It is well known that several geophysical fields exhibit characteristic features at different scales. For some such fields scale-space anisotropy is also present, that is, features contributing significant fraction of energy are oriented in different directions at different scales. Examples of such fields include clouds, rainfall, hurricanes etc. A technique based on wavelet transforms (with two-dimensional directionally oriented Morlet wavelet) is developed to analyze such random fields. This methodology has significant advantage over Fourier transform based techniques and is demonstrated using the analysis of a spatial rainfall field. ¿ American Geophysical Union 1995