变分地磁资料同化的一个事例：来自一维、非线性和稀疏观测的MHD系统的见解
A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system
摘要：
在过去的几百年里，地磁场的长期变化已经被测量，其精度不断提高，现在已经达到了卫星数据的顶峰。然而，众所周知的是，磁场的动力学与堆芯中的速度场的动力学相关联，并且对长期变化进行建模的任何尝试都将涉及磁场和堆芯速度的耦合动力学系统。不幸的是，没有直接观测到速度。独立的确切性质的上述耦合系统-一些版本目前正在建设中-的问题是辩论在本文中是否良好的知识的磁场可以转化为良好的知识的核心动力学。此外，最新和最精确的地磁数据对我们过去和未来的地磁场知识有什么影响？这些问题被投到变分数据同化的语言，而本文考虑的动力系统包括在一组两个过于简化的一维磁场和速度场方程。这个玩具模型保留了从感应方程和Navier-Stokes方程继承的重要特征：存在非线性磁和动量项，并且其对小扰动的线性响应包含Alfvén波。它的结论是变分数据同化原则上确实是适当的，即使速度场仍然隐藏在任何时候，它使我们能够恢复整个演变的两个领域的部分和不规则分布的信息的磁场。这项工作是走向历史地磁资料再同化和地磁预报的第一步。
英文摘要：
Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system -- some version being currently under construction -- the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfvén waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
