PArametric determination of the dynamic ocean topography from geoid, altimetric sea surface heights and SAR derived RAdial SURface Velocities --- PARASURV

动态海洋地形作为海面高度和大地水准面之间的差的大地测量估计尽管关系简单，但仍然是一项困难的任务。主要是现有的测高海面高度观测和大地水准面信息之间的光谱不一致性导致分离过程中的问题。卫星大地水准面信息的精度特征是补充，因为它仅在100 km左右的分辨率下足够精确。相反，大多数衍生模型都是基于网格的--在预定义的网格上以给定的分辨率提供函数值。在它们的生成中，通常使用多步方法，在几个步骤中导出网格。使用规则网格会导致问题，当除了经典使用的大地水准面和高度信息，额外的观测包括到动态地形估计。此外，现有的方法有局限性，适当考虑所使用的数据集的准确性信息。为了避免这些限制，使用一个集成的参数一步的方法提出。数学函数代表大地水准面和动态海洋地形的同时估计。 描述海洋动力学地形的物理模型是不能完全参数化的。动力海洋地形的物理描述不适用于有限参数化。 因此，真实的函数空间的近似是必要的，这可以在具有预定义的平滑特性的有限元方法内完成。在这个项目中，建议使用C <$-光滑有限元对动态海洋地形进行参数化，并将予以实施。这个属性的动机是提案的第二个方面，使用额外的观察。合成孔径雷达得出的径向表面速度应纳入调整，以限制估计，并支持将海面高度测量分为大地水准面和动态海洋地形。在本提案中，应研究随机径向表面速度观测的性质及其在动态地形建模中的应用。

The geodetic estimation of the dynamic ocean topography as the difference between the sea surface height and the geoid remains, despite the simple relation, still a difficult task. Mainly, the spectral inconsistency between the available altimetric sea surface height observations and the geoid information causes problems in the separation process. This is complemented by the accuracy characteristics of the satellite derived geoid information, as it is only sufficiently accurate for a resolution of about 100km.Parametric approaches which describe the dynamic ocean topography with a mathematical function are rarely used. Instead, most of the derived models are grid based -- function values provided on a predefined grid with a given resolution. Within their generation, typically multi-step approaches are used, deriving the grid in several steps. Using regular grids results in problems, when besides the classically used geoid and altimetric information, additional observations are included into the dynamic topography estimation. Furthermore, the existing approaches have limitations properly accounting for the accuracy information of the used data sets. To avoid these limitations, the use of an integrated parametric one-step approach is proposed. Mathematical functions representing the geoid and the dynamic ocean topography are simultaneously estimated. The physical model describing the dynamic ocean topography can not be finitely parameterized. The dynamic ocean topography proper physical description is not applicable for finite parameterization. Thus an approximation of the real function space is necessary, which can be done within a finite element approach with predefined smoothness properties. Within this project the use of C¹-smooth finite elements for the parameterization of the dynamic ocean topography is proposed and shall be implemented. This property is motivated by the second aspect of the proposal, the use of additional observations. Synthetic Aperture Radar derived radial surface velocities shall be integrated into the adjustment to constrain the estimate and support the separation of sea surface height measurements into geoid and dynamic ocean topography. Within this proposal the properties of stochastic radial surface velocity observations and their use for dynamic topography modeling shall be studied.