The Clouds and the Earth's Radiant Energy System (CERES) instrument on board the Tropical Rainfall Measuring Mission (TRMM) satellite provides, for the first time, a large-scale (40 S to 40 N) data set for the atmospheric greenhouse effect and the column-averaged longwave (LW) radiative cooling rates in the broadband (5--100 microns) and the window (8--12 microns) regions. We demonstrate here that the separation into the window and the nonwindow (5--8 microns and 12--100 microns) fluxes provides the first global-scale data set to exhibit the sensitivity of the atmospheric greenhouse effect to vertical water vapor distribution. The nonwindow greenhouse effect varies linearly with the logarithm of column water vapor amount weighted with the atmospheric pressure, while the window component varies quadratically with the water vapor partial pressure. The column cooling rates range from about -170 to -210 W m-2 for the nonwindow region. The window cooling rates are only about 10% to 20% of the above range and approach rapidly to near-zero values for surface temperatures less than 288 K. The nonwindow component of the greenhouse effect and cooling rates are shown to be more sensitive to upper troposphere water vapor, while the window greenhouse effect and cooling rates are shown to be more sensitive to the lower troposphere water vapor amount. In addition, the data reveal that in tropical regions, with warm sea surface temperatures (greater than 297 K) and elevated upper tropospheric water vapor amounts, the continuum emission in the window region leads to enhanced cooling of the column, while the rotational bands in the nonwindow region lead to a net decrease in the longwave cooling of the atmospheric column.