, and ended abruptly at solar max of cycle 24 in 2012 when HadCRUT4 began
a dizzying 5-year rise of 0.37 degrees. Of the various suggested explanations
of the so-called climate hiatus during the first decade of the century, this
one seems particularly plausible.
This correlation can also be seen in Central England Temperature for
1659-2010, extended yet further back to 1550 by Dr. Tim Brown based on
southwest winds in Devon as a proxy. Interestingly the 21-year oscillation
in CET persists even during the Maunder Minimum, making it likely that
the heliomagnetosphere is still active even when sunspot activity
is negligible, as well as making the Gnevyshev-Ohl rule a less plausible
explanation. Solar cycle numbers earlier than -5 are inferred from the
oscillation in CET, whose period during the Maunder Minimum
would appear to be closer to 18 years than the subsequent 21 years.
3. Global Warming since 1850, in three stages.
This graph plots three stages of global surface temperature (both
land and sea), as recorded in HadCRUT4, a dataset assembled from
many hundreds of millions of measurements made at the surface. The first stage
is the 108 years from 1850 to 1958, which trended up at 0.27 degrees
Celsius per century. The next stage is the half century from 1958 to 2008,
which trended up at 1.26 degrees per century. The last stage is the
last ten years, from 2008 to (almost) 2018, which trended up at 3.86
degrees per century.
Detailed numbers for these plots and trends can be seen at
WoodForTrees.org. Click on Raw Data (below the plot) for the numbers.
4. Three natural influences on multidecadal climate
Multidecadal climate refers to climate events that last longer than a
decade. In the graph below, all faster events in the four plots have
been removed with an 11-year moving-average filter, taking out the
11-year sunspot cycle, 7-year El Nino/La Nina events, coolings of at
most 2-3 years due to recent volcanic aerosols, etc.
Climate itself is taken to be HadCRUT4, the blue curve. The three
natural influences plotted below it are as follows.
The human influence, CO2, is not shown. A 63-year filter removes the
faster green (LOD) and purple (HMF) influences, leaving only CO2 and
TSI, which as shown in the previous section accounted remarkably well
for 63-year but less so when TSI was ignored.
5. The CO2 "hockey stick" since 1000 CE
The dark blue line in the plot below gives observed atmospheric CO2 as
measured in Antarctic ice cores for pre-1958 atmosphere and more
directly at the Mauna Loa CO2 observatory since 1958. David
Hofmann, late of NOAA Boulder, has proposed an exponential model of
atmospheric CO2 in excess of the preindustrial level of 280 ppm, which
we have expressed here as a growth rate of 2% a year for that excess,
starting with an excess of 1 ppm (i.e. a total of 281 ppm) in 1772.
This model is suprisingly accurate, namely to within ±5 ppm throughout
the past milliennium. This ±5 ppm band only looks narrower on the right
because it is so steep; however it makes clear that the date 1772 for
when the excess CO2 above 280 was 1 ppm can't be changed much without
spoiling the fit for this century. The date 2014 with a multiplier of
1.02^(2014 - 1772) = 120 (i.e. the formula 280 + 120*1.02^(y - 2014)) would
be an equivalent model because CO2 was at 280 + 120 = 400 ppm in 2014.
6. Residual surface temperature compared with human radiative forcing
Since 1800 global population has increased seven-fold, compounded by
an even greater rise in per capita energy consumption.
There is an evident correlation between the seven-fold rise in each of
global population and technology over the past two centuries and the
atmospheric CO2 "hockey stick" plotted above, suggesting that humans are the
cause of the latter, which in turn could be the cause of the one-degree rise
in global climate over that period.
This correlation suggests However the upward trend in Global climate over
that period is only very vaguely correlated with either, raising the
question of whether
However the fluctuations in climate during that period
interesting whether there is a
has an obvious
Atmospheric CO2 prior to 1958 has been inferred from ice cores taken
by Australian researchers from the Law Dome site in Antarctica, and
Residual surface temperature, the blue curve in the graph below, is HadCRUT4
less the above-mentioned natural influences and filtered with an
11-year moving average filter.
The graph plots RST against Human Radiative Forcing defined as follows.
One benefit of correlating temperature with emitted CO2 rather than
measured atmospheric CO2 is that it makes natural sources of recently
rising CO2 irrelevant to the question of whether humans are responsible
for rising temperature. The above graph is strong evidence that they
7. Atmospheric CO2 as a function of accumulated emissions since 1900.
8. The need to include TSI when forecasting with 63-year climate
63-year climate is HadCRUT4 smoothed with a 63-year moving average
filter. As the three plots in the following figure show, 63-year climate
is not as well modeled by either Radiative Forcing (log(CO2)) or Absorbed
Solar Insolation (ASI = TSI*0.7) alone as by both together.
The three thick gray curves are copies of 63-year HadCRUT4 as smoothed
with a 63-year moving-average filter. The three fits are as follows.
What this graph forecasts with considerable confidence is not
climate in the year 2100 itself, but rather average climate,
averaged over the 63 year window at 2100, i.e. the average of the 63
years 2069-2131. Climate is always changing, and the best we can say
with any confidence about this graph's forecast is that about half
of those 63 years will likely be hotter than forecast and the other
half colder. While we can't say which of those years will be hotter,
we can be pretty sure that there will be some three decades
of hotter-than-forecast climate during the period 2069-2131.
This amounts to an uncertainty principle for modern climate. If we
ask for temperature over a precisely defined short period in time we should
not expect much accuracy in temperature. Conversely if we ask for much
accuracy in temperature we should not expect to be able to achieve it for
too precise a target in time.
9. Miscellaneous graphs, various sources, little or no annotation
Troposphere structure as a function of latitude, and induced tradewinds.