I ran Eureqa on the pure UEP dataset looking for periodicities, ignoring any DiffEq framework
EUP = f(t)
The solution reveals a strong factor along the Pareto front (lower right) of 7.84 rads/year (from a modulated 7.82 with a side-band of 0.014). Since the data is only sampled once per year, this is likely an aliased period of an intra-annual component. IOW, anything above ~6.28 rads/year would be a sub-annual period.
The [anomalistic tidal month](http://en.wikipedia.org/wiki/Lunar_month) of 27.55455 days results in 83.285 rads/year. But subtracting 12 * 2π from this gives 7.887 rads/year, which is very close to 7.84 rads/year.
The reason that this may be important is that a tidal month period can "beat" in synch with a particular time of year or season and this may be amplified enough to be detectable via enough yearly samples.