This work is focused on the characterization and parameterisation of the downward atmospheric irradiance (LW) for clear and cloudy skies. LW is a component of the surface radiation budget that is present throughout the day. Unlike solar irradiance, LW is not measured routinely in extended networks, so it must be estimated indirectly. We evaluated five parameterisations for estimating LW under clear skies. After some consideration regarding the local fitting of the parameterisations, we analysed their different behaviour during day and night and propose a correction model for this effect. We use measurements registered at Tabernas (Spain) from 2001 to 2003. For the locally adjusted parameterisations the root mean square deviation (RMSD) and the mean bias deviation (MBD) are smaller than 5.7 and 0.6%, respectively. The combination of the more complex correction parameterisation of the day/night differences with the locally adjusted formula of Brutsaert and the original formula of Berdalh and Martin leads to estimations with RMSD below 3.1%. Using data registered at Palaiseau (France) the proposed parameterisations yields MBD close to 0% and RMSD below 3.2%. Cloudy conditions were analysed and two different approaches were used to estimate the cloud effect. Both approaches determine all sky LW using a clear-sky formulae and a cloud modification factor, computed with the solar global irradiance on a horizontal surface. The results show that LW can be estimated under all-sky conditions during the daytime with a RMSD of 5.8 and 6.2%, and a MBD of 1.6 and − 2.2% for the Crawford and Duchon scheme and the parameterisation in kt, respectively, at Tabernas. The application of the same parameterisations to Palaiseau yields RMSD of 6.7 and 7.7%, and MBD of − 2.5 and 0.7%. Copyright © 2011 Royal Meteorological Society