This study introduces two new retrievals for ground-based microwave radiometers (MWR) and demonstrates that, together, they solve the misrepresentation issue that makes it challenging to assimilate cloudy-sky brightness temperatures. Multiple studies have shown that assimilating MWR brightness temperatures is beneficial to numerical weather prediction, despite rejecting substantial amounts of valid observations from the assimilation due to the presence of liquid water clouds. Cloud detection complemented with a cloud clearing retrieval makes this rejected data available for direct assimilation.</p> <p>We scrutinize the introduced cloud detection retrieval and cloud clearing retrieval using multiple approaches. For one, we contextualize the new retrievals with reference retrievals. Secondly, we determine the retrieval sensitivity to instrument errors using a Monte Carlo method. And most importantly, we assess the representativeness of the retrieval products, which is crucial for data assimilation, through observation minus background statistics.</p> <p>Our analysis reveals that the new cloud detection retrieval predicts less false positive cloudy-sky cases (-13 % over two years) compared to the established reference. Additionally, the cloud-clearing retrieval improves the representativeness between observation and background to the extent that artificial clear-sky and native clear-sky statistics almost match. Considering the minimal instrumentation required, both retrievals perform surprisingly well for elevation angles from zenith down to 4.8 &deg;.</p> <p>Overall, our findings demonstrate that combining cloud detection and cloud clearing retrievals improves the representativeness between observations and model. This retrieval combination enables the direct assimilation of cloudy-sky brightness temperatures.