That's easy: Louise Monroe of the Edinburgh Police Dept. (by way of the mind of Kate Atkinson).
Kate Shugak, of the Dana Stabenow novels set in Alaska.
You're supposed to let me have your choices over at Petrona! (linked here). Lots of suggestions there, though neither of these two. (I thought Kate Atkinson's main detective is Jackson Brodie, but I have only read one of hers.) I've never read Stabenow, seems as if I should start.