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The asymptotics of weak solutions to the Boussinesq equations with no-slip boundary and moderately ill-prepared data is investigated in rotation-dominant limit regime as the Rossby number, the Froude number and the vertical viscosity tend to zero simultaneously. The new ingredient of this paper is to give a first proof of the three scale singular limit coupled with Ekman boundary layer by introducing an asymptotic profile to the original system. [ABSTRACT FROM AUTHOR]