A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation
A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation
复制标题
亚临界地表准地转方程的数据同化算法
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
E. Titi
中科院分区：
文献类型：
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作者：
M. Jolly;V. Martinez;E. Titi
摘要 在本文中，我们证明了在简化场景中仅使用动力边界上的大空间尺度可观测量，可以通过反馈助推来实现三维准地转方程的数据同化。在此边界上，未知标量（流体的浮力或表面温度）满足表面准地转方程。反馈推动是在这个二维模型上完成的，但最终同步了三维流的流函数。主要的分析困难是由于表面准地转方程中存在非局部耗散算子。这是通过利用合适的单位划分、Sobolev 空间范数的连续性模量以及 Littlewood-Paley 分解来克服的，最终为观测算子建立各种有界性和近似恒等属性。
Abstract In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this boundary, a scalar unknown (buoyancy or surface temperature of the fluid) satisfies the surface quasi-geostrophic equation. The feedback nudging is done on this two-dimensional model, yet ultimately synchronizes the streamfunction of the three-dimensional flow. The main analytical difficulties are due to the presence of a nonlocal dissipative operator in the surface quasi-geostrophic equation. This is overcome by exploiting a suitable partition of unity, the modulus of continuity characterization of Sobolev space norms, and the Littlewood–Paley decomposition to ultimately establish various boundedness and approximation-of-identity properties for the observation operators.
DOI：
10.1016/j.physd.2012.11.005
发表时间：
2012-03
期刊：
Physica D: Nonlinear Phenomena
影响因子：
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作者：
C. Brett;K. F. Lam;K. Law;D. McCormick;M. Scott;A. Stuart
通讯作者：
C. Brett;K. F. Lam;K. Law;D. McCormick;M. Scott;A. Stuart