A good reason for getting up very earily in the morning is to capture fog or low clouds. They create wonderful mood. You can sometimes see these type of weather conditions at other times of the day, they are more likely to be seen before or immediately after sunrise. And even if the fog or low clouds partially obscures the subject, as you can see in this picture of Bled Castle in Croatia, the results will be compelling. This adds mystery and intrigue to the pictures.
The settings for this photo were 1/250, f/5.6, 320 ISO, 70-200mm lens set to 200mm plus a 1.4x teleconverter, thus 280mm of focal length.