I use the weather gnome applet and I just started using (though its just
more a temp gauge) screenlets.

I just use firefox and bookmarked a java applet from my local news
station. But there are some sites that have national weather with a
lot of different features. I can't advise if there is a specific
program that will do that, but if you are looking for something more
advanced you may want to list some preferred features. Also, there is
weatherbug, but I would never touch that after my experience with it
years ago on windows.

I'm assuming you don't have a Doppler setup on your roof, so here is the
next best thing:
www.intellicast.com/.../current.aspx

Wish that I had Doppler on the roof :) I could always have my wife up on
the roof and use her as my Doppler.

There is a weather radar screenlet from here:
http://gtk-apps.org/content/show.php/Weather+Radar+Screenlet?content=121420

Screenlets is in the repositories. You need to run it to use the screenlets.
I have not used Screenlets since I switched to KDE and can't remember how
well it worked.