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

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.地基微波辐射计（Ground-based Microwave Radiometers，GMWRs）可实现连续的热力学廓线反演，但采用经典一维变分（One-dimensional Variational，1D-Var）反演方法时，在多云及降水天气条件下反演精度会出现退化。为解决这一问题，本研究提出了热力学约束卡尔曼滤波变分框架（Thermodynamic-Constrained Kalman Filter Variational Framework，TCKF1D-Var）：该框架以虚位势温度（virtual potential temperature）作为控制变量以实现湿热力学一致性，采用基于比值的代价函数，无需预设背景场与观测误差协方差，并集成了诊断性微物理闭合方案以表征液态水与冰水含量。针对华北地区43个GMWR站点（其中7个站点配备了同步探空仪）开展的验证实验表明，相较于ERA5再分析资料与1D-Var反演结果，TCKF1D-Var可系统性降低温度与湿度的偏差，其中温度偏差的改善在2 km高度以上最为显著，湿度偏差的改善则集中在5.5 km高度以下。在8.5 km高度以下，温度均方根误差与ERA5再分析资料相当，且低于1D-Var反演结果；而湿度误差在近地面有所改善，但由于垂直分辨率不匹配与通道串扰问题，对流层中层的湿度误差出现恶化。通过与EarthCARE卫星同步观测的云液态水含量廓线进行对比评估，结果显示TCKF1D-Var的偏差与误差均为最低，且能最优地复现观测到的分布特征，证实了微物理约束方案的有效性。针对短时强降水的个例分析进一步表明，TCKF1D-Var可增强对流前兆信号，相较于ERA5再分析资料延长了预警有效提前时间，且性能显著优于1D-Var反演结果。上述研究结果凸显了在GMWR反演中嵌入物理约束与微物理闭合方案的重要价值，为提升连续热力学监测能力、支撑高影响天气临近预报提供了切实可行的技术路径。