Abstract GOCE satellite mission enabled us to produce a dramatic improvement in the ability to measure the ocean’s mean dynamic topography (MDT). To promote the application of the new geodetic MDT, it is essential to estimate its error quantitatively. Motivated by this requirement, we carefully assessed the formal error of geodetic MDT based on the classical error propagation law across each harmonic degree and order (D/O) which corresponds to different spatial scale. In the processes above, we presented an efficient method by introducing Fast Fourier Transform Algorithm (FFT) for computation, by which the challenge of high computation load in formal error estimation across each cutoff D/O was overcome. It was found that the MDT formal errors were mainly dominated by geoid formal error across high cutoff D/O. Across low D/O the mean sea surface (MSS) formal error was primarily responsible for the MDT formal error. At the global scale (70 °S-70 °N), the geoid and MSS made similar contributions (0.27 cm) to the MDT formal error (0.38 cm) with a cutoff D/O of 120, corresponding to spatial resolution of 167 km; With a cutoff D/O of 100, 200, and 280, the MDT formal errors were approximately 0.32 cm, 2.0 cm, and 12.5 cm, respectively.

中文翻译：

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不同空间尺度下大地平均动态地形的形式误差评估

摘要 GOCE 卫星任务使我们能够在测量海洋平均动态地形 (MDT) 的能力方面取得巨大进步。为了促进新的大地测量MDT的应用，对其误差进行定量估计是必不可少的。受此要求的推动，我们根据对应于不同空间尺度的每个谐波度数和阶数 (D/O) 的经典误差传播规律，仔细评估了大地测量 MDT 的形式误差。在上述过程中，我们通过引入快速傅立叶变换算法 (FFT) 进行计算，提出了一种有效的方法，克服了每个截止 D/O 的形式误差估计中高计算负载的挑战。发现 MDT 形式误差主要由高截止 D/O 的大地水准面形式误差主导。在低 D/O 中，平均海面 (MSS) 形式误差是 MDT 形式误差的主要原因。在全球尺度（70 °S-70 °N），大地水准面和 MSS 对 MDT 形式误差（0.38 cm）的贡献相似（0.27 cm），截止 D/O 为 120，对应的空间分辨率为 167 km ; 截止 D/O 为 100、200 和 280，MDT 形式误差分别约为 0.32 cm、2.0 cm 和 12.5 cm。