## 1 Introduction  
Cold-sky calibration for spaceborne L-band synthetic aperture radiometers is essential for reducing salinity retrieval errors. The system response to known controlled signals, so-called calibration, is key to the success of the radiometer mission. In order to monitor and forecast sea surface salinity, the assimilation of different radiometer satellites is used to reduce ocean analysis errors, which requires high-quality calibration technology. To support this goal, brightness temperature absolute calibration is the key technology used to obtain high-precision data. The absolute calibration of synthetic aperture radiometers is performed by viewing the deep-sky scene [1]. The calibration stages can be divided into pre-launch calibration and post-launch calibration. During the operation of the satellite, the offset bias of the instruments can introduce measurement errors into the visibilities of synthetic aperture radiometers, resulting in deviation between on-ground characterizations and in-flight ones if the pre-launch calibration coefficient continues to be used. Therefore, in order to avoid greater impact on subsequent data products at all levels, in-orbit cold-sky calibration of the radiometer sensors is required to eliminate systematic deviations and improve data accuracy.  
Periodic cold-sky observation maneuvers are performed over a specific part of Earth's surface to evaluate relative and absolute calibration post-launch, such as Jason3 radiometers, SMOS, Aquarius, and SMAP radiometers [1; 2; 3; 4; 5; 6]. The radiometer antenna patterns' information can be refined by cold-sky maneuvers. For example, the SMAP radiometer antenna points to the cold sky near the Amazonian rainforest, and the backlobe of the antenna observes a transition from ocean to rainforest to correct antenna backlobe spillover. Cold-sky calibration can also be used to calibrate the internal noise diode [2]. The modeled values over cold-sky targets are compared with the measurements of the radiometer for quantification. The simulators of radiometers for cold-sky calibration can be used for calibration program design, which should consider many factors, such as the proportion of land and sea in the antenna pattern and the ground track over the celestial sky [7]. The number of antennas in a synthetic aperture radiometer is much larger than in a real aperture radiometer. For example, the Y-shaped 2D array of MIRAS is formed by three arms about 4.5 m long, with 23 equally spaced antennas each [8]. Additionally, the simulation of a synthetic aperture radiometer for its cold-sky calibration takes much more time, and the quantity is calculated using the traversing method. The influence of the space environment is not considered in traditional cold-sky calibration tactics. In this paper, an effective strategy for the cold-sky calibration of synthetic aperture radiometers is proposed, with consideration of the effect of external thermal environmental variation. The error of the assumption of a spherical Earth is also quantified, which can be used to simplify the simulator for the cold-sky calibration scheme and achieve high-fidelity results with very few computational resources. The offsets in the TB caused by the antenna pattern error between the on-ground and in-flight measurements are assessed, which are mainly due to the influence of antenna uncertainty caused by the space environment alternating between cooling and heating.