Bucket Hat

 A Bucket Hat 

A bush hat is similar to a bucket hat but has a stiffer brim.

A bush hat is a form of wide-brim hat commonly used by military forces

Also known as a Boonie hat by Americans  

 The hat as a fabric tape band of loops is sewn around the hat's crown. This ring is meant to hold additional vegetation/foliage as camouflage. 

Complete with vented crown

Brim up or Brim down, I think with the brim up you will gather a nice puddle in the rain to tip on friends.