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In our previous study, we discovered phase-inversion waves on the lattice shape system. The phase-inversion waves are phenomena changing phase states between adjacent oscillators from in-phase to anti-phase or from anti-phase to in-phase and continuously. The phase-inversion waves can be observed in steady states. In this study, we observe and analyze propagation mechanisms of the phase-inversion waves in the lattice shape system. Furthermore, we predict air temperature data by using the lattice shape system.