Basic Analysis of Global Warming Factors

There are a handful of factors that influence the global mean air and sea surface temperature (GMT, Anom). These include; ocean heat exchanges which can be measured by the Pacific Decadal Oscillation (PDO, the Atlantic Multidecadal Oscillation (AMO), as well as El Nino and La Nina; Total Solar Irradiance (TSI); CO2 and other green house gas (GHG) concentrations; aerosols live volcanic ash; Ozone; Land use such as agriculture; Albedo, the reflectivity of the Earth surface; and other climate forcings.
To get a basic idea of how TSI , PDO and CO2 relate to the temp anomaly, the following three scatter plots relating these to temperature 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 bit of a relationship, but not much.  Given any particular level of Total Solar Irradiance, global temperatures are all over the place.
This graph is for monthly averages.
AnomVTSIFull
A measure of heat exchange between the oceans and global mean air and sea surface temperature can be obtained by equating the temperature anomaly to the Pacific Decadal Oscillation.  When the surface of the ocean is warmer that the air, heat flows from the ocean to the air.  When the PDO is in a cold phase, heat flows from the air to the ocean.  This is simple thermodynamics.  The graph below is a scatter plot of the anomaly as a function of PDO.
AnomVPDO
This is the relationship of the yearly temperature anomaly as a function of atmospheric CO2.  It is expressed as a scatter plot which equates the global mean air and sea surface temperature anomaly to the level of atmospheric CO2.
AnomVCO2Full

The relationship of the monthly temperature anomaly as a function of atmospheric CO2 can be found in the data since 1958.  It is expressed as a scatter plot which equates the global mean air and sea surface temperature anomaly to the level of atmospheric CO2.

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
This quantitative relationship is based on the empirical measures of CO2, PDO, TSI, and GMT.
This mathematical relationship vs the precise measured anomaly are as shown below. “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.  It accounts for 74% of the total variability with three factors.
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
Clearly, TSI and Ocean heat exchange are not the cause of global warming.  This is absolutely provable.  A complete lack of correlation between the temperature anomaly and these two is proof.  Causality required correlation.   This same basic analysis can be done across all of the factors.
Bloomberg published a great article showing, graphically, the contribution of all of the factors.
The science, the empirical quantitative facts, is clear.
CO2 is the cause of the upward trend of global mean air and sea surface temperature.
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