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<H2><A NAME="SECTION0004154000000000000000">SLA_REFRO - Refraction</A>
<A NAME="xref_SLA_REFRO"> </A><A NAME="SLA_REFRO"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Atmospheric refraction, for radio or optical/IR wavelengths.
<DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_REFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REF)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ZOBS</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>observed zenith distance of the source (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>HM</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>height of the observer above sea level (metre)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>TDK</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>ambient temperature at the observer (degrees K)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PMB</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>pressure at the observer (mB)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RH</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>relative humidity at the observer (range 0-1)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>WL</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>effective wavelength of the source (<IMG WIDTH="26" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img21.gif"
ALT="$\mu{\rm m}$">)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PHI</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>latitude of the observer (radian, astronomical)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>TLR</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>temperature lapse rate in the troposphere
(degrees K per metre)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EPS</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>precision required to terminate iteration (radian)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>REF</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TH ALIGN="LEFT" NOWRAP>refraction: <I>in vacuo</I> ZD minus observed ZD (radians)</TH>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>A suggested value for the TLR argument is 0.0065D0. The
refraction is significantly affected by TLR, and if studies
of the local atmosphere have been carried out a better TLR
value may be available.
<DT>2.
<DD>A suggested value for the EPS argument is 1D-8. The result is
usually at least two orders of magnitude more computationally
precise than the supplied EPS value.
<DT>3.
<DD>The routine computes the refraction for zenith distances up
to and a little beyond <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img22.gif"
ALT="$90^{\circ}$"> using the method of Hohenkerk
& Sinclair (NAO Technical Notes 59 and 63, subsequently adopted
in the <I>Explanatory Supplement to the Astronomical Almanac,</I>
1992 - see section 3.281).
<DT>4.
<DD>The code is based on the AREF optical/IR refraction subroutine
of C.Hohenkerk (HMNAO, September 1984), with extensions to
support the radio case. The modifications to the original HMNAO
optical/IR refraction code which affect the results are:
<UL>
<LI> Murray's values for the gas constants have been used
(<I>Vectorial Astrometry,</I> Adam Hilger, 1983).
<LI> A better model for <I>P</I><SUB><I>s</I></SUB>(<I>T</I>) has been adopted (taken from
Gill, <I>Atmosphere-Ocean Dynamics,</I> Academic Press, 1982).
<LI> More accurate expressions for <I>Pw</I><SUB><I>o</I></SUB> have been adopted
(again from Gill 1982).
<LI> Provision for radio wavelengths has been added using
expressions devised by A.T.Sinclair, RGO (private
communication 1989), based on the Essen & Froome
refractivity formula adopted in Resolution 1 of the
12th International Geodesy Association General Assembly
(Bulletin Géodésique <B>70</B> p390, 1963).
</UL>
None of the changes significantly affects the optical/IR results
with respect to the algorithm given in the 1992 <I>Explanatory
Supplement.</I> For example, at <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img174.gif"
ALT="$70^\circ$"> zenith distance the present
routine agrees with the ES algorithm to better than
<IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img175.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.05$"><P>
for any reasonable combination of parameters. However, the
improved water-vapour expressions do make a significant difference
in the radio band, at <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img174.gif"
ALT="$70^\circ$"> zenith distance reaching almost
<IMG WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img130.gif"
ALT="$4\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> for a hot, humid, low-altitude site during a period of
low pressure.
<DT>5.
<DD>The radio refraction is chosen by specifying WL >100 <IMG WIDTH="26" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img21.gif"
ALT="$\mu{\rm m}$">. Because the algorithm takes no account of the ionosphere, the
accuracy deteriorates at low frequencies, below about 30MHz.
<DT>6.
<DD>Before use, the value of ZOBS is expressed in the range <IMG WIDTH="25" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img47.gif"
ALT="$\pm \pi$">. If this ranged ZOBS is negative, the result REF is computed from its
absolute value before being made negative to match. In addition, if
it has an absolute value greater than <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img176.gif"
ALT="$93^\circ$">, a fixed REF value
equal to the result for ZOBS <IMG WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img177.gif"
ALT="$=93^\circ$"> is returned, appropriately
signed.
<DT>7.
<DD>As in the original Hohenkerk and Sinclair algorithm, fixed values
of the water vapour polytrope exponent, the height of the
tropopause, and the height at which refraction is negligible are
used.
<DT>8.
<DD>The radio refraction has been tested against work done by
Iain Coulson, JACH, (private communication 1995) for the
James Clerk Maxwell Telescope, Mauna Kea. For typical conditions,
agreement at the
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img25.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$"> level is achieved for moderate ZD,
worsening to perhaps
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img83.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$"> -
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img178.gif"
ALT="$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0$"> at ZD <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img179.gif"
ALT="$80^\circ$">. At hot and humid sea-level sites the accuracy will not be as good.
<DT>9.
<DD>It should be noted that the relative humidity RH is formally
defined in terms of ``mixing ratio'' rather than pressures or
densities as is often stated. It is the mass of water per unit
mass of dry air divided by that for saturated air at the same
temperature and pressure (see Gill 1982). The familiar
<IMG WIDTH="75" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img180.gif"
ALT="$\nu=p_w/p_s$"> or <IMG WIDTH="75" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img181.gif"
ALT="$\nu=\rho_w/\rho_s$"> expressions can differ from
the formal definition by several percent, significant in the
radio case.
</DL></DL>
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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