The arrangement of the antenna array of the mirrored aperture synthesis (MAS) determines the transformation matrix for solving the cosine visibilities. When the transformation matrix is rank deficient, the solved cosine visibilities will introduce the rank-deficient error. For the two-dimensional (2-D) mirrored aperture synthesis (2-D MAS), the existing literature has discussed the relationship between the arrangement of the antenna array and the rank-deficient error but has not proposed an array that can achieve a full rank transformation matrix, which is called the rank-full array (RFA). Based on a new method for calculating the rank of the transformation matrix (RTM) and the literature on one-dimensional (1-D) RFAs, this letter proves that 2-D RFA cannot be obtained when the reflectors are all metal, and by introducing a reflector made of a magnetic conductor, 2-D RFA can be obtained. Besides, this letter obtained the existence conditions for 2-D RFA. Based on those conditions, two methods are proposed to obtain 2-D RFAs.

In two-dimensional mirrored aperture synthesis (2-D MAS), the rank of the transformation matrix can affect the accuracy of the solved cosine visibilities; therefore, it has an impact on the accuracy of the reconstructed brightness temperature image. In this article, the influence of the rank deficient on the accuracy of the reconstructed brightness temperature image of 2-D MAS is discussed. An analysis of the rank-deficient error is performed by computing its impact on the radiometric accuracy for a reference scene. Two correction methods based on multiple measurements are proposed to correct the rank-deficient error. The simulations and experiments are carried out to demonstrate the effectiveness of the proposed methods.

The assimilation of spaceborne passive microwave measurements often suffers from representativeness errors due to the mismatch between the observation footprints and numerical weather prediction (NWP) model grids. In this article, a new brightness temperature remapping technique based on a deep convolutional neural network (CNN) is proposed to reduce the representativeness error in FengYun-3D (FY-3D) microwave radiation imager (MWRI) observation data assimilation. The remapping technique uses an adapted dataset construction method in which the training data consist of synthetic NWP-model-grid-based MWRI brightness temperature ( $T_{B}$ ) images and synthetic MWRI-observed antenna temperature ( $T_{A}$ ) images. The synthetic $T_{A}$ and $T_{B}$ , which are generated through radiative transfer for TOVS (RTTOV) model and MWRI degradation model, make the network learn the spatial remapping relationship between observation and background $T_{B}$ in data assimilation. In addition, land–sea mask information is input into the CNN to help the network better analyze the coastline area data. The CNN-based remapped MWRI observation data are evaluated through observation minus background (OMB) diagnosis with the Global/Regional Assimilation and PrEdiction System (GRAPES) four-dimensional variational (4D-Var) system. The experimental results illustrate that the bias and standard deviation of OMB with the CNN-based remapped MWRI observation are quantitatively reduced compared with the raw measurements in GRAPES 4D-Var.

Geostationary orbit (GEO) microwave sounding technology, which can continuously monitor Earth and intensively observe weather conditions such as strong convection, has unique advantages. An observing system simulation experiment (OSSE) is an important means to evaluate new meteorological instruments and explore assimilation techniques for new observations. In this paper, an OSSE based on the China Fengyun-4M (FY-4M) GEO microwave satellite is introduced in detail. The nature run (NR) of the OSSE is generated by the Mesoscale Weather Numerical Forecast System of the China Meteorological Administration (CMA-MESO), while the Global Forecast System of the China Meteorological Administration (CMA-GFS) is used to achieve the four-dimensional variational (4D-Var) assimilation and prediction experiment. The atmospheric parameters from the NR are used as inputs to the Radiative Transfer for the TIROS Operational Vertical Sounder (RTTOV) model to simulate the FY-4M GEO microwave brightness temperature. The OSSE results show that assimilating geostationary orbit microwave data has a positive effect on typhoon forecasting. Specifically, the shorter the observation time interval is, the smaller the observation noise, and the better the assimilation effect. There are differences in the role of different frequency band channels in improving forecasts; the best observation effect can only be achieved by setting the observation error appropriately, and the data preprocessing strategy is crucial for improving the assimilation quality. The GEO microwave OSSE further reveals the influence of future FY-4M geostationary microwave observations on typhoon forecasts and the issues that need to be addressed when assimilating these new data.

Mirrored aperture synthesis (MAS) has been proposed as a novel interferometry to achieve higher spatial resolution in passive microwave remote sensing. The phase and amplitude errors for MAS are a crucial problem that has yet to be analyzed. In this letter, a model for the phase and amplitude errors is established. A correction method based on an external source is proposed to correct the phase and amplitude errors. An analysis of the position of the external source is performed by computing its impact on the radiometric accuracy of a reference scene. The imaginary parts of the cross correlations for MAS are analyzed for the first time. Simulations and experiments are carried out to demonstrate the effectiveness of the correction method.

In 2-D mirrored aperture synthesis (2-D MAS), the array configuration determines the rank of the transformation matrix, which can affect the accuracy of the solved cosine visibilities. Ultimately, errors in solved cosine visibilities degrade the quality of reconstructed brightness temperature images. In this letter, the maximum rank of the transformation matrix is analyzed and proven by mathematical induction. An array optimization model of 2-D MAS based on the ``maximum-rank'' criterion is established, and optimal arrays are presented. Finally, the simulations and experiments are carried out to demonstrate the effectiveness of the optimization model.