Stochastic parameterizations are broadly used in climate modeling to represent subgrid scale processes. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to the technical and numerical aspects. In particular, the use of Empirical Orthogonal Functions (EOFs) is well established whenever a spatial structure is required, without considering its possible drawbacks. By applying an energy consistent parameterization to the 2-layer Quasi-Geostrophic (QG) model, we investigate the model sensitivity to the \emph{a priori} assumptions made on the parameterization. In particular, we consider here two methods to prescribe the spatial covariance of the noise. First, by using climatological variability patterns provided by EOFs, and second, by using time-varying dynamics-adapted Koopman modes, approximated by Dynamic Mode Decomposition (DMD). The performance of the two methods are analyzed through numerical simulations of the stochastic system on a coarse spatial resolution, and the outcomes compared to a high-resolution simulation of the original deterministic system. The comparison reveals that the DMD based noise covariance scheme outperforms the EOF based. The use of EOFs leads to a significant increase of the ensemble spread, and to a meridional misplacement of the bi-modal eddy kinetic energy (EKE) distribution. On the other hand, using DMDs, the ensemble spread is confined and the meridional propagation of the zonal jet stream is accurately captured. Our results highlight the importance of the systematic design of stochastic parameterizations with dynamically adapted spatial correlations, rather than relying on statistical spatial patterns.