The total atmospheric attenuation of direct irradiance is often expressed as the product of independent broad band transmittances pertaining to the different depleting materials in the atmosphere. In theory, it is clear however that the broad band transmittances of the two most important attenuating factors, aerosols and water vapour, cannot be considered independent of each other. This is most relevant when trying to isolate the effect of atmospheric aerosols from the measurement of broad band direct irradiance. These questions are addressed in an analytical approach. Several broad band direct transmittance equations and corresponding turbidity parameters are discussed with respect to the analytical results. Simulations made with the SMARTS2 spectral radiative transfer code are used to illustrate the broad band effects.