Only the first few annotated

0. The need to include the Sun in estimating climate sensitivity.

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 origin.

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 65-year moving average or boxcar filter, yielding the thin blue curve in the following figure.

The thick light green curve is 1.7*log2(CO2) indexed after filtering to average zero over the 30 years 1956-1985, that is, an anomaly. The thick light red curve is that plus the Sun, defined as 0.95*TSI*(1 - 0.3)/4. The thin dark blue curve is HadCRUT4. All three curves have been smoothed to a running mean of 65 years and then indexed to zero out their mean over 1956-1985.

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 cooling.

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 is to 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 even-numbered ones.

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 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.
  • Total solar insolation TSI (red), significant only for its slow rise during 1900-1950. While small, any slow influences that one might attribute to humans must also be small during that period because there were only a third as many humans then, and moreover each human was consuming much less energy. Hence any analysis of human influences over a period starting earlier than 1950 will therefore be more accurate when it takes TSI into account.
  • A 63-year cycle often called the Atlantic Multidecadal Oscillation that a number of researchers have linked to millisecond fluctuations in the length of day LOD, whose tiny effect may be amplified considerably by magmatic volatiles as argued here.
  • The 21-year cycle pointed out in the first section (purple).
  • 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.
    The top right corner of this graph is hard to make out. By subtracting 280 from CO2 and plotting the log base 2 of the result, the exponential rise is straightened out to an almost perfectly straight line. The trend this century is 34.25 years per doubling, corresponding to a compound annual growth rate (CAGR) of 2.0%.

    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 thereafter 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.
  • ECO2 is emitted CO2 accumulated since 1900, expressed in units of ppm as per the Carbon Dioxide Information Analysis Center, CDIAC. The carbon in CO2 has mass 12/28.97 of air and the atmosphere has mass 5150 teratonnes, whence 1 ppm of atmosphere corresponds to 12/28.97*5150 = 2133 megatonnes of carbon (2.133 GtC).
  • ECO2/280 changes the ppm units to multiples of preindustrial CO2. In these units preindustrial CO2 is 1, whence preindustrial radiative forcing equals log(1) which is zero.
  • The surface absorbs 55% of our emitted CO2, whence 0.45*ECO2/280 is the amount remaining in the atmosphere. Since surface absorption is reduced by deforestation and other land use changes, further such changes may increase the 0.45 fraction.
  • 0.45*ECO2/280 plus 1 (preindustrial CO2) is expected total atmospheric CO2 based on emitted CO2 since 1860.
  • log base 2 of that is radiative forcing in the case Climate Sensitivity CS equals 1. The graph shows that CS is 1.74. Note that this is neither Equilibrium Climate Sensitivity nor Transient Climate Response but rather the apparent instantaneous effect of the prevailing rate of rise of CO2, sometimes called Observed Climate Sensitivity.
  • 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 are.

    7. Atmospheric CO2 as a function of accumulated emissions since 1900.

    8. The need to include TSI when forecasting with 65-year climate

    65-year climate is HadCRUT4 smoothed with a 65-year moving average filter. As the three plots in the following figure show, 65-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 65-year HadCRUT4 as smoothed with a 65-year moving-average filter. The three fits are as follows.
  • Radiative forcing RF (log2(CO2), blue). RF fits to within a standard deviation of 0.015 degrees (15 mK). Although this is a good fit, it is clear that RF is curving up more than climate, whence its forecast of a further rise of 2.66 degrees by 2100 is likely to be too high.
  • Absorbed solar irradiance (ASI = 0.7*TSI, red). At a standard deviation of 35 mK this is not only a bad fit but a hopeless forecaster of future climate.
  • RF and ASI together (green). This fit is accomplished using multiple linear regression. The fit improves dramatically to 5 mK, confirmed by visual inspection: the model is less curved than the pure RF model, in fact it has essentially the same curvature as the smoothed climate it is intended to model. This model forecasts a more modest rise of only 1.90 degrees, which is more believable than 2.66 degrees given the respective fits.
  • What this graph forecasts with considerable confidence is not climate in the year 2100 itself, but rather average climate, averaged over the 65 year window at 2100, i.e. the average of the 65 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 65 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. Compound Annual Growth Rate (CAGR) of Representative Concentration Pathway 8.5

    10. Miscellaneous graphs, various sources, little or no annotation

    Troposphere structure as a function of latitude, and induced tradewinds.