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We incorporate the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) module in the Community Earth System Model version 2 (CESM2) Community Atmosphere Model Version 6 with interactive chemistry (CAM6‐chem), and couple it with the four mode version of the Modal Aerosol Module (MAM4). The MOSAIC module is used to simulate the thermodynamics of the gas‐aerosol mass exchange, with a special focus on simulating nitrate aerosol. By comparing against ground and satellite observations, we found that the MOSAIC/MAM4 scheme performs reasonably well in simulating spatiotemporal distributions of aerosols, including nitrate aerosol. We conducted a series of model experiments with and without nitrate aerosols, and examined the radiative effect (RE) associated with nitrate aerosols in 1975, 2000, and 2010, and accessed the radiative forcing (RF) of nitrate aerosols between the present day and pre‐industrial periods. Comparing with the nitrate aerosol RE, we predicted relatively small RF of anthropogenic nitrate aerosol from aerosol‐radiation interactions (RFari: −0.014 W m−2) and large RF from aerosol‐cloud interactions (RFaci: −0.219 W m−2). Regional signatures of nitrate RE/RF are noticeable and important: for instance, very small changes in REari in Europe and USA, but 2.8–3 times increases in REari in India and China from 1975 to 2010, while REaci/RFaci in China is a warming effect due to the competing effect between sulfate and nitrate aerosols as cloud condensation nuclei. Key Points: We incorporated the Model for Simulating Aerosol Interactions and Chemistry aerosol module in Community Earth System Model version 2 (Community Atmosphere Model Version 6 with interactive chemistry) modelWe found small radiative forcing due to nitrate‐radiation interactions but large radiative forcing due to nitrate‐cloud interactionsWe found rapid increases in nitrate aerosol REari in China and India since 1975 and positive nitrate aerosol REaci in China after 2000 [ABSTRACT FROM AUTHOR]