The Effects of Estimating a Photoionization Parameter within a Physics-Based Model using Data Assimilation

Data assimilation (DA) is the process of merging information from prediction models with noisy observations to produce an estimate of the state of a physical system.  In ionospheric physics-based models, the solar ionizing irradiance is commonly estimated from a solar index like F10.7.  The goal of this work is to provide the fundamental understanding necessary to appreciate how a DA algorithm responds to estimating an external parameter driving the model’s interpretation of this solar ionizing irradiance.  Therefore, in this work we allow the DA system to find the F10.7 value that delivers the degree of photoionization that leads to a predicted electron density field that best matches the observations.  To this end, we develop a heuristic model of the ionosphere along the magnetic equator that contains physics from solar forcing and recombination/plasma diffusion, which allows us to explore the impacts of strongly forced system dynamics on DA.  This framework was carefully crafted to be both linear and Gaussian, which allows us to use a Kalman filter to clearly see how: 1) while recombination acts as a sink on the information in the initial condition for ionospheric field variables, recombination does not impact the information in parameter estimates in the same way, 2) when solar forcing dominates the electron density field, the prior covariance matrix becomes dominated by its leading eigenvector whose structure is directly related to that of the solar forcing, 3) estimation of parameters for forcing terms leads to a time-lag in the state estimate relative to the truth, 4) the performance of a DA system in this regime is determined by the relative dominance of solar forcing and recombination to that of the smaller-scale processes and 5) the most impactful observations on the electron density field and on the solar forcing parameter are those observations on the sunlit side of the ionosphere.  These findings are then illustrated in a full physics-based ionospheric model using an ensemble Kalman filter DA scheme.