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Surface charges have significant impact on the evolution of surface dielectric barrier discharge (SDBD). In this work, the role of residual surface charges on repetitively nanosecond pulsed SDBD in atmospheric air is investigated using a two-dimensional fluid model, based on the assumption of preserving the distribution of surface charges at the end of the previous high voltage (HV) pulse. In the bipolar mode when the polarity of residual surface charges is opposite to that of the current HV pulse, a lower breakdown voltage and more deposited energy can be observed, showing an obvious enhancement of SDBD. In the unipolar mode, residual surface charges suppress the development of discharges and energy deposition. It is found that more residual surface charges are accumulated during the negative pulsed discharge, which have a more pronounced effect on the subsequent positive pulsed one. This is explained by the fact that the negative surface streamers directly contact the dielectric and charge it, while the positive surface streamers float above the dielectric, forming a ion-rich region near the surface. The results in this work demonstrate the mechanism of how residual surface charges affect discharge dynamics, which can be utilized to regulate energy deposition in SDBDs. [ABSTRACT FROM AUTHOR]