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All three of these apps have some very nice features when used as a stand alone app: They're full-featured weather apps in themselves Their widgets vary in extent and design, so you will want to check each widget to see which one gives you the data you prefer. (For a refresher on how to set up a widget, see Kelly Guimont's “iOS 8: How to Enable Notification Center Widgets.”)
Finally, note that this is an overview of apps and their widgets that looked very good to me, but it's not a TMO formal review. These apps have lots of features that can't be covered in this short introduction.
1. NOAA Radar Pro. It's hard to ignore the expertise of the weather people themselves, NOAA, the National Oceanic and Atmospheric Administration. Their app shows real-time weather radar and alerts for locations you specify. The current conditions are extensive and nicely presented, as shown below. The settings are extensive and technically complete.
NOAA Radar Pro app
The widget is one of the best and shows current conditions, temperature range and a forecast in two hour blocks for the rest of the day.
NOAA Radar Pro widget
2. Weather Pro. This app has a wealth of information presented in the app itself. Just a small part is shown below. One of the things I like is an animated satellite presentation of radar returns (of what looks like water vapor). The weather forecast also predicts the amount of expected rain, in inches (or millimeters).
WeatherPro app
The widget information, added in version 4.0, isn't particularly detailed, however, and just shows the basics. Notable, however, is the inclusion of the current rainfall rate, in inches (or mm)/hour.
WeatherPro widget
3. Weather Underground. This isn't the prettiest of the three weather apps, but there's a wealth of information on its home page, including health related data (pollen, air quality, and so on), astronomical & UV data, webcams, and weather photos. The app is free, and so there is a small panel of ads at the top. If you wish, you can buy one year of ad-free weather as an in-app purchase for US$1.99. Crowd sourcing provides local weather data.
Weather Underground app
Where this app really shines is in the weather part of its two widgets. I like the graph that shows the expected temperature throughout the day. The second widget just takes you back to the app's map of temperatures. This presentation of the daily rise and fall of temperature might be a good widget to combine with, say, another more general widget of your liking, say Yahoo Weather.
Weather Underground widget
Having access to weather information, current conditions, alerts, radar maps, satellite maps, forecasts, astronomical data, and health data all in your hand is one of the coolest things about a modern smartphone always on the Internet. New weather apps are always coming out, but these three, ranging from free to very inexpensive, cover a wide range of information and presentation formats. Best of all, you can have its widget in Notification Center for quick, summary access.