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Abstract A method that enables a mass-flux cumulus parameterization scheme (CPS) to work seamlessly in various model grids across CPS gray-zone resolutions is proposed. The convective cloud-base mass flux, convective inhibition, and convective detrainment in the simplified Arakawa–Schubert (SAS) scheme are modified to be functions of the convective updraft fraction. The combination of two updraft fractions is used to modulate the cloud-base mass flux; the first one depends on the horizontal grid space and the other is a function of the grid-scale and convective vertical velocity. The convective inhibition and detrainment of hydrometeors are also modified to be a function of the grid-size-dependent convective updraft fraction. A set of sensitivity experiments with the Weather Research and Forecasting (WRF) Model is conducted for a heavy rainfall case over South Korea. The results show that the revised SAS CPS outperforms the original SAS. At 3 and 1 km, the precipitation core over South Korea is well reproduced by the experiments with the revised SAS scheme. On the contrary, the simulated precipitation is widespread in the case of the original SAS experiment and there are multiple spurious cores when the CPS is removed at those resolutions. The modified mass flux at the cloud base is found to play a major role in organizing the grid-scale precipitation at the convective core. A 1-month simulation at 3 km confirms that the revised scheme produces slightly better summer monsoonal precipitation results as compared to the typical model setup without CPS.