Ice dams in valleys of metal roof, no attic, solution?

Hi- We have a newer (2005) log house with a metal roof that has many peaks and valleys. We have leaks in most of the rooms where the valleys come down into the house. It has been unusually cold the past few days and I was wondering if these leaks are the cause of ice dams in the valleys on the roof. We have very high ceilings and no attic. My question is, how do we remedy this? Thanks in advance for your help. See picture attached of one of the roof valleys.