Jeremy, you wrote:
"The owners aren't going to want to hear how you saved a few hundred miles (say a day) of time, but cost them an insurance claim because 20 containers went over the side as you were rolling through a F9 extra-tropical cyclone at N55."
The nice thing about this sort of cost from an "algorithmic" point of view, is that it can be incorporated directly into the computation easily, either as a reduction in effective speed or as a separate term in the "cost function". Time is money, and the risk of damage to the vessel or the cargo can easily exceed the time saving that arises from rigorously following great circle paths. Of course, if there is no cost function --if we have no preferences at all specified... no information on risk to vessel, no information on weather or currents-- then it all comes down to travel time, and in that case, a path very close to the GC will necessarily be optimal.
"A good example of this is when I was a young 3rd mate, and I was on a ship exiting the English Channel. There was a good storm south, so the brand new captain decided to do a GC from Bishop Rock to Baltimore, USA in November. We ended up hitting every low rolling off the Polar Vortex and our barograph looked like an EKG. We were nearly a week late and hit 5 storms before we could dive south near the Flemish Cap. We would have done much better taking the "long way" by sailing to the Azores and cutting across at about 30N."
Great story and possibly a good example of the seduction of the GC. It's severely over-emphasized in textbooks, classrooms, and licensing exams, but the tools and the methodologies make it seem so "scientific", so important. That sucks 'em in.
"These days companies often hire weather routing services that use all sorts of algorithms to try to predict the best routes. Still, it's GIGO, so with marginal weather products in certain parts of the world, these services can literally steer you into a tempest."
There's also a lot of voodoo in these systems, and that, strangely enough, is what people pay for and want from these services! There's an oceanographer who is considered the godess of weather routing for the New England to Bermuda races (can't remember her name). From what I understand, she has a relatively solid monopoly on weather-routing advice, which in the case of the Bermuda race is significantly dominated by current analysis (not strictly weather). Riding the right side of a major eddy can cut many hours off a sailing voyage crossing the Gulf Stream. While these issues can all be analyzed with strictly rigorous algorithms based on the best data, sailors in these races still believe that there is an essential "human touch" to the selection of an optimal path. That's what they pay for. They believe in magic.
With ocean Internet rapidly advancing combined with significant advances in global forecasting of major weather systems, I'll suggest/predict that these systems that can "steer you into a tempest" as you say should become quite a bit more trustworthy in the very near future. Weather forecasting is still limited by the chaotic nature of the physics of weather itself which implies that the forecasts will still be limited to about seven days out maximum with only broad-brush statistical predictions after that limit, but as long as the end-users understand those limits and are able to update their routing regularly and quickly, the era when the weather-routing could send you into a major storm should be coming to an end, and very soon. In addition, algorithms that do this sort of routing are increasingly disaster-aware, in the sense that they incorporate a cost for a major failure in the forecasting model. For example, computer models often agree on hurricane tracks over a time scale of three to five days, but sometimes computer models will show extreme sensitivity to initial conditions. This is where the chaotic dynamics take over, and tthe algorithms (or the magic, if we're paying a human expert) have to admit that a policy of weather-ignorance is better than a formal forecast over some timeframe. In other words, the computer itself has to be able to throw up its hands under certain specific circumstances and say, "I give up! I don't know where that hurricane is going. Go home. Do not sail!" The catch, of course, is that managers will tend to view such advice as a failure in the routing product. In addition, there's the problem of the homebrew forecast. We all have friends who believe that they have a "sixth sense" about the weather. These are the people who have gotten into the dangerous habit of adjusting their predictions post facto and are prone to say things like "See? I told you the storm was going to turn north!". Sometimes they're right, and sometimes they're wrong. But by their own memories, they're always right.