Data Assimilation for the Radiation Belt Environment using the Four-Dimensional Variational Method

In this work we implement a four-dimensional variational data assimilation method (4D-Var) to a radiation belt model in order to determine key model parameters. A particular hurdle in implementing the 4D-Var is the computation of the adjoint model. In our work we derive the continuous adjoint model associated with the radiation belt model and discretize them both with a Crank-Nicholson scheme. The resulting adjoint solution is sufficiently accurate for convergence in the 4D-Var assimilation method. We use the 4D-Var assimilation to determine diffusion coefficients (D_LL) within the model that control how particles are distributed throughout Earth's magnetic environment. A series of assimilation experiments are perform to validate the methodology using synthetic data. A more realistic assimilation experiment is performed using Van Allen Probes data for phase space density. The assimilated radiation belt estimate closely match the data by estimating appropriate radial diffusion coefficients for the time-period of the data.