An approximate form for the Chapman grazing incidence function |
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| Institution: | 1. Géosciences Environnement Toulouse (GET), Université de Toulouse, UMR CNRS 5563, IRD UR 234, 16 Avenue Edouard Belin, 31400 Toulouse, France;2. Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), Universités Paris Est Créteil & Paris Diderot, UMR CNRS 7583, 61 Avenue du Général de Gaulle, 94000 Créteil, France;3. Centre Nationale de Recherches Météorologiques (CNRM), Meteo-France & UMR CNRS 3589, 42 Avenue Gaspard Coriolis, 31100 Toulouse, France |
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| Abstract: | Numerical modelling of the ionosphere requires repeated evaluation of the Chapman function Ch(x, χ). This normally involves a numerical integration of the Chapman expression. Approximate values can be obtained using accurate tables of the error function integral, but large numerical errors make this approach unusable for values of χ less than about 80°. Algebraic expressions are obtained for the rapid, direct calculation of the Chapman function, at any zenith angle and for scale heights from 6 to 120 km. The maximum errors in this calculation correspond to an error of about 0.03° in the zenith angle, while the rms error is half this amount. |
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