Towards Data Driven Geodynamo Models Using Variational Data Assimilation

Details Towards Data Driven Geodynamo Models Using Variational Data Assimilation Towards Data Driven Geodynamo Models Using Variational Data Assimilation

Dec 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009agufm.p31c1257d&link_type=abstract

American Geophysical Union, Fall Meeting 2009, abstract #P31C-1257

Mathematics

Logic

[1510] Geomagnetism And Paleomagnetism / Dynamo: Theories And Simulations, [1595] Geomagnetism And Paleomagnetism / Planetary Magnetism: All Frequencies And Wavelengths, [5440] Planetary Sciences: Solid Surface Planets / Magnetic Fields And Magnetism

Scientific paper

In the last decade, fully 3-D, nonlinear numerical dynamo models have allowed for the study of many geomagnetic field features. As the ultimate goal of geodynamo simulations is to explain the features of the real geomagnetic field, variational data assimilation (DA) techniques, in which observations are combined with the underlying dynamical principles governing the system, are a logical next step. The increased resolution and accuracy of geomagnetic field models in recent years can be used to improve estimates of the geodynamo state in earlier years. We present our ongoing effort to develop modern variational DA modules based on the representer method for the Modular Scalable Self-consistent Three-dimensional (MoSST) geodynamo simulator. A variational approach to DA allows inputs (e.g., initial and boundary data, and forcing) to be adjusted to simultaneously fit dynamical equations and observational data by minimizing a cost functional. The present focus of our efforts is to develop tangent linear (TL) and adjoint (ADJ) codes for the nonlinear forcing and the three different time stepping schemes. The adjoint of the numerical time-stepping schemes is calculated in terms of adjoints of the discrete spatial operators. Because the linear parts of these operators are explicitly formed matrices, adjoints of these spatial operators are essentially matrix transposes. The non-linear terms, which must be linearized around a background state, require more care. The TL and ADJ modules will be used to implement a modern variational DA scheme for the geodynamo -- 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 core magnetic and fluid velocity fields. This method will be used to estimate an initial state of the geodynamo, which when propagated forward, will match magnetic data over the last 300 yrs.

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