## 4 Observation Simulations of GMR, GeoSTAR, and GIMS
### Simulation of the Observed Brightness Temperature TA of GMR, GeoSTAR, and GIMS
#### 4.2.3 Geostationary Interferometric Microwave Sounder (GIMS)  
GIMS is a new concept of an atmospheric microwave sounder for China's future geostationary microwave meteorological satellite (FY-4 MW). GIMS is a 50-60 GHz SAIR working in rotating mode with a 70-element circular antenna array. Compared with a conventional stationary SAIR, the rotating SAIR can significantly reduce the number of elements required with the same array aperture at the cost of longer observation periods. The optimized thinned array layout of GIMS is shown in Figure 7a. Seventy antennas sparsely distributed around a 3.7 m diameter circle form the required baselines. Although the snapshot UV plane samples are very sparse and irregular, as shown in Figure 7b, the full samples after a rotation cycle in Figure 7c provide good UV plane coverage. Comparing Figures 6d and 7d, it can be seen that the UV plane samples of GeoSTAR are in a hexagonal uniform grid, but the UV plane samples of GIMS are in a nonuniform polar grid. For the visibility function in the nonuniform polar grid, such a generalized IDFT algorithm does not exist to perform brightness temperature reconstruction. Figure 7: The antenna array (**a**) and resulting UV plane sampling pattern of the GIMS. (**b**) Snapshot samples, (**c**) the full samples after a rotation cycle, and (**d**) partial zoomed-in view. To solve this problem, the visibility samples of GIMS are interpolated from the polar grid to the pseudo polar grid, and then the inverse pseudo polar FFT (PPFFT) is used to reconstruct the brightness temperature distribution [46]. The pseudo polar grid is composed of the intersection nodes between concentric squares and equisloped rays, as shown in Figure 8a. The interpolation from the polar grid to the pseudo polar grid can be implemented by two 1-D interpolations, generally having higher accuracy than 2-D interpolations. For the polar grid of visibility, the equiangular sample points of each circle are 1-D interpolated in the angular direction to obtain equisloped points (as shown in Figure 8b), and then the sample points along each equisloped ray are 1-D interpolated again in the radial direction to square the circles and obtain the pseudo polar grid (as shown in Figure 8c). Finally, the inverse Fourier transform from the pseudo polar grid visibility samples in the spatial frequency domain to the brightness temperature distribution in the spatial domain can be quickly and accurately implemented by inverse PPFFT and the conjugate gradient method. Figure 5d,i shows the simulated 2-D and E-plane 1-D AF of the GIMS with a rectangular window at 50.3 GHz, and the corresponding 3-dB beamwidth and the first SLL are 0.064\({}^{\circ}\) and \(-\)8.8 dB, respectively. The AF with a Blackman window is shown in Figure 5e.j. The 3-dB beamwidth increases to 0.112\({}^{\circ}\), while the first SLL decreases to \(-\)28.5 dB, consistent with GeoSTAR. The simulation parameters of GIMS are shown in Table 3. The simulation process of GIMS is similar to GeoSTAR. The main difference is that the inverse PPFFT algorithm instead of inverse DFT is used to reconstruct the brightness temperature distribution from the visibility for the GIMS. The simulated GIMS observation TA images of Typhoon Hagibis for all 8 channels are shown in Figure 4i-p.  
window is used for GeoSTAR and GIMS. For the relatively transparent channels, i.e., 1-4, the quality degradation of the TA images mainly come from the blurring caused by the limited main lobe beamwidth and side lobe, while for the opaque channels, i.e., channels 5-8, the TA image error is more from the system random noise. GeoSTAR, as a stationary SAIR, has the longest integration time in the simulation configuration, resulting in the smallest system noise. Thus, the TA images of the 5-8 channels appear to have the smallest error.