Data assimilation on the exponentially accurate slow manifold
Data assimilation on the exponentially accurate slow manifold
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DOI：
10.1098/rsta.2012.0300
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发表时间：
2013-05-28
期刊：
影响因子：
5
通讯作者：
Cotter, Colin
中科院分区：
文献类型：
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作者：
Cotter, Colin
我描述了一种数据同化的方法，该方法利用在拉格朗日坐标系中半地转标度的慢流形上定义坐标系的显式映射，并将该方法应用于一个简单的玩具系统，该系统先前已被提出为半地转标度的低维模型。该方法可以扩展到拉格朗日粒子方法，如哈密顿粒子网格和光滑粒子流体力学，应用于旋转浅水方程，许多性质将保留在更一般的欧拉方法中。利用哈密顿标准形式理论，先前已经证明，如果选择系统的初始条件作为映射的像点，那么系统的快速分量在指数长的时间内具有指数小的幅度，并且如果使用辛积分器进行数值时间步进，则该性质保持不变。然后可以使用该映射来参数化慢流形附近的初始条件，允许在不引入任何快速运动程度的情况下执行数据同化（更一般地说，可以选择快速运动的精确量）。
I describe an approach to data assimilation making use of an explicit map that defines a coordinate system on the slow manifold in the semi-geostrophic scaling in Lagrangian coordinates, and apply the approach to a simple toy system that has previously been proposed as a low-dimensional model for the semi-geostrophic scaling. The method can be extended to Lagrangian particle methods such as Hamiltonian particle-mesh and smooth-particle hydrodynamics applied to the rotating shallow-water equations, and many of the properties will remain for more general Eulerian methods. Making use of Hamiltonian normal-form theory, it has previously been shown that, if initial conditions for the system are chosen as image points of the map, then the fast components of the system have exponentially small magnitude for exponentially long times as epsilon -> 0, and this property is preserved if one uses a symplectic integrator for the numerical time stepping. The map may then be used to parametrize initial conditions near the slow manifold, allowing data assimilation to be performed without introducing any fast degrees of motion (more generally, the precise amount of fast motion can be selected).