Retrieving Atmospheric Thermodynamic and Hydrometeor Profiles Using a Thermodynamic-Constrained Kalman Filter 1D-Var Framework Based on Ground-based Microwave Radiometer

Abstract. Ground-based microwave radiometers (GMWRs) provide continuous thermodynamic profiling but suffer from degraded accuracy under cloudy and precipitating conditions when using classical one-dimensional variational (1D-Var) retrievals. To address this, we develop a thermodynamic-constrained Kalman filter variational framework (TCKF1D-Var) that enforces moist-thermodynamic consistency through the use of virtual potential temperature as the control variable, employs a ratio-based cost function independent of prescribed background and observation error covariances, and integrates a diagnostic microphysics closure to represent liquid and ice water. Validation over 43 GMWR sites in North China, including seven with collocated radiosondes, shows that TCKF1D-Var systematically reduces temperature and humidity biases relative to ERA5 and 1D-Var, with the largest improvements above 2 km for temperature and below 5.5 km for humidity. Temperature root-mean-square errors remain comparable to ERA5 and lower than 1D-Var below 8.5 km, while humidity errors are improved near the surface though degraded in the mid-troposphere due to vertical-resolution mismatch and channel cross-talk. Evaluation against collocated EarthCARE cloud liquid water content profiles demonstrates that TCKF1D-Var yields the lowest biases and errors and best reproduces observed distributions, confirming the benefit of the microphysics constraint. Case analyses of short-duration heavy rainfall further show that TCKF1D-Var enhances precursor signals of convection, extending the effective lead time for early warning relative to ERA5 and substantially outperforming 1D-Var. These results highlight the value of embedding physical constraints and microphysical closure within GMWR retrievals, offering a practical pathway to improve continuous thermodynamic monitoring and support high-impact weather nowcasting.