Noise statistics identification for Kalman filtering of the electron radiation belt observations I: Model errors

In this study we present a first attempt to identify errors of the 1-D radial diffusion model for relativistic electron phase space density (PSD). In practice, the model error and characteristics of satellite observations are poorly known, which may cause failure of a Kalman filter algorithm. Correct specification of model errors statistics is necessary for the development of the next generation of radiation belt specification models providing the effective PSD reconstruction and hence the prediction and mitigation of space weather effects in the hazardous space environment. The proposed approach to the identification of errors statistics is based on estimating the unknown bias and the covariance matrix of model errors from the sparse CRRES observations over a period of 441 days, from 28 July 1990 to 11 October 1991. With our technique we demonstrate that model errors are biased. Neglecting the bias when applying a data assimilation algorithm to radiation belt electrons can cause significant errors of the PSD estimate during data gaps. Both the identified bias and the covariance matrix of model errors increase with increase of L shell. Sensitivity of the PSD reconstruction to model errors statistics and advances of the improved physical-based model based on the model errors identification are illustrated by a number of representative examples of the PSD reanalysis. Identification of satellite observations characteristics, and filtration and smoothing algorithms are discussed in the companion paper.