Refraction

From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node214.html | 189 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 189 insertions(+) create mode 100644 src/slalib/sun67.htx/node214.html (limited to 'src/slalib/sun67.htx/node214.html') diff --git a/src/slalib/sun67.htx/node214.html b/src/slalib/sun67.htx/node214.html new file mode 100644 index 0000000..41b8d99 --- /dev/null +++ b/src/slalib/sun67.htx/node214.html @@ -0,0 +1,189 @@ + + + + +Refraction + + + + + + + + + + + + +

+ +

+
+ Next: Efficiency considerations +
+Up: Apparent Place to Observed Place +
+ Previous: Apparent Place to Observed Place +

+Refraction +

+The final correction is for atmospheric refraction. +This effect, which depends on local meteorological conditions and +the effective colour of the source/detector combination, +increases the observed elevation of the source by a +significant effect even at moderate zenith distances, and near the +horizon by over $0^{\circ} + \hspace{-0.37em}.\hspace{0.02em}5$ . The amount of refraction can by +computed by calling the SLALIB routine +sla_REFRO; +however, +this requires as input the observed zenith distance, which is what +we are trying to predict. For high precision it is +therefore necessary to iterate, using the topocentric +zenith distance as the initial estimate of the +observed zenith distance. +

+The full +sla_REFRO refraction calculation is onerous, and for +zenith distances of less than, say, $75^\circ$ the following +model can be used instead: +

$\begin{displaymath} +\zeta _{vac} \approx \zeta _{obs} + + A \tan \zeta _{obs} + + B \tan ^{3}\zeta _{obs} \end{displaymath}$

+where $\zeta _{vac}$ is the topocentric +zenith distance (i.e. in vacuo), + $\zeta_{obs}$ is the observed +zenith distance (i.e. affected by refraction), and A and B are +constants, about $60\hspace{-0.05em}^{'\hspace{-0.1em}'}$ and + $-0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.06$ respectively for a sea-level site. +The two constants can be calculated for a given set of conditions +by calling either +sla_REFCO or +sla_REFCOQ. +

+sla_REFCO works by calling +sla_REFRO for two zenith distances and fitting A and B +to match. The calculation is onerous, but delivers accurate +results whatever the conditions. +sla_REFCOQ uses a direct formulation of A and B and +is much faster; it is slightly less accurate than +sla_REFCO but more than adequate for most practical purposes. +

+Like the full refraction model, the two-term formulation works in the wrong +direction for our purposes, predicting +the in vacuo (topocentric) zenith distance +given the refracted (observed) zenith distance, +rather than vice versa. The obvious approach of +interchanging $\zeta _{vac}$ and $\zeta_{obs}$ and +reversing the signs, though approximately +correct, gives avoidable errors which are just significant in +some applications; for +example about + $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$ at $70^\circ$ zenith distance. A +much better result can easily be obtained, by using one Newton-Raphson +iteration as follows: +

$\begin{displaymath} +\zeta _{obs} \approx \zeta _{vac} + - \frac{A \tan \zeta _{va... + ... + {1 + ( A + 3 B \tan ^{2}\zeta _{vac} ) \sec ^{2}\zeta _{vac}}\end{displaymath}$

+The effect of refraction can be applied to an unrefracted +zenith distance by calling +sla_REFZ or to an unrefracted + $[\,x,y,z\,]$ by calling +sla_REFV. +Over most of the sky these two routines deliver almost identical +results, but beyond $\zeta=83^\circ$ sla_REFV +becomes unacceptably inaccurate while +sla_REFZ +remains usable. (However +sla_REFV +is significantly faster, which may be important in some applications.) +SLALIB also provides a routine for computing the airmass, the function +sla_AIRMAS. +

+The refraction ``constants'' returned by +sla_REFCO and +sla_REFCOQ +are slightly affected by colour, especially at the blue end +of the spectrum. Where values for more than one +wavelength are needed, rather than calling +sla_REFCO +several times it is more efficient to call +sla_REFCO +just once, for a selected ``base'' wavelength, and then to call +sla_ATMDSP +once for each wavelength of interest. +

+All the SLALIB refraction routines work for radio wavelengths as well +as the optical/IR band. The radio refraction is very dependent on +humidity, and an accurate value must be supplied. There is no +wavelength dependence, however. The choice of optical/IR or +radio is made by specifying a wavelength greater than $100\mu m$ for the radio case. +

+ +

+
+ Next: Efficiency considerations +
+Up: Apparent Place to Observed Place +
+ Previous: Apparent Place to Observed Place +

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +

+ + -- cgit