Mathematical modeling of light curves of RHESSI and AGILE terrestrial gamma-ray flashes

  • Marwan AbukhaledEmail author
  • Nidhal Guessoum
  • Noora Alsaeed
Original Article


We consider different distribution functions as possible fits for the light curves (time profiles) of Terrestrial Gamma-ray Flashes (TGFs): the piecewise Gaussian and the piecewise exponential, which correspond to the assumption of exponential growth and decay of the electrons that emit the radiation, and the inverse Gaussian and Ornstein-Uhlenbeck functions, which correspond to the assumption of an exit-time process. We compute maximum likelihood estimations (MLEs) for each of these four functions for a 100 TGFs recorded by the RHESSI and AGILE satellites, and compared those values with MLEs of the lognormal distribution function, which has been very widely used. The analysis of time profiles of these TGFs shows that all five distributions fit the data equally well. The results obtained in this work, combined with the results obtained for the analysis of BATSE and FERMI TGFs (Abukhaled et al. in J. Geophys. Res. Space Phys. 119:5918–5930, 2014) show that the TGF data as recorded thus far by various satellite gamma-ray detectors, are not powerful enough to discriminate between those various mathematical functions, which, if one function were preferred, would identify some physical features of the phenomenon.


Terrestrial Gamma-ray Flash TGF AGILE RHESSI Light curve fitting Maximum likelihood Density functions Stochastic processes Electron cascades Thunderstorms 



The authors acknowledge, with gratitude, the use of the AGILE Terrestrial Gamma-ray Flashes (TGF) catalog available online at and the online repository for RHESSI TGF data available at public/.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Marwan Abukhaled
    • 1
    Email author
  • Nidhal Guessoum
    • 2
  • Noora Alsaeed
    • 3
  1. 1.Department of Mathematics and StatisticsAmerican University of SharjahSharjahUAE
  2. 2.Department of PhysicsAmerican University of SharjahSharjahUAE
  3. 3.Department of Astrophysical and Planetary SciencesUniversity of Colorado BoulderBoulderUSA

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