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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. For
* optical/IR wavelengths, over a wide range of observer heights and
* corresponding temperatures and pressures, the following levels of
* accuracy (arcsec, worst case) are achieved, relative to numerical
* integration through a model atmosphere:
*
* ZR error
*
* 80 0.7
* 81 1.3
* 82 2.4
* 83 4.7
* 84 6.2
* 85 6.4
* 86 8
* 87 10
* 88 15
* 89 30
* 90 60
* 91 150 } relevant only to
* 92 400 } high-elevation sites
*
* For radio wavelengths the errors are typically 50% larger than
* the optical figures and by ZD 85 deg are twice as bad, worsening
* rapidly below that. To maintain 1 arcsec accuracy down to ZD=85
* at the Green Bank site, Condon (2004) has suggested amplifying
* the amount of refraction predicted by sla_REFZ below 10.8 deg
* elevation by the factor (1+0.00195*(10.8-E_t)), where E_t is the
* unrefracted elevation in degrees.
*
* 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.
*
* Reference:
*
* Condon,J.J., Refraction Corrections for the GBT, PTCS/PN/35.2,
* NRAO Green Bank, 2004.
*
* P.T.Wallace Starlink 9 April 2004
*
* Copyright (C) 2004 Rutherford Appleton Laboratory
*
* License:
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program (see SLA_CONDITIONS); if not, write to the
* Free Software Foundation, Inc., 59 Temple Place, Suite 330,
* Boston, MA 02111-1307 USA
*
*-
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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