For the record, all the weather monitoring and forecasting services are still operational (including the obviously non-essential experimental and long-range services) under the life and property clause.
http://www.weather.gov/Of course, of all the services that could benefit from a shutdown, private meteorologists like myself would be first on the list, since for years we have been undercut by the government's free, public-domain forecasts that can be copied at will. Pretty much every other country copyrights their forecasts, models, radar, etc. and makes them available for a very generous license.