A two-step method of crossover adjustment for satellite altimeter data

Crossover adjustment is a crucial method for processing satellite altimetry data. The primary focus in the research of crossover adjustment has been on correcting time-related systematic errors, while studies on correcting geography-related systematic errors are relatively few. Reducing the impact of geography-related systematic errors can improve the detection of finer ocean signals in sea surface height (SSH). To address this problem, a novel approach introduced in the study divides the process for satellite altimetry crossover adjustment into two steps. Compared to other crossover adjustment, the two-step method incorporates the correcting of geography-related systematic errors using a harmonic expansion model. In the first step, a hybrid polynomial model with time as the variable is used to correct for time-related systematic errors. Unlike the traditional crossover adjustment method that constructs observation equations directly through crossover discrepancies, the first step can be processed for each track individually, and an appropriate hybrid polynomial empirical model is selected based on the number of crossover points on the track, thereby mitigating the impact of rank deficiency. In the second step, a harmonic expansion model with latitude and longitude as variables is used to correct for geography-related systematic errors. The parameter of the harmonic expansion are estimated using the Tikhonov regularization principle and the L-curve method to determine the regularization parameter, thereby resolving the issue of rank deficiency. The completion of the two-step process corrects time-related and geography-related systematic errors in satellite altimeter data. Experiments were conducted in the Arabian Sea region (46°∼80°E, 0°∼30°N) using Archiving, Validation and Interpretation of Satellite Oceanographic data (AVISO) Level 2 plus data of Sentinel-3A, Sentinel-3B. The results indicate that the two-step method can reduce the crossover difference from Sentinel-3A and Sentinel-3B by about 4.1 cm, and reduce the discrepancy between Sentinel-3A/Sentinel-3B and Sentinel-6A/Jason-3 by approximately 1.6 cm to 1.8 cm. The tide gauge data is used to validate the two-step method, showing that the STD of the differences between the SSHs processed using this method and the tide gauge data was reduced by 5.3 % to 17.3 %.