| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | void slaRefz ( double zu, double refa, double refb, double *zr )
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| 4 | /*
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| 5 | ** - - - - - - - -
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| 6 | ** s l a R e f z
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| 7 | ** - - - - - - - -
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| 8 | **
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| 9 | ** Adjust an unrefracted zenith distance to include the effect of
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| 10 | ** atmospheric refraction, using the simple A tan z + B tan^3 z
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| 11 | ** model.
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| 12 | **
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| 13 | ** Given:
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| 14 | ** zu double unrefracted zenith distance of the source (radian)
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| 15 | ** refa double A: tan z coefficient (radian)
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| 16 | ** refb double B: tan^3 z coefficient (radian)
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| 17 | **
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| 18 | ** Returned:
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| 19 | ** *zr double refracted zenith distance (radian)
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| 20 | **
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| 21 | ** Notes:
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| 22 | **
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| 23 | ** 1 This routine applies the adjustment for refraction in the
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| 24 | ** opposite sense to the usual one - it takes an unrefracted
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| 25 | ** (in vacuo) position and produces an observed (refracted)
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| 26 | ** position, whereas the A tan Z + B tan^3 Z model strictly
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| 27 | ** applies to the case where an observed position is to have the
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| 28 | ** refraction removed. The unrefracted to refracted case is
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| 29 | ** harder, and requires an inverted form of the text-book
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| 30 | ** refraction models; the formula used here is based on the
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| 31 | ** Newton-Raphson method. For the utmost numerical consistency
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| 32 | ** with the refracted to unrefracted model, two iterations are
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| 33 | ** carried out, achieving agreement at the 1D-11 arcseconds level
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| 34 | ** for a ZD of 80 degrees. The inherent accuracy of the model
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| 35 | ** is, of course, far worse than this - see the documentation for
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| 36 | ** slaRefco for more information.
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| 37 | **
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| 38 | ** 2 At ZD 83 degrees, the rapidly-worsening A tan Z + B tan^3 Z
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| 39 | ** model is abandoned and an empirical formula takes over. Over a
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| 40 | ** wide range of observer heights and corresponding temperatures and
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| 41 | ** pressures, the following levels of accuracy (arcsec) are achieved,
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| 42 | ** relative to numerical integration through a model atmosphere:
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| 43 | **
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| 44 | ** ZR error
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| 45 | **
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| 46 | ** 80 0.4
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| 47 | ** 81 0.8
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| 48 | ** 82 1.5
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| 49 | ** 83 3.2
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| 50 | ** 84 4.9
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| 51 | ** 85 5.8
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| 52 | ** 86 6.1
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| 53 | ** 87 7.1
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| 54 | ** 88 10
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| 55 | ** 89 20
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| 56 | ** 90 40
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| 57 | ** 91 100 } relevant only to
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| 58 | ** 92 200 } high-elevation sites
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| 59 | **
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| 60 | ** The high-ZD model is scaled to match the normal model at the
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| 61 | ** transition point; there is no glitch.
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| 62 | **
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| 63 | **
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| 64 | ** 3 Beyond 93 deg zenith distance, the refraction is held at its
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| 65 | ** 93 deg value.
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| 66 | **
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| 67 | ** 4 See also the routine slaRefv, which performs the adjustment in
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| 68 | ** Cartesian Az/El coordinates, and with the emphasis on speed
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| 69 | ** rather than numerical accuracy.
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| 70 | **
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| 71 | ** Defined in slamac.h: DR2D
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| 72 | **
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| 73 | ** Last revision: 4 June 1997
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| 74 | **
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| 75 | ** Copyright P.T.Wallace. All rights reserved.
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| 76 | */
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| 77 | {
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| 78 | double zu1, zl, s, c, t, tsq, tcu, ref, e, e2;
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| 79 |
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| 80 | /* Coefficients for high ZD model (used beyond ZD 83 deg */
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| 81 | const double c1 = 0.55445,
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| 82 | c2 = -0.01133,
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| 83 | c3 = 0.00202,
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| 84 | c4 = 0.28385,
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| 85 | c5 = 0.02390;
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| 86 |
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| 87 | /* Largest usable ZD (deg) */
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| 88 | const double z93 = 93.0;
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| 89 |
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| 90 | /* ZD at which one model hands over to the other (radians) */
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| 91 | const double z83 = 83.0 / DR2D;
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| 92 |
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| 93 | /* High-ZD-model prediction (deg) for that point */
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| 94 | const double ref83 = ( c1 + c2 * 7.0 + c3 * 49.0 ) /
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| 95 | ( 1.0 + c4 * 7.0 + c5 * 49.0 );
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| 96 |
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| 97 |
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| 98 | /* Perform calculations for zu or 83 deg, whichever is smaller */
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| 99 | zu1 = gmin ( zu, z83 );
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| 100 |
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| 101 | /* Functions of ZD */
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| 102 | zl = zu1;
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| 103 | s = sin ( zl );
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| 104 | c = cos ( zl );
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| 105 | t = s / c;
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| 106 | tsq = t * t;
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| 107 | tcu = t * tsq;
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| 108 |
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| 109 | /* Refracted ZD (mathematically to better than 1mas at 70 deg) */
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| 110 | zl -= ( refa * t + refb * tcu )
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| 111 | / ( 1.0 + ( refa + 3.0 * refb * tsq ) / ( c * c ) );
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| 112 |
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| 113 | /* Further iteration */
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| 114 | s = sin ( zl );
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| 115 | c = cos ( zl );
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| 116 | t = s / c;
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| 117 | tsq = t * t;
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| 118 | tcu = t * tsq;
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| 119 | ref = zu1 - zl + ( zl - zu1 + refa * t + refb * tcu )
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| 120 | / ( 1.0 + ( refa + 3.0 * refb * tsq ) / ( c * c ) );
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| 121 |
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| 122 | /* Special handling for large zu */
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| 123 | if ( zu > zu1 ) {
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| 124 | e = 90.0 - gmin ( z93, zu * DR2D );
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| 125 | e2 = e * e;
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| 126 | ref = ( ref / ref83 ) * ( c1 + c2 * e + c3 * e2 ) /
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| 127 | ( 1.0 + c4 * e + c5 * e2 );
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| 128 | }
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| 129 |
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| 130 | /* Refracted ZD */
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| 131 | *zr = zu - ref;
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| 132 | }
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