2 Beijing Radio Measurement Institute, Beijing 100854, China;
3 Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266237, China
Oceanic eddies are important ubiquitous components of the ocean circulation system and play an essential role in the transportation and distribution of marine materials, energy, heat, and freshwater (Chelton et al., 2011; Chen et al., 2011; Nan et al., 2011; Wang et al., 2012; Sun et al., 2019). Ocean eddies can cause significant elevation differences among sea surface. According to size, oceanic eddies can be classified as either mesoscale or submesoscale eddies (Qiu et al., 2014; Penna and Gaube, 2019; Zhang et al., 2019). Existing high-resolution altimetry satellites have the capability to capture mesoscale oceanic eddies but not smaller eddies in the submesoscale. Therefore, better sampling (broader coverage, higher accuracy, higher spatiotemporal resolution) wide-swath interferometric imaging altimeter has been proposed, e.g., the Surface Water and Ocean Topography (SWOT) (Fu et al., 2012; Fu and Ubelmann, 2014; Xu et al., 2017) and Guanlan (Chen et al., 2019) satellite missions, which plan to launch in 2021 and 2022, respectively. The presence of instrument noise will affect the accuracy of ocean information extraction; therefore, the error analysis of the swath-wide interferometric altimeter plays an essential role before the launch. NASA SWOT workshop proposed an error analysis method based on wavenumber spectrum analysis (Fu et al., 2012; Fu and Ubelmann, 2014), and developed the SWOT Simulator software to directly evaluate the observation error from the perspective of wavenumber spectrum (Gaultier et al., 2016; Qiu et al., 2016). However, there is no complete simulation process of sea surface scattering modeling, radar altimeter echo modeling, imaging processing, and interference processing in the software. To facilitate data processing after the launch of the interferometric altimeter satellite, we shall analyze the ocean errors from the perspective of complete data processing. In this study, we carried out sea surface height extraction and a baseline and random error analysis based on theoretical and systematic simulation of interferometric altimetry. Further, we analyzed the influence of the error on the eddy extraction precision. Due to the limitation of the analysis depth of a single error source and article length, this article only discusses the random errors and baseline errors than other error sources, although they are equally important.2 INTERFEROMETRIC ALTIMETRY PRINCIPLE
Based on the Interferometric Synthetic Aperture Radar (In-SAR) technique (shown as Fig. 1a), an interferometric altimeter can obtain an observation swath extending tens to hundreds of kilometers with a small incidence angle (usually within 10°) near nadir. The angle measurement error of the baseline roll angle can cause significant errors in the height measurement of the sea surface elevation. Derived from the interferometric principle, the relationship between the baseline roll angle measurement error and the interferometric height error is (Jin et al., 2014; Kong et al., 2017):
where, θ is the incidence angle, r is the distance between antenna phase center and the sea surface, is the angle measurement error of the baseline roll angle, ∆α is the angle measurement error of the baseline roll angle.
Figure 1b shows the elevation error caused by the baseline roll angle error increases with the increase of the incidence angle in the cross-track direction. The baseline error of 1 arcsec results in an average height measurement error of 45 cm in the swath, but it can even reach ~80 cm in the distal swath (incidence angle of 10°). The elevation error caused by the baseline roll angle error can be simply recorded as the baseline error.
The random error is the height error caused by the interferometric phase error, and the influencing factors include signal-to-noise ratio (SNR) decorrelation, geometric decorrelation, and angular decorrelation, etc. In this study, ocean signal decoherence is mainly caused by primary and auxiliary SAR imaging error or their registration error. The random error is also related to the incidence angle shown as Eq.2 (Kong et al., 2017).
where, k is radar wave number, σphase is interferometric phase error, B is baseline length, θ is the incidence angle.
The random height error induced from the interferometric phase error is shown in Fig. 2. The error is small in the middle and large on both sides of the edge in the interferometric swath, and the root-mean-square error (RMSE) is 0.85 cm at the gird of 3 km×3 km.3 METHOD
Our method consists of two parts, theoretical simulation and systematic simulation (Fig. 3). The goal of the theoretical simulation is to obtain an arbitrary ideal sea surface with the eddy signals or significant elevation difference. This ideal sea surface can be obtained using a numerical ocean model. Here, we took Regional Ocean Modeling System (ROMS) (Shchepetkin and McWilliams, 2005) sea surface model data as the ideal ocean surface height. The system simulation is the whole process simulation from altimeter observation to data processing, and the simulation process is consistent with the altimeter remote sensing observation and data processing. In this study, the goal of the systematic simulation is to extract the elevation from the ideal sea surface of theoretical simulation and analyze the eddy signal based on the designed parameters of the interferometric altimetry system. The systematic simulation process mainly includes sea surface scattering modeling (Vandemark et al., 2016), radar altimeter echo modeling (Zeng et al., 2010), primary and auxiliary SAR imaging processing (e.g., Range-Doppler algorithm in Cumming and Wong (2005)), and interference processing (Kong et al., 2017). We obtain the baseline error according to the altimeter principle in Eq.1 and add it to the modeling echo in the radar altimeter. Besides, the random phase error is also induced in the interference processing because of the SAR imaging inaccuracy and the registration error of the primary and secondary SAR images. The systematic simulation accuracy of the altimetry system will be analyzed by considering the influence of the random and baseline errors. Finally, the ocean eddies are extracted (Isern-Fontanet et al., 2003; Liu et al., 2016) from theoretical and systematic ocean surfaces and make a comparison in detail.
