  Until now it has been impossible to observationally measure how star cluster
scale height evolves beyond 1Gyr as only small samples have been available.
Here we establish a novel method to determine the scale height of a cluster
sample using modelled distributions and Kolmogorov-Smirnov tests. This allows
us to determine the scale height with a 25% accuracy for samples of 38 clusters
or more. We apply our method to investigate the temporal evolution of cluster
scale height, using homogeneously selected sub-samples of Kharchenko et al.
(MWSC), Dias et al. (DAML02), WEBDA, and Froebrich et al. (FSR).
  We identify a linear relationship between scale height and log(age/yr) of
clusters, considerably different from field stars. The scale height increases
from about 40pc at 1Myr to 75pc at 1Gyr, most likely due to internal evolution
and external scattering events. After 1Gyr, there is a marked change of the
behaviour, with the scale height linearly increasing with log(age/yr) to about
550pc at 3.5Gyr. The most likely interpretation is that the surviving clusters
are only observable because they have been scattered away from the mid-plane in
their past. A detailed understanding of this observational evidence can only be
achieved with numerical simulations of the evolution of cluster samples in the
Galactic Disk.
  Furthermore, we find a weak trend of an age-independent increase in scale
height with galactocentric distance. There are no significant temporal or
spatial variations of the cluster distribution zero point. We determine the
Sun's vertical displacement from the Galactic Plane as $Z_\odot=18.5\pm1.2$pc.
