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

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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.