Relationship between regional and monthly average (only summer months) changes in aerosol optical depth and changes in surface clear-sky shortwave radiation during the 2001–2010 period for (a) East China, (b) Europe, and (c) East U.S. Observed values are shown in grey, CMAQ calculations with direct aerosol radiative feedbacks in red, and CMAQ calculations without aerosol radiative feedbacks in blue. Also, indicated are the slope and correlation coefficient (R) for the individual linear regressions. For each data set (model or observed) there are 33 values, corresponding to each summer month over the 11-year (2001–2010) period. The anomaly is estimated by subtracting the corresponding 11-year average for that month.