Accurate predictions of sea level rise over the coming century will require improved knowledge of the processes controlling accumulation on the great ice sheets. The sparsity of accumulation rate observations, both temporally and spatially, hinder development of this understanding. We introduce a new method to observe accumulation rates (averaged over roughly a decade) using satellite observations of microwave emission at 4.5-cm wavelength, focusing in this paper on Greenland. At this wavelength, scattering by the grain fabric in firn is unimportant relative to quasi-reflection from density (and thus dielectric permittivity) stratification. We show observationally a strong link between random firn density stratification, on scales of millimeters to centimeters, and accumulation rate. We then show theoretically how the observed density stratification can produce and is consistent with observations of polarization of 4.5-cm-wavelength emission. We employ observations from the Scanning Multichannel Microwave Radiometer (SMMR) and previously published ground observations of accumulation rates in Greenland to complete specification of the relationship between accumulation rate and polarization. The relationship is sufficiently accurate to serve as a basis for mapping accumulation rate fields. We compare our satellite-derived maps with previously published maps based on syntheses of ground data. We find broad agreement between the two types of maps, though the satellite-derived map indicates more strongly the importance of topography and prevailing weather patterns in determining detailed accumulation rate patterns. Finally, we discuss possible refinements and the prospects for improved satellite-derived maps based on a new generation of sensors about to be launched. ¿ 2001 American Geophysical Union