Chapman function

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A Chapman function describes the integration of atmospheric absorption along a slant path on a spherical earth, relative to the vertical case. It applies for any quantity with a concentration decreasing exponentially with increasing altitude. To a first approximation, valid at small zenith angles, the Chapman function for optical absorption is equal to

where z is the zenith angle and sec denotes the secant function.

The Chapman function is named after Sydney Chapman.

See also[edit]


  • Chapman, S., Absorption and dissociative or ionising effects of monochromatic radiation in an atmosphere on a rotating earth, Proc. Phys. Soc., London, 43, 1047-1055, 1931
  • Smith III, F. L. and C. Smith, Numerical evaluation of Chapman's grazing incidence integral ch(X,χ), J. Geophys. Res., 77, 3592-3597, 1972

External links[edit]

  • Chapman function at Science World
  • David L. Huestis. "Chapman Function for Atmospheric Attenuation". SRI International. Archived from the original on 2009-11-04.