###### Abstract  
The trajectory-crossing method is an important and effective method for spaceborne SAR (synthetic aperture radar) to detect a two-dimensional current field. However, in practical applications, there are few spaceborne SAR data that meet the requirements of close acquisition time and overlapping trajectories, which makes it difficult to comprehensively analyze the impact of different systems and environmental parameters on current measurement results from real data processing. With the proposal of a SAR constellation plan in the future, the data resources will be constantly enriched, and the trajectory-crossing method will be widely used. It is, thus, necessary to lay some theoretical foundation at present. A two-dimensional sea-surface-current-field simulation method for trajectory crossing spaceborne SAR is proposed in this paper. Based on the principles of the trajectory-crossing method, the proposed method can realize the simulation of two-dimensional sea-surface-current field under given spaceborne SAR system and environmental parameters. In this paper, the simulation process of this method is given, and the simulation experiment is performed. Compared with the current measurement results of SAR data, the simulation experiment shows that the current velocity error is less than 0.03 m/s and the direction error is less than 10 degrees, which proves the reliability of the proposed simulation method. The proposed method lays a foundation for analyzing the influence of various parameters in the application of the trajectory-crossing method. s +
Footnote †: journal: Applied  
article  
[color=gray!20,linewidth=0.5,linewidth=0. verified in some airborne [5] and spaceborne [6] SAR data processing, and there is a lack of further research for the impact of different system and environmental parameters on the current measurement effect. Therefore, simulation is an effective research method. At present, to the best of knowledge, there is no specific simulation method for the trajectory crossing current measurement process. Due to the complexity of sea-surface electromagnetic scattering, the simulation of sea-surface SAR data usually does not start from the original echo but mainly considers the modeling using wave spectrum and modulation transfer function. In 2000, [PERSON] and [PERSON] [7] proposed a sea-surface Doppler spectrum model based on the improved combined sea-surface model, in which the wave-current interaction and the modulation transmission process of sea-surface backscattering were considered [8; 9]. Then, the model was integrated into SAR ocean imaging model and widely used in sea-surface current measurement and simulation [10; 11; 12]. Therefore, this model provides a possibility for the simulation of two-dimensional sea-surface-current field for trajectory crossing spaceborne SAR. Based on the principle of the sea-surface SAR imaging process and trajectory-crossing method, a two-dimensional current field simulation method is proposed in this paper. In the second part, the specific process of the proposed simulation method is given. In the third part, the simulation experiment and verification are conducted. Finally, the above is summarized. Simulation Method of Two-Dimensional Sea-Surface Current Field for Trajectory Crossing Spaceborne SAR  
The trajectory-crossing method needs to use two sets of spaceborne SAR data with overlapping areas, usually from ascending and descending passes, respectively, and their acquisition time should be close. Geometric relationships of different velocity components of sea-surface motion over overlapping area are shown in Figure 1, where the blue and red thick arrows indicate the flight direction of the ascending and descending satellite, respectively. The sea-surface imaging range is \(S\) and \(G\), bounded by blue and red dashed lines, respectively. The middle is the overlapping area of \(S\) and \(G\), where \(V_{tot}\) and \(D_{tot}\) represent the magnitude and direction of current velocity, respectively.