Receiving an emergency alert on your smartphone is pretty hard to miss. It causes your device to vibrate and produce a unique audible signal (much like the emergency broadcast tests you hear on TV).
If you don't want to receive severe weather notifications or AMBER Alerts, you can disable them on your smartphone, but please note that on some devices a class of emergency messages called Presidential Alerts can't be disabled.
To disable Emergency Alerts on your device, go to your Settings menu and scroll to Emergency Alerts or Government Alerts. Disable the alerts you no longer want to receive.