Expressions for the Linke, T-Lvis, and Unsworth-Monteith, T-Uvis, turbidity parameters in the visible region of the solar spectrum are derived. They are based on new determinations of the visible transmittances for the various atmospheric constituents obtained by spectrally integrating the wavelength-dependent atmospheric transmittances. Application of the T-Lvis and T-Uvis expressions for Athens is made for the first time; this is done from measurements of direct solar irradiance in the period 1992-1995. A linear interdependence between T-Lvis and T-Uvis is derived, as in the case of their broadband counterparts. The seasonal, monthly and daily variations of these turbidity parameters are also investigated.