This study presents an analytical expression, derived from radiative theory, for relating water vapor radiances to layer-average relative humidities. This ''radiance-to-humidity transformation'' provides a simple, yet reliable, means of interpreting satellite observations of the upwelling radiation in the 6.3-μm water vapor absorption band in terms of a more familiar water vapor quantity. Despite its simplicity, when compared to detailed radiative transfer calculations of the upper (6.7 μm) tropospheric water vapor radiance, the transformation is demonstrated to be accurate to within ~1 K. Similar levels of accuracy are found when the transformation is compared to detailed calculations of the middle (7.3 μm) and lower (8.3 μm) tropospheric water vapor radiance, provided that the emission from the underlying surface is taken into account. On the basis of these results, the radiance-to-humidity transformation is used to interpret TIROS operational vertical sounder observed water vapor radiances in terms of the relative humidity averaged over deep layers of the upper, middle, and lower troposphere. We then present near-global maps of the geographic distribution and climatological variations of upper, middle, and lower-tropospheric humidity for the period 1981--1991. These maps clearly depict the role of the large-scale circulation in regulating the location and temporal variation of tropospheric water vapor. ¿ American Geophysical Union 1996