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Current solar forecast verification processes place much attention on performance comparison of a group of competing methods. However, forecast verification ought to further answer how the best method within the group performs relative to the best-possible performance which one can attain under that forecasting situation, which makes the quantification of predictability and forecast skill immediately relevant. Unfortunately, the literature on the quantification of relative performance of solar irradiance has hitherto been lacking, and very few studies have focused on the spatial distributions of predictability and forecast skill of solar irradiance. The predictability and forecast skill of an atmospheric process depend on two concepts: (1) the growth of initial error in unresolved scale of motion, and (2) the forecast performance of the standard of reference. Based upon this formalism, predictability and forecast skill of solar irradiance in the United States are quantified and mapped. Through this study, a couple of common misconceptions in regard to irradiance predictability are refuted, and the original formulation of skill score revived. • A formal discussion on predictability of solar irradiance is presented. • A rigorous way of computing the forecast skill score is emphasized. • Predictability of solar irradiance in the United States is estimated. • Bounds of mean square error of ECMWF irradiance forecasts in the United States are derived. [ABSTRACT FROM AUTHOR]