I've never specifically heard the term Weatherwave before, but I've heard a lot about Signalwave and Broken Transmission. It's an interesting enough genre, with a cool concept.
I remember a couple weeks back one of my college roommates was listening to 90's Weather Channel Local on the 8's music while he was studying. I recommended he should also check out the updated soundtrack to the later Weatherscan from the 2000's-22. And so I recommend the same to you.
Weatherscan was a significant, and continuously-run cable program that provided local weather forecasts, a news sidebar, and other indexes. The soundtrack for the program was mostly composed by a man named Trammell Starks. Because of the streaming era and a decline in viewership, Weatherscan stopped operating in 2022 however there is an online unaffiliated emulator that works perfectly and also plays the music that was originally played during Weatherscan's run.
It's not "Weatherwave", nor "broken transmission" or anything like that. It's just simple smooth jazz, new age, and easy listening but some tracks are certainly good on the ears and to be honest is good driving music. However if you wanted to look at the roots of what influenced those genres, it's worth it.
Plus the nostalgia boost. I'm an '04 baby... a lot of those songs are engrained in my memory.
I think there's a bootlegged album on Bandcamp of the entire soundtrack if you're interested. If it's not on there anymore you can find compilations on YouTube.
https://www.youtube.com/watch?v=cXq-_ucfNH8
And if you like that, I think just check out smooth jazz in general. Trammell Starks has more work. Maybe Spyro Gyra would fit your taste.
If you're in operating area, check out SiriusXM's 'Watercolors', channel 66