Optimal assimilation for ionospheric weather – Theoretical aspect

Observation, specification and prediction of ionospheric weather are the key scientific pursuits of space physicists, which largely based on an optimal assimilation system. The optimal assimilation system, or commonly called data assimilation system, consists of dynamic process, observation system and optimal estimation procedure. We attempt to give a complete framework in this paper under which the data assimilation procedure carries through. We discuss some crucial issues of data assimilation as follows: modeling a dynamic system for ionospheric weather; state estimation for static or steady system in sense of optimization and likelihood; state and its uncertainty estimation for dynamic process. Meanwhile we also discuss briefly the observability of an observation system; system parameter identification. Some data assimilation procedures existed at present are reviewed in the framework of this paper. As an example, a second order dynamic system is discussed in more detail to illustrate the specific optimal assimilation procedure, ranging from modeling the system, state and its uncertainty calculation, to the quantitatively integration of dynamic law, measurement to significantly reduce the estimation error. The analysis shows that the optimal assimilation model, with mathematical core of optimal estimation, differs from the theoretical, empirical and semi-empirical models in assimilating measured data, being constrained by physical law and being optimized respectively. The data assimilation technique, due to its optimization and integration feature, could obtain better accurate results than those obtained by dynamic process, measurement or their statistical analysis alone. The model based on optimal assimilation meets well with the criterion of the model or algorithm assessment by ‘space weather metrics’. More attention for optimal assimilation procedure creation should be paid to transition matrix finding, which is usually not easy for practical space weather system. High performance computing hardware and software studies should be promoted further so as to meet the requirement of large storage and extensive computation in the optimal estimation. The discussion in this paper is appropriate for the static or steady state or transition process of dynamic system. Many phenomena in space environment are unstable and chaos. So space environment study should include and integrate these two branches of learning.