ARAMIS: a Martian radiative environment model built from GEANT4 simulations | Journal of Space Weather and Space Climate

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Table 2

Historical SPE events used with their corresponding fits formulas.

SPE event	Spectrum details	Fitting function	Reference
February 1956*	Fluence, differential	$ϕ (E) = 1.0 \times 1 0^{7} [\frac{E + m_{p}}{\sqrt{E (E + 2 m_{p})}}] \exp [\frac{239.1 - \sqrt{E (E + 2 m_{p})}}{100}]$ $\phi (E)=1.0\times 1{0}^7\left[\frac{E+{m}_p}{\sqrt{E\left(E+2{m}_p\right)}}\right]\mathrm{exp}\left[\frac{239.1-\sqrt{E\left(E+2{m}_p\right)}}{100}\right]$	Webber (1963)
November 1960		$ϕ (E) = 6.33 \times 1 0^{8} \exp (\frac{10 - E}{12}) + 4.88 \times 1 0^{6} \exp (\frac{100 - E}{80})$ $\phi (E)=6.33\times 1{0}^8\mathrm{exp}\left(\frac{10-E}{12}\right)+4.88\times 1{0}^6\mathrm{exp}\left(\frac{100-E}{80}\right)$	Wilson et al. (1991b)
August 1972		$ϕ (E) = 2.2 \times 1 0^{7} \exp (\frac{100 - E}{30})$ $\phi (E)=2.2\times 1{0}^7\mathrm{exp}\left(\frac{100-E}{30}\right)$	Wilson et al. (1991b)
October 1989*		$ϕ (E) = 6.104 \times 1 0^{8} [\frac{E + m_{p}}{\sqrt{E (E + 2 m_{p})}}] \exp [\frac{- \sqrt{E (E + 2 m_{p})}}{92.469}]$ $\phi (E)=6.104\times 1{0}^8\left[\frac{E+{m}_p}{\sqrt{E\left(E+2{m}_p\right)}}\right]\mathrm{exp}\left[\frac{-\sqrt{E\left(E+2{m}_p\right)}}{92.469}\right]$	Singleterry Jr et al. (2010)
October 2003 worst hour	Flux, integral	$ϕ (E) = {\begin{array}{l} 4 π \times 1 0^{15} E^{- 6.73}, E \geq 300 MeV \\ 4 π \times 1 0^{4} \exp (- \frac{\sqrt{E^{2} + 1.8 \times 1 0^{4} \times E}}{190}), E < 300 MeV \end{array}$ $\phi (E)=\left\{\begin{array}{l}4\pi \times 1{0}^{15}{E}^{-6.73},\enspace {E}\ge 300\enspace \mathrm{MeV}\\ 4\pi \times 1{0}^4\mathrm{exp}\left(-\frac{\sqrt{{E}^2+1.8\times 1{0}^4\times E}}{190}\right),\enspace {E} < 300\enspace \mathrm{MeV}\end{array}\right.$	OMERE

*m_p is the mass of the proton, approximately 938 MeV.

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