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When I was MUCH younger, the windows were open in the spring, the black-and-white TV was not on all the time, folks did not listen to MP3 players with headphones, and sirens could be heard inside the house.
With the cell phone tied to every waistband, some jurisdictions are turning to products such as Everbridge, Nixle, BlackboardConnect, MyStateUSA, Code Red, and EmergencyE to encourage the public to get their warnings. The National Weather Service offers this “LISTING OF ALTERNATIVE SOURCES OF WEATHER ALERTS”.
Popular smartphone operating systems such as the Android and Iphone offer applications such as Storm and WeatherBug that automatically alert when the resident is in a warning area as well as for areas where the Citizen has an interest.

Of course, amateur radio plays a big part in keeping the resident aware as do local media partners. Even newspapers are joining the electronic media to give their own Twitter and Facebook information.
You may get automated information from your Federal partners with the Integrated Public Alert and Warning System (IPAWS) and the Wireless Emergency Alert system.
Indeed, today, there's no need to go without a warning. However, you must WANT to get one.