While numerical weather prediction models (NWPs) and atmospheric general circulation models (AGCMs) still treat the surface as blackbody in their longwave radiation scheme, recent studies suggest the need of taking realistic surface spectral emissivity into account, especially for the simulated weather and climate in the polar regions. There is little observation or laboratory measurement available for the surface emissivity in the far IR (<650cm^-1). Based on first-principle calculation, we compute the spectral emissivity over the entire longwave spectrum for 11 different surface types. MODIS-retrieved mid-IR surface emissivity at 0.05º by 0.05º spatial resolution is then regressed with the calculated spectral emissivity to determine the surface type for each grid. The derived spectral emissivity data are then spatially averaged onto 0.5º by 0.5º grid boxes and spectrally integrated to the bandwidths used in the RRTMG_LW, a radiation scheme widely used in a variety of AGCM and NWP models. Such band-by-band surface emissivity data are then compared with retrieved surface spectral emissivity from IASI (Infrared Atmospheric Sounding Interferometer) measurement. The comparison shows favorable agreements between two data sets in all the bands covered by the IASI measurements. We further use such data set in conjunction with ECMWF ERA-interim reanalysis to do an off-lien evaluation of the change in OLR and surface upward longwave flux. When the surface spectral emissivity dataset is used instead of blackbody assumption for the entire global surface, the globally averaged difference is ~-1.4 Wm^-2 for all-sky OLR and ~-0.9 Wm^-2 in clear-sky OLR, and the global mean difference of upward longwave flux at surface is ~-21 Wm^-2. Current state-of-the-art GCMs such as NCAR Community Earth System Model (CESM) makes use of an effective blackbody temperature approach to ensure the upward longwave flux at surface being the same as what the Community Land Model calculates. Comparing to such approach, using the actual spectral emissivity data set leads to a reduction of 0.6 Wm^-2 in globally averaged clear-sky OLR and 0.3 Wm^-2 in globally averaged all-sky OLR. The regions with largest differences are desert regions and high-latitude oceans and plateaus.