The only job that is bullshit and meaningless is the job that is not paid enough. Hardly any employee does their job to feel fulfilled, they do it to earn their wage.

Well, in reality it does create an extra hour of daylight. Like now where I live the sun sets at around 19:00 while without DST it would set at 18:00. I don't care that it rises at 7 while without dst it would rise at 6 because most of the society does not function on sun hour but on standard time (whatever that is), so shops open at fixed time not on sunrise, schools start as well on fixed time, and lots and lots of other services are bound to the fixed time instead of on solar time. Thus accepting the reality that the whole life is dictated by some artificial standard time, and not by sunrise and sunset, DST does magically create an extra hour of daylight (if the place you are living in has substantial seasonal difference in daylight duration).

Daylight saving time has no sense if the country is so close to equator as is Samoa. DST works IMHO great (yes I am aware of the biological side effects of switching, but still I like it) in mid and high lattitudes (40+ degrees) where seasonal differences in daytime duration are large.

The phase velocity in your case should not vary much, so i guess that fitting the CFL to the theoreticaly fastest wave should work fine. If you need an accurate and least dispersive method than implicit methods are not very good since they tend to damp the solution so i'd go with an explicit scheme. If you choose FD method then you should be aware that Arakawa A, B, C, D and E grids (staggering methods) produce dispersion (even for the waves that are nondispersive), also you have to be aware that choosing between leepfrog, forward and backward in time produces different dispersions and can affect stability as well. So, what you need is to idealize the problem and solve it analiticaly, and then to employ a couple of methods on this idealized problem, and see which one works best, and then to use this method on nonidealized - real problem, and cross your fingers and hope it'll work. This is really the way to do it. Coming back to the varying phase velocity, this should not be a problem, in meteorology this is the problem that is being solved every day since atmospheric motion is really a wave motion (atmospheric equations of motion can be transformed with some aproximations to the Helmholtz eq), and there are many phase speeds that are involved - from ~ 1cm/s up to the speed of sound. There is no numerical method that does not distort any wave, every method in the book _WILL_ distort your waves, it is up to you to find the method whose distortion will be most acceptable for your problem.