  Long-range spatiotemporal correlations may play important roles in
nonequilibrium surface growth process. In order to investigate the effects of
long-range temporal correlation on dynamic scaling of growing surfaces, we
perform extensive numerical simulations of the (1+1)- and (2+1)-dimensional
Kardar-Parisi-Zhang (KPZ) growth system in the presence of temporally
correlated noise, and compare our results with previous theoretical predictions
and numerical simulations. We find that surface morphologies are obviously
affected with long-range temporal correlations, and as the temporal correlation
exponent increases, the KPZ surfaces develop gradually faceted patterns in the
saturated growth regimes. Our results show that the temporal correlated KPZ
system displays evidently nontrivial dynamic properties when $0<\theta<0.5$,
the characteristic roughness exponents satisfy $\alpha<\alpha_s$, and
$\alpha_{loc}$ exhibiting non-universal scaling within local window sizes,
which differs with the existing dynamic scaling classifications, both in the
(1+1)- and (2+1)-dimensions.
