You will need to find a WMS that contains weather related data that is updated quite frequently. In addition to using this information to build a map, you should be able to build a barometer either as a donut chart or by modifying the idea of creating a timeline. You may find some good information here: https://www.interworks.com/blog/ccrouch/2016/03/22/storm-chasing-tableau-how-create-weather-map
You may also like this one. There is a lot of stuff here and it is where I first learned about creating weather maps with Tableau. https://adventuresinmapping.com/
Thank you Tim for such a good reference.