The Basic Proof Of Global Warming

Anthropogenic Global Warming is the increasing global air and sea temperatures as a result of increasing CO2 in the atmosphere.  The source of the CO2 is from the emissions of carbon based fuels.
The science of global warming approaches the proof from a number of directions.  The first is the physics of CO2 as demonstrated in the laboratory.  The second is the well defined characteristics and theory of CO2 absorption at IR wavelengths. The third is the observation of CO2 and temperature increasing in proportion. Finally, the CO2 increase can be shown as a function of fossil fuel consumption.  There are also a number of points regarding how a scientific analysis is not performed.
The global mean temperature anomaly is available from multiple source, with monthly and yearly resolution going as far back as 1880.  Data is available from https://www.ncdc.noaa.gov/monitoring-references/faq/anomalies.php  Shown below, the global mean air and sea surface temperature has gone from -0.68 C in 1893 to 0.88 in 2007 for a total rise of 1.56 degrees
 YearlyAnom
TSI data is available at http://lasp.colorado.edu/home/sorce/data/tsi-data/.  The extended data set from 1610 to 2003, has a resolution of one year.  Finer resolution data goes back only as far as the launch of the SOURCE satellite.  The yearly resolution for TSI limits some analysis.
TSIVsYEar
It generally comes from Mauna Loa and dates back to 1959. This is the limiting time period for some analysis.
CO2
The Pacific Decadal Oscillation is also available and an excellent indicator of ocean  heat exchange
PDO
To get a basic idea of how TSI , PDO and CO2 relate to the temp anomaly, the following three scatter plots are presented.
The first is the temperature anomaly vs TSI.  There is no doubt that the Sun influences Earth’s temperature, this is obvious. The question is, by how much.  And the answer is, not much compared to other factors.  This is apparent in the relationship shown.  There is little at best.  Given any particular level of Total Solar Irradiance, global temperatures are all over the place.
This graph is for monthly averages.
AnomVTSIFull
Heat exchange with the ocean is a well understood phenomena.  PDO is one of a number of measures of this exchange.  Compared to the whole of global mean temperature anomaly, PDO doesn’t jump out as being a particularly predominant driver of variations in temperature.  The relationship is shown below.
AnomVPDO
On the other hand, CO2 as a driving factor is obvious in the scatter plot here.
AnomVCO2Full

And with more detail, monthly values

Regression

The combined affect of CO2, TSI and Ocean Heat Exchange can be expressed as

Anom = -122.7+0.00944*CO2+0.0804*PDO+.08793*TSI
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For the more technically inclined, the summary of the regression is given in the table.
Coefficients:
                  Estimate      Std. Error      t value  Pr(>|t|)   
(Intercept)   -1.227e+02  6.779e+01   -1.810    0.07620 . 
CO2             9.434e-03   8.110e-04   11.633    5.81e-16 ***
PDO             8.040e-02   2.545e-02     3.159    0.00266 **
TSI              8.793e-02   4.975e-02     1.767    0.08316 . 

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1393 on 51 degrees of freedom
Multiple R-squared:  0.7378,     Adjusted R-squared:  0.7224
F-statistic: 47.84 on 3 and 51 DF,  p-value: 7.466e-15
=======================
The model against the measured anomaly are as shown. “x” marks the predicted anomaly.  The “o” marks the yearly anomaly.  As relationships go, it is quite good on just CO2, TSI, and PDO alone.
AnomPred
In total, the model accounts for 74% of the total variability.
And here is what just PDO and TSI account for, nothing trending upward
Rplot
This isn’t the most precise analysis that can be done. Bloomberg published a great article showing, graphically, the contribution of all of the known factors.
Never the less, the general result is the same.
Clearly, TSI and Ocean heat exchange are not the cause of global warming.  CO2 is the cause.  And this can be done with every single factor included.  I don’t have a super computer, so you’ll have to go to that Guardian article for an exhaustive treatment.  But the science is clear.
CO2 is the cause of the upward trend of global mean air and sea surface temperature.
And the rest of the story is as much a fact.  The increase in CO2 is caused by the burning of fossil fuels. The climate has and continues to change in terms of melting of Earth’s ice, increased and prolonged weather phenomena,  rising sea level, and on and on….

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