Coloring your hair and sun bleaching

[luvme]

My hair naturally medium brown. We moved down south this year and I have noticed that my hair has bleached out to light brown/blonde. My roots and the first 2 inches of my hair near the roots are brown but the rest is bleached out. Is there a way to prevent this? If I color my hair back to brown, how do I protect it from bleaching (or is there really no way to prevent this?) I do wear a hat when I am out in the sun for a long time.

(BTW- this is my first post. I LOVE THIS SITE!)