I have revised my views slightly since I began this thread.
A decrease in Cloud Cover is responsible for most of the warming over the last 30 years and last century, and this decrease in Cloud Cover is directly tied to solar activity variations through solar wind variations inflicting changes on GCRs.
There is an overwhelming amount of evidence to support this viewpoint.
Let's start with nine peer reviewed studies that document that the sun was a likely driver of the 20th Century Warming.Palle Bago and Butler 2001
Palle Bago and Butler 2001, using many formulas they derived in their earlier, 2000 paper, calculated that the solar effects, directly and indirectly, caused 0.5 Degrees C of the 0.55 Degree C warming. This means that they found that 91% of the warming over the past 100 years can be explained by solar variability, directly and indirectly alone. They mention that there is a "possibility" that solar attribution could be less during the most recent decades, but they are not definite with this statement. They simply state that the solar contribution an unknown over the last and most recent decades. This probably has to do with the ACRIM and PMOD TSI Composites and the controversy surrounding these datasets which Scafetta 2009 documents.Georgieva et. al 2005
Georgieva et. al 2005 used the Geomagnetic AA Index to quantify the solar impact on Climate Change, rather than the sunspot number, because using the sunspot number to quantify the solar contribution to climate change, as many studies do, leads to an underestimation of the Solar impact on Climate Change.
The above figure from Georgieva et. al shows the Geomagentic AA Index with the broken line, and the Global Temperature Anomalies with the solid line. They find that the correlation coefficient between the AA Index and Global Temperatures is 0.85, meaning that the sun can explain 85% of the variances in temperatures over the last ~150 years. Cliver et. al 1998
Cliver et. al 1998 also used the Geomagnetic AA Index to estimate the solar contribution to climate change.
Above figure: From Cliver et. al 1998. The AA Index is the dotted line, and the solid line are the temperature anomalies.
They found that 50-100% of the warming could be due to the sun, but it should be noted that this analysis does not include other factors like volcanic activity and anthropogenic greenhouse gas emissions when estimating the total contribution. Nonetheless, this study also shows that other studies which do include these factors are only at the lower end of the 50-100% range for the solar contribution over the last 100-150 years. It also supports other studies with a larger solar contribution to climate change because of the remarkable correlation with the AA Index and temperatures.Solheim et. al 2012
Solheim et. al 2012 found that the solar signal is reinforced by the Atlantic Ocean, and this reinforcing signal in the Atlantic Ocean is calculated to be from 63-72% of the variances in temperatures over the entire timeframe. They get a lower solar contribution to land based stations, but the reinforced signal is probably what would lead to a more accurate solar contribution, since most of the world is covered by oceans, and likely, reinforcing the solar signals. Link et. al 2011
The box that represents the % solar contribution from Link et. al 2011 actually represents the probability whether the entire trend over the last 100-150 years is natural. The authors calculate that the probability of the warming being caused by solar activity over this entire timeframe is 40-90%. It should be noted that these probabilities go up significantly over shorter timeframes like 1900-1950 and 1960-2005.Scafetta and West 2008
Scafetta and West 2008 adresses the uncertainty raised in the first paper. If a TSI curve that shows an upward trend from Solar Cycle 21 to 22 is used from the ACRIM TSI composite rather than the flat PMOD TSI composite, then a higher contribution from the sun would be needed. The authors find that up to 69% of the variances in temperatures can be explained by solar activity.
The image above from Scafetta and West 2008 shows the divergence between the PMOD and ACRIM TSI datasets, which makes attribution to past climate change even harder. The red curve is the ACRIM TSI composite, the blue curve is the PMOD TSI Composite, and the black curve and green line are the Global Temperature anomalies. Scafetta and West 2007
The ACRIM verses PMOD controversy continues in this paper. 50% or more of temperatures can be attributed to the solar forcing, depending if the ACRIM TSI composite is used or not. This further adds on to resolving the uncertainty between the PMOD and ACRIM datasets during the ACRIM Gap.
The graph above from Scafetta and West 2007 shows the excellent correlation between solar activity and temperatures. It also shows that a large portion of the warming can be attributed to solar activity. Over the last 30 years, a significant portion of the warming can be attributed to solar activity if the ACRIM TSI composite is used. Ogurtsov 2007
Ogurstov 2007 estimated that the solar contribution directly and indirectly caused about 0.25-0.35 degrees C of the warming that took place during the 20th Century. Using the Skeptical Science trend calculator gives an approxiate warming of 0.6 Degrees C during the 20th Century. This means that 41-59% of the trend upward can be attributed to solar activity over the past 100 years.Blanter et. al 2008
Blanter et. al 2008 found that temperatures correlated remarkably well for all periods between the solar activity indicies and the observed temperatures for stations in Europe and the United States during the 20th Century. They used a finding from a previous study that the temperatures at weather stations correlated remarkably well if they were up to a 1000 km distance from each other. They also state in the abstract that these changes can "possibly" be extended onto a Global scale. Being that they found that solar activity can account for all temperature changes over the 20th Century, I reduced the range slightly from 100% to somwhere in the 90-100% range to account for the anthropogenic forcings.
I will be posting more papers later on this thread that support a natural solar and oceanic cause for recent warming, and not anthropogenic.