Earlier quoted context omitted.
Setting aside the names of the authors, this is a very bad paper. They take temperature data sets, "adjust" [1] them by attempting to remove the biggest recent factors (volcanism, solar and el nino cycles) affecting temperatures , then do a piece-wise regression analysis to look at trends in 10-year chunks. This is just bad methodology, akin to what a junior graduate student with a failing thesis might do to find sig…
Your summary of the article is wrong. The authors model temperature using time series over solar irradiance, volcanic activity, and southern oscillation. They calibrate that model using time series over global surface temperatures. This allows them to isolate and remove each of the three listed confounding factors. The resulting time series fits a super-linear curve -> accelerating global warming.
No, it isn’t. You’re just rephrasing what I said with more words: they attempted to adjust for three of the biggest factors that affect temperature, then did a piecewise regression to estimate a 10-year window.
You can’t do it in a statistically valid way. Full stop. The authors admit this, but want you to ignore it.