Recent studies have shown non-negligible impact of the representation of surface spectral emissivity on the polar radiation budget and on the simulated climate changes. While the surface spectral emissivity can be easily incorporated into the RRTMG_LW, one of the most widely used longwave radiation schemes in current weather and climate models, the errors due to the way of representing surface emissivity in the RRTMG_LW have not been quantified. Using a line-by-line radiative transfer model (LBLRTM) as benchmark, we quantify such errors in the RRTMG_LW. The benchmark calculation is done using the LBLRTM and a 3-angle Gaussian quadrature formula to compute radiative flux and cooling rates, in which the angular dependence of surface emissivity was explicitly taken into account. The RRTMG_LW model, on the other hand, can only use band-averaged surface emissivity and do not include any explicit dependence with the zenith angle. Using typical sounding profiles in the tropics, mid-latitude summer, sub-arctic winter, and Sahara desert, we compare the outgoing longwave radiations and longwave radiative cooling rates as computed by the LBLRTM and by the RRTMG_LW model. The comparisons show that the largest fractional difference in OLR is 0.9%, which is obtained for the case of subarctic winter profile. The largest radiation cooling rate discrepancy happens at the lowest level near to the surface with a fractional difference of ~15% (i.e. ~0.1K/day), among which ~5% discrepancies are due to the representation of surface emissivity alone and the rest 10% can be attributed to the simplified representation of atmospheric radiative transfer in the RRTMG_LW. Above 800 hPa, the discrepancies are less than 1% and almost exclusively caused by the RRTMG_LW formulation. For the mid-latitude and tropical profiles, window band of 820-980cm^-1 contributes most among all 16 RRTMG_LW bands to the discrepancies in the cooling rates. For the sub-arctic winter and Sahara desert profiles, the largest contribution comes from a far-IR band of 500-630cm^-1.