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# atoi13

erfa.atoi13(type, ob1, ob2, utc1, utc2, dut1, elong, phi, hm, xp, yp, phpa, tc, rh, wl)

  Observed place to CIRS. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

  Parameters:
    type const char array
    ob1 double array
    ob2 double array
    utc1 double array
    utc2 double array
    dut1 double array
    elong double array
    phi double array
    hm double array
    xp double array
    yp double array
    phpa double array
    tc double array
    rh double array
    wl double array
  Returns:
    ri double array
    di double array

  Notes

  Wraps ERFA function `eraAtoi13`. The ERFA documentation is:

      - - - - - - - - - -
       e r a A t o i 1 3
      - - - - - - - - - -

      Observed place to CIRS.  The caller supplies UTC, site coordinates,
      ambient air conditions and observing wavelength.

      Given:
         type   char[]   type of coordinates - "R", "H" or "A" (Notes 1,2)
         ob1    double   observed Az, HA or RA (radians; Az is N=0,E=90)
         ob2    double   observed ZD or Dec (radians)
         utc1   double   UTC as a 2-part...
         utc2   double   ...quasi Julian Date (Notes 3,4)
         dut1   double   UT1-UTC (seconds, Note 5)
         elong  double   longitude (radians, east +ve, Note 6)
         phi    double   geodetic latitude (radians, Note 6)
         hm     double   height above the ellipsoid (meters, Notes 6,8)
         xp,yp  double   polar motion coordinates (radians, Note 7)
         phpa   double   pressure at the observer (hPa = mB, Note 8)
         tc     double   ambient temperature at the observer (deg C)
         rh     double   relative humidity at the observer (range 0-1)
         wl     double   wavelength (micrometers, Note 9)

      Returned:
         ri     double        CIRS right ascension (CIO-based, radians)
         di     double        CIRS declination (radians)

      Returned (function value):
                int      status: +1 = dubious year (Note 2)
                                  0 = OK
                                 -1 = unacceptable date

      Notes:

      1)  "Observed" Az,ZD means the position that would be seen by a
          perfect geodetically aligned theodolite.  (Zenith distance is
          used rather than altitude in order to reflect the fact that no
          allowance is made for depression of the horizon.)  This is
          related to the observed HA,Dec via the standard rotation, using
          the geodetic latitude (corrected for polar motion), while the
          observed HA and (CIO-based) RA are related simply through the
          Earth rotation angle and the site longitude.  "Observed" RA,Dec
          or HA,Dec thus means the position that would be seen by a
          perfect equatorial with its polar axis aligned to the Earth's
          axis of rotation.

      2)  Only the first character of the type argument is significant.
          "R" or "r" indicates that ob1 and ob2 are the observed right
          ascension and declination;  "H" or "h" indicates that they are
          hour angle (west +ve) and declination;  anything else ("A" or
          "a" is recommended) indicates that ob1 and ob2 are azimuth
          (north zero, east 90 deg) and zenith distance.

      3)  utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
          convenient way between the two arguments, for example where utc1
          is the Julian Day Number and utc2 is the fraction of a day.

          However, JD cannot unambiguously represent UTC during a leap
          second unless special measures are taken.  The convention in the
          present function is that the JD day represents UTC days whether
          the length is 86399, 86400 or 86401 SI seconds.

          Applications should use the function eraDtf2d to convert from
          calendar date and time of day into 2-part quasi Julian Date, as
          it implements the leap-second-ambiguity convention just
          described.

      4)  The warning status "dubious year" flags UTCs that predate the
          introduction of the time scale or that are too far in the
          future to be trusted.  See eraDat for further details.

      5)  UT1-UTC is tabulated in IERS bulletins.  It increases by exactly
          one second at the end of each positive UTC leap second,
          introduced in order to keep UT1-UTC within +/- 0.9s.  n.b. This
          practice is under review, and in the future UT1-UTC may grow
          essentially without limit.

      6)  The geographical coordinates are with respect to the ERFA_WGS84
          reference ellipsoid.  TAKE CARE WITH THE LONGITUDE SIGN:  the
          longitude required by the present function is east-positive
          (i.e. right-handed), in accordance with geographical convention.

      7)  The polar motion xp,yp can be obtained from IERS bulletins.  The
          values are the coordinates (in radians) of the Celestial
          Intermediate Pole with respect to the International Terrestrial
          Reference System (see IERS Conventions 2003), measured along the
          meridians 0 and 90 deg west respectively.  For many
          applications, xp and yp can be set to zero.

      8)  If hm, the height above the ellipsoid of the observing station
          in meters, is not known but phpa, the pressure in hPa (=mB), is
          available, an adequate estimate of hm can be obtained from the
          expression

                hm = -29.3 * tsl * log ( phpa / 1013.25 );

          where tsl is the approximate sea-level air temperature in K
          (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
          52).  Similarly, if the pressure phpa is not known, it can be
          estimated from the height of the observing station, hm, as
          follows:

                phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );

          Note, however, that the refraction is nearly proportional to
          the pressure and that an accurate phpa value is important for
          precise work.

      9)  The argument wl specifies the observing wavelength in
          micrometers.  The transition from optical to radio is assumed to
          occur at 100 micrometers (about 3000 GHz).

      10) The accuracy of the result is limited by the corrections for
          refraction, which use a simple A*tan(z) + B*tan^3(z) model.
          Providing the meteorological parameters are known accurately and
          there are no gross local effects, the predicted astrometric
          coordinates should be within 0.05 arcsec (optical) or 1 arcsec
          (radio) for a zenith distance of less than 70 degrees, better
          than 30 arcsec (optical or radio) at 85 degrees and better
          than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

          Without refraction, the complementary functions eraAtio13 and
          eraAtoi13 are self-consistent to better than 1 microarcsecond
          all over the celestial sphere.  With refraction included,
          consistency falls off at high zenith distances, but is still
          better than 0.05 arcsec at 85 degrees.

      12) It is advisable to take great care with units, as even unlikely
          values of the input parameters are accepted and processed in
          accordance with the models used.

      Called:
         eraApio13    astrometry parameters, CIRS-observed, 2013
         eraAtoiq     quick observed to CIRS

      This revision:   2022 August 30

      Copyright (C) 2013-2023, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.