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<H2><A NAME="SECTION0004152000000000000000">SLA_REFCO - Refraction Constants</A>
<A NAME="xref_SLA_REFCO"> </A><A NAME="SLA_REFCO"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Determine the constants <I>a</I> and <I>b</I> in the
atmospheric refraction model
<IMG WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img148.gif"
ALT="$\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$">, where <IMG WIDTH="11" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img149.gif"
ALT="$\zeta$"> is the <I>observed</I> zenith distance
(<I>i.e.</I> affected by refraction) and <IMG WIDTH="24" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img150.gif"
ALT="$\Delta \zeta$"> is
what to add to <IMG WIDTH="11" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img149.gif"
ALT="$\zeta$"> to give the <I>topocentric</I>
(<I>i.e. in vacuo</I>) zenith distance.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_REFCO (HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REFA, REFB)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>HM</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<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>REFA</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="37" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img151.gif"
ALT="$\tan \zeta$"> coefficient (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>REFB</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img152.gif"
ALT="$\tan^{3} \zeta$"> coefficient (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>Suggested values for the TLR and EPS arguments are 0.0065D0 and
1D-8 respectively.
<DT>2.
<DD>The radio refraction is chosen by specifying WL >100 <IMG WIDTH="26" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img21.gif"
ALT="$\mu{\rm m}$">. <DT>3.
<DD>The routine is a slower but more accurate alternative to the
sla_REFCOQ routine. The constants it produces give perfect
agreement with sla_REFRO at zenith distances
<IMG WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img153.gif"
ALT="$\tan^{-1} 1$"> (<IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img154.gif"
ALT="$45^\circ$">) and <IMG WIDTH="54" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img155.gif"
ALT="$\tan^{-1} 4$"> (<IMG WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img156.gif"
ALT="$\sim 76^\circ$">).
At other zenith distances, the model achieves:
<P> <IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img83.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$"> accuracy for <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img157.gif"
ALT="$\zeta<80^{\circ}$">,<P> <IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img158.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.01$"> accuracy for <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img159.gif"
ALT="$\zeta<60^{\circ}$">, and
<P> <IMG WIDTH="39" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img112.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.001$"> accuracy for <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img160.gif"
ALT="$\zeta<45^{\circ}$">. </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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