(a) Looks good, capturing zero crossings is something I've been thinking about, having used [a simple metric that compares sign changes between two time series](http://contextearth.com/2017/10/25/improved-solver-target-error-metric/). SiZer should be similarly useful as well.
(b) That looks interesting in terms of certain wavenumbers being involved in the standing wave patterns -- come to think of it, that's why the standing waves stand out. Perhaps similar in origin to the Tropical Instability Waves along the equator.
The frustrating aspect of spatiotemporal patterns is that while the spatial aspect is stable (due to the fixed boundary conditions), the temporal aspect can be highly erratic. So finding a stable standing wave pattern is just the start.
Here's another view of the wavelet scalograms that I've created from the last few days. I didn't get a chance to experiment with all the different wavelet windowing functions. The Gabor appears best for isolating periodicities but the MexicanHat or DGaussian may be better for pattern matching.