  We study dynamical surface gravity in a general spherically symmetric setting
using Painlev\'{e}-Gullstrand (PG) coordinates. Our analysis includes several
definitions that have been proposed in the past as well as two new definitions
adapted to PG coordinates. Various properties are considered, including general
covariance, value at extremality, locality and static limit. We illustrate with
specific examples of "dirty" black holes that even for spacetimes possessing a
global timelike Killing vector, local definitions of surface gravity can differ
substantially from "non-local" ones that require an asymptotic normalization
condition. Finally, we present numerical calculations of dynamical surface
gravity for black hole formation via spherically symmetric scalar field
collapse. Our results highlight the differences between the various definitions
in a dynamical setting and provide further insight into the distinction between
local and non-local definitions of surface gravity.
