This app was mentioned in 2 comments, with an average of 3.00 upvotes
Weird that nobody gave you the actual SK emergency alert app
https://play.google.com/store/apps/details?id=ca.sk.gov.saskalert
Install this app, and you will get the push alerts for tornado watches and other types of storms. When you are driving around and there is a tornado warning where you are, your phone will go off, making that blaring noise.
The City of Saskatoon also has https://www.saskatoon.ca/services-residents/fire-emergency/notifynow which is good for flooding, fires power outages and other storm type things.