Calgary Weather Map can be added to your home screen so it opens like a normal app — full screen, no browser address bar, its own icon. It takes about fifteen seconds.
There is nothing to download and no App Store involved. It's the same website, just launched in its own window. No account, no tracking, still free.
Look for the small install icon at the right-hand end of the address bar — a monitor with a downward arrow — and click Install. The map then opens in its own window without browser tabs.
Being straight about the limits: this is a website in an app window, not a native app. It needs a connection to fetch current conditions, and it does not send push notifications — if a hail-alert notification is what you're after, that isn't built yet. Tell us if you want it; it moves up the list when people ask.
Press and hold the icon on your home screen and choose Remove App (iPhone) or Uninstall (Android). Nothing is left behind — it never had an account or stored anything about you beyond your °C/°F preference.