In this work we review and recalibrate existing models, and present a novel comprehensive model for estimation of the downward atmospheric longwave (LW) radiation for clear and cloudy sky conditions. LW radiation is an essential component of thermal balances in the atmosphere, playing also a substantial role in the design and operation of solar power plants. Unlike solar irradiance, LW irradiance is not measured routinely by meteorological or solar irradiance sensor networks. In most cases, it must be calculated indirectly from meteorological variables using simple parametric models. Under clear skies, fifteen parametric models for calculating LW irradiance are compared and recalibrated. All models achieve higher accuracy after grid search recalibration, and we show that many of the previously proposed LW models collapse into only a few different families of models. A recalibrated Brunt-family model is recommended for future use due to its simplicity and high accuracy (rRMSE = 4.37%). To account for the difference in nighttime and daytime clear-sky emissivities, nighttime and daytime Brunt-type models are proposed. Under all sky conditions, the information of clouds is represented by cloud cover fraction (CF) or cloud modification factor (CMF, available only during daytime). Three parametric models proposed in the bibliography are compared and calibrated, and a new model is proposed to account for the alternation of vertical atmosphere profile by clouds. The proposed all-sky model has 3.8-31.8% lower RMSEs than the other three recalibrated models. If GHI irradiance measurements are available, using CMF as a parameter yields 7,5% lower RMSEs than using CF. For different applications that require LW information during daytime and/or nighttime, coefficients of the proposed models are corrected for diurnal and nocturnal use. (C) 2017 Elsevier Ltd. All rights reserved.