Mean dynamic topography and oceanographic parameters estimated from an inverse model and satellite geodesy, with link to model result in one single NetCDF file (392 MB), including the inverse data error covariance

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography-the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99-110, 2012, doi:10.1016/j.jog.2011.07.0069; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie, 2012, http://nbn-resolving.de/nbn:de:hbz:5n-29199). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.

地转表面流速可由平均动力地形（mean dynamic topography）的梯度推导得到——平均动力地形为平均海面与大地水准面（geoid）之差。因此，独立观测得到的平均动力地形数据是海洋环流模式的重要输入参数与约束条件。
要实现与观测动力地形数据的良好拟合，不仅需要特定海洋模式网格上的平均动力地形数据，还需其逆协方差矩阵（inverse covariance matrix）的相关信息。然而，基于卫星重力场模型（satellite-based gravity field models）与测高海面高度测量（altimetric sea surface height measurements）计算平均动力地形并非易事。
为此，我们此前已开发出一套一体化方法，可在无需使用常规滤波手段的前提下，以一致的方式整合这两类不同观测数据集（Becker等，《地球动力学杂志》，2012，59(60):99-110，DOI:10.1016/j.jog.2011.07.0069；Becker，《重力场、测高与水文数据的一致组合以构建动态海洋地形模型》，2012，http://nbn-resolving.de/nbn:de:hbz:5n-29199）。该组合方法可覆盖观测的全频谱范围，还能直接求解任意网格上平均动力地形的法方程（normal equations，即误差协方差矩阵（error covariance matrix）的逆），这正是海洋数据同化（ocean data assimilation）的必要条件之一。
本文报告了我们在筛选与优化处理测高数据集方面取得的进展。我们重点针对Jason-1与Envisat的沿轨测高数据（along-track altimetry data）开展预处理流程，以获取平均海面剖面。在此过程中完成了严格的方差传播，首次实现了平均海面完整协方差矩阵的获取。
将该平均剖面与GRACE/GOCE组合重力场模型相结合，可得到北大西洋海域的平均动力地形模型，该模型基于一套明确的假设条件。我们证实，将带有完整误差结构的大地测量获取的平均动力地形融入三维稳态反演海洋模式后，相较于此前的估算结果，该模式模拟的海洋学特征得到了显著改善。