;+ ; NAME: ; CHAP ; ; PURPOSE: ; Chapman grazing incidence integral function ; ; CATEGORY: ; TIMED/SEE Level 2 ; ; CALLING SEQUENCE: ; ch=chap(chi,rs,h) ; ; INPUTS: ; chi zenith angle in degrees, floating point scalar ; rs distance from center of Earth in cm, floating point scalar ; h scale heights in cm, floating point array (or scalar) ; ; OUTPUTS: ; ch path length enhancement factor, floating point array (or scalar) ; ; COMMON BLOCKS: ; none ; ; PROCEDURE: ; Calculates Chapman grazing incidence integral using fit function. ; Result is a path length factor to be multiplied by the ; vertical column density. For low zenith angles, this factor is ; approximately equal to 1/cos(chi). An array of scale heights ; (e.g., one for each atmospheric species) may be used. ; Designed for use with solar zenith angles on the Earth, ; but is sufficiently general that it may be used for any body ; on any planet. (Dimensions are also arbitrary as long as they ; are self-consistent, i.e., rs and h must be in the same units.) ; Note - at large h and small chi, fit function can go slightly less ; than 1, which is non-physical. Therefore, fit is constrained to be ; greater than or equal to 1. ; REFERENCE: ; Smith & Smith, JGR, 77, 3592, 1972 ; ; MODIFICATION HISTORY: ; 1/00 Adapted from FORTRAN function by Stan Solomon ; ;+ function CHAP, chi, rs, h hg=rs/h x=sqrt(0.5*hg*(cos(chi*!pi/180.)^2)) sp = 0.56498823/(0.06651874+x) w=where(x le 8.) if w(0) ne -1 then $ sp(w)=(1.0606963+0.55643831*x(w))/(1.0619896+1.7245609*x(w)+x(w)^2) chap=sqrt(0.5*!pi*hg)*sp > 1. return, chap end