A simulation of the earth's clear-sky long-wave radiation budget is used to examine the dependence of clear-sky outgoing long-wave radiation (OLR) on surface temperature and relative humidity. the simulation uses the European Centre for Medium-Range Weather Forecasts global reanalysed fields to calculate clear-sky OLR over the period from January 1979 to December 1993, thus allowing the seasonal and interannual time-scales to be resolved. the clear-sky OLR is shown to be primarily dependent on temperature changes at high latitudes and on changes in relative humidity at lower latitudes. Regions exhibiting a ‘super-greenhouse’ effect are identified and are explained by considering the changes in the convective regime associated with the Hadley circulation over the seasonal cycle, and with the Walker circulation over the interannual time-scale. the sensitivity of clear-sky OLR to changes in relative humidity diminishes with increasing relative humidity. This is explained by the increasing saturation of the water-vapour absorption bands with increased moisture. By allowing the relative humidity to vary in specified vertical slabs of the troposphere over an interannual time-scale it is shown that changes in humidity in the mid troposphere (400 to 700 hPa) are of most importance in explaining clear-sky OLR variations. Relative humidity variations do not appear to affect the positive thermodynamic water-vapour feedback significantly in response to surface temperature changes.