## 4 Results and Discussion  
An antenna pattern similar to the one in [13] is used for the selection of an optimized calibration location and the brightness temperature calculation for an L-band synthetic aperture radiometer. The results are shown as follows. Figure 8a shows the antenna brightness temperatures for the radiometer antenna beams when the cold-sky maneuver is emulated. The spacecraft rotates over 180\({}^{\circ}\) from its normal Earth-observing attitude to an orientation pointing toward the celestial sky, where the radiometer antennas are looking into the sky. Each point in the figure represents the projection of the center of the field of view of the antenna at each satellite position on the ground, and the color represents the brightness temperature value (unit: K) of the single antenna obtained while inverting the spacecraft here. The ground track, colored green, shows the lower brightness temperature, while the main beam of the antenna is looking toward the sky at this time, and Earth's surface is the ocean. The yellow and red colors show the brightness temperature change as the spacecraft crosses from land to ocean or otherwise. The integral of the power incident on the antenna is relatively low and constant when the satellite flies over an ocean far from land. The signal emitted from all kinds of sources surrounding the antenna is very stable at the same time. The dominant element of the signal is the direct emission of the sky, which enters the main lobe of the antenna. Additionally, the timing is suitable for the cold-sky maneuver from Earth's surface, and the direct emission from upwelling from the atmosphere into the back lobes of the antenna and the sum of the sun and moon entering into the side lobes of the antenna are also small and stable in the meantime. There are also some differences between the descending pass and the ascending pass at the same inverted position, as shown in this figure. For example, the antenna temperatures at the same location during the ascent orbit are slightly lower than the antenna temperatures at the descent orbit in the Pacific region. The appropriate geometry for the Aquarius CSC is chosen by the threshold corresponding to a weighted land fraction between 0.02% and 0.03% [9]. Figure 8b shows the results of the area selected by the criterium of a weighted land fraction <0.03%, based on a previous study, and the radiometer system operates on the sun-synchronous orbit parameter with an equatorial altitude of about 600 km. The figure shows the region with minimal interfering radiation from Earth among the data from 15 January 2021 04:24:00.000 to 19 January 2021 08:24:00.000. The red dot represents a suitable region to perform cold-sky calibration. Although the spherical approximation of the Earth model is simple and fast to implement in the computation, it can introduce some significant errors in geolocations and local incidence angles [9]. The antenna temperature Ta bias between the Earth ellipsoid model and the simplified spherical model in the cold-sky observation of the radiometer system is simulated in Figure 9. The differences are very apparent from the comparison of these two Earth models, especially when the spacecraft flies across the coastline, which is relatively larger than 1 K. For example, significant errors can happen at some land-ocean crossing geolocations, such as the ocean area at 60 degrees south latitude near the South Pole, the Bering Strait, the ocean near the Amazon forest, and so on. Therefore, the simplified spherical model of Earth is not suitable for antenna spillover or sidelobe calibration mode design, which can lead to significant errors, although the computation is efficient. As for cold-sky calibration design over an open-ocean area, the simplified spherical model of Earth can be used to improve efficiency. The spacecraft is usually kept inverted into the sky for a few minutes during cold-sky calibration. For example, the maneuvers before and after the external calibration measurement period each take about 20 min on SMOS [1].