The significance is analyzed for the possible influence of variations of solar constant upon the energetic balance of the atmosphere. (realclimate.org)
The 4 W / m2 solar constant change you quote (which is at the high end), is around 0.7 W / m2 in global annual mean radiaitve forcing, compared to 2.4 W / m2 from CO2 + CH4 + N2O — still a small number. (realclimate.org)
Again, could you be kind enough to provide me with 1 or 2 of your best PEER - REVIEWED references on solar constant variation and terrestial climate change? (dotearth.blogs.nytimes.com)