In this work, two types of superlattice patterns with spatiotemporal asymmetry are observed for the first time using a dielectric barrier dis- charge device with an array electrode. The device consists of a square array water electrode and a plate water electrode. Experimental and theoretical studies are conducted on the formation mechanism of the spatiotemporally asymmetric patterns. By solving the Laplace equation, the electric field in the gas gap presents periodic spatial distribution, and the array electrode surface possesses a stronger transverse electric field. Using this device, two new types of square superlattice patterns are observed in the discharge of a mixture of air and argon. We employ a high-speed camera and photomul- tiplier tubes to conduct spatiotemporal dynamics measurements on one of the patterns. The results reveal a pronounced spatiotemporal asymmetry.During the positive half-cycle, one substructure exhibits two discharge events. The second begins near the voltage zero-crossing and extends into the negative half-cycle, whereas no similar behavior is observed during the negative half-cycle. To estimating the plasma parameters, the emission op- tical spectra are measured by a spectrograph. Theoretically, the Poisson equation is solved using COMSOL. The results not only explain the spati- otemporal sequence of the pattern discharge, but also reveal the underlying mechanism of the observed asymmetry. It is found that the secondary dis- charge of the substructure in the positive half-cycle is induced by the trans- verse transport of wall charges, which is driven by the stronger transverse electric field. These findings elucidate the pattern's formation mechanism and open a new direction for studying pattern dynamics in asymmetric di- electric barrier discharges.