From space observation with passive narrowband instruments such as MODIS, it is hard to retrieve the microphysical and optical properties of sub-visible cirrus with optical depth around 0.1 or less. As a result, longwave radiation budget computed from narrowband derived cloud products systematically underestimates the warming effect of these thin cirrus clouds. How accurately can we compute longwave thin cirrus cloud radiative forcing from retrieved cloud properties? This study address this question by comparing theoretical calculations with observations with measurements made during CRYSTAL-FACE. The CERES programmable-azimuth-plane-scan (PAPS) during CRYSTAL-FACE provides multi-angle broadband longwave and window measurements. Such measurements are compared with model calculations using cloud optical property product of CERES Single Scanner Footprint TOA/Surface Fluxes and Clouds (SSF), derived from MODIS. Theoretically, a cloud model for simulating the upwelling cirrus cloud radiance and brightness temperature in the entire infrared channels is constructed. In the model, thirty in-situ size distributions are used to calculate the mean scattering properties of ice crystals in cirrus clouds. The clear sky optical thickness and upwelling LW (longwave) and WN (window) radiance are simulated using a line-by-line radiative transfer model and the discrete-ordinate-method radiative transfer model, respectively. The broadband radiances are integrated over the window channels and entire longwave range. By study the limb-darkening differences between model calculations and CERES broadband measurements, we can estimate the errors of computed longwave energy budget. This study contributes to a better understanding of thin cirrus on LW radiative forcing.