There are a large number of image processing compression methods. Altho
their underlying theory is general, many implementations are for only 8-bit
data. There is also some precedent in the literature for scaling
elevations to 8 bits for research purposes. In adir512, scaling
destroys 
, or
slightly more than 2 bpp, or 65K bytes. The
resulting file is now quantized in 6 meter intervals, so the maximum error
introduced by this is 3 meters, and the average error is 1.5. Datasets
with a greater maximum elevation will have larger errors.
After scaling the elevations, the binary file is one byte per element, or 262,144 bytes. Gzip compresses this file to 103,413 bytes. Note that this size, plus the destroyed bits, is still less than the gzipped original file, showing in yet another way that altho gzip is an excellent compression program, it can be suboptimal.
Converting the scaled file to a GIF file (which is exact, but requires 8-bit data) gives a 123,986 byte result, somewhat worse than gzip. LJPEG gives 64,935 bytes, showing that elevation data has similar statistical characteristics to photographic images. This may be partly due to smoothing during the data generation, in which cliffs in the real world can be smoothed into gradual slopes.