slocum is an open source project which provides weather forecasts to the bandwidth impaired (primarily sailors). It includes a weather specific compression algorithm which results in forecasts attachments that are the fraction of the size of saildoc forecasts.

Joshua Slocum (February 20, 1844 -on or shortly after November 14, 1909) was a Canadian-American seaman and adventurer, a noted writer, and the first man to sail single-handedly around the world. In 1900 he told the story of this in Sailing Alone Around the World. He disappeared in November 1909 while aboard his boat, the Spray. (wikipedia)

In "Sailing Alone Around the World" he talks about his tin clock:

"My tin clock and only timepiece had by this time lost its minute-hand,

but after I boiled her she told the hours, and that was near enough on a long stretch."

If Slocum was able to successfully circumnavigate via celestial navigation using a clock with no minute hand, then modern day sailors should be able to get by using weather forecasts without floating point precision.