The presence of surface meltwater on ice caps and ice sheets is an important glaciological and climatological characteristic. We describe an algorithm for estimating the depth and hence volume of surface melt ponds using multispectral ASTER satellite imagery. The method relies on reasonable assumptions about the albedo of the bottom surface of the ponds and the optical attenuation characteristics of the ponded meltwater. We apply the technique to sequences of satellite imagery acquired over the western margin of the Greenland Ice Sheet to derive changes in melt pond extent and volume during the period 2001--2004. Results show large intra- and interannual changes in ponded water volumes, and large volumes of liquid water stored in extensive slush zones.