Climate changes all the time since the Earth exists.
We don’t know what a desirable climate is; neither can we determine if and how changes will have a positive or a negative outcome for life on Earth, in particular human life.
But we always are afraid of any change, because of its uncertain outcome.

How to assess climate changes?

Surface temperature has been chosen as parameter describing climatic evolution. Of course other parameters such as, rainfalls, ice cover, soil biological activity are also measurable climatic outcome. But temperature can be considered as the leading climatic parameter. Temperature anomalies averaged over monthly periods are used here. They are expressed as the difference between the current value and the mean over a reference period (1961-1990 in this case) at one place and at a given date.

Click on the images to see them in full.

 

Driving Forces for Climate Change

The most frequently cited driving forces for climate change are:

Solar input variation (Spot)

Solar input is the most important factor that will determine ice ages, although with very long cycles (Milankovich cycles). The medium term impact of solar spot cycles or other related oscillations is unknown.

 

Carbon dioxide emissions and atmospheric concentration (CO2).

It is undisputable that carbon dioxide concentration is increasing and that it is due to the extraction and combustion of fossil fuels from their deposits. Since the beginning of the industrial age it is estimated that 1’300’000’000’000’000 kg or 2.91·10¹³ kmole of CO₂ have been emitted (source: CDIAC), of which 68% remained in the atmosphere to increase the pre-industrial concentration of approx. 280 ppm to today’s concentration of 390 ppm. It is also undisputable that long wave radiations (infrared range) are partially absorbed by this gas in a logarithmic dependence on its concentration in air (Lambert-Beer law).  Temperature increases as consequence of this energy absorption. While the physical link between CO₂ concentration and temperature is a given, the quantitative impact, taking into account complex feedback mechanisms, is not clear

Recent data from the Mauna Loa Observatory:

Aerosols (TRAN)

Finely divided solid or liquid particles remain suspended in air for a long time and have an influence on the portion of sunlight that is reflected away or absorbed by the atmosphere and the ground (albedo). Volcanic eruptions are the largest producers of such aerosols. Sources from human activities are not quantified. Net incoming solar radiation can be used as a proxy for the effectof aerosols on the climate.

The large outliers are coinciding with volcanic eruptions (e.g. El Chichón in 1982 and Mt. Pinatubo in 1991).

Oceanic oscillations

The El Niño- La Niña phenomenon in the Pacific and the Atlantic Multi Decadal Oscillations are known to have a strong influence on medium term (a few years) weather changes. These oscillations are integral parts of the on-going climate; they are no external input to it. But to dissociate the influence of primary factors such as solar input and greenhouse gases it is necessary to examine the correlation. Other ocean currents and oscillations may also have similar effect.

El Niño- La Niña (MEI):

 

Atlantic oscillations (AMO):

 

Correlation

An unknown function relating temperature anomalies to the other determining factors is sought:

T_A = f(CO₂, TRAN, MEI, AMO, Spot)

With the help of the new software “formulize” available for free on www.nutonian.com the search for an adequate formula is now possible, even on a simple home computer. Also, cloud computing can be switched on to enhance the calculation performance (a commercial service).

For the period 1958 to 2010 monthly series of publicly available data were taken from NOAA ESRL (http://www.cdc.noaa.gov/PublicData/) and from the Met Office Hadley centre (http://www.metoffice.gov.uk/hadobs/index.html). This is the only time period for which all the parameters are simultaneously available with very few exceptions for the solar transmission.

No pre-formatting, smoothing or moving average calculations has been made. When one piece of data is missing the monthly observation is ignored. The software takes care of all these impediments.

Correlation A.

Following result was obtained after approx. 3 hours running on 16 cores on the cloud:

TA = 0.2440446458*AMO + 0.1134248525*delay(AMO, 5) + 0.06428597063*delay(MEI, 2) + 0.006701866248*delay(CO2, 9) + delay(TRAN, 2)*delay(TRAN, 10) – 3.046514859

Statistical parameters:

R² Goodness of Fit             0.95780349

Correlation Coefficient    0.91538746

Maximum Error                   0.30868463

This is a fair correlation, as can be better seen in graphical form:

 

Interpretation

• All parameters but solar spots have found a place in the correlation. This does not mean that solar activity does not play a role, but if so it should be quite a minor one.
• The sensitivity to CO₂ is 0.0067. This means that for each ppm a temperature variation of 0.0067 degrees can be expected. For the time period considered the concentration was raised from 316 to 390 ppm. According to the correlation equation this should result in a temperature increase of 0.0067*(390-316) = 0.50 K, a 0.1 K increase per decade.
  Or, extrapolating since the beginning of the industrial era, the CO₂ contribution may have been 0.0067*(390-288) = 0.68 K.
  This is higher than what a zero order static atmospheric model would indicate, see my paper on Two-Layers-Climate-Model.
• The relatively stable period between 1998 and 2010 is well represented by the equation. This means that, to an increasing trend related to CO₂, decreasing mechanisms were in place.
• Instead of smoothing or calculating running averages, the equation is taking time lags into account: 9 months for CO₂, 2 and 10 months for volcanic eruptions, and 5 and 2 months respectively for AMO and MEI.
• Aside of the time lags the correlation equation is amazingly very simple.

