Collaborative Research: CSEDI--Variational Approaches to Geomagnetic Data Assimilation

这个项目的目标是开发一种方法来结合地球的历史和正在进行的测量？用计算机模拟地球的磁场？S动态地核，即地磁场产生的地方。类似的方法，一般称为数据同化（DA），在大气科学中广泛使用，以提高由大气流动数值模式产生的天气预报的可靠性。我们将这些方法应用于地磁场，将有助于改进磁场产生的模型，更好地了解地球的物理过程。并改进了对地磁场慢时间变化的估计，即历史上和更遥远过去的地磁场长期变化（SV）。这种改进的SV将在各种科学研究中具有价值，包括地球自转、地球动力学、地磁和古气候。地磁数据分析的发展最终将使对地球未来演化的预测更加准确。S磁场。该项目建立在以前的地磁序列数据分析工作的基础上，适应了海洋和大气科学变分数据分析方法的最新发展。我们工作的关键组成部分包括为most（模块化可扩展自洽三维）地球动力学模型开发切线和伴随代码，使用这些代码实现现代变分数据分析方案（所谓的代表方法），以及对地磁数据集的初步应用。在变分方法中，模型输入（初始和边界数据、强迫）被调整以同时拟合动力方程和观测数据。这种技术方法提供了一种自然的方法，可以使用近年来的高质量数据来改进对过去时代的磁场和岩心流量的估计，允许动态一致地同时估计岩心中磁场和流体速度场的时间演变，以及在地表观测到的结果信号。更一般地说，变分数据分析提供了一个比较地球动力学模型输出和数据的通用框架，并将允许对动力学假设进行严格的检验。为变分数据分析开发的切线和伴随工具也将应用于数值地球动力学模型的敏感性和稳定性分析。

The objective of this project is to develop methods for combining historical and ongoing measurements of the Earth?s magnetic field with numerical computer models for Earth?s dynamic core, where the geomagnetic field is generated. Similar methods, generally referred to as data assimilation (DA), are widely used in atmospheric sciences to improve reliability of weather forecasts generated by numerical models of atmospheric flows. Our application of these methods to the geomagnetic field will allow development of improved models of magnetic field generation, better understanding of physical processes in Earth?s core, and improved estimation of the slow time variations of the geomagnetic field, i.e. geomagnetic secular variation (SV) in the historical and more distant past. Such improved SV will be of value in diverse scientific studies, including Earth rotation, geodynamics, geomagnetism, and paleoclimate. Ultimately, development of geomagnetic DA will result in improved forecasts of the future evolution of the Earth?s magnetic field.The project builds on previous work with sequential DA in geomagnetism, adapting recent developments of variational DA methods in ocean and atmospheric sciences. Key components of our effort include development of tangent linear and adjoint codes for the MoSST (Modular Scalable Self-consistent Three-dimensional) geodynamo model, use of these codes to implement a modern variational DA scheme (the so-called representer method), and initial applications to geomagnetic datasets. In the variational approach model inputs (initial and boundary data, forcing) are adjusted to simultaneously fit dynamical equations and observational data. This technical approach provides a natural way to use high quality data from recent years to improve magnetic field and core flow estimates for past epochs, allowing dynamically consistent simultaneous estimation of the time evolution of the magnetic and fluid velocity fields in the core, and the resulting signals observable at the surface. More generally, variational DA provides a common framework for comparing geodynamo model outputs to data, and will allow rigorous tests of dynamical hypotheses. The tangent linear and adjoint tools developed for variational DA will also have applications to sensitivity and stability analysis of the numerical geodynamo models.