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Long-range spatiotemporal correlations may play important roles innonequilibrium surface growth process. In order to investigate the effects oflong-range temporal correlation on dynamic scaling of growing surfaces, weperform extensive numerical simulations of the (1+1)- and (2+1)-dimensionalKardar-Parisi-Zhang (KPZ) growth system in the presence of temporallycorrelated noise, and compare our results with previous theoretical predictionsand numerical simulations. We find that surface morphologies are obviouslyaffected with long-range temporal correlations, and as the temporal correlationexponent increases, the KPZ surfaces develop gradually faceted patterns in thesaturated growth regimes. Our results show that the temporal correlated KPZsystem 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.

Kinetic roughening and nontrivial scaling in the Kardar-Parisi-Zhang growth with long-range temporal correlations