 

Correlation B:

Depending on the search conditions different formulas can be obtained. Here is another result obtained in 5 hours with an Intel Mobile Core 2 Duo T5600 mobile computer at 1833 MHz.

TA = 0.09362477205*delay(MEI, 2) + 0.2932284049*cos(AMO + 0.03104125154*CO2
+ delay(AMO, 6) – 0.06208250307*delay(MEI, 2)) + delay(TRAN, 11) – 0.1405903365
– cos(delay(TRAN, 1))

Statistical parameters:

R² Goodness of Fit             0.96413895

Correlation Coefficient    0.92205205

Maximum Error                   0.30733298

 Interpretation of Correlation B

• This correlation has a slightly better fit than the first one. However the interpretation of its formula is less intuitive.
• Here too solar spots were contemplated over the iterative computation, but at the end no correlation was found for them.
• The major factors are El Niño- La Niña (MEI) and volcanic activities (TRAN). CO₂ and AMO are embedded in a cosine function, thus just providing an oscillating impact of ± 0.293 K over a very long cycle.
• This means that it is possible to fairly represent the current temperature evolution without a continuously increasing impact of the CO₂ concentration!

Discussion

• A fitting correlation equation is not the justification for cause-effect relationship. However, the link between CO₂ concentration and temperature is plausible for physical reasons and is confirmed in the first correlation; however, the second one arrives at an even slightly better result without needing the CO₂ ramping.
• With correlation equations no prediction can be made for the future. Attempts were made to extrapolate the correlation equation for another 50 years. To do this, scenarios must be assumed, for example by using the same “formulize” software, to evaluate a time dependency for each influencing parameter, and to extrapolate them over the next 50 years. With Correlation A or Correlation B two very distinct projections are obtained:

  and 

In case A the temperature is increasing steadily and takes one more degree over the next 50 years. In the other case a kind of long term oscillation takes place.

• At this point no over-interpretation shall be made!
  The time regressions and projections into the future of the five parameters is of very bad quality. The data used to establish a model is only over a period of 50 years, not enough for a serious validation. Therefore, the extrapolation may be valid for the next few years, not more.
• A better simulation job will require costly multidimensional dynamic models. This is why zillions of dollars are poured into scientific institutions.
  But the constraint of validation will remain: when reliable measurement data is available for a quite short period of time, any scenario extrapolation will be limited to a fraction of this period. Model experts must remain modest and shall not overstate their ability to fine tune their models and the initiation parameters.
• For Carbon Dioxide it shall be remembered that according to the Lambert Beer logarithmic law, the IR absorption by CO₂ will tend to saturation as the concentration will increase. Also, as feedback mechanisms are globally negative, stabilizing effects will also develop. Again, see my paper on Two-Layers-Climate-Model.
• The whole question of water vapor and cloud formation cannot be addressed in this simple exercise, but we know how important these phenomena are, in particular as feedback mechanism and for biomass production.
• Data quality is important. There are still on-going discussions on the selection of representative stations over the globe, on averaging temperature measurements (a physical nonsense[1], but a useful tool for temperature anomalies), and on further alleged data massaging. It is of the utmost importance that raw, unfiltered data is made publicly available. With analysis tools like the formulize software and further modeling ideas better insights can be gained, also outside of the cozy and warming climate research community.
• Basically we don’t know in what direction the climate will evolve. It may remain so despite of all research done on this topic. The known and unknown unknowns…
• In a Pascalian bet, one could argue that curbing CO₂ emissions is of prime importance: if these efforts have no effect on the climate they remain benign, and if they actually have an impact, then we will have made the right thing. But we know for sure that a heavy burden to reduce CO₂ emissions will be on the shoulder of populations who have much more important development priorities and cannot afford being restrained by such idealistic views.
  And by the way: Pascal had to wait upon his death to know if he won his bet, and could not communicate the result to us!
• I leave it to people who might earn a salary to perform finer experimentations with better datasets and more computing power.
• As ever: more research is needed (which means: please increase the budget)!

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