Vertical velocity damping at the top of the atmosphere

A vertical velocity ($w$) damping term is used to prevent reflection of acoustic waves off the upper model boundary and is defined as a Raleigh damping term

$${\cal{D}}_w = \kappa_w \left(w-w_{ref}\right)$$ (119)

where $\kappa_w$ is a characteristic timescale and only varies in the vertical and is zero except in the uppermost layers where it increases approaching a maximum value at the upper boundary. This is akin to a Raleigh damping to the basic state value ($w_{ref}=0$) to avoid reflections off the model top (downward). This term is included in the $D_w$ term in Eq. 32.