### Abstract

We propose stochastic processes to be used to model the total electron content (TEC) observation. Based on this, we model the rate of change of TEC (ROT) variation during ionospheric quiet conditions with stationary processes. During ionospheric disturbed conditions, for example, when irregularity in ionospheric electron density distribution occurs, stationarity assumption over long time periods is no longer valid. In these cases, we make the parameter estimation for short time scales, during which we can assume stationarity. We show the relationship between the new method and commonly used TEC characterization parameters ROT and the ROT Index (ROTI). We construct our parametric model within the framework of Bayesian statistical inverse problems and hence give the solution as an a posteriori probability distribution. Bayesian framework allows us to model measurement errors systematically. Similarly, we mitigate variation of TEC due to factors which are not of ionospheric origin, like due to the motion of satellites relative to the receiver, by incorporating a priori knowledge in the Bayesian model. In practical computations, we draw the so-called maximum a posteriori estimates, which are our ROT and ROTI estimates, from the posterior distribution. Because the algorithm allows to estimate ROTI at each observation time, the estimator does not depend on the period of time for ROTI computation. We verify the method by analyzing TEC data recorded by GPS receiver located in Ethiopia (11.6°N, 37.4°E). The results indicate that the TEC fluctuations caused by the ionospheric irregularity can be effectively detected and quantified from the estimated ROT and ROTI values.

Original language | English |
---|---|

Pages (from-to) | 1772-1782 |

Number of pages | 11 |

Journal | Radio Science |

Volume | 51 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 1 2016 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Electrical and Electronic Engineering
- Earth and Planetary Sciences(all)

### Cite this

*Radio Science*,

*51*(11), 1772-1782. https://doi.org/10.1002/2016RS005959

**Study of TEC fluctuation via stochastic models and Bayesian inversion.** / Bires, A.; Roininen, L.; Damtie, B.; Nigussie, M.; Vanhamaki, Heikki Antero.

Research output: Contribution to journal › Article

*Radio Science*, vol. 51, no. 11, pp. 1772-1782. https://doi.org/10.1002/2016RS005959

}

TY - JOUR

T1 - Study of TEC fluctuation via stochastic models and Bayesian inversion

AU - Bires, A.

AU - Roininen, L.

AU - Damtie, B.

AU - Nigussie, M.

AU - Vanhamaki, Heikki Antero

PY - 2016/11/1

Y1 - 2016/11/1

N2 - We propose stochastic processes to be used to model the total electron content (TEC) observation. Based on this, we model the rate of change of TEC (ROT) variation during ionospheric quiet conditions with stationary processes. During ionospheric disturbed conditions, for example, when irregularity in ionospheric electron density distribution occurs, stationarity assumption over long time periods is no longer valid. In these cases, we make the parameter estimation for short time scales, during which we can assume stationarity. We show the relationship between the new method and commonly used TEC characterization parameters ROT and the ROT Index (ROTI). We construct our parametric model within the framework of Bayesian statistical inverse problems and hence give the solution as an a posteriori probability distribution. Bayesian framework allows us to model measurement errors systematically. Similarly, we mitigate variation of TEC due to factors which are not of ionospheric origin, like due to the motion of satellites relative to the receiver, by incorporating a priori knowledge in the Bayesian model. In practical computations, we draw the so-called maximum a posteriori estimates, which are our ROT and ROTI estimates, from the posterior distribution. Because the algorithm allows to estimate ROTI at each observation time, the estimator does not depend on the period of time for ROTI computation. We verify the method by analyzing TEC data recorded by GPS receiver located in Ethiopia (11.6°N, 37.4°E). The results indicate that the TEC fluctuations caused by the ionospheric irregularity can be effectively detected and quantified from the estimated ROT and ROTI values.

AB - We propose stochastic processes to be used to model the total electron content (TEC) observation. Based on this, we model the rate of change of TEC (ROT) variation during ionospheric quiet conditions with stationary processes. During ionospheric disturbed conditions, for example, when irregularity in ionospheric electron density distribution occurs, stationarity assumption over long time periods is no longer valid. In these cases, we make the parameter estimation for short time scales, during which we can assume stationarity. We show the relationship between the new method and commonly used TEC characterization parameters ROT and the ROT Index (ROTI). We construct our parametric model within the framework of Bayesian statistical inverse problems and hence give the solution as an a posteriori probability distribution. Bayesian framework allows us to model measurement errors systematically. Similarly, we mitigate variation of TEC due to factors which are not of ionospheric origin, like due to the motion of satellites relative to the receiver, by incorporating a priori knowledge in the Bayesian model. In practical computations, we draw the so-called maximum a posteriori estimates, which are our ROT and ROTI estimates, from the posterior distribution. Because the algorithm allows to estimate ROTI at each observation time, the estimator does not depend on the period of time for ROTI computation. We verify the method by analyzing TEC data recorded by GPS receiver located in Ethiopia (11.6°N, 37.4°E). The results indicate that the TEC fluctuations caused by the ionospheric irregularity can be effectively detected and quantified from the estimated ROT and ROTI values.

UR - http://www.scopus.com/inward/record.url?scp=85000751817&partnerID=8YFLogxK

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U2 - 10.1002/2016RS005959

DO - 10.1002/2016RS005959

M3 - Article

AN - SCOPUS:85000751817

VL - 51

SP - 1772

EP - 1782

JO - Radio Science

JF - Radio Science

SN - 0048-6604

IS - 11

ER -