Why doesn't the Sun cross the meridian at noon?
Observers attempting to locate the North Celestial Pole have suggested using the position of the Sun at noon. But, they have noticed they may be off as much as a half-hour. Why is that? The straightforward answer is noon is your local MEAN solar time.  And your particular location probably won't coincide with an hourly longitude. For example, Phoenix, Arizona is located just about mid-way between longitudes 105 and 120 degrees West. As a result, local solar noon actually occurs around 12:30pm. Keep in mind that time-zones are multiples of 15 degrees starting with Greenwich, England. So, a preferable method of locating the meridian is to use planetarium software to determine the time of transit of the Sun for your physical location (actual longitude/latitude).