To analyze the effect of baseline error on ocean signal, a combined-strategy of low-pass filtering, empirical orthogonal function (EOF) decomposition, and linear fitting, is proposed for error removal of the finally systematic sea surface. The strategy is as follows: compared with the sea elevation signal, the random noise is a type of high-frequency signal. Therefore, as far as possible, useful ocean signals can be retained through low-pass filtering. Then, the single sea surface height (SSH) image is divided into several sub-images in along-track direction to form a sub-image sequence. Then, EOF analysis is applied to the sequence to extract the signal mode. The first few valid modal components can be selected using EOF decomposition and modal signal validity analysis (Li et al., 2000; Wenzel and Schröter, 2014). From the retained modal signal, the baseline error can be estimated by linear fitting in the cross-track direction, because of the characteristic of the approximate linear increase of the baseline error. Then, the estimated baseline error can be removed from the retained EOF signal to obtain a "clean?sea surface elevation. The "clean?sea surface elevation can be compared with the originally theoretical simulated surface.4 RESULT AND DISCUSSION
Through three scenarios, we analyzed the effects of the altimeter system's baseline error and random error in data processing for the ocean surface obtained from the theoretical simulation and systematic simulation, and ocean surface signal extraction accuracy. The designed parameters of the interferometric altimetry system are shown in Table 1.
Scenario 1: Altimeter system does not contain baseline error, only random error is considered because of imaging error or registration error of primary and secondary images.
Figure 4 shows the intermediate result of the theoretical and systematic simulation of the altimeter system. It can be seen that the random error only makes the sea surface obtained from the systematic simulation rough compared with the theoretical simulation. However, the ocean eddy signal is still clear and distinct.
Scenario 2: Altimeter system contains baseline error, and the random error in data processing is also taken into account at the same time.
Figure 5 shows the theoretical simulated surface (Fig. 5a), systematic simulated surface (Fig. 5b), and the surface after error removal from Fig. 5b using the proposed combined-strategy (Fig. 5c & d). To estimate the error in the sea surface obtained from the systematic simulation and evaluate the error removal effect of the combined-strategy, we subtracted Fig. 5b–d from Fig. 5a to get the sea surface error and the residual error (Fig. 6). Figure 6a shows that the error distribution pattern is consistent with that interferometric principle in Section 2; therefore, the baseline error is the main error source in the sea surface obtained from the systematic simulation. However, it can be seen that Fig. 6b is almost the same as Fig. 6a, and it shows the effect of random error removal using low-pass filtering is relatively weak because of the low proportion of simulated high-frequency noise. Table 2 also confirms the poor remove effect, and residual error decreased by only 0.2 (0.1) cm on average (RMSE). However, the proposed EOF and linear fitting combined-strategy have a noticeable effect for baseline error elimination shown in Fig. 6c. Table 2 shows the final residual error decreases from 2.7 (3.1) cm to 0.1 (1.0) cm on average (RMSE), and the residual error is mainly distributed at image edges in the swath. And, more remarkable, the final residual error conforms to the distribution characteristics of random error in Fig. 2, and the residual error in the margin in the swath is significant, the middle is small. It indicates that the random error is the noise floor in the systematic processing, and it cannot be eliminated by a particularly effective method at present. However, the low-pass filtering method was tried in this study and played a weak error removal effect, and other methods need to be further considered.
Scenario 3: Eddy extraction and analysis based on Scenario 2
Ocean eddies can be extracted by various methods (Isern-Fontanet et al., 2003; Mason et al., 2014; Liu et al., 2016). We extracted ocean eddies from the theoretical simulated surface, the systematic simulated surface, and the surface after error removal in Fig. 5, separately. In the theoretical simulated surface, Eddy 1 and Eddy 2 were detected (Fig. 7a). A dark blue area of low sea surface height can be seen separating the two eddies. In Fig. 7b, the existence of the baseline error slightly enlarges the boundary of Eddy 1. In contrast, it dramatically reduces the boundary of Eddy 2, mainly because of the reduced area of low sea surface height values between the two eddies in the right swath. Figure 7c shows that the effect of error removal using low-pass filtering is weak, i.e., the detected eddies are almost the same as Fig. 7b. Figure 7d shows that the height characteristics of the theoretical simulated surface are entirely restored, and the range of the area of low sea surface height is also restored; consequently, the extracted eddies are almost identical to those of the ideal sea surface shown in Fig. 7a. The sea surface height after baseline error removal through the proposed combined-strategy is perfect.5 CONCLUSION
A new generation of altimetry satellites provides the possibility for better observation of the sea surface, especially for the submesoscale ocean signals. Before satellite launch, data processing and the related error analysis based on interferometric altimetry are particularly important, and they directly affect the satellite's ability to capture ocean signals. Because ocean eddies can cause significant elevation differences on the sea surface, this is very convenient for the theoretical simulation and systematic simulation for wide-swath interferometric altimetry. Therefore, in this study, the sea surface height extraction, sea surface error analysis, and ocean signal extraction are realized using the theoretical simulation and the systematic simulation. In particular, by analysis of three scenarios of the random error in data processing, baseline error in the altimetry system, and sea surface eddy extraction, the proposed combined-strategy of low-pass filtering, EOF decomposition, and linear fitting achieves a superior effect in systematic baseline error removal, thus significantly improving the ability of satellite altimetry to capture ocean signal. Through simulation experiments, the final error decreases from 2.7 (3.1) cm to 0.1 (1.0) cm on average (RMSE). The residual errors have the same distribution characteristics as random errors, and it is proved the noise floor in the altimeter data processing. It has also been proved that, after error removal, the sea surface can be recovered, and the ocean eddies are accurately extracted.6 DATA AVAILABILITY STATEMENT
The theoretical sea surface can be simulated by ROMS model or other ocean models. NASA SWOT workshop use ROMS model data for error analysis and developed a SWOT error simulator. A large number of ideal sea surfaces were provided in its doc folder in SWOT error simulator at the website: https://github.com/SWOTsimulator/swotsimulator/tree/master/doc/images.
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