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SUBROUTINE sla_REFZ (ZU, REFA, REFB, ZR)
*+
* - - - - -
* R E F Z
* - - - - -
*
* Adjust an unrefracted zenith distance to include the effect of
* atmospheric refraction, using the simple A tan Z + B tan**3 Z
* model (plus special handling for large ZDs).
*
* Given:
* ZU dp unrefracted zenith distance of the source (radian)
* REFA dp tan Z coefficient (radian)
* REFB dp tan**3 Z coefficient (radian)
*
* Returned:
* ZR dp refracted zenith distance (radian)
*
* Notes:
*
* 1 This routine applies the adjustment for refraction in the
* opposite sense to the usual one - it takes an unrefracted
* (in vacuo) position and produces an observed (refracted)
* position, whereas the A tan Z + B tan**3 Z model strictly
* applies to the case where an observed position is to have the
* refraction removed. The unrefracted to refracted case is
* harder, and requires an inverted form of the text-book
* refraction models; the formula used here is based on the
* Newton-Raphson method. For the utmost numerical consistency
* with the refracted to unrefracted model, two iterations are
* carried out, achieving agreement at the 1D-11 arcseconds level
* for a ZD of 80 degrees. The inherent accuracy of the model
* is, of course, far worse than this - see the documentation for
* sla_REFCO for more information.
*
* 2 At ZD 83 degrees, the rapidly-worsening A tan Z + B tan**3 Z
* model is abandoned and an empirical formula takes over. Over a
* wide range of observer heights and corresponding temperatures and
* pressures, the following levels of accuracy (arcsec) are
* typically achieved, relative to numerical integration through a
* model atmosphere:
*
* ZR error
*
* 80 0.4
* 81 0.8
* 82 1.5
* 83 3.2
* 84 4.9
* 85 5.8
* 86 6.1
* 87 7.1
* 88 10
* 89 20
* 90 40
* 91 100 } relevant only to
* 92 200 } high-elevation sites
*
* The high-ZD model is scaled to match the normal model at the
* transition point; there is no glitch.
*
* 3 Beyond 93 deg zenith distance, the refraction is held at its
* 93 deg value.
*
* 4 See also the routine sla_REFV, which performs the adjustment in
* Cartesian Az/El coordinates, and with the emphasis on speed
* rather than numerical accuracy.
*
* P.T.Wallace Starlink 19 September 1995
*
* Copyright (C) 1995 Rutherford Appleton Laboratory
*-
IMPLICIT NONE
DOUBLE PRECISION ZU,REFA,REFB,ZR
* Radians to degrees
DOUBLE PRECISION R2D
PARAMETER (R2D=57.29577951308232D0)
* Largest usable ZD (deg)
DOUBLE PRECISION D93
PARAMETER (D93=93D0)
* Coefficients for high ZD model (used beyond ZD 83 deg)
DOUBLE PRECISION C1,C2,C3,C4,C5
PARAMETER (C1=+0.55445D0,
: C2=-0.01133D0,
: C3=+0.00202D0,
: C4=+0.28385D0,
: C5=+0.02390D0)
* ZD at which one model hands over to the other (radians)
DOUBLE PRECISION Z83
PARAMETER (Z83=83D0/R2D)
* High-ZD-model prediction (deg) for that point
DOUBLE PRECISION REF83
PARAMETER (REF83=(C1+C2*7D0+C3*49D0)/(1D0+C4*7D0+C5*49D0))
DOUBLE PRECISION ZU1,ZL,S,C,T,TSQ,TCU,REF,E,E2
* Perform calculations for ZU or 83 deg, whichever is smaller
ZU1 = MIN(ZU,Z83)
* Functions of ZD
ZL = ZU1
S = SIN(ZL)
C = COS(ZL)
T = S/C
TSQ = T*T
TCU = T*TSQ
* Refracted ZD (mathematically to better than 1 mas at 70 deg)
ZL = ZL-(REFA*T+REFB*TCU)/(1D0+(REFA+3D0*REFB*TSQ)/(C*C))
* Further iteration
S = SIN(ZL)
C = COS(ZL)
T = S/C
TSQ = T*T
TCU = T*TSQ
REF = ZU1-ZL+
: (ZL-ZU1+REFA*T+REFB*TCU)/(1D0+(REFA+3D0*REFB*TSQ)/(C*C))
* Special handling for large ZU
IF (ZU.GT.ZU1) THEN
E = 90D0-MIN(D93,ZU*R2D)
E2 = E*E
REF = (REF/REF83)*(C1+C2*E+C3*E2)/(1D0+C4*E+C5*E2)
END IF
* Return refracted ZD
ZR = ZU-REF
END
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