Sea state bias (SSB) is a crucial error of satellite radar altimetry over the ocean surface. For operational nonparametric SSB (NPSSB) models, such as two-dimensional (2D) or three-dimensional (3D) NPSSB, the solution process becomes increasingly complex and the construction of their regression functions pose challenges as the dimensionality of relevant variables increases. And most current SSB correction models for altimeters still follow those of traditional nadir radar altimeters, which limits their applicability to Synthetic Aperture Radar altimeters. Therefore, to improve this situation, this study has explored the influence of multi-dimensional SSB models on Synthetic Aperture Radar altimeters. This paper proposes a deep learning-based SSB estimation model called SNSSB, which employs a Siamese network framework, takes various multi-dimensional variables related to sea state as inputs, and uses the difference in sea surface height (SSH) at self-crossover points as the label. Experiments were conducted using Sentinel-6 self-crossover data from 2021 to 2023, and the model is evaluated using three main metrics: the variance of the SSH difference, the explained variance, and the SSH difference variance index (SVDI). The experimental results demonstrate that the proposed SNSSB model can further improve the accuracy of SSB estimation. On a global scale, compared to the traditional NPSSB, the multi-dimensional SNSSB not only decreases the variance of the SSH difference by over 11%, but also improves the explained variance by 5-10 cm2 in mid- and low-latitude regions. And the regional SNSSB also performs well, reducing the variance of the SSH difference by over 10% compared to the NPSSB. Additionally, the SNSSB model improves the computational efficiency by approximately 100 times. The favorable results highlight the potential of the multi-dimensional SNSSB in constructing SSB models, particularly the five-dimensional (5D) SNSSB, representing a breakthrough in overcoming the limitations of traditional NPSSB for constructing high-dimensional models. This study provides a novel approach to exploring the multiple influencing factors of SSB.

中文翻译：

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探索Siamese网络估计合成孔径雷达高度计海况偏差


海况偏差（SSB）是海洋表面卫星雷达测高的一个关键误差。对于可操作的非参数 SSB (NPSSB) 模型，例如二维 (2D) 或三维 (3D) NPSSB，求解过程变得越来越复杂，并且随着相关变量维数的增加，其回归函数的构建提出了挑战。目前大多数高度计的SSB校正模型仍然遵循传统天底雷达高度计的模型，这限制了它们在合成孔径雷达高度计中的适用性。因此，为了改善这一现状，本研究探讨了多维SSB模型对合成孔径雷达高度计的影响。本文提出了一种基于深度学习的SSB估计模型SNSSB，该模型采用Siamese网络框架，以与海况相关的各种多维变量作为输入，并利用自交叉点处的海面高度（SSH）差异作为标签。使用2021年至2023年的Sentinel-6自交叉数据进行实验，并使用三个主要指标评估模型：SSH差异方差、解释方差和SSH差异方差指数（SVDI）。实验结果表明，所提出的SSSB模型可以进一步提高SSB估计的精度。在全球范围内，与传统的NPSSB相比，多维SNSSB不仅使SSH差异的方差降低了11%以上，而且在中低纬度地区改善了解释方差5~10 cm2。并且区域 SNSSB 也表现良好，与 NPSSB 相比，SSH 差异的方差减少了 10% 以上。 此外，SNSSB模型将计算效率提高了约100倍。良好的结果凸显了多维 SNSSB 在构建 SSB 模型方面的潜力，特别是五维 (5D) SNSSB，代表着克服传统 NPSSB 在构建高维模型方面的局限性的突破。本研究为探索SSB的多重影响因素提供了一种新方法。