Abstract: To improve the dynamical performance of the unified weather-climate modeling system, this study implements the RWDM6 (Revised WRF Double-Moment 6-class) double-moment bulk microphysics scheme within the GRIST (Global-to-Regional Integrated Forecast System) global nonhydrostatic model, replacing the original MG (Morrison-Gettelman) parameterization. A comprehensive time-step size sensitivity analysis is performed to evaluate the scheme improvements. Comparative evaluations demonstrate that the RWDM6 scheme exhibits superior performance in simulating critical meteorological fields, including thermodynamic profiles, relative humidity distributions, cloud fraction, cloud radiative forcing, and precipitation. The scheme effectively mitigates the cold and moist biases in the mid-upper troposphere while simultaneously reducing the warm and dry biases in the stratosphere. The RWDM6 implementation also corrects the systematic overprediction of total cloud fraction at mid-high latitudes, with vertical cloud structure analysis indicating these improvements primarily arise from enhanced representation of mid-and low-level clouds. Furthermore, RWDM6 reduces the underestimation of shortwave cloud radiative forcing in tropical and Arctic regions while ameliorating the overestimation of longwave cloud radiative forcing over Southeast Asia and mid-latitude marine areas. Through improved microphysical process representation, the new parameterization decreases precipitation biases in tropical convergence zones, collectively enhancing the GRIST model's predictive capability. Time-step size sensitivity experiments reveal that the MG scheme produces spatially inconsistent bias patterns in simulated precipitation, cloud radiative effects, and humidity fields across different time-step sizes. For instance, the negative bias in tropical shortwave cloud radiative forcing attenuates with decreasing time steps, while the positive bias over the Southern Ocean amplifies, exhibiting opposing response characteristics. Although these MG-derived biases show non-monotonic dependencies on time-step variations, they collectively highlight the scheme's inherent sensitivity to time-step size. In contrast, RWDM6 simulations demonstrate significantly improved statistical consistency across different time-step sizes configurations, with markedly reduced sensitivity of microphysical parameterization errors on timestep variations. This enhanced stability primarily stems from RWDM6's prognostic treatment of precipitation particles compared to MG's diagnostic approach, making it particularly suitable for highresolution applications with smaller time-step size. These characteristics indicate that the RWDM6 scheme exhibits superior adaptability for models employing variable resolution configurations or dynamic mesh refinement techniques, demonstrating strong potential for implementation within GRIST's flexibleresolution unified modeling framework across weather and climate timescales.