I am fitting a new door cill to the front door porch. One of the frame timbers had rot at the bottom. I have cut off 4 inches leaving a 45 degree splice and now need to glue in a new piece. I was going to dowell it for added strengh. It clearly needs to be weatherproof and have gap filling properties as my saw cut wasn't 100%. What is going to be the best glue for the job?