Providing an accurate picture of the weather conditions in the pilot's area of interest could be a highly useful application for ground-to-air data links. The problem with using data links to transmit weather pictures is the large number of bits required to exactly specify a weather image. To make transmission of weather maps practical, a means must be found to compress this image. The Polygon-Ellipse (PE) encoding algorithm developed in this report represents weather regions as ellipses, polygons, and exact patterns. The actual ellipse and polygon parameters are encoded and transmitted; the decoder algorithm redraws the shape from their encoded parameter values and fills in the included weather pixels. Special coding techniques are used in PE to compress the encoding of the shape parameters to achieve further overall compression. The PE algorithm contains procedures for gracefully degrading the fidelity of the transmitted image when necessary to meet a specified bit limit. Pictorial examples of the operation of this algorithm on both Terminal Doppler Weather Radar (TDWR) and ASR-9 radar-generated weather images are presented.