  Passive random walker dynamics is introduced on a growing surface. The walker
is designed to drift upward or downward and then follow specific topological
features, such as hill tops or valley bottoms, of the fluctuating surface. The
passive random walker can thus be used to directly explore scaling properties
of otherwise somewhat hidden topological features. For example, the walker
allows us to directly measure the dynamical exponent of the underlying growth
dynamics. We use the Kardar-Parisi-Zhang(KPZ) type surface growth as an
example. The word lines of a set of merging passive walkers show nontrivial
coalescence behaviors and display the river-like network structures of surface
ridges in space-time. In other dynamics, like Edwards-Wilkinson growth, this
does not happen. The passive random walkers in KPZ-type surface growth are
closely related to the shock waves in the noiseless Burgers equation. We also
briefly discuss their relations to the passive scalar dynamics in turbulence.
