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Geophysical turbulence has a wide range of spatiotemporal scales that requires a multiscale prediction model for efficient and fast simulations. Stochastic parameterization is a class of multiscale methods that approximates the large-scale behaviors of the turbulent system without relying on scale separation. In the stochastic parameterization of unresolved subgrid-scale dynamics, there are several modeling parameters to be determined by tuning or fitting to data. We propose a strategy to estimate the modeling parameters in the stochastic parameterization of geostrophic turbulent systems. The main idea of the proposed approach is to generate data in a spatiotemporally local domain and use physical/statistical information to estimate the modeling parameters. In particular, we focus on the estimation of modeling parameters in the stochastic superparameterization, a variant of the stochastic parameterization framework, for an idealized model of synoptic-scale turbulence in the atmosphere and oceans. The test regimes considered in this study include strong and moderate turbulence with complicated patterns of waves, jets, and vortices.