Weather is a major contributing factor in aviation accidents, incidents and delays. Doppler weather radar has emerged as a potent tool to observe weather. Aircraft carry an onboard radar but its range and angular resolution are limited. Networks of ground-based weather radars provide extensive coverage of weather over large geographic regions. It would be helpful if these data can be transmitted to the pilot. However, these data are highly voluminous and the bandwidth of the ground-air communication links is limited and expensive. Hence, these data have to be compressed to an extent where they are suitable for transmission over low-bandwidth links. Several methods have been developed to compress pictorial data. General-purpose schemes do not take into account the nature of data and hence do not yield high compression ratios. A scheme for extreme compression of weather radar data is developed in this thesis that does not significantly degrade the meteorological information contained in these data. The method is based on contour encoding. It approximates a contour by a set of systematically chosen ‘control’ points that preserve its fine structure upto a certain level. The contours may be obtained using a thresholding process based on NWS or custom reflectivity levels. This process may result in region and hole contours, enclosing ‘high’ or ‘low’ areas, which may be nested. A tag bit is used to label region and hole contours. The control point extraction method first obtains a smoothed reference contour by averaging the original contour. Then the points on the original contour with maximum deviation from the smoothed contour between the crossings of these contours are identified and are designated as control points. Additional control points are added midway between the control point and the crossing points on either side of it, if the length of the segment between the crossing points exceeds a certain length. The control points, referenced with respect to the top-left corner of each contour for compact quantification, are transmitted to the receiving end. The contour is retrieved from the control points at the receiving end using spline interpolation. The region and hole contours are identified using the tag bit. The pixels between the region and hole contours at a given threshold level are filled using the color corresponding to it. This method is repeated till all the contours for a given threshold level are exhausted, and the process is carried out for all other thresholds, thereby resulting in a composite picture of the reconstructed field. Extensive studies have been conducted by using metrics such as compression ratio, fidelity of reconstruction and visual perception. In particular the effect of the smoothing factor, the choice of the degree of spline interpolation and the choice of thresholds are studied. It has been shown that a smoothing percentage of about 10% is optimal for most data. A degree 2 of spline interpolation is found to be best suited for smooth contour reconstruction. Augmenting NWS thresholds has resulted in improved visual perception, but at the expense of a decrease in the compression ratio. Two enhancements to the basic method that include adjustments to the control points to achieve better reconstruction and bit manipulations on the control points to obtain higher compression are proposed. The spline interpolation inherently tends to move the reconstructed contour away from the control points. This has been somewhat compensated by stretching the control points away from the smoothed reference contour. The amount and direction of stretch are optimized with respect to actual data fields to yield better reconstruction. In the bit manipulation study, the effects of discarding the least significant bits of the control point addresses are analyzed in detail. Simple bit truncation introduces a bias in the contour description and reconstruction, which is removed to a great extent by employing a bias compensation mechanism. The results obtained are compared with other methods devised for encoding weather radar contours.