Monthly- averaged climate and turbidity data from five sites in North America and Europe are employed to evaluate the relationships among month ly-averaged observed beam irradiation ((H) over bar (b) and (H) over bar (bn)), clear-sky beam irradiation ((H) over bar (bc) and (H) over bar (bnc)), -sunshine duration ((s) over bar), and daylength ((S) over tilde), Linear regression model fits to (H) over bar (b)/(H) over bar (bc) = a + b((s) over bar/(S) over bar) and (H) over bar (bn)/(H) over bar bnc = a + b((s) over bar/(S) over bar) indicate that the intercept (a) and slope (b) of the fits are close to 0.0 and 1.0, respectively. Thus, in locations where the absence of empirical data prevents finding the 'true' values of these coefficients. it is proposed that a = 0 and b =1 be used to estimate the clear-sky beam irradiation from observed irradiation and sunshine duration. The analysis has utility in turbidity studies and solar applications, such as the performance prediction of solar energy systems, where the average daily clear-sky beam irradiation needs to be known.